INVITED RESEARCH REPORT

The Atomic Constants, Light, and Time

by BARRY SETTERFIELD and TREVOR NORMAN © August 1987 PREPARED FOR: Lambert T. Dolphin Senior Research Physicist

FOREWORD That a major revolution in nuclear physics, astronomy and cosmology is underway these days is perhaps not obvious to the general public, or even perhaps to the average research scientist who is not working directly in one of these fields. It was but 300 years ago this year that Sir Isaac Newton published his "Principia," launching the western world boldly forward towards the era of modern physics. An explosive increase in the body of knowledge about our physical universe has resulted. The most rapid changes in this body of knowledge, however, seem to have occurred just in the past few years and appear to be taking place even now at an accelerated rate. As startling and profound as Albert Einstein's Special and General Theories of Relativity were when they first appeared, shortly after the turn of this century, advances in particle physics and in astronomy in the past three or four decades have been even more radical in their implications. It is now known that certain atomic constants governing the atom and its inner workings are the very same constants that likewise describe phenomena in space-time on the largest scale of observables in the universe. Thus, for some as yet unexplained reasons, the realm of the smallest physical observables is coupled to the grandest scale of events and happenings amongst the stars and galaxies. All science rests upon some form of philosophical presupposition, or upon basic assumptions made at the start of a hypothesis. Good science means questioning basic assumptions from time to time, or altering one's weltanschaung in the light of new findings. Today's scientific theories are built on the foundations laid by the previous generation, and a good many of our

theories are certainly valid because they work so well and have stood the test of time. But old theories do give way to new, and hopefully a net gain in understanding follows. The progress of science occurs mostly by observation and experiment, though some scientific discoveries are the result of pure mathematical studies later tested and found to fit observable data in the universe. Scientific instruments extend the range of the five senses by orders of magnitude in all directions. Observations and experimental data are used to fit the data to a curve and to find an equation that will allow extrapolation into uncharted waters. It is an unwritten law, known as Occam's Razor, that the simpler equation (or theory) is to be preferred to the complex, even if both fit the data. This principle propels the scientist to look for "Grand Unified Theories" and to find simpler models to replace the too-complex. Often a new scientific theory is found to fit the experimental data very well --- at first, and everyone rejoices. Then more precision measurements are made. When the new data are in small differences between theory and experiment are frequently discovered. Whenever this happens concerted efforts (often by many research groups) are launched spontaneously to find the reasons for the discrepancies and to revise the older theory. Growth in science also depends on new ways at looking at old data, at carefully looking for the exceptions to the rule, or by following hunches, intuition or "leaps of faith" to see where they lead. Choosing to study observational anomalies that apparently run counter to the prevailing assumptions of the day is not guaranteed to prove popular with all scientists. Many scientists have never taken a class in the history of science so as to be aware of how the body of scientific evidence has developed over time, or they would be, perhaps, less afraid of change. Some researchers may be so engrossed in the excitement of their current studies that they fail to take into account new evidence from other disciplines, or to question the assumptions upon which prevailing models rest. Everyone tends to forget that much of today's scientific orthodoxy came out from yesterday's unpopular heresies. It is the mark of a good scientist to not be afraid to question what has been taken for granted (perhaps for decades), by others. The authors of this report raise a scientific discussion, which, if true, has profound implications not only for physics but also for philosophy as well. As far as I can discern, their arguments are sound, their homework has been done, and they "have done their sums correctly." The authors of this report discuss the possibility that the velocity of light is not a constant. This notion is not so unreasonable when one considers the history of "c". When the Danish Astronomer Roemer, (Philosophical Transactions, June 25, 1677), announced to the Paris Academie des Sciences in September 1676 that the anomalous behavior of the eclipse times of Jupiter's inner moon, Io, could be accounted for by a finite speed of light, he ran counter to the current wisdom espoused by Descartes and Cassini. It took another quarter century for scientific opinion to accept the notion that the speed of light was not infinite. Until then it had never been the majority view that this physical quantity was finite. The Greek philosophers generally followed Aristotle in the belief that the speed of light was infinite. However there were exceptions such as Empedocles of Acragas (c. 450 B.C.) who spoke of light, "traveling or being at any given moment between the earth and its envelope, its movement being unobservable to us," (The Works of Aristotle translated into English, W.D. Ross, Ed., Vol. III, Oxford Press 1931: De Anima, p4l8b and De Sensu, pp446a-447b). Around 1000 A.D. the Moslem scientists Avicenna and Alhazen both believed in a finite speed for light, (George Sarton, "Introduction to the History of Science," Vol.I, Baltimore, 1927, pp709-12). Roger Bacon (1250 A.D.) and Francis Bacon (1600 A.D.) accepted that the

speed of light was finite though very rapid. The latter wrote, "Even in sight, whereof the action is most rapid, it appears that there are required certain moments of time for its accomplishment...things which by reason of the velocity of their motion cannot be seen--as when a ball is discharged from a musket," (Philosophical Works of Francis Bacon, J.M. Robertson, ed., London, 1905, p363). However, in 1600 A.D. Kepler maintained the majority view that light speed was instantaneous, since space could offer no resistance to its motion, (Johann Kepler, "Ad Vitellionem paralipomena astronomise pars optica traditur," Frankfurt 1804). It was Galileo in his "Discorsi...îpublished in Leyden in 1638, who proposed that the question might be settled in true scientific fashion by an experiment over a number of miles using lanterns, telescopes and shutters. The Academia del Cimento of Florence reported in 1667 that such an experiment over a distance of one mile was tried, "without any observable delay," ("Essays of Natural Experiments made in the Academie del Cimento," translated by Richard Waler, London, 1684, p157). However, after reporting the experimental results, Salviati, by analogy with the rapid spread of light from lightning, maintained that light velocity was fast but finite. Descartes, who died in 1650, strongly held to the instantaneous propagation of light and accordingly influenced Roemer's generation of scientists who accepted his arguments. He pointed out that we never see the sun and moon eclipsed simultaneously. However if light took, say, one hour to travel from earth to moon, the point of co-linearity of the sun, earth, and moon system causing the eclipse would be lost and visibly so, (Christiaan Huygens, "Traite de la Lumiere...îLeyden, 1690, pp4-6, presented in Paris to the Academie Royale des Sciences in 1678). It was Christiaan Huygens in 1678 who demolished Descartes' argument by pointing out, on Roemer's measurements, that light took of the order of seconds to get from moon to earth, maintaining both the co-linearity and a finite speed. However it was only Bradley's independent confirmation published January 1, 1729 that caused the opposition to a finite value for the speed of light to cease. Roemer's work, which had split the scientific community, was at last vindicated. After 53 years of struggle, science accepted the observational fact that light traveled at a finite speed. Until recently that finite speed has been generally been taken to be a fixed and immutable constant of the universe in which we live. I first became aware of the research investigations of Trevor Norman and Barry Setterfield four years ago. I had stumbled across, almost by accident, a short technical paper in which they described an analysis of the known experimental measurements to date of the velocity of light. Their data seemed to show that a small (but statistically significant) decrease in "c" had occurred during the past 400 years. I followed the subsequent printed responses solicited from scientists around the world on the issues raised by the original paper and found Norman and Setterfield competently answered the questions raised by critics of their theory. I knew from experience that major changes in scientific theories often start out from just this kind of beginning. I have learned to sort out new ideas such as these when they appear in print and to pay close attention to a few of them, for it is out of papers like this one that change and progress in science often come. At first I was both cautious and skeptical, though interested. I remember speculations when I was an undergraduate in physics at San Diego State University (near the famous 200 inch Hale Telescope on Mt. Palomar), concerning the red shift of light from distant galaxies, and the apparent expansion of the universe outwards from a point of singularity. These ideas were not, I recalled, well received by all when they were first propounded. I had heard of the

possibility of "tired light," but always assumed the speed of light had been dependably constant for billions of years. So out of curiosity I wrote to Barry Setterfield soon after reading their article. I received a prompt and courteous reply. There followed a lengthy exchange of comments, articles and references between the three of us. I have since talked to several other respected and competent scientific colleagues in the United States and abroad who also take Norman and Setterfield's work seriously and this has given me increased confidence that they are onto something new and important. Last year Trevor Norman was instrumental in establishing an electronic mail connection between our two organizations to facilitate discussions between the three of us. In all honesty I can say that it has taken me four years to get comfortable (and enthused about) their findings. It has been very good for me to do my homework in the process of evaluating what they have written. I have had to dig out my Quantum Mechanics, Nuclear Physics, Relativity and Cosmology textbooks from graduate school at Stanford University, and get up to date a bit by reading more recent works. When I learned recently that Norman and Setterfield had now carried their work to the stage where a thorough report had been drafted, I offered my assistance in hopes their findings could be better known. If indeed the velocity of light has changed or is changing, a certain set of related other physical "constants" have changed as well. The authors have not set out to "prove" that this is indeed the case. They have however amassed and carefully studied a great body of data that suggests that the some of most "sacred" of the physical constants are not constant after all. Their report is written in accord with perfectly orthodox scientific standards. That is, they have collected and analyzed the available data and formed a hypothesis. This hypothesis (that the velocity of light has decreased with time) is testable. It is a perfectly valid hypothesis until further data proves otherwise. I believe it is timely and appropriate to call wider attention to this hitherto little known investigation. This report is therefore presented to invite discussion, comment, rebuttal, and hopefully to provoke researchers to look for further evidence which could support or refute the authors' conclusions. The authors and I have agreed that papers and comments should be solicited so that a follow on report might be published by us on this important subject. The reader, whether scientist or layman, is welcome therefore to contact either of the authors or myself in this regard. Norman and Setterfield also have available a small supplement to this report which addresses some of the ramifications of different universal timescales, which logically follow from possible real changes in such basic constants as the velocity of light. I recommend that those readers with interests in the latter area write the authors directly for a copy of this supplement. I myself found it most helpful and stimulating. Lambert T. Dolphin Senior Research Physicist Geoscience and Engineering Center SRI International August 1987

INDEX ABSTRACT.

I. INTRODUCTION. II. C DECAY PROPOSAL HISTORICALLY. (A). Dynamical c variation discussed. (B). The speed of Light and relativity. (C). Reactions and arguments. III. MEASURED VALUES OF C. (A). The Roemer-type determinations. (B). The Bradley-type observations. (C). Toothed wheel experiments. (D). Rotating mirror results. (E). Kerr Cell results. (F). The six methods used 1945-1960. (G). The post-1960 results. (H). The ratio ESU/EMU and waves on wires. (I). Conclusions from collective data. IV. PHYSICAL QUANTITIES AFFECTED BY C DECAY. (A). Maxwell's Laws and the electronic charge. (B). Atomic rest-masses. (C). The atom and Planck's constant. (D). Atomic orbits and related quantities. (E). Radioactive decay. V. TIME AND GRAVITATION. (A). Atomic time. (B). Gravitation. (C). Length, time and c. (D). Lasers and a test for c decay. VI. DATA CONCLUSIONS AND ULTIMATE CAUSES. (A). General conclusions from all data. (B). Conclusions from c data. (C). Conclusions from refined atomic data. (D). Ultimate causes and the c equation. VII. CONSEQUENCES. (A). Radioactive radiation intensities. (B). Stellar radiation intensities. (C). The red-shift. (D). The Doppler formula. (E). The missing mass. (F). Superluminal jets. (G). Final comments. REFERENCES APPENDIX I: Non-technical summary.

SELECTED PROFESSIONAL COMMENT TABLE 1. Roemer method values. TABLE 2. Results of Bradley's observations. TABLE 3. Bradley aberration method values. TABLE 4. Toothed wheel experimental values. TABLE 5. Rotating mirror experiments. TABLE 6. Kerr cell values of c. TABLE 7. Results by six methods 1945-1960. TABLE 8. Results 1960-1983 - mainly Laser. TABLE 9. C values by the ratio of ESU/EMU. TABLE 10. C values by waves on wires. TABLE 11. Refined List of c data. TABLE 12. Options with changing c. TABLE 13. Values of the electronic charge, e. TABLE 14. Values of the specific charge e/(mc). TABLE 15. Experimental values of h/e, 2e/h, h/e². TABLE 16. The Rydberg constant, R. TABLE 17. The proton gyromagnetic ratio. TABLE 18. Other c independent quantities. TABLE 19. Half-lives of the main heavy radio-nuclides. TABLE 20. The Newtonian gravitational constant G. TABLE 21. Comparison of curves fitted to Table 11 data. TABLE 22. Results of analysis of speed of light data. TABLE 23. Summary of behavior of atomic quantities. TABLE 24. Consistent trends in 7 atomic quantities. FIGURE I. Pulkova aberration results. FIGURE II. Best 23 c values by 8 methods 1740-1940. FIGURE III. Typical curve fit on table 11 c data. FIGURE IV. Typical curve fit detail 1870-1983. FIGURE V. Probable atomic clock behavior all curves. Acknowledgements: We are indebted to Flinders University, South Australia, for the use of facilities, and for the patience and help of Ron, Kai, Judy and Ian at the I.L.L. desk. Thanks also to Dr. R.O. Hampton (biologist, Waite Research Institute) for his impressions and valued comments as an 'outsider' in the fields addressed. The comments and suggestions of Professor P.P. Martins Jr., CETEC, Brazil, Professors D.H. Kenyon and D. Meredith, San Francisco State University, along with Dr. G. Mortimer, Adelaide University, South Australia, and Drs. J. Rice and M. Murray of Flinders University, are deeply appreciated. The very useful discussions with Dr. D.R. Humphreys, Sandia National Labs., Albuquerque, U.S.A. and Col.(ret.) Dr. W.T. Brown, (formerly Chief of Science and Technology Studies, Air War College, Assoc. Professor, U.S. Air Force Academy), and the late Dr. Brian Daily, (formerly Dean of the Faculty of Science, Adelaide University), have made a major contribution to the form and content of this presentation. THE ATOMIC CONSTANTS, LIGHT, AND TIME.

by Trevor G. Norman* and Barry Setterfield** *School of Mathematical Sciences, Flinders University, South Australia 5042. **Present address: P.O. Box 318, Blackwood, S.A., 5051, Australia.

ABSTRACT:The behavior of the atomic constants and the velocity of light, c, indicate that atomic phenomena, though constant when measured in atomic time, are subject to variation in dynamical time respectively. Electromagnetic and gravitational processes govern atomic and dynamical time respectively. If conservation laws hold, many atomic constants are closely linked with c. Any change in c affects the atom. For example, electron orbital speeds are proportional to c, meaning that atomic time intervals are proportional to 1/c. Consequently, the time dependent constants are affected. Therefore, Planck's constant, h, may be predicted to vary in proportion to 1/c as should the half-lives of radioactive elements. Conversely, the gyromagnetic ratio,  , should be proportional to c. Any variation in c, macroscopically, therefore reflects changes in the microcosm of the atom. A systematic, non-linear decay trend is revealed by 163 measurements of c in dynamical time by 16 methods over 300 years. Confirmatory trends also appear in 475 measurements of 11 other atomic quantities by 25 methods in dynamical time. Analysis of the most accurate atomic data reveals that the trend has a consistent magnitude in all quantities. Lunar orbital data indicate continuing c decay with slowing atomic clocks. A decay in c also manifests as a red-shift of light from distant galaxies. These variations have thus been recorded at three different levels of measurement: the microscopic world of the atom, the intermediate level of the c measurements, and finally on an astronomical scale. Observationally, this implies that the two clocks measuring cosmic time are running at different rates. Relativity can be shown to be compatible with these results. In addition, gravitational phenomena are demonstrably invariant with changes in c and the atom. Observational evidence also demands consistent atomic behavior universally at any given time, t. This requires the permeability and metric properties of free space to be changing. In relativity, these attributes are governed by the action of the cosmological constant, , proportional to c2, whose behavior can be shown to follow an exponentially damped form like = a + ekt (b + dt). This is verified by the c data curve fits.

DEFINITION: A dynamical second is defined as 1/31,556,925.9747 of the earth's orbital period and was standard until 1967. Atomic time is defined in terms of one revolution of an electron in the ground state orbit of a hydrogen atom. The atomic standard by the caesium clock is accurate to limits of ±8 x 10 -14.

THE ATOMIC CONSTANTS, LIGHT, AND TIME I. INTRODUCTION:-

There are two basic clocks by which cosmic time is commonly measured. One is atomic time that is governed by the period taken for an electron to move around once in its orbit. In essence, it is electromagnetic in character. The other is dynamical time whose units are subdivisions of the period that the earth takes to make one complete orbit of the sun. Obviously, this clock is governed by gravitation. Dynamical time was kept universally until 1967 when the atomic standard was introduced using the caesium clock. Dirac and Kovalevsky have pointed out 360 that if the two clock rates were different, 'then Planck's constant as well as atomic frequencies would drift'. The observational evidence suggests that these two clocks do run at different rates. The lunar and planetary orbital periods, which comprise the dynamical clock, have been compared with atomic clocks from 1955 to 1981 by Van Flandern and others 1. Assessing the evidence in 1984, T.C. Van Flandern came to a conclusion, with a dilemma. He stated that1 ëthe number of atomic seconds in a dynamical interval is becoming fewer. Presumably, if the result has any generality to it, this means that atomic phenomena are slowing down with respect to dynamical phenomena ... (though) we cannot tell from the existing data whether the changes are occurring on the atomic or dynamical level.íIn either event, atomic quantities bearing units that involve time should show the same correlated variation when measured in dynamical time. Among those quantities would be Planck's constant, h, the gyromagnetic ratio,  ', radioactive decay constants, , and the speed of light, c. The electron rest-mass, m, should also vary from energy considerations and by the definition of force/acceleration. Dimensionless constants and those with mutually canceling time dependent terms remain invariant if conservation laws are to be upheld. The observational limits set for the 'cosmological variation' of many constants are actually limits on energy conservation. In these cases, a ratio of atomic quantities with mutually canceling time units, such as hc, is usually measured. No conclusion can thus be drawn about any variability in c or h separately. The only statement that is valid is that ' h must vary precisely as 1/c within the observational limits. Those limits are absolutely upheld here. Theory and experimentally observed effects agree only if distances remain unaffected by the difference in the run-rate between the two clocks. Wavelengths and atomic orbit radii are thus invariant along with the Avogadro Number, N 0. As electron orbital velocities are time dependent, it follows that higher velocities produce shorter time intervals on the atomic clock, seen dynamically. Slowing atomic clocks thus imply slowing electron velocities seen from the dynamical time-frame. In addition, those atomic quantities with time units on the denominator should decay while those with time units on the numerator should increase. The measured values of a number of quantities are examined first, confirming the atomic slow-down in dynamical time. Van Flandern's dilemma as to which clock varies is investigated later. For conservation laws to be valid, the atom and dynamical processes will act in completely consistent ways in their own time-frames leaving all quantities invariant there, no matter which clock is in fact varying. However, when dynamically constant orbital periods are measured atomically, the different clock rates will appear as a variation in the gravitational constant, G, seen atomically. This is what Van Flandern observed originally1. The reverse, or dynamical observation of atomic phenomena, is examined here. Light is produced by atomic processes and its velocity, c, has been measured for 300 years. The subsequent analysis concentrates on this basic quantity initially. It is found that there is a statistically significant decay when c is measured in dynamical time. All 16 methods of c

measurement give a decay both individually and collectively. The main points raised in the discussion on c decay in the scientific literature are reviewed. If conservation laws are valid, a slow-down in c, measured dynamically, should be matched by a proportional change in electron orbit velocities and other atomic processes. Conservation laws require that the time dependent atomic quantities should also be c dependent. An atomic interval, d , is thus proportional to 1/c, being longer when c is lower. This is precisely the effect that Van Flandern has noted. Consequently, changes in c are either the cause, or the result, of changes in the atom. Light speed thus emerges as a key factor interlinking the atomic constants. The values of these atomic constants, measured dynamically, are found to vary in a way that is consistent with c decay and slowing atomic clocks. Observationally, 16 methods of measurement of various atomic quantities show a statistically significant atomic slow-down. It is also implied in 3 other cases. The data from all 16 methods of measuring c, and 25 methods of measuring the atomic constants, are treated uniformly. All readily available data have been tabulated, comprising 194 atomic, 281 radio-nuclide, and 163 c values. They include those results rejected by the experimenters themselves or their immediate peers and their reasons for rejection are quoted. The rejected data are often used, but are omitted from refined analysis. Data are treated by a standard least-squares linear fit to discover trends. The slope of this fit decreases with time for all c-dependent quantities. The students t-distribution is applied to the least-squares data mean and to the correlation coefficient, r, to find the confidence interval in the data trend and linear fit. Note that for the sake of convenience in presentation, all methods of measuring a particular atomic quantity are tabulated together, including the best adjusted values. Some of these methods may not measure the quantity directly. However, the different systems of measurement are indicated in the column marked 'Method'. In these cases, an analysis is made of each method individually and the trend confirmed. This indicates that the trend is not unique to a particular system of measurement but is a genuine effect. This is also the case with the best adjusted values. Indeed, it is in just those cases where an atomic constant has been found varying that the earlier data were gradually omitted from adjusted analysis as more 'correct' newer values were found. The adjusted value was thus determined on the 'best' data that was then available and so long-term changes in this value also indicate a slowing atomic clock. A summary of the measured trends in 12 atomic quantities is presented in Table 23. The results from all data are given first for each quantity, then those for the most accurate measurements. More details of the speed of light data are given in Table 22 and Figures III and IV. Since it covers a greater time range, the decreasing decay rate from the c data is more readily apparent than with other quantities. In Table 23, the rate of change in an atomic quantity per year is divided by the value of that quantity for all the most accurate data. This allows a cross-comparison of results. In Table 24 the non-linear slow-down is evident and is shown to be concordant in magnitude from the measurements of 7 atomic quantities. It should be noted that the measured rate of slowing is tapering off very rapidly. Future monitoring will be required to discern which of several possibilities will be followed. The full analysis summarized by Tables 22-24 therefore shows that the slowing of atomic processes in dynamical time has formal statistical significance, which upholds Van Flandern's statements. This then raises some issues which are mainly associated with c decay.

The issue of relativity with c variation was essentially addressed with recent papers by Breitenberger6, Mermin7 and Singh8. They show constancy of c was not essential as relativity theory can be deduced without c at all. On a neo-Newtonian level, a variation in c as the limit velocity for energy propagation suggests that a gravitational permeability term should be included in equations. When this is done, a resemblance to relativistic terms is noted. Gravitational potentials on both approaches are then proportional to Gm/c2, which is constant for all c because of mutually canceling, c-dependent terms. For the same reason, the basic equation E=mc2 is also completely valid. Under these circumstances, gravitational terms in general relativity hold dynamically. Furthermore, all gravitational phenomena are thus shown to be invariant with changes in the atom or c, leaving the dynamical clock unaffected. However, in its own time-frame, the atom acts in a completely consistent way leaving all atomic constants without variation. This suggests that relativity also holds when considered by the atomic standard. A constant dynamical interval, dt, could also be written as c.d . The 2 general relativistic equations involving time intervals written as (c2.d ) would thus be valid dynamically if the time interval were measured atomically. An equation in dynamical time results that is independent of c. In other words, from relativistic and neo-Newtonian theory, the dynamical clock is completely invariant with any change in c or atomic behavior. The implication is that the behavior of the atomic clock is variable intrinsically, or is subject to c-dependent external factors, such as the permeability of free space, which leave the dynamical clock unaffected. Furthermore, conservation laws seem violated if gravitational phenomena were causing these data trends. It seems that the atomic clock is slowing down rather than the dynamical clock speeding up. Van Flandern's dilemma thus appears to be solved and relativity is upheld. One final constraint appears necessary. Light speed must have the same value at any instant in all dynamical frames throughout the universe. This constraint has recently been upheld experimentally by Barnet et al. 9. They demonstrated that light from distant quasars arrived here with the same velocity as light from more local astronomical sources. That means consistent atomic behavior universally at any given time t. This requires the permeability, or energy density, and metric properties of free space to be changing. This option is favored by general relativity where these properties are controlled57 by the action of the cosmological constant, . A change in therefore seems to be the root cause of the observed variations. In the Schwarzschild metric, the term /c2 appears which requires to be proportional to c 2 for energy conservation. This also follows as there has dimensions of time-2. We can thus write = kc2, with k a true constant of about 10-66 cm-2. This allows a /k substitution for c2 in electromagnetic and other equations. A universe under the action of , essentially exhibits a form of simple harmonic motion with varying as the radius89 . An exponentially damped sinusoid would be typical behavior90 . This is born out by the c observations which follow the equation c = [a + e kt(b + dt)]1/2, where one solution gives k = - 0.0048, a = 9.029 x 1010, b = 4.59 x 1013, d = -2.60 x 1010, t is the year. However, most properties of this complex expression are closely reproduced by a much simpler polynomial c = a + bt 2 + dt8, where a = 299792, b = 0.01866 and d = 3.8 x 10-19. This equation also has a superior fit to the c data. In conclusion, theory and observation indicate that electromagnetic wave amplitude energies, and hence photon intensities, are proportional to 1/c. Consequently, although stellar and radioactive processes were more vigorous in the past, proportional to c, the net radiation intensity remained unchanged with temperatures unaffected. The latter follows since thermal conductivity is proportional to c. This approach receives observational support since light

from distant objects is undimmed by c decay. However, for light in transit, increasing amplitude energy is made at the expense of wavelength energy. Wavelengths are thus proportional to 1/c giving a red-shift to light from distant galaxies. Note that the observed redshift, z, is a net result since the action of causes galactic motion towards the observer. This research thus holds the potential to resolve some perplexing problems of science. II. THE C DECAY PROPOSAL HISTORICALLY: (A). DYNAMICAL C VARIATION DISCUSSED: In October 1983 the speed of light, c, was declared a universal constant of nature defined as 299,792.458 Km/s and as such is now used in the definition of the meter. However, in a recent article on this subject, Wilkie² points out that ëmany scientists have speculated that the speed of light might be changing over the lifetime of the universeíand concludes that ëit is still possible that the speed of light might vary on a cosmic timescale.íVan Flandern 1 agrees. He states that ëAssumptions such as the constancy of the velocity of light ... may be true in only one set of units (atomic or dynamical), but not the other.í Historically, the literature, particularly from the 1920's to the 1940's, amplifies this conclusion and indicates that if c is varying it is doing so in dynamical units, not atomic. Thus, the values for c obtained by Michelson alone were as follows in Table A (with full details in Table 5). TABLE A

DATE VALUE OF C (km/s) 1879.5 299,910 ±50 1882.8 299,853 ±60 1924.6 299,802 ±30 1926.5 299,798 ±15 These results are not typical of a normal distribution about today's fixed value. However, the 1882.8 result is confirmed by the values from two other experiments. One by Newcomb in 1882.7 yielded a c value of 299,860 ±30 Km/s, while Nyren using another method in 1883 obtained a definitive value of 299,850 ±90 Km/s (see discussion below for details). In other words, Michelson's 1882.8 result was completely consistent with the other values obtained that year. The mean of these three values (299,854 Km/s) lies above today's value by 61.8 Km/s, though the standard deviation of these three values is only ±5 Km/s. The quoted probable errors thus seem to be conservative. Assuming no c variation, the least squares mean for all these data show they are distributed about a point 53 Km/s above today's value. The mean error is ±45.8 Km/s, which places today's value beyond its lower limit. If the students t-distribution is applied to these data, the hypothesis that c has been constant at its present value from 1879.5 to 1926.5 can be rejected with a confidence interval of 98.2%. One would expect that other results from this type of experiment would lie below today's value by a similar amount to restore the normal distribution. This is not observed.

Assuming, then, that the variation is real, it represents a measured decay of 112 Km/s in 47 years. A linear, least squares fit to these data gives a drop of 1.62 Km/s per year. The resulting correlation coefficient r = -0.879, and this decay correlation is significant at the 98.9% confidence level from the t-statistic. This is not an isolated instance: similar trends occur with all methods of c measurement, individually and collectively, involving 163 data points. Some are illustrated in Figures I and II. Despite a preference for the constancy of atomic quantities, Dorsey3 did concede that 'As is well known to those acquainted with the several determinations of the velocity of light, the definitive values successively reported...have, in general, decreased monotonously from Cornu's 300.4 megameters per second in 1874 to Anderson's 299.776 in 1940...' In fact, even Dorsey's reworking of the original data left c values generally above those currently prevailing. The continuing drop in the measured value of c with each new determination elicited further remarks on the topic until the mid 1940's. By then the wealth of comment can be gauged by the representative sample in the final reference (360) given below. The listing includes 18 from Nature alone. A variety of possible decay curves for c was espoused, and the resulting experiments invalidated some proposals. The effects of c variation on some other quantities were discussed, and a number of scenarios eliminated by experiment. (B). THE SPEED OF LIGHT AND RELATIVITY: De Bray4, after listing the four most recent determinations of c commented 'If the velocity of light is constant, how is it that, INVARIABLY, new determinations give values which are lower than the last one obtained, ...There are twenty-two coincidences in favor of a decrease of the velocity of light, while there is not a single one against it' (his emphasis). De Bray then made a key point in stating that 'Vrkljan has shown (Zeits. fur Phys., Vol.63, pp 688-691; 1930) that a decrease in the velocity of light is not in contradiction with the general theory of relativity.' Again, Canuto and Hsieh 5 point out that the gravitational field equations in general relativity contain a single factor M = Gm/c 2 as a constant of integration. All the equations demand is that the net result, M, is constant without saying anything about compensating variations in individual terms. Likewise, a recent paper by Breitenberger 6 states that 'The special theory of relativity is shown to be independent of the assumption that the velocity of light, c, is a universal constant. ...Existing theory-dependent arguments purporting to demonstrate the constancy of c are shown to be inadequate.' Furthermore, 'natural units furnished by atomic standards' should replace length and time intervals, in line with Van Flandern's option if c is changing dynamically. The proposals advocated by Mermin 7 and Singh8 are also relevant. They show that relativity theory can be deduced without introducing c at all. In IV (B) below, mention is made of the fact that the basic equation, E = mc2;, may be deduced without relativity theory, and that it, too, is valid in a changing c scenario. The constancy of c in the atomic frame implies the validity of relativity there. From the above, and statements below in V (A) and IV (B), c decay and relativity seem compatible dynamically. Additionally, Einstein's base for relativity also appears valid dynamically provided that c (1) remains independent of the motion of the source and (2) has the same value at any instant in all dynamical frames throughout the universe. Point (2) has been experimentally verified by Barnet et al. 9. Using the aberration method, they reported that light from distant quasars arrived here with the same velocity as light from nearby stars. They concluded that c had remained constant to within 0.4% throughout the life of the universe.

These results do not necessarily set limits on a cosmological variation of c at all. Rather, they completely affirm the principle that c has a universal value at any given time t. This is also confirmed by the 1976 results of Baum and Florentin-Nielsen10. A further comment on this point occurs in the final discussion. (C). REACTIONS AND ARGUMENTS: Three reactions to the decrease in the measured value of c were summarized by Dorsey 3, after admitting that the idea of c decay had 'called forth many papers.' He stated that 'Not a few of their authors seem to be very favorably impressed by the idea of a secular variation, some seem to be favorable to it but unwilling to commit themselves, and some are strongly critical.' Dorsey himself was in the last category as eventually was R.T. Birge. Nevertheless, in 1941 even Birge 11 acknowledged that 'these older results are entirely consistent among themselves, but their average is nearly 100 km/s greater than that given by the eight more recent results'. In this, history repeated itself. In 1886, Newcomb 12, who had obtained some of those 'older results' mentioned by Birge, stated that the still older results around 1740 were also consistent but placed c about 1% higher than in his own time. This persistent trend was countered by three arguments. Initially, it was deemed contrary to Einsteinian theory, but, as indicated above, the truth appears to be otherwise. The second argument recognized, as Newcomb and Birge's statements do, that the measured values of c were differing with time. Dorsey3 proposed in 1944 that perhaps the measuring equipment was at fault or that it was an artifact of more sophisticated procedures. However, his lengthy analysis still left the early c values above c now. He concluded that all measurements prior to 1928 were unreliable, extended their error limits, and claimed that c decay could be rejected on these grounds. However, Dorsey did not address the main problem. He failed to demonstrate why the measured values of c should show a systematic trend with the mutual unreliability of the equipment. Indeed, if c was constant, error theory indicates that there should have been a random scatter about a fixed value. This is not observed. Instead, the analysis below shows a statistical decay trend for c measured by 16 different methods, individually as well as collectively. This tends to negate Dorsey's contention since it represents one chance in 43 million of being the coincidence that he might have implied (trends could be increasing, decreasing or static). Furthermore, in the seven instances where the same equipment was used in a later series of experiments, a lower c value has always resulted at the later date. Dorsey had no satisfactory explanation for this phenomenon. Birge13 gave a third reason for rejecting c decay. After noting that wavelengths and length standards were experimentally invariant over time, he stated that 'if the value of c...is actually changing with time, but the value of (wavelength) in terms of the standard meter shows no corresponding change, then it necessarily follows that the value of every atomic frequency...must be changing. Such a variation is obviously most improbable....' Ironically, this is the very effect that Van Flandern observed experimentally. Indeed, the analysis below shows that when the basic equations are worked through with energy conservation in mind, the conclusion emerges that the emitted frequency of light from atoms is the quantity varying with c and wavelengths do remain unchanged. The constraint of energy conservation based on constant length standards (including dynamical and atomic distances) alone appears to give predicted trends in the values of other atomic constants that are consistent with measurement

and observation. As Birge pointed out in his article, invariant length and wavelength standards are upheld experimentally. More recently, it has been suggested that measured values became 'locked' around some canonical value, an effect called 'intellectual phase locking'. This hardly accounts for the confirmatory trends in other atomic constants, nor the lower values obtained when the same cmeasuring equipment was used for a later experiment. Dorsey's reworked results also deny it. Furthermore, when many of the measurements were being made, c behavior was still a matter for debate and appropriate descriptive curves were discussed. However, since the 1940's, a different attitude to the value of c has prevailed which may itself be a form of intellectual phase-locking. As one reviewer pointed out, Aslakson's measurements with the 'SHORAN' navigation system in 1949 required a higher value for c than was currently accepted to agree with geodetic distances. He delayed publication for several years while he sought for supposed errors in his system. As it turned out, his experimental value was correct, within its error limits, and the accepted c value was too low for reasons discussed later. The importance of experimental results compared with accepted norms is thereby well illustrated. Accordingly, it seems appropriate to re-examine all experimental determinations of c and related atomic quantities to establish what these results actually reveal. The initial results of the investigation are hereby presented. III. MEASURED VALUES OF C:(A). THE ROEMER-TYPE DETERMINATIONS: The Roemer-type measurements are based on the eclipse times of Jupiter's satellite Io. These fall behind schedule as the earth in its orbit draws away from Jupiter and pick up again as the earth approaches Jupiter. Light travel time across the earth's orbit radius (1.4959787 x 108 Km) delays the eclipses and allows a calculation of c. Initially these results differed. Observations by Cassini 14 (1693 and 1736) gave the orbit radius delay as 7 minutes 5 seconds. Roemer in 1675 gave it as 11 minutes from selected observations15. Halley16 in 1694 noted that Roemer's 1675 figure for the time delay was too large while Cassini's was too small. Newton17 listed the delay as 'seven or eight minutes' in 1704 and 1713. All but Roemer suggested a delay shorter than today's value, yet estimates of Roemer's c value range18 from 193,120 to 327,000 Km/s. Roemer's selective procedure and time for Io's period affects his c value. An examination of the best 50 Roemer values was undertaken by Goldstein19 in 1975 after initial work20 in 1973. The correction21 of a procedural error, only recently noted, 'gave a light travel time 2.6% lower than the presently accepted value. The formal uncertainty is ±1.8%' Roemer's value thus becomes 307,600 ±5400 Km/s. The investigations are continuing22. Table 1 lists the results obtained by this method that have been found in the literature to date. If the uncertain 1675 and 1693 values are omitted, the data mean is 1701 Km/s above c now. On this basis, the hypothesis that c has been constant at its present value during these experiments can be rejected at the 96.5% confidence interval. If the other alternative is explored, a least squares linear fit to the data gives a decay of 25.9 Km/s per year, with r = -

0.982. The decay correlation is significant at the 99.97% confidence interval. In view of initial uncertainties, only the Glasenapp and Harvard values are included in the final analysis of Table 11. TABLE 1 - ROEMER METHOD VALUES

AUTHORITY MEDIAN DATE ORBIT RADIUS DELAY (sec) C (Km/s) 1. Roemer

1675

-

307,600 ±5400

2. Cassini

1693

425.0

352,000

3. Delambre

1738 ±71

493.2

303,320

4. Martin

1759

493.0

303,440

5. Encyc.Brit. 1771

495.0

302,220

6. Glasenapp

1861 ±13

498.57

300,050

7. Sampson

1876.5 ±32

498.64

300,011

7. Harvard

1876.5 ±32

498.79 ±0.02

299,921 ±13

1. Provisional correction only (see text). 2. Uncorrected observations by Cassini 94. 3. Mean of 1000 observations from 1667-1809. Delambre95 and Newcomb 96. 4. Value deduced by Martin 97. 5. Generally accepted value 98. 6. Reduction of 320 eclipses 1848-1873 by Glasenapp99 using 5 methods. Result mean of 4 as method 1 comprehensively covered in method 5. See also Kulikov 100 and Newcomb96. 7. Reduction of Harvard observations 1844-1909 done in 1909. Official Harvard reductions, and those by Sampson (see Whittaker101). TABLE 2 - RESULTS OF BRADLEY'S OBSERVATIONS

LOCATION STARS

DATE

AUTHORITY ABERRATION ANGLE (arc-seconds)

1. Kew

8 stars

1726-27 Bradley

2. Kew

Draconis 1726-27 Busch

20.2495

2. Kew

Draconis 1726-27 Auwers

30.3851 ±0.0725

3. Kew

Draconis 1726-27 Newcomb

20.53 ±0.12

2. Wanstead

23 stars

1727-47 Busch

20.205

2. Wanstead

23 stars

1727-47 Auwers

20.460 ±0.063

4. Greenwich Draconis 1750-54 Bessel

20.25

20.475

4. Greenwich Draconis 1750-54 Peters

20.522 ±0.079

1. Bradley's102 observational mean was 20.2 arc-seconds. However, he took the mean of the two extreme limits to get 20.25 (see also Sarton103). 2. Busch's reworkings were disputed by Auwers who also corrected for collimation and screw errors104. 3. Auwer's reworking corrected for a theoretical latitude variation by Newcomb 105. 4. Bessel and Peters both rejected Bradley's observations of Feb. 20, 21, and 23 in 1754 as disagreeing with all others and giving large remainders. Their values above omit these observations106.

(B). THE BRADLEY-TYPE OBSERVATIONS: To illustrate this technique, consider a drop of rain falling vertically. The rain has an aberration angle towards a car moving with constant speed, the angle depending on the rain's velocity. Similarly, a star's aberration angle (K) can be measured due to c and the essentially constant orbital speed of the earth. A constant value Kc = 6144402 has been adopted from the current I.A.U. value of K = 20.49552 arc-seconds. Table 2 gives the results from Bradley's observations from 1726 to 1754 on 24 stars. The final average value omitting both of Busch's disputed reworkings was 20.437 arc-seconds. The average date is 1740 for a c value of 300,650 Km/s, just 858 Km/s above the present value for c. If Busch's reworkings are accepted, this mean figure increases to 1632 Km/s above c now. Table 3 lists 63 aberration determinations from 1740 to 1930 given by Kulikov 23 and Newcomb 24. Only the dated values are included and repeats are omitted. Basically the same type of equipment was used during this time with basically the same error margins, while observational methods were substantially unaltered. The mean of all data is 76.2 Km/s above c now. The t-statistic thus indicates that the hypothesis that c equaled c today during these experiments can be rejected at the 93.9% confidence interval. Figure I presents the results from the Pulkova Observatory. That mean is 88 Km/s above c now for a mean date of 1879. However, one mean value does not give the full picture. If Table 3 is split into 50 year segments, and the mean c value in each segment is taken, and the difference of the mean from c now is noted, the results become: TABLE B

DATE

C MEAN (Km/s) DIFFERENCE (Km/s)

1765 ±25 300,555

763

1865 ±25 299,942.5

150

1915 ±25 299,812

20

The difference column indicates the trend for the mean to become successively higher further back in time. This suggests that the above statistical rejection of a constant c proposal is all the more justified for these experiments. A least squares linear fit to all data also supports the likely alternative proposition, as it gives a decay of 4.83 Km/s per year. The Pulkova results in Fig. I indicate a decay of 6.27 Km/s per year with an acceptance of the decay correlation r = - 0.947 at the 99.9% confidence level. Newcomb 24 quotes errors for all these data as approximately three times the size of those for the following observations. Consequently, only the definitive values of Nyren (1883) and Struve (1841) and the comprehensively treated Bradley value with Lindenau are used in the final discussion. TABLE 3 - BRADLEY ABERRATION METHOD: PULKOVA VALUES MARKED * SEE FIG. I

AV.YR.

TIME OF OBS.

OBSERVER

K (Arc Seconds)

C VALUE (Km/s)

1740

1726-1754

Bradley: Reworked Average

20.437

300,650

1783

1750-1816

Lindenau: ±fr. weights

20.450 ±0.011

300,460 ±170

*1841

1840-1842

Struve: corrected 1853

20.463 ±0.017

300,270 ±250

*1841

1840-1842

Folk-Struve

20.458 ±0.008

300,340 ±120

*1843

1842-1844

Struve: ±fr. mean error

20.480 ±0.011

300,020 ±170

1843

1842-1844

Lindhagen-Schweizer

20.498 ±0.012

299,760 ±180

1858

1842-1873

Nyren-Peters

20.495 ±0.013

299,800 ±190

1864.5

1862-1867

Newcomb: weighted av.

20.490

299,870

1866.5

1863-1870

Gylden

20.410

301,050

1868

1863-1873

Nyren and Gylden

20.52

299,440

1870

1861-1879

Nyren-Wagner

20.483 ±0.003

299,980 ±50

1873

1871-1875

Nyren

20.51

299,580

1879.5

1879-1880

Nyren

20.52

299,440

1880.5

1879-1882

Nyren

20.517 ±0.009

299,480 ±130

*1883

1883-1883

Nyren: wtd. av. all obs.

20.491 ±0.006

299,850 ±90

1889.5

1889-1890

Kustner

20.490 ±0.018

299,870 ±260

1889.5

1889-1890

Marcuse

20.490 ±0.012

299,870 ±180

1889.5

1889-1890

Doolittle

20.450 ±0.009

300,460 ±130

1890.5

1890-1891

Comstock

20.443 ±0.011

300,560 ±170

1891.5

1890-1893

Becker

20.470

300,170

1891.5

1891-1892

Preston

20.430

300,750

1891.5

1891-1892

Batterman

20.507 ±0.011

299,630 ±170

1891.5

1891-1892

Marcuse

20.506 ±0.009

299,640 ±130

1891.5

1891-1892

Chandler

20.507 ±0.011

299,630 ±170

1892.5

1891-1894

Becker

20.475 ±0.012

300,090 ±180

1893

1892-1894

Davidson

20.480

300,020

1894.5

1894-1895

Rhys-Davis

20.452 ±0.013

300,430 ±190

1896

1893-1899

Rhys-Jacobi-Davis

20.470 ±0.010

300,170 ±150

1896.5

1896-1897

Rhys-Davis

20.470 ±0.011

300,170 ±170

1897

1897-1897

Grachev-Kowalski

20.471 ±0.007

300,150 ±100

1898.5

1898-1899

Rhys-Davis

20.470 ±0.011

300,170 ±170

1898.5

1898-1899

Grachev

20.524 ±0.007

299,380 ±100

1899

1899-1899

Grachev

20.474 ±0.007

300,110 ±100

1900.5

1900-1901

Internat. Lat. Serv.

20.517 ±0.004

299,480 ±60

1901.5

1901-1902

Doolittle

20.513 ±0.009

299,540 ±130

1901.5

1901-1902

Internat. Lat. Serv.

20.520 ±0.004

299,440 ±60

1903

1903-1903

Doolittle

20.525 ±0.009

299,360 ±130

1904.5

1904-1905

Ogburn

20.464 ±0.011

300,250 ±170

1905

1905-1905

Doolittle (wtd. av.)

20.476 ±0.009

300,080 ±130

1905

1904-1906

Bonsdorf

20.501 ±0.007

299,710 ±100

1906

1906-1906

Doolittle (wtd. av.)

20.498 ±0.009

299,760 ±130

1906.5

1904-1909

Bonsdorf et. al.

20.505 ±0.008

299,650 ±120

1907

1907-1907

Doolittle

20.504 ±0.009

299,670 ±130

1907

1906-1908

Bayswater

20.512 ±0.007

299,550 ±100

*1907.5 1907-1908

Orlov

20.491 ±0.008

299,860 ±120

1907.5

1907-1908

Internat. Lat. Serv.

20.525 ±0.004

299,360 ±60

1908

1908-1908

Doolittle

20.507 ±0.012

299,630 ±180

*1908.5 1908-1909

Semenov

20.518 ±0.010

299,460 ±150

1908.5

Internat. Lat. Serv.

20.522 ±0.004

299,410 ±60

1908-1909

1909

1909-1909

Doolittle

20.520 ±0.009

299,440 ±130

*1909.5 1904-1915

Zemtsov

20.500

299,730

*1909.5 1909-1910

Semenov

20.508 ±0.013

299,610 ±190

1910

1910-1910

Doolittle

20.501 ±0.008

299,710 ±120

*1914

1913-1915

Numerov

20.506

299,640

*1916

1915-1917

Tsimmerman

20.514

299,520

1922

1915-1929

Kulikov

20.512 ±0.003

299,550 ±50

1923.5

1911-1936

Spencer-Jones

20.498 ±0.003

299,760 ±50

*1926.5 1925-1928

Berg

20.504

299,670

1928

1928-1928

Spencer-Jones

20.475 ±0.010

300,090 ±150

1930.5

1930-1931

Spencer-Jones

20.507 ±0.004

299,630 ±60

1933

1915-1951

Sollenberger

20.453 ±0.003

300,420 ±50

*1935

1929-1941

Romanskaya

20.511 ±0.007

299,570 ±100

1935.5

1926-1945

Rabe (gravitational)

20.487 ±0.003

299,920 ±50

Whittaker101, Kulikov 107, suggest K = 20.511: c is then above c(now) for most values.

CLICK HERE TO SEE FIGURE I http://www.setterfield.org/report/fig1.jpg TABLE 4 - TOOTH WHEEL EXPERIMENTAL VALUES

EXPERIMENTER DATE

NUMBER BASE (meters) C VALUE (Km/s)

1. Fizeau

1849.5

28

8633

315300

2. Fizeau

1849.5

28

8633

313300

3. Fizeau

1855

-

8633

305650

4. Fizeau (?)

1855

-

8633

298000

5. Cornu

1872

658

10310

298500 ±300

6. Cornu

1874.8

624

22910

300400 ±300

7. Cornu-Helmert

*1874.8 624

22910

299990 ±200

8. Cornu-Dorsey

*1874.8 624

22910

299900 ±200

9. Young/Forbes

1880

5484

301382

12

10. Perrotin/Prim

1900.4

1540

11862.2

300032 ±215

11. Perrotin

*1900.4 1540

11862.2

299900 ±80

12. Perrotin

1901.4

-

299880 ±50

13. Perrotin

*1902.4 2465

45950.7

299860 ±80

14. Perrotin/Prim

*1902.4 2465

45950.7

299901 ±84

-

1. Fizeau108 journal value - base too short for accuracy. Wheel of 720 teeth at 12.6 revs/sec gave minimum intensity. 2. Textbook value109. Difference arising from interpretation of Fizeau's length measure of 70,948 leagues of 25 to the degree. 3. Values 2, 3, and 4 appeared110 in 1927 but were omitted in all more comprehensive discussions. Dorsey111 pointed out that further values were promised, but none are extant. 4. It is probable that this may be a bad citation for Foucault's result of 1862. 5. Cornu112. Rejected by Cornu113 due to systematic errors. Crude apparatus with low precision114. 6. Cornu115. Working to 4 figures only. Newcomb116 gives the wrong years for these determinations. This error copied by Preston117. 7. Result corrected by Helmert 118, discussed, verified119 despite Cornu's protest. Accepted by Birge120. Newcomb121, Preston117 and Michelson122 incorrectly attribute this value to Listing123. Michelson124 also misquoted the value. Probable error assessed by Todd125. 8. Cornu's result re-analyzed by Dorsey126 . 9. No probable error given and spread of results attributed to c varying with wavelength in vacuo127. Criticized severly by Newcomb128 and Cornu 129. Aluminum wheel of 150 teeth used. 10. Prim's analysis of after Perrotin's death - treatment method unsatisfactory - completely discarded by Prim 130. 11. Perrotin131. 12. Perrotin's 132 mean of the 1900.4 and 1902.4 determinations. 13. Perrotin133. 14. Prim's130 analysis of the 1902.4 determination after Perrotin's death.

(C). TOOTHED WHEEL EXPERIMENTS: In this method, an intense beam of light is chopped by a rotating toothed wheel, traverses a distance of several miles, returns via a mirror and is viewed between the teeth of the wheel. At certain speeds of rotation, the returning light will be blocked by the teeth, at other speeds it will be visible. From those measured speeds and the known distance, c is derived. This is often called the Fizeau method after its pioneer. Table 4 lists 14 results from this method. Those results marked (*) are usually considered reliable. The values obtained by Fizeau and Young / Forbes reflected problems with short baselines. Fizeau's pioneering experiments have been described as25 'admittedly but rough approximations...intended to ascertain the possibilities of the method.' Newcomb 26 pointed out that the performance of Young and Forbes' apparatus did not do justice to their method since the 12 experimental results 27 varied by over 4,000 Km/s.

The mean of the best data alone indicates that c was 117.7 Km/s above the current value for a mean date of 1891. This gives a confidence interval of 99.4% that c was not constant at its current value during these experiments. Additionally, a least squares linear fit to all 14 data points gives a decay of 164 Km/s per year, while the best data alone give a decay of 2.17 Km/s per year. These data all suggest a decay in c. This conclusion is reinforced by the fact that Perrotin obtained his value essentially using Cornu's equipment some 27 years later 28. Perrotin's mean is 65 Km/s below the mean of Cornu's reworked results, indicating that the decay effect was not primarily due to equipment limitations. (D). ROTATING MIRROR RESULTS: For this method, a beam of light is reflected from a rotating mirror to a distant fixed mirror and returned. The rotating mirror has meanwhile moved through an angle which results in the returned beam undergoing a measurable deflection from which c may be calculated knowing the path length and mirror rotation rate. This is often called the Foucault method. Table 5 lists the rotating mirror results. The pioneer experiments by Foucault29 were hampered by trouble with the screw of the micrometer and diffraction distortion 30, leaving his value uncertain. In 1880, Michelson 31 discarded his exploratory value of 1878. Newcomb also rejected his own 1880.9 and 1881.7 values (299,627 and 299,694 Km/s in air respectively) due to systematic errors from vibrations of an unbalanced mirror and irregular pivots. Two pairs of images were seen in the micrometer. As a consequence, Newcomb 32 insisted that his 'results should depend entirely on the measures of 1882.' To avoid criticism, these two values were included in the 1881.8 in vacuo mean with the 1882 result. If these uncertain values are omitted, the mean value is 40.3 Km/s above c today with a confidence level of 93.9% that c did not have its present value during those experiments. This is supported as a least squares linear fit to the six data points gives a decay of 1.85 Km/s per year with r = -0.932 and a confidence interval in the decay correlation of 99.6%. TABLE 5 - ROTATING MIRROR EXPERIMENTS

EXPERIMENTER DATE

NUMBER BASE (meters) C VALUE (Km/s)

1. Foucault

1862.8

80

20.0

298,000 ±500

2. Michelson

1878.0

10

152.4

300,140 ±480

3. Michelson

*1879.5 100

605.40

299,910 ±50

4. Newcomb

1881.8

2,550.95

299,810

5. Newcomb

*1882.7 66

3,721.21

299,860 ±30

6. Michelson

*1882.8 563

624.65

299,853 ±60

7. Michelson

*1924.6 80

35,426.23

299,802 ±30

8. Michelson

*1926.5 1600

35,426.23

299,798 ±15

255

9. Pease/Pearson

*1932.5 2885

1,610.4

299,774 ±10

* Values generally accepted as reliable. 1. Foucault134 obtained a deflection of 0.7 mm with 500 revs/sec from a one-faced mirror with 'very unfavorable limitations' experimentally (Todd 135). 2. Michelson136 obtained a deflection of 7.5 mm with 130 revs/sec from a one-faced mirror and a 'crude piece of apparatus' (Michelson 137). De Bray138 has incorrect baseline and probable error. 3. Michelson139 obtained a deflection of 133.2 mm with 257.3 revs/sec from one-faced mirror. Corrected result in Michelson140. Newcomb 141 misquotes the corrected value. Todd135 quoted erroneous figures from an incorrect Abstract 142 that someone had prepared from Michelson143. 4. Mean of 2 rejected values and accepted final value. Average deflection 18 cm from 4-faced mirror speeds of 114-268 revs/sec. The three series comprised 255 experiments. The shorter path length of series 1 is quoted. 5. Newcomb 144. Accepted result of 3rd series. 6. Michelson145. Average deflection of 138 mm from 1-faced mirror speeds pf 129-259 revs/sec. 7. Michelson146. Polygonal mirror method combining features of the toothed wheel and rotating mirror. Measurements on the undisplaced image. Glass octagon used at 528 revs/sec. The corrected value for the series in Michelson147 is omitted from the Birge148 list but appears in Froome and Essen149 and Table 11 below. 8. Michelson150 used polygonal mirrors of 8, 12, 16 faces. Zero deflection at 264-528 revs/sec used. Result corrected for group velocity by Birge 151. Final values from the 5 mirrors agreed within ±1 Km/s. Michelson152 and others 153 make misleading statements and quote incorrect values. 9. Michelson/Pease/Pearson154. Michelson died as series began. Mirror speeds of 585-730 revs/sec for 32 faces used. Null position not used. Convenient speeds gave deflections near 0.01 mm. Micrometer problems noted155. Unstable baseline156 gave regular and irregular variations in c values hourly, daily, and in periods up to 1 year.

For Pease and Pearson, a long baseline on unstable alluvial soil seemed to cause varying c values with33 'A correlation between fluctuations in the results and the tides on the sea coast' and lunar phases34. Omitting their final result gives a mean value 52.1 Km/s above c now in 1899. This gives a confidence interval of 95.6% that c did not equal c now during that time. In addition, a decay of 1.74 Km/s per year results, with r = -0.905 and a confidence level of 98.2% in the decay correlation. It is also worthy of note that Michelson's determinations 1879.5 and 1882.8 were both with the same equipment, as were the 1924.6 and 1926.5 pair35. On both occasions a lower value for c was recorded at the later date, ruling out equipment variation as the cause and enhancing the suspicion that a decay in c itself was responsible. As mentioned above, the concordance of Newcomb's 1882.7 result with Michelson's 1882.8 value and the definitive aberration value of Nyren in 1883 lends credence to the notion that c was actually higher at the time of those measurements. (E). KERR CELL RESULTS:

This method is similar to the toothed wheel, but the light beam is chopped electrically. The transit times of electrons in detection tubes, light passing through glass, liquids, and air, all systematically result in an estimate of c below the real value. Birge11 applied uniform corrections to four results by this method. In so doing he noted that 'The base line in each case was about 40 meters' and gives the probable error for each as about 10 Km/s indicating similar experimental conditions. Any trend should not be an instrumental effect. The results are given in Table 6. The linear fit of data gives a decay of 1.03 Km/s per year with r = -0.81 at the 90.5% confidence level. The systematic errors give low values for c, but a decay is still apparent. These systematic errors seem not to be the cause of the decay trend, therefore, but shift this trend into a lower range of c values. (F). THE SIX METHODS USED 1945-1960: Froome and Essen 36 and Taylor et al. supply 23 data points as the evidence from these six new methods which are listed in Table 7. Three radar values are omitted as they did not measure atmospheric moisture, which critically affects the radio refractive index. Under these circumstances the final c value is somewhat spurious 37. Also omitted on the basis of Mulligan and McDonald's statements 38 are two early spectral line results with errors due to imperfect wavelength measurements. Results spread over 180 and 500 Km/s also disqualify two quartz modulator values39 of 1950. The linear fit gives a decay of 0.19 Km/s per year with a confidence level of 99.0% in the data showing c as higher than now during those 15 years. Five of the six methods gave a decay individually, radar being the exception due to the removal of a signal intensity error in the later results 40. TABLE 6 - KERR CELL VALUES* OF C

EXPERIMENTER DATE NUMBER VALUE OF C (Km/s) 1. Mittelstaedt

1928.0 775

299,786 ±10

2. Anderson

1936.8 651

299,771 ±10

3. Huttel

1937.0 135

299,771 ±10

4. Anderson

1940.0 2895

299,776 ±10

* Uniform corrections applied to all experiments by Birge 157. 1. Preliminary report by Karolus and Mittelstaedt158 with a final report by Mittelstaedt 159. De Bray has incorrect base length 160. 2. Initial report by Anderson161 and final corrections including the phase velocity given by Anderson162. 3. Report by Huttel 163. Uncorrected original value 299,768 ±10 Km/s. 4. Improved techniques removed glass from the light path. Other variables also altered. Dorsey164 stated the precision essentially as for his earlier experiment at ±14 Km/s. However, Birge165 puts it at ±6. Average again ±10 Km/s.

TABLE 8 - RESULTS 1960-1983 - MAINLY LASER

DATE EXPERIMENTER

REFERENCE VALUE OF C (Km/s)

1.

1966

Karolus

190

299,792.44 ±0.2

2.

1967

Simkin et. al.

191

299,792.56 ±0.11

3.

1967

Grosse

192

299,792.50 ±0.05

4.

1972

Bay/Luther/White

193

299,792.462 ±0.018

5.

1972

NRC/NBS

194

299,792.460 ±0.006

6.

1973

Evenson et. al.

195

299,792.4574 ±0.0011

7.

1973

NRC/NBS

194

299,792.458 ±0.002

8.

1974

Blaney et. al.

196

299,792.4590 ±0.0008

9.

1978

Woods/Shotton/Rowley 197

299,792.4588 ±0.0002

10. 1979

Baird/Smith/Whitford

198

299,792.4581 ±0.0019

11. 1983

NBS(US)

199

299,792.4586 ±0.0003

1. Modulated light. Baseline error corrected 1967 (see Froome and Essen 200). 2. Microwave interferometer. 3. Geodimeter. 4-11. Laser methods. Discussion in Mulligan 201. 6. Result corrected for new definition by Blaney et. al. 196.

TABLE 7 - RESULTS* BY SIX METHODS 1945-1960

DATE EXPERIMENTER

REFERENCE MEASUREMENT METHOD VALUE OF C (Km/s)

1.

1947

Essen,Gordon-Smith

166

Cavity Resonator

299,798 ±3

2.

1947

Essen,Gordon-Smith

166

Cavity Resonator

299,792 ±3

3.

1949

Aslakson

167

Radar

299,792.4 ±2.4

4.

1949

Bergstrand

168

Geodimeter

299,796 ±2

5.

1950

Essen

169

Cavity Resonator

299,792.5 ±1

6.

1950

Hansen and Bol

170

Cavity Resonator

299,794.3 ±1.2

7.

1950

Bergstrand

171

Geodimeter

299,793.1 ±0.26

8.

1951

Bergstrand

172

Geodimeter

299,793.1 ±0.4

9.

1951

Aslakson

173

Radar

299,794.2 ±1.4

10. 1951

Froome

174

Radio Interferometer

299,792.6 ±0.7

11. 1953

Bergstrand (av. date)

175

Geodimeter

299,792.85 ±0.16

12. 1954

Froome

176

Radio Interferometer

299,792.75 ±0.3

13. 1954

Florman

177

Radio Interferometer

299,795.1 ±3.1

14. 1955

Scholdstrom

178

Geodimeter

299,792.4 ±0.4

15. 1955

Plyler,Blaine,Connor

179

Spectral Lines

299,792 ±6

16. 1956

Wadley

180

Tellurometer

299,792.9 ±2.0

17. 1956

Wadley

180

Tellurometer

299,792.7 ±2.0

18. 1956

Rank,Bennett,Bennett 181

Spectral Lines

299,791.9 ±2

19. 1956

Edge

182

Geodimeter

299,792.4 ±0.11

20. 1956

Edge

182

Geodimeter

299,792.2 ±0.13

21. 1957

Wadley

180

Tellurometer

299,792.6 ±1.2

22. 1958

Froome

183

Radio Interferometer

299,792.5 ±0.1

23. 1960

Kolibayev (av. date)

184

Geodimeter

299,792.6 ±0.06

Geodimeters (8 values): Decay of 0.22 Km/s per year Cavity Resonators (4 values): Decay of 0.53 Km/s per year Radio Interferometers (4 values): Decay of 0.04 Km/s per year Tellurometers (3 values): Decay of 0.20 Km/s per year Spectral lines (2 values): Decay of 0.10 Km/s per year Radar (2 values): Error removal gave higher c value in 2nd result

* Data as discussed by Froome and Essen185 and Taylor et. al.186. 1. Mean preliminary value from the two modes used in the final experiment. See Froome and Essen, Table III, p.61. 6. Reference in the name of Bol only. This value by DuMond and Cohen 187 is corrected for the 'skin effect' mentioned by Froome and Essen 188. 11. Weighted mean result 189 for period 1949-1957.

Froome and Essen 41 made an important statement, reiterating that 'As with the unit of length, errors in the unit of time have never yet presented a limitation in the accuracy of measuring the velocity of light.' A variation in c cannot be attributed to these causes, therefore. It also becomes apparent that the linear fit decay rate is decreasing with time. Table C lists the mean

decay rates in Km/s per year and the date. The first value is derived by taking the two most conservative individual values by the Roemer method rather than the means. One was the 1877 official Harvard reductions. The other was Roemer's 1675 value. Here, for comparison purposes only in Tables C and D, the minimum point in the quoted error limit was used. Roemer's value thus became 302,200 Km/s. TABLE C

DATE

DECAY (Km/s/yr)

1776 ±100 11.31 1838 ±98

4.83

1861 ±120 2.79 1887 ±14

2.17

1903 ±24

1.85

1934 ±6

1.03

1953 ±7

0.19

This would seem to indicate that any decay is following a non-linear pattern. These two facts have a bearing on the post 1960 results. A tapering rate of decay may get to the stage where it is undetectable or ceases, depending on the decay pattern. The significance of this is enforced by the results of equation (34) and the remarks pertaining thereto. (G). THE POST 1960 RESULTS: Table 8 lists 11 values of c that were obtained between 1960 and 1983. Eight of these used laser techniques. A linear fit of all 11 data points gives a decay of 0.0026 Km/s per year. The eight laser values alone give a decay of 0.00013 Km/s per year. The last six give a 0.00004 Km/s per year INCREASE, while the last five and four values give c as constant, or decaying at 0.000097 Km/s per year respectively. The first seven data points 1966-1973 show a decay of 0.0058 Km/s per year. Confidence intervals for c not constant were about 50% in all cases. Minimum laser values were recorded in 1973. The only conclusion to be drawn from these figures of low statistical confidence is that any decay during this period would have occurred at a very slow rate, perhaps may have ceased altogether, or c may have begun to increase at some time in this period. The reason for these inconclusive observations becomes apparent later. A method used to overcome the problem is mentioned below, and the results indicate continuing decay at a rate lower than that prior to 1960. CLICK HERE TO SEE FIGURE II http://www.setterfield.org/report/fig2.jpg

TABLE 9 - C VALUES BY THE RATIO OF ESU/EMU

EXPERIMENTERS

DATE MEAN VALUE (Km/s)

RANGE ERROR OR PRECISION

REFERENCE

1. Weber/Kohlrausch 1856

310,700

±20,000 Km/s

202

2. Maxwell

1868

284,000

±20,000 Km/s

203

3. W.Thomson/King

1869

280,900

288,000-271,400

204

4. McKichan

1874

289,700

299,900-286,300

205

5. Rowland

1879

-

301,800-295,000

206

6. Ayrton/Perry

1879

296,000

Errors of 1/100

207

7. Hockin

1879

296,700

-

208

8. Shida

1880

295,500

Precision of 1%

209

9. Stoletov

1881

-

300,000-298,000

210

10. Exner

1882

287,000

Errors up to 8/100

211

11. J.J.Thomson

1883

296,400

±20,000 Km/s

212

12. Klemencic

1884

301,880

303,100-300,100

213

13. Colley

1886

301,500

Errors up to 2/100

214

14. Himstedt

*1887 300,570

301,460-299,990

215

15. Thomson et. al.

1888

292,000

Precision of 1.75%

216

16. W.Thomson

1889

300,500

-

212

17. Rosa

*1889 300,000

301,050-299,470

217

18. J.Thomson/Searle

*1890 299,600

Errors of 1/500

218

19. Pellat

*1891 300,920

Errors of 1/500

219

20. Abraham

*1892 299,130

299,470-298,980

220

21. Hurmuzescu

*1897 300,100

Errors of 1/1000

221

22. Perot/Fabry

*1898 299,730

Errors of 1/1000

222

23. Webster

1898

302,590

Precision of 1%

223

24. Lodge/Glazebrook

1899

300,900

Errors up to 4/100

224

25. Rosa/Dorsey

*1906 299,803

±30 Km/s

225

NOTE:- All Table 9 values from uniform treatment by Abraham43. Froome and Essen226 applied a uniform correction of 95 Km/s to these results for air to bring them to c in vacuo. Numbers 3, 4, and 11. Mean value from Froome and Essen 212. 14. Mean date of 3 experiments. 25. Recently corrected value to vacuum conditions etc. (see text).

TABLE 10 - C VALUES BY WAVES ON WIRES

EXPERIMENTER

DATE No.

C VALUE (Km/s)

RANGE OR ERROR (Km/s)

REFERENCE

1. Blondlot

1891

12

302,200

312,300-295,500

227

2. Blondlot

1893

8

297,200

302,900-292,100

228

3. Trowbridge/Duane

1895

7

300,300

303,600-292,300

229

4. Saunders

1897

6

299,700

299,900-293,400

230

5. MacLean

1899

-

299,100

-

231

6. Mercier

1923

5 sets

299,795

±30

232

NOTE:- Table 10 values in air from discussion by Blondlot43. Number 5: MacLean used a free space technique. Number 6: Mercier value corrected to in vacuo (see text).

(H). THE RATIO ESU/EMU AID WAVES ON WIRES: The charge on a capacitor is measured in electrostatic and electromagnetic units in the first of these methods. The wavelength and frequency of a radio wave transmitted along a pair of parallel wires are measured in the second. The values of c obtained by these two methods did not achieve high accuracy except in two cases. A glance at Tables 9 and 10 tells the story. The variation in c values obtained during a determination by these method could go as high as 16,000 Km/s or more. In the cases of numbers 1, 2, and 11 in Table 9, Fowles 42 estimated the error as ±20,000 Km/s. In general the spread of values of the velocity in any one determination ranged from 1% to 5%. This is in marked contrast to the 0.02% or lower obtained by the optical methods. These values have thus been omitted from the main analysis. Despite this, the waves on wires experiments listed in Table 10 still exhibit a decay trend of 7.47 Km/s per year. After a lengthy treatment of the esu/emu ratio experiments, Abraham43 concluded that the values marked with an asterisk in Table 9 were the most accurate. Although the errors of these eight experiments vary up to about 0.5%, they, too, exhibit a decay trend of about 24 Km/s per year with a mean about 189 Km/s above c now.

The two shining exceptions to the low precision are the Rosa/Dorsey value from the ratio of electrostatic to electromagnetic units, and that of Mercier from the waves on wires. Both of these values have recently been reassessed44 : the first with the best value for the unit of resistance and air humidity (see also Florman45), the second for atmospheric conditions. Froome and Essen 46 also point out that these experiment were the only ones by those two methods that were 'as accurate as the direct measurements of the speed of light at that time...'. Accordingly, these two alone from Tables 9 and 10 are included in the following analysis. (I). CONCLUSION FROM COLLECTIVE DATA: When all 163 values involving 16 different methods are used, the linear fit to the data gives a decay of 38 Km/s per year. If only the best data from Table 9, chosen by Abraham43, are coupled with all other figures, then 146 values indicate a decay of 43 Km/s per year. The data mean is 753 Km/s above c now and the hypothesis that c has been constant at today's value over the last 300 years can be rejected with a confidence interval of 97.2%. Nevertheless, if we summarize from the above discussion the difference of the best data means from c now in Km/s at the mean date, we obtain the following: TABLE 11 - REFINED LIST OF C DATA (See Figs. II, III, IV)

NO. DATE OBSERVER

METHOD

VALUE OF C (Km/s)

1

1740

Bradley

Aberration

300,650

2

1783

Lindenau

Aberration

300,460 ±160

3

1843

Struve

Aberration

300,020 ±160

4

1861

Glasenapp

Jupiter Satellite

300,050

5

1874.8 Cornu (Helmert)

Toothed Wheel

299,990 ±200

6

1874.8 Cornu (Dorsey)

Toothed Wheel

299,900 ±200

7

1876.5 Harvard Observat.

Jupiter Satellite

299,921 ±13

8

1879.5 Michelson

Rotating Mirror

299,910 ±50

9

1882.7 Newcomb

Rotating Mirror

299,860 ±30

10

1882.8 Michelson

Rotating Mirror

299,853 ±60

11

1883

Aberration

299,850 ±90

12

1900.4 Perrotin

Toothed Wheel

299,900 ±80

13

1902.4 Perrotin

Toothed Wheel

299,860 ±80

14

1902.4 Perrotin/Prim

Toothed Wheel

299,901 ±84

15

1906.0 Rosa and Dorsey

Electromag. Units 299,803 ±30

16

1923

Waves on Wires

Nyren

Mercier

299,795 ±30

17

1924.6 Michelson

Polygonal Mirror

299,802 ±30

18

1926.5 Michelson

Polygonal Mirror

299,798 ±15

19

1928.0 Mittelstaedt

Kerr Cell

299,786 ±10

20

1932.5 Pease/Pearson

Polygonal Mirror

299,774 ±10

21

1936.8 Anderson

Kerr Cell

299,771 ±10

22

1937.0 Huttel

Kerr Cell

299,771 ±10

23

1940.0 Anderson

Kerr Cell

299,776 ±10

24

1947

Essen,Gordon-Smith Cavity Resonator

299,798 ±3

25

1947

Essen,Gordon-Smith Cavity Resonator

299,792 ±3

26

1949

Aslakson

Radar

299,792.4 ±2.4

27

1949

Bergstrand

Geodimeter

299,796 ±2

28

1950

Essen

Cavity Resonator

299,792.5 ±1

29

1950

Hansen and Bol

Cavity Resonator

299,794.3 ±1.2

30

1950

Bergstrand

Geodimeter

299,793.1 ±0.26

31

1951

Bergstrand

Geodimeter

299,793.1 ±0.4

32

1951

Aslakson

Radar

299,794.2 ±1.4

33

1951

Froome

Radio Interferom. 299,792.6 ±0.7

34

1953

Bergstrand

Geodimeter

35

1954

Froome

Radio Interferom. 299,792.75 ±0.3

36

1954

Florman

Radio Interferom. 299,795.1 ±3.1

37

1955

Scholdstrom

Geodimeter

299,792.4 ±0.4

38

1955

Plyler et. al.

Spectral Lines

299,792 ±6

39

1956

Wadley

Tellurometer

299,792.9 ±2.0

40

1956

Wadley

Tellurometer

299,792.7 ±2.0

41

1956

Rank et. al.

Spectral Lines

299,791.9 ±2

42

1956

Edge

Geodimeter

299,792.4 ±0.11

43

1956

Edge

Geodimeter

299,792.2 ±0.13

44

1957

Wadley

Tellurometer

299,792.6 ±1.2

45

1958

Froome

Radio Interferom. 299,792.5 ±0.1

46

1960

Kolibayev

Geodimeter

299,792.6 ±0.06

47

1966

Karolus

Modulated Light

299,792.44 ±0.2

299,792.85 ±0.16

48

1967

Simkin et. al.

Microwave Interf. 299,792.56 ±0.11

49

1967

Grosse

Geodimeter

299,792.50 ±0.05

50

1972

Bay,Luther,White

Laser

299,792.462 ±0.018

51

1972

NBS (Boulder)

Laser

299,792.460 ±0.006

52

1973

Evenson et. al.

Laser

299,792.4574 ±0.0011

53

1973

NRC, NBS

Laser

299,792.458 ±0.002

54

1974

Blaney et. al.

Laser

299,792.4590 ±0.0008

55

1978

Woods et. al.

Laser

299,792.4588 ±0.0002

56

1979

Baird et. al.

Laser

299,792.4581 ±0.0019

57

1983

NBS (US)

Laser

299,792.4586 ±0.0003

TABLE D

METHOD DATE DIFFERENCE (Km/s) Roemer*

1675

2408

Bradley

1765

763

Bradley

1865

150

Roemer*

1877

129

Fizeau

1891

117.7

Foucault

1899

52.1

Foucault

1905

40.3

Bradley

1915

20.0

Various

1953

0.72

The Roemer method is again represented by two individual values as in Table C. However, it is desirable to use only the most reliable values to determine the true situation. Birge11 summarized the best 13 values by six methods in the period 1874.8 to 1940, including those of Rosa/Dorsey and Mercier. Let us take Birge's basic list as definitive, as did Huttel 47, Bergstrand48, and Cohen and DuMond49. These same data were advocated by de Bray50,51, and Mittelstaedt52. If the Table 7 and 8 values are added with the remaining starred data from Table 4, then a core of 51 of the most reliable results by 14 methods emerges. The most conservative estimates by the Roemer method are the official 1876.5 ±32 value and the 1861 ±13 result. Newcomb 26 lists Nyren's 1883 treatment as the most definitive value by the Bradley method. Its best conservative early data are Lindenau's and Struve's 1843 value with Bradley's reworked average. These total an extra six points from two other methods. Thus, 57

best possible data by 16 methods can be listed as in Table 11 and associated Figures II, III, IV. These Table 11 data give a mean c value at 52.5 Km/s above c now. Statistically, these data give a confidence interval of 99.46% that c was above its present value. A least squares linear fit indicates a decay of 2.79 Km/s per year with r = - 0.878 and a confidence of 99.99% in the decay correlation. Non linear fits give an improvement on the value of r. Initial independent analyses of these data at Newcastle University53 concluded that 'Any two stage curve fit gives a highly significant improvement over the assumption of a constant c value. Residuals reduced from 22,000 to under 2000.' Thus 16 different methods of measurement by almost 50 different instruments all exhibit the decay trend. The only values that went against the trend were all rejected by the experimenters themselves or their peers. If this were simply the result of equipment unreliability and improved measurement techniques as Dorsey implied in 1944, then it would be a most unusual phenomenon in itself. Yet historically the measurements and past equipment have only been called into question because their values for c differed from those currently prevailing. This itself argues against any 'intellectual phase-locking'. The other option is that all 16 methods were registering c correctly within their error margins, but that c itself has changed. The above results are typical of a decaying quantity. The atom and atomic constants now need to be examined to see if they support the idea and answer Birge's criticism. TABLE 12 - OPTIONS WITH CHANGING C

OPTION I

OPTION II

OPTION III

2  0 = CONST:  01/c

0 = CONST: 01/c2

 0 1/c:  0 1/c

THEN

THEN

THEN

V = m2/(40r) = C-IND* V = q2/(40r) = C-IND* From Options Iand II therefore

therefore

m2 /0 = C-IND*

q2/0 = C-IND*

m2/0 = C-IND* = q2/ 0

magnetic pole m 1/c

unit charge q 1/c

m 1/c:q 1/c

NOTE:- The symbol () is taken to mean 'proportional to' throughout this article. * C-IND means that the expression is independent of variation in c. N.B. For observed results of wavelength and frequency to hold, atomic and dynamical length standards and distances remain unchanged. Potentials V are thus taken over constant distance r.

IV. PHYSICAL QUANTITIES AFFECTED BY C DECAY:-

(A). MAXWELL'S LAWS AND THE ELECTRONIC CHARGE: If energy is to be conserved as c decays, then Maxwell's Laws must hold. Therefore if the electric permittivity is  0 and the magnetic permeability is  0 for free space, then as 2 1/2  0 0 = [1/c ]

(1)

there will be three valid possibilities as illustrated in Table 12. In each case the electric and magnetic potential, V, is conserved. An additional requirement is that wavelengths and atomic or dynamical distances must be invariant from the experimental results mentioned in Birge's assessment 13 of the c decay proposal. Atomic orbit radii are thus required to be invariant and consequently also N 0, the Avogadro Number, if these experimental results are to be upheld. From the point of view of Table 12, the key requirement is the constancy of q 2/ 0. This has 54 55 been demonstrated over astronomical time by Dyson , Peres , Bahcall and Schmidt56 and Wesson57 on the basis of experiment and also by the observed abundances of radioactive elements. This cosmological constancy is an important result. Conservation also requires that the volt V = hf/2e, of measured potential V, is c independent, along with the energy hf. The Josephson frequency is f and h is Planck's constant. This definition by Cohen and Taylor 58 and Finnegan et al.59, demands the constancy of the electronic charge, e, quite independently of  0. Theory therefore favors Option I from Table 12. The value of e has been measured by the oil-drop and X-ray methods. The former obtains a value of e in association with  0, while the latter obtains e via the Avogadro Number, N0. Table 13 lists the results from both methods along with the best adjusted values. The Avogadro Number, N0, is experimentally implied as invariant as noted above. The X-ray method essentially measures N0, and then, from the relation F = N0e, where F is the Faraday, the electronic charge is determined. A linear fit to the X-ray data yields a decay of 0.0000148 x 10-10 ESU/year with a confidence in e not constant at the last X-ray value (31) of 63.72%. Given the invariance of N 0, this measured constancy of e also establishes the constancy of F from the above equation. Furthermore, this constancy of e is completely independent of  0. A least squares linear fit to the oil-drop data gives an increase of 0.000383 x 10-10 ESU per year with a confidence interval of 76.8% in e not constant at the final oil-drop value. The adjusted value results are similar. Given the experimental constancy of e independent of  0, from the X-ray results, these oil drop results indicate the constancy of  also. An increase of 0 -10 0.000026 x 10 ESU per year results from the analysis of all data in Table 13. A confidence level of 55.4% in e not constant at its 1973 value is obtained. Theory and experiment thus combine to validate the invariance of e,  0, F and N0. TABLE 13 - VALUES OF THE ELECTRONIC CHARGE e

AUTHORITY

DATE VALUE OF e x 10-10 ESU METHOD REF.

1. Millikan

1913

4.8049 ± 0.0022

OD

233

2. Millikan

1917

4.8071 ± 0.0038

OD

234

3. Millikan

1917

4.8059 ± 0.0052

OD

234

4. Millikan

1920

4.803 ± 0.005

OD

235

5. Wadlund#

1928

4.7757 ± 0.0076

XR

236

6. Backlin#

1928

4.794 ± 0.015

XR

237

7. R.T.Birge

1929

4.801 ± 0.005

AV

238

8. Bearden

1931

4.8022

XR

239

9. Soderman

1935

4.8026 ± 0.003

XR

240

10. Backlin

1935

4.8016

XR

241

11. Bearden

1935

4.8036 ± 0.0005

XR

242

12. DuMond/Bollman

1936

4.799 ± 0.007

XP

243

13. R.T.Birge

1936

4.8029 ± 0.0005

AV

244

14. DuMond/Bollman

1936

4.805

XM

245

15. Backlin/Flemberg

1936

4.7909 ± 0.0114

OD

246

16. Ishida et. al.

1937

4.8453 ± 0.0030

OD

247

17. Dunnington

1938

4.8025 ± 0.0004

XM

248

18. Dunnington

1938

4.8036 ± 0.0048

OM

248

19. Bollman/DuMond

1938

4.803

AV

249

20. R.T.Birge

1939

4.8022 ± 0.0010

AV

250

21. Miller/DuMond

1939

4.801 ± 0.002

XR

251

22. Miller/DuMond

1939

4.8005 ± 0.0004

XM

251

23. DuMond

1940

4.80650

AV

252

24. Hopper and Laby

1940

4.8137 ± 0.0030

OD

253

25. R.T.Birge

1941

4.8025 ± 0.0010

XM

254

26. R.T.Birge

1944

4.8030 ± 0.0021

AV

255

27. R.T.Birge

1944

4.8021 ± 0.0006

XM

255

28. DuMond and Cohen 1947

4.80193 ± 0.0006

XM

256

29. DuMond and Cohen 1947

4.8024 ± 0.0005

AV

257

30. Bearden and Watts

4.80217 ± 0.00006

AV

258

31. DuMond and Cohen 1952

4.80220 ± 0.0001

XM

259

32. DuMond and Cohen 1952

4.80288 ± 0.00021

AV

259

33. Cohen et. al.

4.80286 ± 0.00009

AV

260

1950

1955

34. Cohen and DuMond 1963

4.80298 ± 0.00020

AV

261

35. Cohen and DuMond 1965

4.80313 ± 0.00014

AV

262

36. Taylor et. al.

1969

4.80325 ±0.0000021

AV

263

37. Cohen and Taylor

1973

4.803242 ±0.0000014

AV

264

NOTE:- # Pioneer results 'not as accurate as the oil drop value' and 'likely to contain various unsuspected sources of systematic error' (Birge238). Omitted from analysis as did Birge238 and Bearden242. OD = oil drop: OM = oil-drop mean: XR = X-ray: XM = X-ray Mean: XP = X-ray powder method (imprecise): AV = best adjusted value. CORRECTED VALUES: OD values 2, 15, 16, 24, by Birge255. Value 1 used the Birge 1944 air viscosity and his 1929 corrections as for 2. Value 3 by Dunnington 248. XR values 8-10 by DuMond252. XR method gives e independent of  0.

These above data indicate that Option I from Table 12 is upheld, and will be followed here, despite the advantages of the symmetry of Option III. The permeability of free space, 0 , is thus proportional to 1/c 2. Variation in this permeability is also one possible cause of the timedependence of c. Wesson57 has already noted this suggestion for other reasons by Creer. The systematic variation of c under these conditions may be indicative of a systematic alteration of the physical character of the universe due to expansion or contraction under, perhaps, the action of the cosmological constant. (B). ATOMIC REST-MASSES: Chemical and nuclear reactions obey the standard equation E = mc2

(2)

which O'Rahilly 60 has demonstrated can be derived non-relativistically and without any assumptions about c behavior. For energy E to be conserved in all chemical and nuclear reactions requires that m ~ 1/c 2

(3)

The symbol ~ means 'proportional to' throughout this report. That this result is not unexpected for charged particles follows from the classical relation for their effective mass m as given by French 6l where 2 m = q2/(6 0 rc )

and the particle has charge q and radius r.

(4)

An experimental check of this proposal that atomic rest-masses should increase with time is given by Table 14. Here e/(mc) is listed for electrons, rather than just m, in order to eliminate the effects of other measured quantities, namely e and c, and the result is in EMU/gm. In the majority of early cases, m was determined by conversion from this same ratio. The fine structure method (marked FS in Table 14) used the Faraday to obtain e/(mc). However, F has already been demonstrated as invariant in the previous section, leaving a valid result. A leastsquares linear fit to all data gives a decay of 679.9 EMU/gm. per year, with a confidence interval for e/(mc) not being constant at the 1973 value of 99.17%. However, eight different methods were used to determine e/(mc). The results of each method individually still show a decay (except for the two methods that are represented by single observations) and results are listed with Table 14. This reinforces the conclusion that the quantity m is actually varying as the result is completely independent of the method used in the measurement. Note that the issue of mass and gravitation is dealt with later in V (B). From this it becomes apparent that rest-masses are invariant when measured in their own time-frames, whether dynamical or atomic. However, when atomic rest-masses are measured dynamically the above variation is noted. TABLE 14 - VALUES OF THE SPECIFIC CHARGE e/(mc)

AUTHORITY

DATE e/(mc) x 10 7 EMU/gm METHOD REF

1. J.J.Thomson

1900

1.7591 ±0.0005

CF

265

2. Bestelmeyer

1910

1.76 ±0.02

MM

238

3. Paschen

1916

1.768 ±0.003

FS

266

4. Babcock

1923

1.761 ±0.001

ZE

267

5. Gerlach

1926

1.766

MM

238

6. Wolf*

1927

1.7690 ±0.0018

CF

268

7. Houston*

1927

1.7617 ±0.0008

FS

269

8. Babcock

1929

1.7606 ±0.0012

ZE

270

9. Perry/Chaffee*

1930

1.7611 ±0.0010

DV

271

10. Campbell/Houston 1931

1.7579 ±0.0025

ZE

272

11. Dunnington

1932

1.7592 ±0.0015

MD

273

12. Kirchner*

1932

1.7590 ±0.0009

DV

274

13. Kinsler/Houston*

1934

1.7570 ±0.0007

ZE

275

14. Shane/Spedding*

1935

1.75815 ±0.0006

FS

276

15. Houston#

1937

1.7590 ±0.0005

FS

277

16. Dunnington*

1937

1.75982 ±0.0004

MD

278

17. Williams*

1938

1.75797 ±0.0005

FS

279

18. Shaw*

1938

1.7582 ±0.0013

CF

280

19. Bearden*

1938

1.76006 ±0.0004

XR

281

20. Chu*

1939

1.76048 ±0.00058

FS

282

21. Robinson*

1939

1.75914 ±0.0005

FS

283

22. Goedicke*

1939

1.7587 ±0.0008

CF

284

1.75913 ±0.00027

FS

285

23. Drinkwater et. al.* 1940 24. Birge

1941a 1.7592 ±0.0005

MM

254

25. DuMond/Cohen

1947

1.75920 ±0.00038

MM

256

26. Bearden and Watts 1951

1.758912 ±0.00005

IM

258

27. Bearden and Watts 1951

1.758896 ±0.000028

MM

259

28. Gardner

1951

1.75890 ±0.00005

MD

286

29. DuMond/Cohen

1952

1.75888 ±0.00005

MM

259

30. Cohen et. al.

1955

1.75890 ±0.00002

MM

260

31. Cohen/DuMond

1965

1.759796 ±0.000006

MM

262

32. Taylor et. al.

1969

1.7588028 ±0.0000054 MM

263

33. Cohen and Taylor

1973

1.7588047 ±0.0000049 MM

264

MM. Mean of Methods etc.(10): Decay = 630.5 EMU/gm/year FS. Fine Structure (8): Decay = 3620 EMU/gm/year ZE. Zeeman Effect (4): Decay = 3756 EMU/gm/year CF. Crossed Fields (4): Decay = 61.61 EMU/gm/year MD. Magnetic Deflection (3): Decay = 265.9 EMU/gm/year DV. Direct Velocity (2): Decay = 10500 EMU/gm/year XR. X-ray Refraction (1): IM. Indirect Method (1):

* Corrected by Birge287: # Corrected in DuMond252 .

Conversely, when dynamical phenomena are measured atomically, a variation in the gravitational constant, G, is noted. (C). THE ATOM AND PLANCK'S CONSTANT: For energy to be conserved in atomic orbits, the electron kinetic energy must be independent of c and obey the standard equation as given by Wehr and Richards62

E k = mv2/2 = (Ze2)/(80a) = C-IND

(5)

where the expression C-IND represents independence of c throughout this report. From Table 12 the term e2/ 0 is also c independent as are atomic and dynamical orbit radii. Thus, the atomic orbit radius, a, in (5) may be described as a = C-IND

(6)

However, from (5) as a result of (3), there comes the conclusion that for atomic particles v~c

(7)

Now from Bohr's first postulate (the Bohr Model is used for simplicity throughout as it gives correct results to a first approximation61) comes the relation62 mva = nh/2

(8)

where h is Planck's constant. As a result of (3), (6) and (7) and remembering that n is an integer, we have from (8) that h ~ 1/c

(9)

The value of h is thus expected to increase with time if c is decaying. An experimental check with the data in Table 15A does not negate the proposition. Again, h/e is tabulated as h was determined from this ratio in the majority of cases. A linear fit to the data gives an increase in h/e of 0.00014 x 10-17 erg-sec/ESU per year with a confidence level in h/e not being constant at its 1973 value of 99.99%. It may be objected that the continuous X-ray data (CX in Table 15A) may be expected to show an increase in h/e with time. This results since the X-ray spectrum does not fall linearly to zero. Up to 1937, the exact position of the short-wave cutoff in the spectrum was estimated by the 'projected tangent method'. In 1936, DuMond and Bollman used a spectrometer with better resolution and found the exact cutoff was not where the projected tangent predicted. In 1943, Ohlin, using even more sensitive equipment noted 'knees' and 'valleys', which further changed the estimated position of the cutoff. In the period 1936-1943 the value of h/e jumped 1.376 to 1.379 x 10 -17 erg-sec/ESU due to better resolution by the CX method. TABLE 15A - EXPERIMENTAL VALUES OF h/e

AUTHORITY

DATE h/e x 10-17 erg-sec/ESU METHOD REF

1. Duane/Palmer/Yeh*

1921

1.37494

CX

288

2. Lawrence*

1926

1.3753 ±0.0027

CP

289

3. Lukirsky/Prilezaev#

1928

1.3715

PE

290

4. Feder*

1929

1.37588

CX

291

5. Olpin#

1930

1.372

PE

292

6. Van Atta#

1931

1.3753 ±0.0025

CP

293

7. Kirkpatrick/Ross*

1934

1.37541 ±0.0001

CX

294

8. Millikan#

1934

1.375

PE

235

9. Whiddington/Woodroofe# 1935

1.3737 ±0.0018

CP

295

10. Schaitberger*

1935

1.3775 ±0.0004

CX

296

11. DuMond/Bollman*

1936

1.37646 ±0.0003

CX

245

12. Dunnington

1938

1.3763 ±0.0003

XM

248

13. Wensel

1939

1.3772 ±0.0006

OP

297

14. Ohlin

1939

1.3787

CX

298

15. R.T. Birge

1940

1.37929 ±0.00040

IV

250

16. R.T. Birge

1941

1.37933 ±0.00023

IV

254

17. Schwarz/Bearden

1941

1.3775

CX

299

18. Panofsky et. al.

1942

1.3786 ±0.0002

CX

300

19. DuMond/Cohen

1947

1.3786 ±0.0004

CX

256

20. DuMond/Cohen

1947

1.37926 ±0.00009

AV

257

21. Bearden et. al.

1951

1 .37928 ±0.00004

XM

301

22. Bearden and Watts

1951

1.379300 ±0.000016

AV

258

23. DuMond/Cohen

1952

1.37943 ±0.00005

AV

259

24. Felt/Harris/DuMond

1953

1.37913

AV

302

25. Cohen et. al.

1955

1.37942 ±0.00002

AV

260

26. Cohen/DuMond

1965

1.379474 ±0.000013

AV

262

27. Taylor et. al.

1969

1.3795234 ±0.0000046 JE

263

28. Cohen and Taylor

1973

1.3795215 ±0.0000036 JE

264

CX = continuous X-ray: CP = critical potentials: PE = photoelectric effect: XM = X-ray Mean: OP = optical pyrometry: IV = indirect value: AV = best adjusted value: JE = ac Josephson effect.

* Values corrected by DuMond 252 or Dunnington248. # These results 'much less accurate' than the X-ray values (DuMond303 ). They are tabulated for completeness, but omitted from analysis.

TABLE 15B - 2e/h FROM THE ac JOSEPHSON EFFECT (ref. 264)

LAB. DATE

2e/h (GHz/V)

ERROR (ppm)

1.

NBS. 1970.33 483593.718 ±0.060 0.12

2.

NPL. 1970.50 483594.2 ±0.4

0.8

3.

NSL. 1970.52 483593.84 ±0.05

0.1

4.

PTB. 1970.79 483593.7 ±0.2

0.4

5.

NSL. 1971.49 483593.80 ±0.05

0.1

6.

NBS. 1971.57 483593.589 ±0.024 0.05

7.

NPL. 1971.58 483594.15 ±0.10

8.

NSL. 1972.26 483593.733 ±0.048 0.1

9.

NPL. 1972.28 483594.00 ±0.10

0.2

0.2

10. NBS. 1972.29 483593.444 ±0.024 0.05 11. PTB. 1972.38 483593.606 ±0.019 0.04 NOTE:- The NBS 1968 value was 483597.6 ±1.2, (2.4 ppm). Ref. 186.

The argument goes that the increasing value of h is entirely attributable to better equipment. This ignores the fact that the CX method is only one of eight used to determine h/e. Furthermore, Sanders64 has pointed out that the increasing value of h can only partly be accounted for by the improvements in instrumental resolution and changes in the accepted values of other constants. Indeed, a reviewer who had a preference for the constancy of atomic quantities noted that instrumental resolution 'may in part explain the trend in the figures, but I admit that such an explanation does not appear to be quantitatively adequate.' This point is amplified by the post 1947 results, which largely avoid the problem. Even these values give h/e increasing at 0.0000115 X 10-17 erg-sec/ESU per year, with a confidence in h/e not constant at the 1973 value of 96.7%, or 99.3% if the indirect Birge values of 1940 and 1941 are included. As the best adjusted values generally only included the most recent data and omitted the more 'aberrant' early data, the trend noted in those figures alone reflect the general situation and may be validly used. However, Sanders' statement is verified by two other considerations. Firstly, the measurements of 2e/h by the ac Josephson effect for 1970-1972. The results are more accurate than those of h/e and are listed in Table 15B. When the results from each of the four laboratories are considered individually, a decay in the value of 2e/h is recorded, with NBS giving the greatest. Treatment of all 11 values of 2e/h gives a decay of 0.0936 GHz/V/year

with a confidence of 96.2% that this quantity was not constant at the 1972.38 value. Since the minute drifts in voltage standards are positive as well as negative 168, these unidirectional results are the more noteworthy. Furthermore, they were predicted by Dirac and Kovalevsky360 if the atomic clock run-rate differed from the dynamical clock. Secondly, in Table 15 C., the Hall resistance, h/e 2, affirms these conclusions with an increase of 0.0159 ohms/year and a confidence in R h not constant at the 1985 value of 92.9%. As this approach predicts that h must vary precisely as 1/c, it follows that for all values of h and c hc = CONSTANT

(10)

Experiments by Bahcall and Salpeter65, Baum and Florentin-Nielsen10, and Solheim et al.66 indicate that this holds over astronomical time. Indeed, with a redshift z of distant astronomical objects, Noerdlinger67 obtained the result that d[ln(hc)]/dz 3 x 10-4 . These cosmological results upholding (10) experimentally, have often been interpreted as setting limits on the variability of either h or c on a universal time-scale. However, in each case an assumption is made about the constancy of the other term. The results that uphold (10) within the experimental limits say only that h must vary precisely as 1/c, which also upholds (9). Since the standard relations hold for energy E that E = hc/= hf

(11)

where is the wavelength of light emitted by the atom and f is the frequency, it follows for energy conservation that from (9) and (10) substituted in (11) TABLE 15C - THE QUANTIZED HALL RESISTANCE Rh = h/e 2

IDENTIFICATION

DATE Rh (ohms BI85)

ERROR (ppm)

1. Klitzing et. al.

1980

25812.776 ±0.036

1.39

2. Klitzing et. al.

1981

25812.79 ±0.04

1.55

3. NBS (US)

1983.5 25812.8495 ±0.0031 0.12

4. ETL, NPL, VSL mean 1984.0 25812.8418 ±0.0044 0.17 5. LCIE (France)

1984.5 25812.8502 ±0.0039 0.15

6. PTB (FRG)

1935.0 25812.8469 ±0.0048 0.18

NOTE: 1, 2 in REF. 336 p.519-537. 3-6 in CODATA Bulletin 63, 1986, E.R. Cohen and B.N. Taylor p.9, The 1986 Adjustment of the Constants.

TABLE 16 - THE RYDBERG CONSTANT R

AUTHORITY

DATE RVALUE (cm-1)

REF

1. Rydberg

1890

109721.6

304

2. Bohr

1913

109737

305

3. Paschen

1916

109737.35 ±0.06

266

4. Birge

1921

109737.36 ±0.2

306

5. Pickering/Fowler

1925

109737.36 ±0.06

305

6. Houston

1927

109737.335 ±0.016

269

7. Houston

1927

109737.313 ±0.060

269

8. Birge

1929

109737.42 ±0.06

238

9. Chu

1939

109737.314 ±0.020

282

10. Drinkwater et. al.

1940

109737.311 ±0.009

285

11. Birge

1941

109737.303 ±0.017

287

12. DuMond and Cohen 1947

109737.30 ±0.05

256

13. Bearden and Watts

1951

109737.323 ±0.024

258

14. Cohen

1952

109737.311 ±0.012

307

15. DuMond and Cohen 1952

109737.309 ±0.012

259

16. Cohen et. al.

109737.309 ±0.012

260

17. Cohen and DuMond 1963

109737.31 ±0.03

261

18. Cohen and DuMond 1965

109737.31 ±0.01

262

19. Csillag

1966

109737.307 ±0.007

308

20. Taylor et. al.

1969

109737.312 ±0.011

263

21. Cohen, Taylor

1973

109737.3177 ±0.0083

264

22. Hansch et. al.

1974

109737.3141 ±0.0010

309

23. Weber/Goldsmith

1978

109737.3149 ±0.00032

310

24. Petley et. al.

1979

109737.31513 ±0.00085 311

25. Amin et. al.

1981

109737.31521 ±0.00011 312

1955

NOTE:- Values 3-5 and 8 are corrected using Birge238 constants. Values 7 and 11 corrected by Birge287. Values 6, 9, 10, 18, 19 corrected by Taylor et. al.263. Values 20-24 as discussed in Hansch313.

TABLE 18 - OTHER C INDEPENDENT QUANTITIES

QUANTITY

FORMULA

Bohr Magneton

0* = he/(4mc)

Zeeman Displacement/gauss

Z* = (e/mc)/(4c)

Schrodinger constant (fixed nucleus) S = 82m/h2 Compton wavelengths

c = h/mc

de Broglie wavelengths

d = h/(mv) = hc/E

Faraday

F = N0 e

Volt

V = hf/2e

f~c = C-IND

(12) (13)

The result in (12) and (13) was supported by experimental evidence at a time when c was measured as varying 13. This treatment of the atom based on conservation thus overcomes Birge's objection. Atomic frequencies should vary as c, as in (12), even though Birge13 considered that 'Such a variation is obviously moat improbable.' Therefore, unchanging length standards, in both atomic and dynamical units, along with energy conservation, give results which are concordant with theory and experiment. Varying length standards would nullify (12). In keeping with invariant wavelengths for emitted light, de Broglie wavelengths of moving particles, d, are given by h/(mv) = hc/E, and from (3), (7), (9), (10) and (11), this quantity is independent of c. Likewise the Compton wavelength, c, given as h/(mc), will also be cindependent. (D). ATOMIC ORBITS AND RELATED QUANTITIES: The expression for the energy of a given electron orbit n is given by Wehr and Richards62 and French 68 as E n = -22e4m/(h2n2)

(14)

which from (3) and (9) is independent of c. With orbit energies unaffected by c decay, electron sharing between two atomic orbits results in the 'resonance energy' that forms the covalent bond being c independent (see Brown69 ). A similar argument also applies to the dative bond between co-ordinate covalent compounds. Since the electronic charge is taken as constant, the ionic or electrovalent bond strengths are not dependent on c.

Related to orbit energy is the Rydberg constant R. An application of (3) and (9) to the standard definition 62,68 of R results in R = 22e4m/(ch3) = CONSTANT

(15)

as the variable quantities mutually cancel. Experimental evidence listed in Table 16 agrees with (15). Omitting the 1890 value, which was not corrected to vacuo or for the infinite nucleus, the linear data fit gives an increase of 0.000495 cm-1 per year, with a confidence in R not constant at the 1981 value of 56.01%. This strongly suggests that the Rydberg constant has not varied. Its measured stability to 7 figures contrasts markedly with c values. The Fine Structure constant, , appears in combination with the Rydberg constant in defining some other quantities. An application of (10) to the definition 70 of gives = 2e2/(hc) = CONSTANT

(16)

Bahcall and Schmidt56 determined that for distant astronomical sources, was (1.001 ±0.002) times its current value. Thus (16) is in accord with observation and holds on a cosmological time-scale. TABLE 17 - THE PROTON GYROMAGNETIC RATIO  '

AUTHORITY

DATE  ' (Rad./sec./gauss)

REF

1. Thomas/Driscoll/Hipple

+1949 26752.31 ±0.26

314

2. DuMond and Cohen

1952

26752.70 ±0.80

259

3. Cohen et. al.

1955

26753.00 ±0.40

260

4. Wilhelmy*

1957

26755.00 ±1.20

315

5. Driscoll and Bender

1958

26751.465 ±0.08

316

6. Yanovskii et. al.

1959

26752.00 ±1.50

317

7. Capptuller

+1960 26752.50 ±7 0.99

318

8. Vigoreaux

1962

26751.440 ±0.070

319

9. Yagola/Zingerman/Sepetyi

1962

26751.20 ±0.20

320

10. Yanovskii and Studentsov

1962

26750.60 ±0.50

321

11. Cohen and DuMond

1963

26751.92 ±0.07

262

12. Driscoll and Olsen

1964

26751.555 (mean)

322

13. Yagola/Zingerman/Sepetyi +1966 26751.05 ±0.20

323

14. Driscoll and Olsen

1968

26751.526 ±0.099

322

15. Hara et. al.

1968

26751.384 ±0.086

324

16. Studentsov et. al.

1968

26751.349 ±0.045

325

17. Taylor/Parker/Langenberg 1969

26751.270 ±0.082

263

18. Olsen and Driscoll

1972

26751.384 ±0.054

326

19. Cohen and Taylor

1973

26751.301 ±0.075

264

20. Olsen and Williams

1975

26751.354 ±0.011

327

21. Wang (Chiao, Liu, Shen)

1977

26751.481 ±0.048

328

22. Vigoureaux and Dupuy

1978

26751.178 ±0.013

329

23. Kibble and Hunt

+1979 26751.689 ±0.027

330

24. Williams and Olsen

1979

25. Chiao, Liu and Shen

+1980 26751.572 ±0.095

332

26. Chiao and Shen

1980

332

27. Forkert and Schlesok

+1980 26751.32 ±0.41

333

28. Forkert and Schlesok

1980

26751.55 ±0.13

333

29. Tarbeyev

1981

26751.257 ±0.040

334

30. Tarbeyev

1981

26751.228 ±0.016

334

26751.3625 ±0.0057 331

26751.391 ±0.021

* Included in Table for completeness but omitted from trend analysis. NOTE:- Values 1-17 as corrected by Taylor et. al.335 except for the best adjusted values 2, 3, 11 and 19. Values 18, and 20-30 as discussed by Williams, Olsen and Phillips336 except 21 from p.507 and 29 from p.484 of the same publication. + High field values: a decay of 0.0312 rad/sec/gauss per year, similar to the trend from all values.

It may be thought from (8) that orbital angular momentum is not conserved. However, the rate of precession of the orbital angular momentum vectors about their resultant is given by French 72 as PRECESSION = W/h

(17)

where W is the magnetic potential energy, which from Table 12 is c independent. As this quantity W also defines the doublet fine structure splitting in ergs, it follows that this, too, is c independent. Applying this and (9) to (17) results in angular momentum being conserved in atomic orbits as PRECESSION ~ c

(18)

The gyromagnetic ratio,  , as defined by French72 also appears to be c-dependent as = e/(2mc) ~ c

(19)

Table 17 suggests a decay of 0.0294 rad/sec/gauss per year in  , with a 99.9% confidence interval that was not constant at the 1981 value. Table 18 summarizes some quantities that are c independent through mutually canceling c dependent terms. (E). RADIOACTIVE DECAY: As (3) and (7) apply to nucleons as well as electrons, the velocity, v, at which nucleons move in their orbitals seems to be proportional to c. As atomic radii are c independent, and if the radius of the nucleus is r, then the alpha particle escape frequency * (the decay constant) as defined by Glasstone73 and Von Buttlar74 is given as * = Pv/r

(20)

where P is the probability of escape by the tunneling process. Since P is a function of energy, which, from the above approach is c independent, then * ~ c

(21)

For decay processes, Von Buttlar75 defines the decay constant as * = Gf = mc2g2|M|2f/(2h)

(22)

where f is a function of the maximum energy of emission and atomic number Z, both c independent. M, the nuclear matrix element dependent upon energy, is unchanged by c, as is the constant g. Planck's constant is h, so for decay, * ~ c

(23)

An alternative formulation by Burcham76 leads to the same result. TABLE 19: HALF-LIVES OF THE MAIN HEAVY RADIO-NUCLIDES

DATE: ELEMENT:

1904

1913

1930

1936

1944

1950

1958

1966

1978

BEHAVIOR/YEAR

TREND/UNIT

Thallium 207

-

3.47

4.71

4.71

4.76

4.76

4.79

4.78*

4.77

m

+ 1.5 x 10 -2

+ 3.1 x 10 -3

Thallium 208

-

3.1

3.1

3.2

3.1

3.1

3.10

3.10*

3.053

m

- 8.4 x 10-4

- 2.7 x 10-4

Thallium 210

-

1.4

1.32

1.32

1.32

1.32

1.32

1.30*

1.30

m

- 1.2 x 10-3

- 9.2 x 10-4

Lead 210

-

16.5

22

16

22

22

19.4

21

22.3

y

+ 7.0 x 10 -2

+ 3.1 x 10 -3

Lead 211

#38*

36.0

36.0

36.0

36.1

36.1

36.1

36.1*

36.1

m

+ 2.0 x 10 -3

+ 5.5 x 10 -5

Lead 212

#11.3*

10.6

10.6

10.6

10.6

10.6

10.64

10.64*

10.64

h

+ 8.1 x 10 -4

+ 7.6 x 10 -5

Lead 214

21.4*

26.8

26.8

26.8

26.8

26.8

26.8

26.8

26.8

m

+ 4.4 x 10 -2

+ 1.6 x 10 -3

Bismuth 210

-

5.0

4.9

4.85

5.00

5.0

5.01

5.0

5.01

d

+ 1.2 x 10 -3

+ 2.4 x 10 -4

Bismuth 211

-

2.10

2.16*

2.15

2.16

2.16

2.16

2.15*

2.15

m

+ 5.4 x 10 -4

+ 2.5 x 10 -4

Bismuth 212

55

60.0

60.5

60.8

60.5

60.5

60.5

60.6*

60.60

m

+ 4.8 x 10 -2

+ 7.9 x 10 -4

Bismuth 214

#28

19.5

19.7

19.7

19.7

19.7

19.7

19.9

19.7

m

+ 3.5 x 10 -3

+ 1.7 x 10 -4

Polonium 210

-

136

136.3*

136.5

140

140

140*

138.4

138.38

d

+ 5.1 x 10 -2

+ 3.6 x 10 -4

Polonium 216

-

0.14

0.145*

0.14

0.158

0.160

0.158

0.15*

0.15

s

+ 2.0 x 10 -4

+ 1.3 x 10 -3

Polonium 218

3.0

3.0

3.05

3.05

3.05

3.05

3.05

3.05

3.05

m

+ 7.2 x 10 -4

+ 2.3 x 10 -4

Radon 219

4.0*

3.90

3.92

3.92

3.92

3.92

3.92

4.00*

3.96

s

+ 1.8 x 10 -4

+ 4.5 x 10 -5

Radon 220

60

54.0

54.5

54.5

54.5

54.5

(54.5)

55.0*

55.6

s

- 3.0 x 10-2

- 5.4 x 10-4

Radon 222

3.65*

3.85

3.823

3.825

3.825

3.82

3.823

3.825

3.8235

d

+ 1.2 x 10 -3

+ 3.1 x 10-4

Radium 223

-

10.5

11.2

11.2

11.2

11.2

11.7

11.43*

11.435

d

+ 1.3 x 10 -2

+ 1.1 x 10 -3

Radium 224

4.0

3.64

3.64

3.64

3.64

3.64

3.64

3.64*

3.66

d

- 2.7 x 10-3

- 7.3 x 10-4

Radium 226

732*?

2000?

1590

1580

1590

1620

1622

1620

1600

y

+ 4.8 x 10 0

+ 3.0 x 10-3

Radium 228

-

5.5

6.7

6.7

6.70

6.7

6.70

5.77*

5.76

y

- 2.1 x 10-3

- 3.6 x 10-4

Actinium 227

-

-

20.0

20

-

21.7

21.6

21.6*

21.773

y

+ 4.1 x 10 -2

+ 1.8 x 10 -3

Actinium 228

-

6.2

6.13

6.13

6.13

6.13

6.13

6.13*

6.13

h

- 7.8 x 10-4

- 1.2 x 10-4

Thorium 227

-

19.5

18.9

18.9

18.9

18.9

18.2

18.5*

18.718

d

- 1.3 x 10-2

- 6.9 x 10-4

Thorium 228

-

2

1.90

1.90

1.90

1.90

1.91

1.91

1.9131

y

- 8.8 x 10-4

- 4.6 x 10-4

Thorium 230

-

?

7.6*

7.6

8.30

8.0

8.30*

8.00

8.00 E4 y

+ 8.4 x 10 -3

+ 1.0 x 10 -3

Thorium 231

-

36?

24.6

24.5

24.6

24.6

25.6

25.5*

25.52

h

- 1.0 x 10-1

- 3.9 x 10-3

Thorium 232

-

3?

1.65*

1.65

1.39

1.39

1.39

1.41

1.41 E10

y

- 2.0 x 10-2

- 1.7 x 10-2

Thorium 234

22.3

24.6

23.8

24.5

24.1

24.1d

24.5*

24.1

24.10

d

+ 1.3 x 10 -2

+ 5.4 x 10 -4

Protact. 231

-

-

1.25

1.20

3.2

3.2

3.43

3.25*

3.28 E4 y

+ 4.5 x 10 -2

+ 1.3 x 10 -2

Protact. 234

-

-

6.7

-

6.7

6.7

-

6.66

6.75

h

+ 5.1 x 10 -4

+ 7.5 x 10 -5

Protact. 234m

-

-

1.14

1.15

1.14

1.14

1.18

1.17*

1.1725

m

+ 8.4 x 10 -4

+ 7.1 x 10 -4

Uranium 234

-

-

3.0?

-

2.69

2.35

2.48

2.50

2.45 E5 y

- 1.0 x 10-2

- 4.0 x 10-3

Uranium 235

#7.3

-

-

-

7.07

7.07

(7.13)

7.1

7.038 E8

y

- 6.5 x 10-4

- 9.2 x 10-5

Uranium 238

-

6?

4.40

4.5

4.51

4.5

(4.56)

4.51

4.468 E9

y

- 1.6 x 10-2

- 3.5 x 10-3

# For 1904: Several decaying elements involved, increasing half-life: Ommited from analysis. ? Approximate values - retained in analysis. Seconds = s: Minutes = m: Hours = h: Days = d: Years = y.

NOTE:- Behavior/Year from least squares linear fit to data. Trend/Unit = (Behavior/Year)/(1978 value). REFERENCES: 1904: Rutherford337, *values Soddy338. 1913: Rutherford339. 1930: Curie et. al.340, *values from Rutherford 341. 1936: Crowther342. 1944: Seaborg343. 1950: Glasstone 344. 1958: Strominger et. al. 345, *values US Navy346, bracketed values Korsunsky347. 1966: Gregory348, *values Goldman 349. 1978: Lederer and Shirley350 in Friedlander et. al.351.

For electron capture, the relevant equation from Burcham 77 is * = K2|M| 2f/(23)

(24)

where f is here a function of the fine structure constant, the atomic number Z, and total energy, all c independent. M is as above. K 2 is defined by Burcham78 as K2 = g2m5c4 /(h/2)

(25)

With g independent of c, application of (3) and (9) to m, h and c results in K2 proportional to c so that for electron capture * ~ c

(26)

This approach thus gives * proportional to c for all radioactive decay. Table 19 lists the experimental evidence for slowing decay rates of the main naturally occurring heavy radionuclides which, generally, were the first to be noted and have their half-lives recorded. They support the contention of increasing half-lives by an almost two-thirds majority, despite increasing efficiencies of particle counters which tend to reverse the trend. The most pessimistic conclusion is that they do not invalidate the proposal. The decay coupling constant, g, used above, also called the Fermi interaction constant, bears a value 57 of 1.4 x 10-49 erg-cm3 . Conservation laws therefore require it to be invariant with changes in c. The weak coupling constant, gw, is a dimensionless number that includes g. Wesson57 defines g w = [gm2c/(h/2)3] 2 where m is the pion mass. From (3) and (9) and constant g, this equation also leaves gw as invariant with changes in c. This is demonstrable in practice since any variation in gw would result in a discrepancy between the radiometric ages for and decay processes57. That is not usually observed. The fact that gw is also dimensionless hinted that it should be independent of c for reasons that become apparent shortly. Similar theoretical and experimental evidence also shows that the strong coupling constant, gs has been invariant over cosmic time57. Indeed, the experimental limits that preclude variation in all three coupling constants also place comparable limits on any variation in e or vice versa 57. The indication is, therefore, that they have remained constant on a universal time scale. The nuclear g-factor for the proton, gp, also proves invariant from astrophysical observation 57. Generally, therefore, the dimensionless coupling constants may be taken as invariant with changing c. V. TIME AND LENGTH:(A). ATOMIC TIME:

If the above list of constants is examined, it is discovered that those which are measured as varying all have units involving time. These include electron velocities, c itself, Planck's constant h, frequencies f, precession rates, the gyromagnetic ratio  , and radioactive decay rates. Even rest-mass involves time from its definition of force/acceleration. It is noticeable that the constants which remain invariant with mutually canceling c-dependent terms are those whose units are time independent. They include the fine structure constant , the Rydberg constant R, wave-lengths , energy per unit wavelength hc, the volt, and the electronic charge. The dimensionless constants are also invariant if conservation is to be upheld. TABLE 20 - MEASUREMENTS OF THE NEWTONIAN GRAVITATIONAL CONSTANT, G

NO. EXPERIMENTER DATE METHOD

VALUE OF G x 108 dynecm2/gm2

REF

1.

Cavendish

1798

6.754 ±0.041

352

2.

Reich

#1838 static torsion

6.64 ±0.06

353

3.

Baily

#1843 static torsion

6.63 ±0.07

353

4.

Cornu/Baille

1872

6.618 ±0.017

354

5.

Jolly

#1873 Jolly balance

6.447 ±0.11

353

6.

Eotvos

1886

static torsion

6.657 ±0.013

353

7.

Richarz/K-Menzel 1888

Jolly balance

6.683 ±0.011

353

8.

Wilsing

#1889 Jolly balance

6.594 ±0.15

353

9.

Poynting

1891

Jolly balance

6.6984 ±0.004

355

10.

Boys

1895

static torsion

6.658 ±0.007

353

11.

Braun

1895

dynamic torsion

6.658 ±0.002

355

12.

Richarz/K-Menzel 1896

Jolly balance

6.685 ±0.011

356

13.

Braun

1897

dynamic torsion

6.649 ±0.002

353

24.

Burgess

#1901 dynamic torsion

6.64

353

15.

Heyl

1930

dynamic torsion

6.6721 ±0.0073

357

16.

Zahradnicek

1933

dynamic torsion

6.659 ±0.004

355

17.

Heyl/Chrzanowski 1942

dynamic torsion

6.6720 ±0.0049

357

18.

Rose et. al.

1969

rotating table

6.674 ±0.003

357

19.

Pontikis

1972

resonance torsion

6.6714 ±0.0006

357

static torsion

static torsion

20.

Renner

1973

dynamic torsion

6.670 ±0.008

353

21.

Karagioz

1976

dynamic torsion

6.668 ±0.002

353

22.

Rose et. al.

1976

rotating table

6.6699 ±0.0014

355

23.

Sagitov

1977

dynamic torsion

6.6745 ±0.003

353

24.

Stacey et. al.

1978

geophysical

6.712 ±0.037

358

25.

Luther/Towler

1981

dynamic torsion

6.6726 ±0.0005

359

# Omitted from analysis since data (a) only given to 3 figures, or (b) has high error, or no error given, or (c) aberrant compared with other values.

Summarizing the above approach, we may say that the atom sees no change in c! Atomic time is based on the time an electron takes to travel its orbit once. Seen dynamically then, atomic time intervals, d , vary as 1/c. For the atom, light has always traveled the same distance in one of its seconds, its light emitting frequency has always been constant, Planck's constant never varies and radioactive decay rates remain unchanged. It is only as we look at the atom from our dynamical time frame that any change is noted. A constant dynamical interval, dt, may thus be written c.d . This implies that general relativistic equations hold as their time 2 intervals, written as (c 2.d , would be valid dynamically if time,  , was measured atomically. Since both c and are invariant in the atomic frame, the equations are automatically valid there. The change observed in c macroscopically is thus an indication of a variation occurring on the atomic level, with the run rate of the atomic clock being affected. This atomic variation with c answers the key criticism made by Birge in 1934. He stated19 that 'if the value of c...is actually changing with time, but the value of (wavelength) in terms of the standard meter shows no corresponding change then it necessarily follows that the value of every atomic frequency...must be changing. Such a variation is obviously most improbable. Unfortunately,' he lamented 13, 'it is not possible to make a direct test, since one cannot compare directly an atomic frequency with any macroscopic standard of time.' Today, however, evidence comes from analysis of lunar occultations and planetary orbital data. The moon and planets all appear from the measurements to have different angular acceleration rates in atomic time compared with dynamical time. On these results, Van Flandern concludes that 1 'the number of atomic seconds in a dynamical interval is becoming fewer. Presumably, if the result has any generality to it, this means that atomic phenomena are slowing down with respect to dynamical phenomena...(though) we cannot tell from existing data whether the changes are occurring on the atomic or dynamical level.' The above analysis verifies these conclusions, and the dilemma seems to dissolve by considering gravitation. (B).GRAVITATION: REVISED IN LATER REPORT (C). LENGTH, TIME AND C:

The atomic unit of time is given by one revolution of an electron in the ground state orbit of a hydrogen atom (see Roxburgh 82). Froome and Essen 83 note that there was a consistent standard from 1820 to 1955 for the dynamical second as 1/86,400 of the earth's rotational period checked by stellar transit times. Goudsmit et al.84 point out that from 1956 the same standard was redefined as 1/31,556,925.9747 of the earth's orbital period. Atomic clocks became available in 1955 (see Morrison 85 and Van Flandern1) and Wilkie 2 notes that our time became regulated by atomic seconds in 1967. At that date the old standard interval was redefined as 9,192,631,770 periods of radiation of caesium 133 in the ground state 86. The above work suggests that the number of caesium transitions per dynamical second are becoming fewer. However, up to 1967, timing of events in the measurement of c were not affected by this. Furthermore, there has been a consistent meter length standard since 1798, formalized in 1875 and redefined in 1960 as 1,650,763.73 vacuum wavelengths of the Krypton 86 orange line (see Froome and Essen87). In 1983 it was redefined as the distance light travels in 1/299,792,458 seconds as noted by Wilkie 2. There will be no difference in the length standard if c varies provided measurements are done in atomic seconds. If c was to increase and measurements were in dynamical time for the new definition of the meter, then fewer wavelengths of a given spectral line would fit in the interval and the meter would have to be lengthened to restore the definition. (D). LASERS, AND A TEST FOR C DECAY: TABLE 21 - COMPARISON OF CURVES FITTED TO ALL TABLE 11 DATA NOTE:- Typical dates only reproduced from the full Table 11 analysis to avoid a lengthy table.

DATE 

OBSERVED C VALUE (Km/s)

LINEAR DECAY, EXPON. or LOG.

POWER CURVE

PARABOLA, and COSEC2

CRITICAL, OVER, UNDER DAMPED

SQ. ROOT OF CRITICALLY DAMPED

POLYNOMIAL APPROX. TO ROOT DAMPED

1740

300,650

300,378

300,397

300,700

300,697

300,752

300,701

1783

300,460

300,258

300,267

300,379

300,340

300,344

300,379

1843

300,020

300,090

300,091

300,047

300,018

300,005

300,047

1861

300,050

300,040

300,039

299,974

299,953

299,941

299,974

1876.5

299,921

299,997

299,995

299,920

299,908

299,898

299,921

1883

299,860

299,979

299,977

299,900

299,891

299,882

299,901

1906

299,803

299,914

299,912

299,843

299,844

299,839

299,844

1926.5

299,798

299,857

299,855

299,809

299,815

299,814

299,809

1937

299,771

299,828

299,826

299,798

299,805

299,805

299,798

1947

299,795 (av)

299,800

299,799

299,791

299,798

299,799

299,791

1957

299,792.6

299,772.2

299,772.1

299,787.5

299,793.3

299,795.2

299,787.5

1967

299,792.5

299,744.3

299,745.1

299,787.9

299,790.9

299,793.0

299,787.9

1973

299,792.4574

299,727.5

299,728.9

299,789.9

299,790.4

299,792.6

299,789.9

1983

299,792.4586

299,699.6

299,702.0

299,796.2

299,791.2

299,793.1

299,796.3

ALL TABLE 11 DATA RESIDUALS: 2.883 2.813 910 924 **1013 911 = ±(Observed - Predicted): (Sum of Residual squares)/n: 657 866 **1058 660

Linear decay:-

r2 = With a = 0.7704: c = a + bt 305242

b=2.79495

Exponential:-

r2 = 0.7705: e = aebt

With a = 305285

b = -9.3131 x10-6

Logarithmic:-

r2 = 0.7705: c = a10bt

With a = 305285

r2 = Power Curve:- 0.7863: c = atb

With a = 342871

b=4.0446x 106

b=0.0177239

*Parabola:-

r2 = 0.9704: With a = c = aT2 + 0.018679 bT + d

b=0

*Cosec 2:-

r2 = 0.9703: c=a cosec2 bT

b= 2.494912x 10-4

*Critical Damping:-

c=a+ With a = (d + ft)ebt 301924

b=0.00308

d= 4.733 x 106

f = -2870

Root Damped:-

c= [a + ekt(b + dt)]

a = 9.029 x 1010

b = 4.59 x1013

d = -2.6 x 1010

k = -0.0048

*Polynomial:-

c= aT8 + bT2 + d

With a = 3.8 x 10-19

b= 0.01866

d= 299787.23

With a = 299787.23

d= 299787.23

* Maximum r2 left minimum values unadjusted. These curves essentially unaffected by post 1967 values. For parabolas etc., T = (1961 - t): for cosec2 curves, T = (4335 + t). Minima In 1961 result for each.

** Higher residuals for the preferred curve mainly result from the 1740 value compared with the others.

It is significant that the eight laser values from 1972 to 1983 were using the atomic time and frequency standards. It is therefore inevitable that the constancy of c in the atomic time frame will be reflected in the measurements. It is for this reason that no statistically significant trend was revealed in that period. If any trend was occurring, and the figures up to 1967 indicated a rapidly flattening decay rate, it could only be picked up by a comparison between clock rates. Van Flandern did this 1 with lunar orbit data from 1978 to 1981. Though c was not considered, the results give nï/n = -Pï/P = -cï/c = (3.2 ±1.1) x 10-11/yr

(34)

where (ï) indicates a time derivative, P is the moon's orbital period, n is the mean motion and c is light speed. This yields the result that the mean decay rate for c by time comparisons around 1980 was 0.0096 m/s per year. Planetary ranging techniques 93 gave initial results in 1978 of nï/n equal to (12.4 ±6.6) x 10-11 per year or a c decay rate of 0.037 m/s per year. However, the combined average for Mercury, Venus and Mars was 30 x 10-11 per year in 1978. This gives a c decay rate of 0.089 m/s per year at that date. By 1983, Canuto et al. (item 30, Table 24) gave  ï/at (1 ±8) x 10 -12 /yr. These results suggest that cï/c is flattening out fast (see Table 24). Two possibilities now exist. The decay rate may either taper rapidly to zero, or bottom out and become an increase. The preferred curve forms on page 55 also allow both options. However the coefficients used in the specific example require the second option to be followed. Minor adjustment would give the first. Van Flandern's clock comparisons over an ever increasing period thus hold the key to discerning the precise behavior of c, cross-checked by data from the gyromagnetic ratio,  ', the Hall resistance, h/e 2 and 2e/h. VI. DATA CONCLUSIONS AND ULTIMATE CAUSES:(A). GENERAL CONCLUSIONS FROM ALL DATA: The proposal of c decay and slowing atomic clocks has been examined using 638 values of the relevant atomic quantities measured by 41 methods. This has comprised 194 atomic, 281 radio-nuclide, and 163 c values. Of these, the 16 different methods of measurement of c all individually show a decay. Again, the 15 methods employed for the 104 atomic values predicted to vary and the method used for the 281 radio-nuclides, all confirm the expected trend. This means that 32 methods of measurement and 548 values support c decay and slowing atomic clocks directly. The remaining 9 methods and 90 values give indirect support to the proposal. This can hardly be the result of intellectual phase locking. Further, the odds against 32 methods showing this trend by coincidence are about one in 10 15, assuming that some would be expected to show an increase, others a decrease, and some no trend at all. These odds also seem to stretch Dorsey's explanation of equipment unreliability, systematic errors, and improved techniques too far. If c and associated atomic quantities were true constants, measurements should produce results similar to those for all values of e in Table 13. There, a random fluctuation about a

fixed value occurs, regardless of the size of the error limits. The alternative example is R from Table-16, which is stable to seven figures, despite error limits. Both e and Ralso have low statistical probabilities of any change compared with the modern values. All this is in sharp contrast with the c values and related atomic quantities. These contrasts indicate that the data do not support constant c, but instead favor slowing atomic processes compared with dynamical phenomena as Van Flandern concluded. TABLE 22 - RESULTS OF ANALYSIS OF SPEED OF LIGHT DATA

REF. MEAN DATE DATA C MEAN Km/s C VALUE c.f. NOW Km/s DECAY RATE Km/s/yr CONF 1.

~1700 ±100

4

301,098

1,305

12.48

91.0%

2.

1740 ±14

4

300,277

485

9.92

80.7%

3.

1812 ±72

6

300,265

473

5.19

99.1%

4.

1833 ±93

18

299,962.4

170

4.66

99.6%

5.

1865 ±25

16

299,942.5

150

4.97

89.7%

6.

1877 ±1

1

299,921.5

129

-

-

7.

~1880 ±100

63

299,868.7

76.2

4.83

93.9%

8.

1887 ±14

5

299,910.2

117.7

2.17

99.4%

9.

~1890 ±100

57

299,844.9

52.5

2.79

99.5%

10.

1899 ±24

5

299,844.6

52.1

1.74

95.6%

11.

1903 ±23

4

299,840.8

48.3

1.84

89.6%

12.

1905 ±27

6

299,832.8

40.3

1.85

93.9%

13.

1915 ±25

45

299,812.0

19.5

-

-

14.

1934 ±6

4

-

-

1.03

90.5%

15.

1953 ±6

23

299,793.2

0.72

0.19

99.0%

16.

1961 ±6

15

299,792.64

0.18

0.030

82.7%

17.

1970 ±4

7

299,792.477

0.019

0.0058

64.1%

18.

1975 ±7

11

299,792.470

0.012

0.00262

-

19.

1979 ±5

4

299,792.4586

0.00063

0.000097

50.2%

REFERENCE:1, 6: Results from the Roemer eclipse method. The four most conservative values used in 1. Item 6 represented by a single value based on a large number of observations. 2, 3, 5, 7, 13: All used the Bradley aberration method. Item 13 had a large scatter of points rendering the decay value unreliable. 4: Best results from seven methods (aberration, eclipse, toothed wheel, rotating mirror, polygonal mirror, waves on wires, ratio of ESU/EMU).

8: Most reliable values from the Fizeau toothed wheel method. 9: Summary of the best data available based on the Birge list (reference 11). 10, 12: The Foucault rotating mirror method was used to obtain these values. 11: Summary of Michelson's 4 prime values. The first two used a rotating mirror. In the second two, a polygonal mirror technique allowed an adjustment to a null position. Each of Michelson's determinations was lower than the previous one. In 7 instances by different experimenters the same equipment was used and always resulted in a lower c value at the later date. 14: The Kerr Cell chopped the light beam electrically like a toothed wheel. A built-in defect in the method gave systematically low results. The decay was still observed, but shifted to a lower range of c values. The confidence interval in this case refers to the decay trend and not the mean value. 15 - 19: Combined results from six modern methods in item 15. Each gave a decay individually as well as collectively. Item 16 used 9 methods, with c values from 1954-1967 inclusive. Item 17 had 4 methods with the first 7 values from Table 8. Item 18 includes all 11 data points from Table 8 with 4 methods involved. The last 4 laser results in Table 8 give Item 19.

CLICK HERE TO SEE FIGURE III http://www.setterfield.org/report/fig3.jpg CLICK HERE TO SEE FIGURE IV http://www.setterfield.org/report/fig4.jpg (B). CONCLUSIONS FROM C-DATA: Table 21 makes a comparison with observed values of c for eight types of curve based on the Table 11 data. If all 163 c data points are used, then least squares analyses give higher decay rates than with the Table 11 data. Decay for all data ranges around 40 Km/s per year, but only 2.5 Km/s per year for Table 11 data. Again, measured trends of all related atomic constants do serve to confirm c decay and points do not exhibit a normal distribution about today's values. However, the fewer values involved for each quantity, and their shorter time range, do not allow the same formulation of the decay's precise nature that the c data does. Nevertheless, a cross-comparison of the best atomic results not only endorses the non-linear slow-down in atomic processes, but their values give consistent magnitudes for all 7 varying quantities. This is demonstrated in the next section. A summary of all results of the c data analysis appears in Table 22. Note that in the case of item 18 in Table 22, the dynamical measurements of c are compared with the atomic standard using all data in Table 8 to obtain an estimate of the decay rate for a mean date of 1975. The results from Table 22 are used in Table 24 as outlined in the next section. (C). CONCLUSIONS FROM REFINED ATOMIC DATA: Thus far, the atomic data for Tables 13 - 19 have generally been treated as a whole without refinement. Table 23 overcomes this difficulty. The observed trend for all data is maintained

in refined analysis, though less extreme in form, as the scatter of points is reduced and the true trend becomes more closely defined experimentally. Items 1-3 in Table 23 are the c data which has already been dealt with. Items 4-6 and 24 were also handled when the electronic charge was considered. Items 7-11 consider the specific charge e/(mc) with item 7 summarizing all results. These items derive from a consideration of Table 14 where e/(mc) is listed. Item 8 gives the most conservative early results by a single method, namely the crossed-fields values from Table 14 numbers 1, 6, 18, and 22 for a mean date of 1926. Item 9-11 (Table 23) treats the most conservative values by 6 methods. All excessively high or low values were omitted. This gives a range from Dunnington's maximum of 1.7592 in 1932 to the low in 1965 of 1.758796. The values so treated thus become numbers 1, 11, 12, 15, 21, 23-33. To obtain a mean date of 1938, 11 points were used omitting numbers 27, 29, and 31-33. For a mean date of 1945 all 16 points were used, while a mean date result for 1952 was obtained using all values between 1951 and 1955 inclusive. The decay rate in parts per million at these dates closely corresponds with that of the c data as evidenced by Table 24. Items 12 and 13 in Table 23 consider h/e from Table 15A with item 12 summarizing all results. The best modern data all have values prefixed by 1.379 and until 1940 there was deviation from this. For a mean date of 1947 all 6 data of the above prefix between 1940-1952 inclusive were used. As the 2e/h results from Table 15B were more accurate than h/e for later dates, they were considered instead in items 14 and 15. Item 14 in Table 23 is the summary. The refined data was considered in the range greater than or equal to the prefix 483593.6 and less than or equal to 483593.8. This gave 5 points with a mean date of 1971. For both h/e and 2e/h the trend rate in parts per million closely approximate to that for the c data (see Table 24). TABLE 23 - SUMMARY OF BEHAVIOR OF ATOMIC QUANTITIES

REF. CONST. DATA

METH.

DATES

VALUE

TREND/YR.

CONF.

1.

c

163

16

1675-1983

299792.4586

- 38

-

2.

c

146

16

1675-1983

-

- 43

97.2 %

3.

c

57

16

1740-1983

-

- 2.79

99.99 %

4.

*e

37

2

1913-1973

4.803242

+ 0.000026

55.4 %

5.

*e

8

1

1913-1940

-

+ 0.000383

76.8 %

6.

*e

15

1

1928-1952

-

- 0.0000148

63.7 %

7.

e/(mc)

33

7

1900-1973

1.7588047

- 0.0000679

99.2 %

8.

e/(mc)

4

1

1900-1939

-

- 0.00000616

77.7 %

9.

e/(mc)

11

6

1900-1955

-

- 0.00000303

99.99 %

e/(mc)

16

6

1900-1973

-

- 0.00000592

99.98 %

e/(mc)

5

3

1951-1955

-

- 0.00000067

99.98 %

10. 11.

12.

h/e

28

5

1921-1973

1.3795215

+ 0.00014

99.99 %

13.

h/e

6

3

1940-1952

-

+ 0.00000324

99.50 %

14.

2e/h

13

1

1966-1973

483593.606

- 0.535

95.5 %

15.

2e/h

5

1

1970-1973

-

- 0.0239

66.5 %

16.

'

30

2

1949-1981

26751.228

- 0.0294

99.9 %

17.

'

12

2

1958-1973

-

- 0.0131

93.6 %

18.

'

7

2

1968-1980

-

- 0.00109

99.92 %

19.



281

35

1904-1978

1 unit

- 0.0001129

85.5 %

20.



42

6

1913-1978

-

- 0.00000202

-

21.

*R

25

1

1890-1981

109737.31521

+ 0.000495

56.01 %

22.

*G

25

6

1798-1981

6.6726

- 0.000114

57.83 %

hc

cosmologically proven constant - time terms mutually cancel.



cosmologically proven constant - time terms mutually cancel.

**e 2/ 0

measured as constant cosmologically - time independent.

23.

24.

25.

LEGEND:REF. = reference number. CONST. = atomic quantity. DATA = number of data used. METH. = number of methods. DATES = years of observations. VALUE = last value by experiment (not the same as the current best adjusted value). TREND/YR = the trend per year from the least squares linear fit in units of the atomic quantity. CONF. = confidence interval that the data mean is not equal to the current value. NOTE:- Items 1-3, 7-20 list all data first, then treat the best data only in each quantity. Items 1, 8, 15, 20 have low confidence intervals due to small data numbers and/or large standard deviations. REFERENCE:1, 2, 3: c = light speed in Km/s. For 2, values with errors 0.5% are omitted. For 3, refined data only, based on Birge (see reference 11) plus post 1945 values. For 1, all data are used. 4, 5, 6: e = electronic charge in ESU x 10-10. For 4, all data used. For 5, only oil-drop data employed. For 6, X-ray data only. 7-11: m = electron rest mass. Specific charge e/(mc) in EMU/gm x 107. 12. 13: h = Planck's constant. h/e in units of (erg-sec/ESU) x 10 -17. 14, 15: 2e/h in units of GHz/V. Values from ac Josephson effect. 16-18:  ' = gyromagnetic ratio in units of rad/sec/gauss.

19, 20: = radioactive decay constants. All units reduced to unity. In this case METH. column refers to the number of elements only. 21: R= Rydberg constant for infinite nucleus in units of cm-1. It combines variables c, h, and m so that time terms cancel. 22: G = Newtonian gravitational constant in units of dyne-cm2/gm2 x 108. 23-25: see listing under references 10, 54-57 and 65-67 at end of report. = fine structure constant,  0 = permittivity of free space, * The statistical treatment indicates these quantities to be absolute constants. The values of Rare stable to 7 figures. The values of e and G have a normal distribution about today's value. This is in sharp contrast to the other constants discussed. 2 ** From 4-6 and 25,  0 must be an absolute constant. As  0 0 = 1/c , free space permeability 0 is implied as proportional to 1/c2.

Items 16-18 give the gyromagnetic ratio results, ', with 16 being the already given summary. Table 17 shows that all recent data are prefixed by 26751. Those data outside that prefix were rejected. For a mean date of 1966, all 12 data of the correct prefix were used from 1958 to 1973. For a mean date of 1974 values between 1968-1980 were used with the prefix narrowed to 26751.3 which had a clear majority over other values for the decimal. The refined results are again in accord with the c data trend in parts per million. The radioactive decay constant, , appears in items 19 and 20 in Table 23. Here, for the purposes of comparison, each decay constant has been reduced to unity and an overall general result obtained for item 19. The best data is taken as being those that show a trend of less than 7 x 10-5 per year when the 1904 value is omitted. The relevant elements become Pb211, Bi 211 Bi 212 (which also omits the 1913 value), Ra224, Th234 (which also omits the 1913 value), and finally U235. The latter was included as the best result from the long-lived nuclides. The mean date for these 6 elements is 1951, and again the results are largely in accord with the refined c data trend. The consistent trend in 7 atomic quantities, including c, is listed in Table 24. The non-linear nature of the trend is clearly revealed. In 1700 the rate of change per quantity for c (or cï/c) was -4.16 x 10-5. By 1905 it had dropped to about -6.1 x 10-6. Around 1945 two other atomic quantities placed it about -2 x 10-6. In the period 1952-1966, c and two other quantities placed it in the order of -1 to -6 x 10 -7. From 1970-1974 the decay measured by three quantities ranged from 2 to 5 x 10 -8. In the mid 1970's it was about 10-9, while the late 1970's saw it drop to 10 -10. The slowing announced by Van Flandern in the early 1980's were of the order of 10 10 to 10 -11. It is important to continue the measurements to discover whether the trend will drop to zero rate of change, taper off slowly, or perhaps reverse and become an increase. (D). ULTIMATE CAUSES AND THE C EQUATION: The above data presentation indicates strongly that both light speed and atomic processes, including atomic time, are undergoing a uniform decay process. Furthermore, experiments mentioned above indicate that all atomic clocks are ticking in unison for light speed to have some universal value at any instant. Rather than invoke some property of light or the atom that might suggest they have an intrinsic notion of time, it would seem more logical to search for properties of free space that uniformly affect both. The place to commence would seem to

be equation (1) as light speed and atomic behavior are both affected by the permeability of free space. Put into a context of general relativity, this implies that the energy density of free space, and consequently its metric properties, are altering. Wesson and others 57 have pointed out that these properties are under the control of the cosmological constant, . This immediately links atomic variations with the behavior of the cosmos. TABLE 24 - CONSISTENT TRENDS IN 7 ATOMIC QUANTITIES

REF

MEAN DATE

ATOMIC QUANTITY

DATA POINTS

RATE OF CHANGE PER QUANTITY

1.

1700

c

4

-4.16 x 10-5

2.

1740

c

4

-3.31 x 10-5

3.

1812

c

6

-1.73 x 10-5

4.

1833

c

18

-1.55 x 10-5

5.

1865

c

16

-1.65 x 10-5

6.

1880

c

63

-1.61 x 10-5

7.

1887

c

5

-7.24 x 10-6

8.

1890

c

57

-9.31 x 10-6

9.

1899

c

5

-5.80 x 10-6

10.

1903

c

4

-6.13 x 10-6

11.

1905

c

6

-6.17 x 10-6

12.

1926

e/(mc)

4

-3.50 x 10-6

13.

1934

c

4

-3.43 x 10-6

14.

1938

e/(mc)

11

-1.72 x 10-6

15.

1945

e/(mc)

16

-3.37 x 10-6

16.

1947

h/e

6

+2.34 x 10-6

17.

1951



6

-2.02 x 10-6

18.

1952

e/(mc)

5

-3.79 x 10-7

19.

1953

c

23

-6.33 x 10-7

20.

1961

c

15

-1.00 x 10-7

21.

1966

 '

12

-4.89 x 10-7

22.

1970

c

7

-1.94 x 10-8

23.

1971

2e/h

5

-4.96 x 10-8

24.

1974

 '

7

-4.08 x 10-8

25.

1975

c

11

-8.73 x 10-9

26.

1978



-

-3.00 x 10-10

27.

1978



-

-1.24 x 10-10

28.

1979

c

4

-3.25 x 10-10

29.

1980



-

-3.20 x 10-11

30.

1983



-

-1.00 x 10-12

NOTE:Symbols as in Table 23. Atomic time =  . The value of e is invariant, while  ', , and are proportional to c. Since m is proportional to 1/c 2, and h to 1/c, then e/(mc) is also proportional to c as is 2e/h. But h/e increases as c decays. The data for items 26, 27, 29 come from ref. 1 and 93. Item 30 in Physical Review Letters, 51:18, p.1609, Oct. 31, 1983, since no evidence of 'orbit stretching' (New Scientist, Nov. 17, 1983, p.494) with Gï/G essentially = 0. But orbit distances are invariant atomically and dynamically as is Gï/G on our approach. Item 30 may thus be spurious. CONCLUSION:Data from items 25-30 suggest cï/c and  ï/is rapidly tapering to a zero rate of change. The critically damped curve form on page 55 (and the overdamped case) accommodates this behavior with a minor change in the values of the coefficients, tapering rapidly to the time axis. The underdamped case is clearly invalidated by these and other results. The polynomial will be valid only to its turning point under these conditions. However, CODATA Bulletin 63 for November 1986 gives values for  ' and 2e/h which support the curve as presented, exhibiting a slight increase after its minimum point just below the time axis. A choice between the options can only be made by continuing measurement of  , , 2e/h, and h/e2.

In the Schwarzschild metric, the term /c2 appears which requires to be proportional to c2 for energy conservation. This also follows as there has dimensions of time-2, and as pointed out above it is those time-dependent quantities which are varying. We can thus write = kc2 , with k a true constant of dimensions cm-2. Once the value for k is established, then a /k substitution may be made for c 2 in electromagnetic and other equations. Now a universe under the control of essentially exhibits some form of simple harmonic motion with varying as the radius of the cosmos 89. An exponentially damped sinusoid would thus be typical  behavior90. This form is typical of the behavior of many electrical, mechanical, and other systems88. Taking the square root of this exponentially damped sinusoid equation immediately gives us the behavior of c. Table 21 makes it clear that c could well be following this type of curve as it provides an extremely good fit to the data. The exact form that was chosen was c = [(a + ekt(b + dt)], which is the critically damped example 88. In the overdamped case, where the equations explicitly contain the sinusoid term, the curve form that fits the data is virtually indistinguishable from this one88 . The underdamped case fitting the data also has a similar form, but the predicted future behavior is vastly different. As a consequence, the above

example may be considered typical of the other data fits. One solution gives k = -0.0048, a = 9.029 x 1010, b = 4.59 x 1013, d = -2.60 x 1010, and t is the year AD. Residuals are reduced somewhat by taking the coefficients to a higher number of significant figures. This example is fitted to the data in Figures III and IV. However, most properties of this complex formula for c are reproduced by a simpler polynomial, c = a + bT2 + dT8, where a = 299792, b = 0.01866 and d = 3.8 x 10-19, where T = (1961 - t). This equation also has a superior fit to the c data. The only region where this expression differs from the more complex one is the future reaction of c, as a rapid rise is predicted. By contrast, the exponentially damped form, as it stands, suggests a small rise in c over a long period, although minor adjustments to the coefficients allow cï/c to taper to zero. This latter result is supported by the Table 24 data. The former result may be supported by the 3 standard deviation increase in 2e/h reported by Cohen and Taylor in CODATA Bulletin 63 for November 1986. Their  ï'/ ' shows a similar increase of about 6 x 10-7/yr like the curve cï/c. Clock comparisons and Rh data are needed to cross-check. VII. CONSEQUENCES:(A). RADIOACTIVE RADIATION INTENSITIES: The energy of a photon, E, is constant in both time systems and is related to the kinetic energy so that E may be written, as in equation (11), E = hf = mc 2 = C-IND

(35)

where m is the effective mass of the photon. This means that the photon momentum, mc, is proportional to 1/c as a result of (3). Now photon momentum is related to light pressure and energy density361 such that if electromagnetic energy density is W, we can write W ~ 1/c

(36)

For an electromagnetic wave, where E 0 and H0 are the maximum amplitudes of the electric and magnetic components respectively, the energy density is362  E 02/ 8= W = H02 / 8l/c

(37)

where is the permittivity and the permeability of free space. Thus the amplitude energies of electromagnetic waves increase as c decreases. The flux of energy denoted by the Poynting Vector, S, is therefore given by362 S = Wc = C-IND

(38)

Some consider the intensity to be given by the square of the electric amplitude, E 02, but we will call this quantity the relative energy along with Ditchburn 363, and denote the flux, S, as the intensity of radiation. Consider the decay of a radioactive atom in which a gamma ray is emitted. When the speed of light is 10 times higher than now, that gamma ray has a relative energy or energy density that is 1/10th of its current value in accord with (37). If it is composed of only one wavecrest now, it was composed of only one wavecrest then. Therefore, it requires 10 radioactive atoms to

decay in unit time back then to give the same total energy flux, S, or intensity, equal to that now. This is precisely the situation outlined above with decay rates proportional to c. Thus (38) takes into account the higher production rate of photons by radioactive decay. This means that radioactivity in all its forms was intrinsically less of a problem with higher c. (B) STELLAR RADIATION INTENSITIES: REVISED IN LATER PAPER. (C). THE RED SHIFT: REVISED IN LATER REPORT (D). THE DOPPLER FORMULA: REVISED IN LATER REPORT (E). THE MISSING MASS: The discussion concerning the 'missing mass' needed to hold clusters of galaxies together as well as that within galaxies themselves has elicited a number of possible solutions over the last decade. This c-decay proposal has the potential to overcome the problem in several ways. Firstly, the fact that the proposal requires the sign of and k (in = kc2) to be negative is in contrast to the usually assumed positive sign for an expanding cosmos on the basis of the redshift. However, as Landsberg and Evans point out, it is in ideal agreement with a straight mathematical approach to Cosmology375 , a fact hitherto ignored. Furthermore, they state that its acceptance would virtually solve the missing mass problem375. This is certainly the case as negative acts as a form of gravity over large distances since the acceleration is given by 376 a = -r/3. This contrasts with normal gravity , which diminishes over large distances. The missing mass problem may also be enhanced by misleading red-shift. and Doppler information due to c decay across a cluster of galaxies. (F). SUPERLUMINAL JETS: If an event occurred at exactly the speed of light when c was 10 times its present value, and we received the signal with c equal to c now, then that event would appear to occur at exactly c now. (G). FINAL COMMENTS: The evidence given by the c, atomic, and astronomical data is therefore seen to lead on a trail that gives new insight into the behavior of the universe. One advantage has been the potential solution to a number of problems that science has faced. This report has dealt with some, mainly in the area of astronomy. However, others requiring further investigation lie in the fields of geology and paleontology. Some outlines are already apparent. It seems possible that the decay in the speed of light may yet be shown to have supplied a driving mechanism for some natural selection and observed preponderances in the fossil record. Other aspects of astronomy are also in view. It is hoped to deal with these questions in detail in the second report. In the meantime, Van Flandern's final comment after discussing the slow-down in

atomic time seems appropriate1: 'The implications of this result for our understanding of the origin and ultimate fate of the universe are profound, although not yet fully elaborated.'

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368. Kittel, C., and H. Kroemer, 'Thermal Physics', second edition, p.402, W.H. Freeman and Co., San Francisco, 1980. 369. Jaroff, L., A Star of Another Colour, summarising Nature article in Time, p.72, December 2, 1985. 370. Anonymous, Ancient Chinese suggest Betelgeuse is a young star, New Scientist, p.238, October 22, 1981, quoting Fang Li-zhi in Chinese Astronomy and Astrophysics, Vol. 5, p.1, 1981. 371. Margon, B., The Origin of the Cosmic X-ray Background, Scientific American, Vol. 248, No.1, pp.104-119, January 1983. 372. Narlikar, J., Was There a Big Bang?, New Scientist. Vol 91, pp.19-21, 1981. Also quoted in Science Frontiers, No.17, Fall 1981. 373. Anonymous, Cosmic Background Not So Perfect, New Scientist, Vol.92, p.23, 1981. Also quoted in Science Frontiers, No.18, Nov.-Dec. 1981. 374. Audouze, J., and G. Israel, editors, Cambridge Atlas of Astronomy, p.382, Cambridge University Press, 1985. 375. Landsberg, P.T., and D.A. Evans, 'Mathematical Cosmology', p.93-94, Oxford University Press, 1979. 376. Ibid, p.69. 377. Pearson, T.J., et al., Superluminal expansion of quasar 3C273, Nature, Vol.290, pp.365368, also p.363, April 2, 1981. Many recent examples.

APPENDIX I: NON-TECHNICAL SUMMARY INTRODUCTORY CONCEPT Time and its measurement has an important place in our lives. To the scientist, time is one of three basic quantities, the others being mass and distance. These three quantities allow physicists to describe anything in the cosmos. If time is doing something unexpected, our view of the universe may be faulty. We are all familiar with the 'pips' that give the exact time from our radio stations. When we hear them, we usually check our watches in order to make sure they are keeping 'correct' time as dictated by the pips. In so doing, we implicitly assume that those pips are keeping time without variation. In this situation, we have two methods of measuring time. There is the standard given by the pips, and there are our watches. We all know that our watches are less reliable than the standard and that they require periodic correction if that standard is to be maintained by them. In like fashion, there are two basic clocks by which cosmic time is usually measured. The first we are well familiar with. It goes by the name of DYNAMICAL TIME. The basic unit of dynamical time is the period it takes the earth to go once around the sun. Subdivisions of this

period give us hours, minutes, days, seconds and so on. If we say that I a person is 35 years old, we mean that the individual concerned has been on this planet for 35 of its orbits around the sun. This is time we are all accustomed to. A moment's thought makes it apparent that dynamical time is governed by gravitation. The earth's orbital process is the result of the sun's gravitational pull. Dynamical time is thus a gravitational clock. The second clock is used in a variety of ways, but has one basic feature common to all: the atom and atomic behavior. This ATOMIC CLOCK is used to measure the age of the rocks, the fossils, the moon, the stars and the universe itself. There is an actual timepiece called the caesium clock which ticks away this atomic standard. Until 1967, all our time was regulated by the dynamical clock. Since then, atomic time has been gradually introduced world-wide using the caesium clock. An atom can be thought of as a miniature solar system. There is the central nucleus made up of protons and neutrons in tight motion about each other similar to a multiple sun system such as the star Castor. Then the electrons move about this central nucleus like planets around a star. The intervals on the atomic clock are defined as the period taken for one revolution of an electron around the nucleus of an ordinary hydrogen atom. CLOCKS THAT DON'T KEEP TIME Just as the time kept by our wrist watches seems to drift against the standard kept by the 'pips', so also there seems to be a variation between the two cosmic timepieces. From 1955 until 1981, Dr. Thomas Van Flandern of the U.S. Naval Observatory in Washington measured by an atomic clock the time taken for the moon to complete its orbit around the earth. The moon in its orbit is keeping dynamical time since it is a form of gravitational clock. One method of checking its orbital period is by occultation, that is when the moon passes in front of a distant star. Looking at the results of these measurements, Van Flandern concluded that the atomic clock was slowing down relative to the dynamical standard. In other words, there were fewer and fewer ticks of the atomic clock in the time it took the moon to orbit the earth once. Van Flandern was not sure which clock was the one that was varying. It is at this point that the report to which this Appendix is attached comes into focus. Not only does it solve the dilemma, it also completely reinforces Van Flandern's conclusion. THE ATOM AND LIGHT If atomic time is drifting against the dynamical standard, then other atomic quantities measured in dynamical time should also show the effect. It makes no difference which clock is in fact varying, the observed result will be the same. The quantities to look at will be those that bear units involving time. One of the prime candidates is the speed of light. All light comes from atomic processes, and the speed of light is measured in kilometers per second. Note the time-tag on this physical quantity. Now the atom will act in a completely consistent way if the usual laws of conservation are valid. In other words, the atom will not be able to detect any change within itself as all of its processes are geared to each other. It is only as we look at atomic processes from outside, in dynamical time, that any change will be noted. We then have to check to see if it is atomic phenomena or gravitational processes that are changing. In either scenario it can be shown

that theory will agree with observation only if distances (one of the three basic quantities) remain unaffected. Seen from outside the atom, dynamically, an atomic second will get longer if the atomic clock is slowing down. This means that there were more atomic seconds in a dynamical interval in the past. Now in one atomic second, light will always travel the same distance. Therefore, more atomic seconds in a dynamical interval means that light will have traveled further. Consequently, if atomic processes were faster in the past, the speed of light would have been faster. This provides a useful cross-check on atomic behavior. The speed of light is usually given the shorthand symbol of 'c'. THE SPEED OF LIGHT OBSERVATIONS There have been 16 different methods for measuring the speed of light, c. A brief summary of how those methods worked can be found in the main report under the relevant headings. When each method is taken individually, the measured values show a decay in c with time. When all 163 values are taken together, they still reveal a decay in c. However, it is desirable to use only the best data. Accordingly, those values which had been rejected by the experimenters themselves, or their fellow scientists, were set aside, along with those values which had a large margin of error. The 57 best possible data points that were left still show a decay in c with time. The drop is something like 1500 kilometers per second over a period of 300 years. These refined data are listed in 11, and illustrated in the Figures II, III, and IV. All date in this report are treated uniformly. Firstly, all the readily available data have been tabulated. Those data regarded as unreliable by the experimenters themselves, or their peers, have been noted and the reasons listed. We often use these rejected data, but they are omitted from our refined analysis. Any trend in the data is discovered by a mathematical procedure called a 'least squares linear fit'. This means that a straight line is put through the data in the optimum position having due regard to all the observations. If the line is horizontal, there is no variation with time and the quantity will be considered a true constant. If the line slopes, the data is taken to indicate some systematic trend with time. A further check is applied to discover how significant these trends are. There is the correlation coefficient, r, which indicates how well the line fits the data points. Values of r range between 0 and 1. If all points lie on the line then r = 1, no matter whether the line is sloping or horizontal. A value for r above 0.8 is often accepted as indicating a good fit to the data. Confidence intervals, expressed as a percentage, are then applied to the data trend and the linear fit. It is customary to acknowledge that the result should be taken seriously if the confidence interval lies in the 90% to 100% range. Using these procedures indicates that c does decay with time, and that the decay does have a formal statistical significance. This suggests that the speed of light was indeed higher in the past, and that atomic processes were faster as Van Flandern indicated. Light from distant galaxies thus took less time in transit as atomic processes and light speed are inextricably linked. This means that if the atomic clock has registered an age of, say, 10 billion years for the universe, then light will have traveled a distance of 10 billion light years in that atomic period. However, the dynamical clock could have registered a completely different age. No matter what dynamical age is appropriate, this result means that light could have got back from those parts of the universe 10 billion light years away in that appropriate dynamical interval. Note in passing that some claim the evidence suggests an atomic age for the universe

of 15 or 20 billion years. In this case, the values in the above examples would be adjusted accordingly. RELATIVITY AND LIGHT A changing c scenario bothers some people because of Einstein's use of c in relativity theory. However, it can be shown that relativity is still valid with changing c. Some physicists have proposed an approach that deduces relativity without light entering the argument at all. Others have shown that changes are possible in the physical quantities involved in the equations provided that the effects are mutually canceling. This approach is shown to be valid and one example appears in the next section. OTHER ATOMIC QUANTITIES If the trend indicated by Van Flandern's observations and the decaying speed of light is genuine, then other atomic quantities that have a time-tag on them should also show the effect. This is the third leg of the tripod of evidence. The first leg involved observations on an astronomical scale in which Van Flandern recently highlighted the problem. In the second leg, the observations of c on an intermediate scale over the last 300 years also indicated an atomic slow-down. Finally, there is this third leg in which the microcosmic world of the atom itself is explored. In all, we have considered about 25 different methods by which these various atomic quantities have been measured. Their treatment statistically was the same as for the c data. A united testimony emerges. Those quantities with the time tag 'per second', as c had, all displayed a statistically significant decay with time, like c. Those quantities that had the units of 'seconds', like Planck's constant (h erg-seconds), would be expected to move in the opposite way and increase with time. Again, in each instance a statistically significant increase in the measured value has been recorded. AN ATOMIC CROSS-CHECK An interesting cross-check can then be made. There are some atomic quantities that combine both those values that are decreasing, like c, with those that are increasing, like Planck's constant, h. The ratio hc should in fact be absolutely constant as all the time terms cancel out. This is despite the fact that the individual parts making up the quantity have been measured as varying. When hc is measured over the lifetime of the universe, by examining the most distant astronomical objects, the testimony is that it is an absolute constant. The same is found for all those similar quantities containing mutually canceling time-dependent parts. Note that if only one of those mutually canceling parts, like c, was varying, and the other, like h, was not, then hc would not be measured as being constant. We would then suspect that our theoretical approach was in error, that atomic processes may be unchanging with time, and that some other effect was causing c to decay. Instead of that, those atomic quantities with mutually canceling time-dependent terms show a stability, a constancy, in some cases to over six figures since measurements began. In other cases there is a small random fluctuation about some fixed value. This behavior should be emulated by c and those other time-dependent quantities if they were indeed true constants. This is not observed. The conclusion is that the atom itself is, in fact, registering a slow-down

in its processes, and the third leg of the tripod of evidence is in place. There is thus a united testimony from three levels of measurement to the validity of this effect. Tables 23 and 24 summarize the statistical treatment on all atomic quantities. From Table 24, it becomes apparent that the best data show a completely concordant slow-down in all relevant quantities, including c, over dynamical time. The size of the change for each quantity is virtually the same. In other words atomic processes are indeed acting in unison with c and each other as the slow-down occurs. Furthermore, in each case the slope of the best fit straight line through the data points lessens with time. That is to say the line becomes more and more horizontal. This indicates that the atomic slow-down is best described by a curve of lessening gradient as in figures III and IV rather than the sloping straight line of Figure II. As a consequence, it would seem that the further back in the past we go, the more quickly the atomic clock ticked. It therefore registers a systematically old date when compared with the dynamical standard. RADIOACTIVE DECAY AND STARS All forms of dating by the atomic clock are subject to this effect. This includes radiometric dating whether it be the uranium/lead, thorium/lead, lead/lead, rubidium/strontium, potassium/argon, carbon 14 or any other. The rate at which a radioactive element decays from, say, uranium to lead or from potassium to argon, is dependent upon how fast the atomic clock ticks. In Table 19, the decay rates of two-thirds of the main naturally occurring radioactive elements indicate a slowing atomic clock, despite improved measurement techniques which tend to reverse the trend. Since the radioactive elements are absolutely tied to the atomic clock, they, like the speed of light, will register an atomic age for the cosmos of, say, 10 billion years no matter what age is recorded by the dynamical clock. Despite more rapid radioactive decay in the past, proportional to c, the equations demand that the actual intensity of radiation be proportional to 1/c. For example, if the speed of light was 10 times its present value at some stage in the past, then radioactive decay would have occurred 10 times more quickly. However, although 10 times as much radioactive decay was occurring in a given interval, the intensity of radiation from each decaying atom was only 1/10th of today's value. Accordingly, the total observed intensity would only be the same as today's level. In a word, radioactive decay was far safer and much less of a problem in the past with higher c than it is today. A similar situation occurs with regard to the dating given by the ages of stars since stars burn their fuel a process related to radioactive decay. Thus stars go through their life cycle more rapidly with higher values for c. Hand in hand with this faster aging process, proportional to c, goes a radiation intensity proportional to 1/c. Therefore, even though the amount of light coming from a star was proportionally greater, this was exactly offset by the fact that its intensity was lower. Consequently, net observed light intensities were unchanged, with solar and planetary temperatures unaffected. A CHOICE IS NEEDED. Experimental measurements thus support the conclusion that atomic time is slowing against dynamical time. The question now arises whether it may not in fact be dynamical time that is varying. If this were the case, it would mean that atomic intervals were constant and that dynamical time was speeding up, with shorter and shorter intervals. The earth would thus be

going faster and faster around the sun and also spinning faster on its axis. In either case, whether the variation is atomic or dynamical, the result remains unchanged, namely that atomic time registers as systematically old against the dynamical standard which we are all used to. The difficulty is fairly readily resolved, however. It can be demonstrated that gravitational phenomena are completely independent of any changes in the atom or c. In other words, if the atom is varying, the dynamical clock is not affected. Furthermore, the physical behavior of the gravitational constant, G, would be in contradiction to conservation laws and theory if the atom were not changing. Thirdly, things tend to slow down, wear out, and get older, rather than speed up and go faster with time as a dynamical variation would require. Dynamical variation would seem to break this physical principle which is called the 2nd law of Thermodynamics. In addition, if c decay is taken as causing the atomic changes rather than the other way round, the dynamical clocks are not affected at all. Each scenario conspires to indicate varying atomic processes and constant dynamical ones. We begin to get to the basic reason for all the observed variations if we consider atomic changes and c decay both as symptoms instead of being the root cause of the trouble. However, the observations require every atom to tick in unison throughout the cosmos and for all light to behave uniformly. This united slowing of atomic clocks and decaying light speed indicates that the properties of free space must be altering, like the magnetic permeability. Relativity points out that these properties are controlled by what is called the cosmological constant, . Furthermore, for conservation to be valid, , must be proportional to c2 . We can therefore write a equivalent for c in our equations. Atomic processes and c are consequently under the control of as a decay in means a decay in c and slowing atomic clocks. However, not only governs the properties of space, it also manipulates the behavior of the universe, so the atomic slow-down warns us of cosmic changes. THE BEHAVIOR OF THE UNIVERSE We are all familiar with the force that exists in a stretched rubber-band tending to snap it back to its minimum position. The cosmological constant, , acts in precisely the same way. Perhaps it would be more accurate to consider an expanded balloon which has the same force acting to restore it to its smallest size. That is roughly a picture of the universe. The cosmos expanded to its maximum size extremely rapidly in the process scientists call the 'Big Bang'. Following that event, has been acting in such a way as to deflate the cosmological balloon. At its maximum extension, the rubber in the balloon is thinnest, and thickest when collapsed. In a like manner, we may consider the fabric of space to become 'thicker' with time under the action of . Put scientifically, the permeability, or energy density of free space, has increased, and the metric properties of space have changed. This slows both light and the atomic clocks uniformly. A rubber band, or balloon under the action of such a force will begin to follow a special form of behavior. This behavior is more complete when a weight on the end of a spring is set in motion. It is called simple harmonic motion. The force acting within the spring plays a similar role to . At the maximum extension of the spring the force is at a maximum, while the spring in its rest position has the minimum force exercised. The magnitude of the force is thus given by the extension. In like manner, was greatest when the universe was at its maximum size and became less as the cosmos collapsed. There are a set of equations that describe the behavior of under these circumstances. To give it the full title, the behavior is that of an

exponentially damped sinusoid. The curve for is a typical example of this. Since c is related to , it is possible to test this approach by fitting a related curve to the c data. The test is passed as a result. The details of equations are given on page 7, and the curve fit to the c data is illustrated in Figure IV. ASTRONOMICAL OBSERVATIONS The concept of a collapsing universe seems to be at variance with popular notions of an expanding cosmos. However, the reason for believing that the universe is expanding actually turns out to be evidence for a decay in the speed of light! By way of explanation, we are all familiar with the wail of a police siren and the manner in which the siren's pitch drops once it has passed us. Light behaves in a similar way to sound. If an object is coming towards us and emitting light, the 'pitch' of that light is higher than normal. If it is receding from us the 'pitch' of the light drops, just like that of the siren. More correctly, we should say that for recession, the wavelength of light is increased, or moves towards the red end of the rainbow spectrum. As we look at the light from distant galaxies, we find that it is shifted towards the red end by progressively greater amounts for increasingly more distant objects. This effect is called the red-shift. It has usually, though not always, been interpreted as indicating that the distant galaxies are moving away from us and that the universe is expanding. Some controversy has surrounded this interpretation of late, however, and a variety of alternatives explored. The decay in c offers a valid mechanism for the effect. Most are familiar with the wave-like properties of light. The distance from the crest or trough of any wave to the mid-point is called the amplitude. Some wave energy is locked up for light in the wave amplitude. The equations demand that, for a decay in c, the amplitude energy increases. That means the crests must go higher and the troughs get deeper as c decays. This is also the reason that radiation intensities increase. However, for energy to be conserved with light in transit, the wave amplitudes must grow at the expense of the wavelength. Energy is therefore taken from the wavelength which gets longer or redder, since longer wavelengths have less energy. As c decays, a red shift will consequently occur in light from distant objects. The further away those objects are, the more c has decayed and the greater will be the resultant red-shift. Far from indicating an expanding universe, the red-shift gives evidence for slowing c and atomic processes. QUASARS AND THE MAXIMUM VALUE FOR C The red-shift may also supply details as to the upper maximum value that c attained. Coming uniformly from every direction in space are the two background radiations, one in the X-ray region of the spectrum, the other in the microwave portion. It is customary to attribute the microwave background to the 'echo of the Big Bang'. However some like Narlikar dispute this contention. He pointed out that the microwave background looked very similar to light from stars, galaxies, or other celestial objects that had simply been red-shifted. It was back in 1983 that Bruce Margon, Professor of Astronomy at the University of Washington, noted that the two backgrounds had a great deal in common and that one behaved very much as the other. The only difference he noted was that the microwave differed from the x-ray by a wavelength factor of ten million. This being the case, we get a value for c virtually at the time of the Big Bang of about 10 million times c now. Since we know that the universe is say 10 to 15 billion years old in atomic time, this value of 10 million times c now allows us to put in an important origin point on the c decay graph. This origin point is thus determined by observation, given the validity of the proposal by Margon. The c data tie in the points down this end of the curve,

and the form of the decay is fixed by generally accepted theory. This allows some confidence to be placed in the final result. It also supplies a possible answer to one of the problems associated with quasars. They are the most distant astronomical objects on the red-shift data and are hyperactive, ultra-luminous centers of galaxies. The source of this intense activity has been somewhat conjectural. However it is safe to say that with a higher value for c in the past, the stars in the centers of all galaxies, (the 'old' or Population II stars) would go through their life cycle much more rapidly. Many stars end their life in a spectacular outburst called a supernova which produces as much light as 100 million normal stars. The end product also results in vast X-ray emission. With a life cycle that was shortened by higher c, there would be many stars going through a supernova process at any one time and X-ray emission would be intense. This would enhance the X-ray producing process of any black holes at galactic centers. The reason for the X-ray background may therefore have been tracked down as well as a possible explanation for the quasar ultra-luminosity. THE CURRENT STATE OF THE COSMOS The quasars supplying the microwave background would appear to be virtually at rest after the Big Bang expansion and before the collapse set in. As the collapse started, the red-shift would be partly offset as any motion towards an observer produces the reverse effect (or blue shift). Between the microwave and the X-ray backgrounds would be a relatively small region of space where the red-shift factor dropped from 10 million down to the quasar value of about 2. That region of space represents the area where the action of built up the contraction speed of the cosmos to its terminal velocity This would make it difficult to find quasars in that region and to date only relatively few objects are known beyond red-shift 3. This rapidly dropping red-shift over a small distance means that few objects are involved. It also means that there is no effective background radiation in the wavelengths from X-rays to microwaves. Apart from the microwave background, then, the observed red-shift is a net result of c decay coupled with universal contraction The c data curve indicates that cosmological contraction is virtually at a minimum. This is deduced by the fact that the decay pattern has tapered off to a nearly zero rate of change as evidenced by Table 24. Consequently, one is permitted to speculate as to what will happen next. The form of the decay curve for c or both allow two possibilities. The exponentially damped motion could taper to a zero rate of change quite quickly and stay there. This is suggested by the Table 24 results. Alternatively, it is also possible that once the minimum is reached, the motion could slowly climb back to a slightly higher equilibrium point. This suggests that, perhaps, a slight universal re-expansion may occur, though it will be a small effect over some time. This option is supported by some values of the relevant constants that were published in 1986 and a value for h in 1987. Before it can be definitely decided, all data must show a consistent trend. Future monitoring of the situation is therefore absolutely essential. CONCLUDING COMMENTS When all the best-fit date curves are extrapolated back in atomic time, they each show essentially the same features. This family of curves is illustrated in Figure V. From them, the collapse in the run rate of the atomic clock appears to have started roughly 600 million years ago in atomic time. Up until then the run rate followed a slightly sloping straight line. The

rollover to the collapse seems to have been complete about 50 million years ago atomically and the final steep linear collapse set in. These dates correspond to important events in the fossil record. It was about 600 million years ago on the atomic clock that the Cambrian fossils recorded a burst of life geologically. It was also about 50 million years ago, atomically, that the present geological era, the Cenozoic, commenced with its mammal dominance. This report has dealt mainly with physics and astronomy. In the second report, it is hoped to demonstrate that c decay has supplied the mechanism guiding natural selection into some of the changes recorded by these fossils and explore other implications in astronomy, geology and biology. CLICK HERE TO SEE FIGURE V http://www.setterfield.org/report/fig5.jpg

This report was converted and formatted in HTML by Derek Miller ([email protected]) May 10, 1999. March 8, 2203. Greek letters are in Symbol font and may not be correctly rendered by all browsers. Corrections, May 14, 1999, August 19, 1999.

History of the Speed of Light Experiments Barry Setterfield | Preface | Part 1 | Part 2 | Part 3 | Part 4 |

An Infinite Speed of Light? Ole Roemer Analysis of Roemer’s Work A Modern Look at Roemer’s Work Delambre Glasenapp Sampson and the Harvard Values Miscellaneous Values Conclusions from Roemer-type experiments Preface: The following paper was started by Barry Setterfield in 1987. Shortly after the data and rough paper were complete, he was asked by a senior research scientist at Stanford Research Institute International to put together a white paper for internal study. This paper was done with Trevor Norman, then of Flinders University in Adelaide Australia. The paper was published by Flinders University due to internal reorganization at SRI at that time. At that point, Gerald Aardsma, then of Creation Research Institute in southern California, telephoned both SRI and Flinders and asked them if they knew that Setterfield was a young earth creationist. This information caused both Flinders and SRI to retract support for the paper, although the Flinders staff had, before that telephone call, been interested enough in the paper to ask for a seminar hosted by Setterfield and Norman regarding the subject of the speed of light and the statistical analysis. The seminar was cancelled, Setterfield was told he was unwelcome on the campus from that time on, Norman was instructed not to have anything further to do with Setterfield if he wanted to keep his job at

the university. Norman later resigned his position. The paper, however, had been published and is available on the web here: http://www.setterfield.org/report/report.html The massive responses to the Norman-Setterfield paper caused the paper which follows here, the history of the research of the speed of light up to the mid twentieth century, to be put on hold. We have decided to include this material in a book which is currently in progress. Because there have been a great number of requests for information on the history of the speed of light research we have decided to make this section of the book available now, before it is quite ready for the book. This page will be changed in parts rather frequently as we get endnotes and diagrams into their proper places. Other illustrations will be in the book, and we beg the reader’s indulgence regarding references to them until they are put in. Thank you. Helen and Barry Setterfield Note: endnotes are listed repeatedly in many cases rather than using ‘op.cit’ or’ ibid’ too many times. This is done to help the reader and avoid confusion. It is not being done to try to ‘impress’ anyone with the number of references!

Part 1: Early Measurements An Infinite Speed of Light? For many ages, men thought that light had no speed. It simply was. It was instantaneous. If speed was referred to, it was referred to as infinite. Aristotle thought that. Most of the Greek philosophers did as well. There were a few strange people who thought the speed of light might be finite, albeit extremely fast: Empedocles, in 450 B.C., the Moslem scientists Avicenna and Alhazen about 1000 A.D. Both Roger Bacon (1250 A.D. ) and Francis Bacon (1600 A.D.) argued against an infinite speed for light. But that was at the same time Kepler and Decartes were arguing for an infinite speed of light. It was not really considered debatable. Of course the Bacons were wrong and the speed of light was infinite! Nevertheless, such a consistent scattering of scientific philosophers through the ages disputed an infinite speed of light that it occurred to Galileo that there should be some way to check this and settle it once and for all. So Galileo devised an experiment using lights, shutters, and telescopes to be set up on hills a number of miles apart. The Academia del Cimento of Florence set up Galileo’s experiment using a distance of about a mile. The conclusion they reached was that the speed of light was infinite. Either that or, of course, it was too fast to be measured in that manner over just one mile… But some things were coming together which would allow the speed of light to be measured. Galileo had discovered the first four satellites of the planet Jupiter in January of 1610.1 This would provide a source of measurement, as it was discovered later that the moons would eclipse behind Jupiter at regular intervals. It was not until almost fifty years later, however, that a device which could be used accurately enough in timing was invented. In 1657, Huygens had invented a clock with a free-swinging pendulum, 2 capable of

counting seconds. This was improved upon with his 1673 version.3

Ole Roemer More was needed. Ole Roemer, born in Denmark on September 25, 1644, had begun studies in mathematics and astronomy at Copenhagen University in 1662. Ten years later, in 1672, he was appointed to the newly constructed observatory in Paris. In 1675, he discovered that the epicycloid was the best shape for teeth in gears and communicated to Huygens that such gears would be advisable in his clocks.4 This resulted in an improvement so significant that clocks of this caliber made the determination of longitude possible. With such accurate clocks and the knowledge that Jupiter’s moons eclipsed regularly, it was now be theoretically possible to measure the speed of light, and determine whether or not this speed was really infinite. The eclipses provided a regular astronomical phenomenon that was visible from both a standard observatory and the place whose longitude was to be determined. The Paris Observatory was chosen as the standard. One more thing was needed, however: accurate tables were needed to predict eclipse times. Picard, then later Cassini and Roemer, made a series of observations so that the tables could be prepared. Cassini published the first reliable times for these astronomical events.5 Roemer collected more than seventy observations by Picard and himself of Jupiter’s inner moon, Io, from 1668 to 1677. Of these, half came from the period 1671-1673, when Jupiter was at the most distant point in its orbit and consequently moving the most slowly as seen from earth. At any given time, Io would take approximately one day, 18 hours, and 28.5 minutes to complete one revolution around its giant parent planet. The times when it either went into eclipse behind Jupiter, or emerged from eclipse could thus be accurately predicted. The giant planet itself takes about 12 years to go around the sun once. The earth in its orbit thus periodically comes its closest to Jupiter, then swings away, until 6 months later, at the opposite part of its orbit, the earth is a its furthest point from Jupiter. During the course of these observations, Roemer noticed something: as the earth drew away from Jupiter, the eclipse times of Io fell further and further behind schedule. However, once the furthest point in our orbit was passed, and the earth began to approach Jupiter, the eclipse times began to catch up again. How could the position of the earth in its orbit affect the time it took Io to go around Jupiter once and be eclipsed? It didn’t, said Roemer. What is happening is that the light carrying the information from the Jupiter-Io system is taking time to travel across the diameter of the earth’s orbit, so the eclipse information takes longer to get to the earth when it is at the furthest point in its orbit. This was the discovery that Roemer announced to the Paris Academie des Sciences in September of 1676. He then predicted to them that the eclipse of Io that was due on November 9 of 1676 at 05 hours, 25 minutes and 45 seconds would, in fact, be ten minutes late. They listened. They doubted. Then they watched. On November 9, 1676, the eclipse was observed at the Observatoire Royale at precisely 05 hours, 35 minutes, and 45 seconds, exactly as Roemer had predicted, evidently because of the time it took the light to travel. It might be expected that with the above information Roemer would pronounce a definitive value for the

speed of light (or “c”), but this was not his main purpose. His prime concern was to demonstrate that light was not transmitted instantaneously, but had instead a definite velocity, as evidenced by the observations. In this he eventually succeeded. The main factor that was unknown to Roemer, and that prevented accurate calculation of the speed of light was the radius of the earth’s orbit. Without that knowledge it was impossible to know exactly how far the light had traveled and thus also impossible to determine its speed. Today we know the radius of the earth’s orbit to be 1.4959787 x 108 Km,6 a value that is adopted in all the following calculations. Due to the precision needed in the measuring devices, there would have been further problems for Roemer if he had tried to calculate the speed of light. First of all, though Huygenian clocks could count seconds, the metal in the pendulum rod was temperature sensitive. A rise of 5° C caused a loss of 2.5 seconds per day.7 With temperature variation on a daily scale, it is possible that Roemer’s clocks were accurate only to five seconds. While this accuracy was quite sufficient to pick up a ten minute time difference in the observations, it was not until 1869, about 200 years later, that temperature effect was corrected for by making only evening transit timings for Jupiter’s moons. The other major problem Roemer would have faced had to do with human error in observation. Io is about 3632 kilometers in diameter, and it goes into or emerges from its total eclipse in a period of 3.5 minutes. During the time that it goes into eclipse, it becomes progressively fainter until the observer times the disappearance of the last speck of light from the fast-fading satellite. When Io is emerging from Jupiter’s shadow, the first speck of light is timed. With a small telescope, this timing can be accurate to within ten seconds,8 which would approximate what Roemer achieved with his equipment. Obviously, an exact timing of the moment of extinction of the disappearing Io is going to be easier than the exact timing of its reemergence out of darkness. Consequently, it comes as no surprise that Roemer’s value for the period of Io in its orbit as timed by its emergence from Jupiter’s shadow varied from 8 seconds up to 29 seconds longer than the timing of its disappearance. The average variation was about 20.7 seconds. As the November 9 eclipse timing in 1676 was one of a re-emergence, it is inevitable that it would be timed late. Roemer’s period for Io’s orbit in November was 27 seconds longer than in June of 1676.9 Analysis of Roemer’s Work A variety of values for the speed of light have been extracted from Roemer’s figures. They range from 193,120 Km/s up to 327,000 Km/s.10 If we take Roemer’s delay as being the ten minutes that he quoted, less the 27 seconds due to the late emergence timing for November, less a further 5 seconds for the clock running fast in the cold November weather, we end up with a delay of the order of 568 seconds. In 1915, Danish mathematician K. Meyer rediscovered Roemer’s own observations in an original notebook. Meyer’s calculations show that “the increment in the distance from Jupiter to the earth between August 23 (the last eclipse of Roemer’s list before that of November 9, and the one on which it is probable he based his startling prediction) and November 9 of 1676 was 1.14 r” where r is the radius of the earth’s orbit.11 We thus divide 568 seconds by 1.14, giving us 498.2 second for the delay across the radius of the earth’s orbit of 1.4959787 x 108 Km. This results in a value for c of 300,280 Km/s -- but this is little more than a ‘guesstimate’. Roemer estimated the delay across the diameter of the earth’s orbit as about 22 minutes, a result that he obtained by averaging what he considered his best figures.12 In 1686, in his first edition of “Principia”, Newton quoted the radius delay discovered by Roemer as ten minutes, but in his own revision in the second edition, he quotes it as seven or eight minutes. By contrast, in 1693 Cassini, from his own observations, gave the delay for the orbit radius as 7 minutes and 5 seconds.13 Halley noted that Roemer’s figure of 11 minutes for the time delay across the radius was too large, while that of Cassini was too small.14 Cassini

agreed about the delay but debated its cause. Newton noted the orbit radius delay in 1704 in these words: “Light is propagated from luminous bodies in time, and spends about seven or eight minutes of an hour in passing from the sun to the Earth.” 15 Newton quoted the radius delay discovered by Roemer as ten minutes,16 but in his own revision in the second edition, he quotes it as seven or eight minutes.17 In May of 1706, a translation of sections of Newton’s “Opticks” appeared in French quoting the figure as eight minutes.18 This gives a speed of light equal to 311,660 Km/s. In describing Roemer’s method in the section on Astronomy in the Encyclopedia Britannica for 1711, the conclusion is presented from the latest observations that “it is undeniably certain that the motion of light is not instantaneous since it takes about 16.5 minutes of time to go through a space equal to the diameter of the earth’s orbit…And…it must be 8.25 minutes coming from the sun to us.”19 This gives a 1710 value of c equal to 302,220 Km/s. Apart from Roemer’s statement about the 11 minutes, it seems that Cassini, Halley, Flamstead, and Newton quote figures that suggest that the speed of light prior to 1700 may have been higher than now. The orbit delay quoted in the Encyclopedia Britannica tends to confirm this, as does Bradley’s comment about his own method. Roemer’s statement thus leaves an element of ambiguity that is in contrast with the other observers of his day. This suggests that a closer examination of Roemer’s figures is needed. By 1729, Bradley had published his findings on the aberration of light and wrote that “…from when it would follow, that Light moves, or is propogated as far as from the Sun to the Earth in 8 minutes 12 seconds…”. This gives the result that c was equal to 304,000 Km/s. Bradley then commented that his result was “…as it were a Mean betweist what had at different times been determined from the Eclipses of Jupiter’s satellites.” 20 A Modern Look at Roemer’s Work In 1973, an attempt was made by Goldstein et al to reanalyze 40 of Roemer’s original observations to come to some definite conclusions. What Goldstein and his team did was to adopt a model for the Jupiter-Io system and calculate the eclipse times for any given position of the earth. They chose the forty most reliable eclipse times from Roemer’s diary which were then compared with times from their model. They concluded that “The best fitting value for the light travel time across one astronomical unite [the radius of the earth’s orbit] does not differ from the currently accepted value by one part in 200.” Their final statement was that “the velocity of light did not differ by 0.5% in 1668 to 1678 from the current value.”21 Does this negate the idea of any variation in c? No, it does not. An immediate problem with the analysis surfaces when we look at what was done in 1973. As Goldstein and his co-workers point out, their method results in what is known as a “root mean square” (rms) deviation of observed times compared with the model of 118 seconds. In other words, the predicted times from their model disagreed with Roemer’s observations by an average of almost two minutes! The claim that c did not differ by 0.5% about 1675 is therefore meaningless. An rms error of 118 seconds in about 1000 seconds for the observed delay across the diameter of the earth’s orbit is an 11.8% error, which is equivalent to ± 35,000 Km/s in the value of c. Any suggested variation in c is very liberally covered by this error margin! Mammel has noted another, even more interesting, difficulty.22 1973 The actual visible phase of Io was not projected back over a period of 300 years to get the exact times of eclipses from the model. To do this would have involved knowing the orbital period of the satellite to an accuracy of better than one part per billion. So instead, Golstein et al calculated via an adjustment made on what was seen now, or the empirical initial point. . To get this initial point they used the current value of the speed of light to adjust the average time of observation to get the best agreement with the average predicted time. Consequently,

their answer gave them back the same value of c that they started with! Instead they should have been adjusting c to account for the variation in the apparent period of Io. In other words, because they started with an assumption that the speed of light was constant, their conclusions included that assumption. After pointing out this problem, Lew Mammel Jr. went on to correct the conceptual error and do his own calculation from the data used by Goldstein et al. As he is not a supporter of any variation in c, his results are the more interesting. He found that he had to subtract 6% of the nominal delay time for each datum to get the best fit. The predicted delay times were therefore being reduced by 6%, meaning that the value of c was 6% higher than now. This places Roemer’s value for the speed of light at 317,700 Km/s, with an expected error of 8.6%. The conclusion is that when Roemer’s data is re-worked by the current Goldstein method, it suggests that c was somewhat above its current value, in good accord with the statements by Cassini, Halley, Flamstead and Newton, who were contemporary observers with Roemer. It might also be noted here that in the last ten years, since about 1995 or so, observations of Io, the moon that was used for the Roemer data, has shown that its orbit is changing, thus making it virtually impossible to go back in time and determine the exact eclipse times Roemer and his colleagues were seeing. Delambre In 1792 the Paris Academie des Sciences decided to compile a definitive set of tables of the motions of Jupiter’s satellites. This was accomplished by Delambre in 1809 and published in 1817.23 For this task, Delambre processed all observations of Io and the other satellites in the 150 years since 1667. In all, nearly one thousand observations of those moons were processed. Unfortunately, Delambre’s manuscripts containing his calculations have been lost, so that it is impossible to cross-check his results. Irksome though this may be, all are forced to admit that Delambre’s final result of 8 minutes 13.2 seconds for the earth orbit radius delay was generally received as definitive for the median date of 1738 ± 71 years. Even Newcomb admitted this and at the same time acknowledged that it was “remarkable that the early determinations of the constant of aberration agreed with Delambre’s determination,” even though “there was an apparent difference of 1 per cent” when they were compared to the c values of the mid-1800’s.24 To see the agreement, Bradley’s value from the aberration constant as mentioned above is 303,440 Km/s, while Delambre’s result is 303,320 Km/s. The figure is quoted to the nearest tenth of a second, but if the accuracy was about 0.5 seconds, resulting from the known rapid development of both telescopes and time-pieces, the error margin would be about ± 310 Km/s. Glasenapp In 1874, S.P. Glasenapp of Pulkova Observatory discussed the results from all available observations of Io between 1848 and 1873 – 320 eclipses in all. 25 He analyzed each eclipse according to the following five different correction procedures: 1. All eclipse observations were reduced to the center of the satellite. Variation in satellite brightness with apparent distance from Jupiter’s center was corrected for at the instant of eclipse. Another term we shall call z was added to give the exact dependence. 2. Without the reduction to Io’s center and without the z term. 3. Without reduction to the center of Io, but including the z term. 4. Excluding the 50 Leiden observations. 5. As for alternative 1, with an additional correction to the mean noon based on Newcomb’s

assumption of periodic variations of earth’s rotation. The 5 corrections resulted in the following 5 values 1. 2. 3. 4. 5.

500.84 sec. 497.43 sec. 494.67 sec. 497.15 sec. 505.03 sec.

Glasenapp pointed out that the large variation in results was due to the impossibility of determining the exact apparent brightness of Io in absolute units at the moment of the eclipse. He did not indicate which results were to be preferred. However, as the first is included in the more comprehensive results of the fifth, it appears justifiable to take the mean of the second, third, fourth, and fifth, and omit the first. When this is done, the orbit radius delay becomes 498.57 ± 0.1 seconds. This error has been adopted, as it was the daily accuracy of the timepieces around 1800 that would be checked by daily star transit observations. 26 Observational accuracy with larger instruments would be somewhat better than that as times are quoted in hundredths of a second. Accordingly, an average result for the speed of light of 300,050 ± 60 Km/s for the median date of 1861 can be derived.27 Sampson and the Harvard Values In 1909, Sampson derived a value for the orbit radius delay of 498.64 seconds from his private reductions of the Harvard observations since 1844.28 However, the official Harvard readings themselves gave a result of 498.79 ± 0.02 seconds, the error being due to the inequalities in Jupiter’s surface. The Sampson result thus becomes 300,011 Km/s for the speed of light, while the official Harvard reductions give 299,921 ± for the same median date of 1876.5 ± 32 years. Miscellaneous Values In 1759, B. Martin deduced a time of 8 minutes 13 seconds for the orbit radius light delay.29 A light speed of 303,440 Km/s results. In 1770, Richard Price indicated that his research gave a value of 8.2 minutes or 492 seconds for the orbit radius delay, resulting in a light speed, or c, of 304,060 Km/s.30 In 1778, J Bode published a value of 8 minutes 7.5 seconds for the orbit light delay, giving a c of 306,870 Km/s.31 In 1785, Boscovich published his time of 486 seconds, equivalent to 307,810 Km/s.32 These values appear to be the only other independent assessments of the orbit radius delay for light. Most others appear to take Cassini’s, Newton’s or Roemer’s figures and build upon them. As various estimates of the radius of the earth’s orbit flourished, so did a wide variety of proposals for the peed of light. However, the one basic requirement was the measured time delay, and the above appear to be the full compliment of available measurements. Once that basic fact had been determined, our modern knowledge of the orbit radius allows a consistent treatment of these observations. This was the one factor lacking in the derivation of c from these basic observations up until the early 19th century. But by that time, Delambre’s figure of 8 minutes 13.2 seconds was already being widely quoted. Conclusions from Roemer-type experiments The above results may be best summarized in a table. This is done in Table 1 below. When treated statistically, the Table 1 values yield the following results:

TABLE 1 Roemer-type Experiments

Authority *Roemer

Seconds delay

Date 1673 ± 5

Value of c Km/sec 317,700

Comment Corrected method

? *Newton Delambre Martin Price Encyc. Brit. #Bode #Boscovich Glasenapp Sampson Harvard

1706 1738 ± 71 1759 1770 1771 1778 1785 1861 ± 13 1877 ± 32 1877 ± 32

480 493.2 493.0 492.0 495.0 487.5 486.0 498.57 498.64 498.79

311,660 303,320 ± 310 303,440 304,060 302,220 306,870 307,810 300,050 ± 60 300,011 299.921 ± 13

Approximate value Mean of 1000 observs.

Accepted value

Mean of 320 observs. Private reduction Harvard reduction

Upon omitting the approximate values of Roemer and Newton, a least squares linear fit to the 9 data points gives a decay of 36.35 Km/s per year. When the next two most aberrant values marked # are omitted, the linear fit to the 7 remaining data points produces a decay of 28.3 Km/s per year with r = -0.945, which is significant at the 99.93% confidence level. Furthermore, the mean of these 7 points is 301,860 Km/s, which is 2067 Km/s above the current value of 299,792.458. The t statistic therefore indicates with a confidence of 98.48% that c has not been constant at this current value during the time covered by these data points. These c values are thus consistent with a slowing trend.

References Robert Grant, History of Physical Astronomy, London, 1852

1

Oeuvres completes de Christiaan Huygens, vol. II, chapt. VII, Letter 370, Published by the Societe Hollendaise des Sciences, the Hague, 1888-1937 2

S Goudsmit and R. Claiborne, ed.., Time, Life Science Library, p. 96

3

Oeuvres completes de Christiaan Huygens, op.cit. pp. 607-616

4

5

G.D. Cassini, Ephemerides Bononienses Medicecrum Syderum Ex Hypotheses et Tabluis, Bologne, 1668

J. Audouze; G. Israel, ed.; Cambridge Atlas of Astronomy, Cambridge University Press, 1985, p. 422

6

7S

Goudsmit and R. Claiborne, ed.., Time, Life Science Library, p.97

McMillan and Kirszenberg, “A Modern Version of the Ole Roemer Experiment,” Sky and Telescope, Vol 44, 1972, p. 300 8

9

I.B.Cohen, “Roemer and the First Determinaton of the Velocity of Light:, Isis, Vol. 31, 1939, p. 351 C. Boyer, Isis, Vol. 33, 1941 p.28

10

I.B. Cohen, op.cit., p. 353

11

Journal des Scavans, December 7, 1676; also, Philosophical Transactions, Vol. XII, No. 136, June 25, 1677, pp 893-894 12

G.D. Cassini, Divers ouvrages d’astronimie, (Amsterdam, 1736) p. 475

13

Philosophical Transactions., vol XVIII, No. 214, Nov-Dec 1694, pp 237-256

14

I. Newton, ‘Opticks’, The Second Book of Opticks, Part III, Proposition XI

15

I. Newton, Principia Mathematica, London, 1687, authorized by Pepys, July 5, 1688, Scholium to Proposition XCVI, Theorem L. 16

17

I. Newton, Philosophiae Naturalis Principia Mathematica, Cambridge, 1713

18

I Newton (translator unknown), Les Nouvelles de la Republique des Lettres, May 1706

19

Encyclopaedia Britannica, 1771, Vo. 1, p. 457

20

J. Bradley, Philosophical Transactions, Vol. 35, No. 406, 1729, pp 653 and 655

21

S.J. Goldstein, J.D. Trasco, T.J. OGburn III, Astronomical Journal , Vo. 78, NO. 1, Feb. 1973, p. 122

Lew Mammel Jr., AT&T Bell Labs, Naperville, Ill. USA, Dec. 2 and Dec. 7, 1983, News Groups: Net Astro. Message ID: <795 ihuxr. UUCP> and <800 ihuxr. UUCP> 22

J.B.J. DeLambre, Tables ecliptiques des satellites de Jupiter, Paris, 1817; also in Histoire de l’astronomie moderne, Vol. II, Paris, 1821, p. 653 23

24

S. Newcomb, Nature, May 13, 1886, p. 29. Also C. Boyer, Isis, vo. 33, 1941, p. 39

S.P. Glazenap (Glasenapp), “Sravnenie nablyudenii sputnikav Yupitera” (A Comparative Study of the Observations of Eclipses of Jupiter’s Satellites), Sankt-Petersburg, 1874 25

26

S Goudsmit and R. Claiborne, ed.., Time, Life Science Library, p. 193

Note: Newcomb in Ref. 24 quotes “results between 496 s [seconds] and 501 s could be obtained”. This gives a mean of 498.5 s and c = 300,096 Km/x. K.A. Kulikov, Fundamental Constants of Astronomy (translated from Russian and published for NASA by the Israel Program for Scientific Translations, Jerusalem. Original dated Moscow, 1955 ), p. 58, quotes the weighted mean of 498.82 second. This gives a speed of light as 299,904 Km/s. 27

E.T. Whittaker, A History of the Theories of Aether and Electricity…, Dublin, 1910, p. 22. Also Cohan, ref. 11, p. 358. 28

29

C. Boyer, Isis, Vol. 33, 1941. p. 37

30

Ibid. p. 38

31

Ibid.

32

Ibid.

Part 2: The Bradley-Type Experiments Bradley’s Circumstances Observing with Bradley Bradley’s Discovery Bradley’s Initial Results Results on Seven More Stars Table 2: Bradley’s Results from Stars at Kew Re-processing Bradley’s Results Table 3: Results of Bradley’s Observations Other Aberration Values Table 4: Bradley Method Values

Bradley’s Circumstances James Bradley was born in 1693, and educated at Balliol College, Oxford.1 His astronomical instructor was one of the finest of that period in England, his uncle, the Rev. James Pound. In 1717, Edmond Halley ushered him into the scientific world and by 1721 Bradley had been appointed to the Savilian chair of astronomy at Oxford. He also lectured in experimental philosophy from 1729 until 1760. Upon the death of Halley in 1742, Bradley succeeded to his position as Astronomer Royal. At that time, the Copernican theory of the earth and planets orbiting the sun was still the subject of some debate. If the idea was correct, the new telescopes held the promise of being able to pick up the apparent displacement of the nearer stars relative to the more distant stars of the stellar background as the earth moved in its orbit. The same effect is seen when a nearby tree changes its position against the background of buildings as you walk near it in the park. The effect is called parallax. Picard, about 1671, had noticed annual variations in the position of the pole star but hesitated to attribute them to parallax or refraction.2 Hooke in 1674 and Flamsteed from 1689 to 1697 decided that parallax was the cause. However, Cassini the Younger and Manfredi, around 1699, carefully noted that the variation was opposite that required for parallax. Observing with Bradley In December of 1725, Samuel Molyneux decided to settle the question of parallax and started observing at Kew with an excellent instrument built by the famous mechanic George

Graham. He chose the star Gamma [γ ] Draconis since it passed overhead and no correction was needed for refraction. He looked at the star on December 3, 5, 11, and 12 and was joined by Bradley on the 17th. Bradley noted the star was further south on this occasion than Mosyneux observed it. Suspecting an instrumental error, he observed again on the 20th. It was even further south than on the 17th. They noted that it was in the opposite sense to what parallax predicted, as well as being at the time of the year when parallax changes would be expected to be minimal.3 After continued observation and equipment testing, it was concluded that the effect was not instrumental. The star stopped its southerly movement about the beginning of March 1726 when it was found to be about twenty seconds of arc (written 20”) further south than in December. By definition, 60 arc seconds total 1 arc minute (written 1’), while 60 arc minutes equal 1 degree (1°). A full circle comprises 360 degrees. The star’s declination then started to increase, moving northward, and in June returned to the December value. This motion continued until it again became stationary in September, differing by 39: from its March value. By December 1726, it had returned to its original position. An annual motion of γDraconis had been established. Its cause was not parallax. (Indeed, because of the immense distances involved, the annual parallax effect is about 100 times smaller for even the nearer stars.) Bradley wondered if nutation might be responsible, that is the oscillation of the axis of the earth under the influence of the Moon. Today we know this to have an 18 year period. Such an observation would have been of importance in establishing Newton’s Law of Gravitation which had been propounded in 1687. But if what Bradley and Molyneux had observed was nutation, all stars would be affected almost equally. Bradley then ordered another instrument from Graham which could examine stars other than on the zenith. In August 1727, he started observing eight stars and found that they described ellipses on the celestial sphere whose major axes were about 40” long and lay parallel to the plane of the earth’s orbit (the ecliptic). However, geometrically speaking, the minor axes of these ellipses were proportional to the sine of the angle between the star’s direction and the ecliptic. Therefore, nutation (or wobble of the earth on its axis) had to be ruled out as the cause of what was being seen as the apparent ellipses of the stars. As it eventuated, about 20 years later, in 1748, Bradley confirmed nutation by observation, and hence, Newton’s Laws.4 Bradley’s Discovery It was against this background, and with some perplexity of mind as to the cause of the observed effect, that Bradley was invited to go sailing on the Thames, so the apocryphal story goes. He became intrigued with the behavior of the flags on the sail boats. Why, when the wind was blowing in a constant direction, did the flags swing to a different one when the yachts changed course? The answer came that the cause was the net result of the yacht’s motion plus the wind. The earth also had an annual motion, Bradley reasoned, and the only other factor, equivalent to the wind, was the light from the stars coming in a constant direction towards the earth. As the earth swung around in its orbit, so did the apparent position of the stars, just like the flags on the yachts. It is called aberration, and, in this case, the aberration of light. A more everyday example is that when we walk through vertically falling rain with an umbrella, the faster we walk, the more we have to tilt the umbrella as the rain appears to come at us from an increasing angle. Knowing how fast we are walking and measuring the

rain’s angle then tells us how fast the rain is falling. If we walk at a constant rate, then this simple trigonometric relationship tells us that the rain’s speed multiplied buy the angle is always a constant value, no matter what the rain does. If the rain falls faster, the angle gets less. If the rain falls more slowly, the angle gets greater. We may write it this way: (angle) x (rain speed) = constant µ ( walking speed) where the symbol µ means ‘proportional to’. Since the motion of the earth in its orbit is essentially constant, Bradley knew that this same relationship could be applied to the figures tumbling through his excited mind, provided he used the appropriate units. The aberration angle, K,he had measure from the stars. If the speed of light was c, equivalent to the rain speed, then as written above Kc = constant. On the accepted figures today the result is Kc = 6,144,402 where K is in arc-seconds and c in kilometers per second.5 Bradley concluded “that Light moves, or is propagated as far as from the Sun to the Earth in 8 minutes, 12 seconds.”6 Bradley had confirmed not only the Copernican model for the solar system, but also the hotly debated idea of a finite value for c. His discovery was announced on the first of January, 1729.

Bradley’s Initial Results Bradley’s observations of aberration go in three periods. First, from 1726 to 1727 there was his study of γDraconis, then seven other stars at Kew. Second, from 1727 to 1747, he studied 23 stars at Wanstead in Essex where his uncle had been Rector. (The Rev. James Pound had died during 1724, before his nephew made the all-important discovery for which he had been training him.) Finally, as Astronomer Royal, Bradley made another series of observations on γDraconis from 1750 to 1754 from Greenwich. Bradley quotes his result for γDraconis in period one as 20” .2 for the major axis when the 39” was transferred to the ecliptic pole. When measured in radians, the pure mathematical unit used in some calculations, 20.2 arc seconds becomes 1/10210 radians. From the simple trigonometric relationship used in the example with the flags on the boats, 10210 was also equal to the speed of light divided by the earth’s orbit speed. Thus, if V is the orbit speed, Bradley could then write c/V = 10210 But orbit speed is equal to distance traveled divided by time taken. The time taken is one year in seconds, or 365.25 x 24 x 60 x 60. The distance traveled is the circumference of a circle, or 2πr, where r is the radius, or the distance of the earth from the sun. Therefore, he could substitute for V in the first equation and come up with Tc/(2πr) = 10210 However, he did not know the distance from the earth to the sun with any degree of accuracy, so r was in question. Therefore, the simple way out of the problem was to recognize that if the time taken for light to travel across the orbit radius r – or that distance – was t, then this equaled distance r divided by the speed of light, c, or r/c (the inverse of what he already had

in the second equation). Thus, he could announce that light took t = r/c = T/(10210 x 2π) = 8 minutes 12 seconds to get from sun to earth. Bradley, comparing the two extreme values of Roemer and Cassini for this ‘light equation,’ commented, “The Velocity of Light therefore deduced from the foregoing Hypothesis, is as it were a Mean betwixt what had at different times been determined from the Eclipses of Jupiter’s Satellites.”7 Bradley noted that the declination of the star was increasing by an arc second in three days, which indicates he could easily measure to 0”.3 as he noted its daily motion. On p. 655, he indicated that the above calculation for t could give a result to about 5 seconds, indicating an error of perhaps 0”.2. Other re-workings in Table 3 below reduce the error to below ± 0”.1. If we take the probable error as being one-tenth of an arc second in 20”.2, then from Kc = 6144402, a value for c of 304,000 ± 1500 Km/s results from Bradley’s initial work. Results on Seven More Stars Though the work on γDraconis in this first period resulted in K = 20” .2, Bradley’ s treatment of the other seven stars also examined, then revised, his mean aberration value to 20.25 arc seconds. His results for all eight stars are examined in Table 2. TABLE 2 Bradley’s Results from Stars at Kew8

Star and Comment

Magnitude

35 Camelopardus * τPersei (estimate) βDraconis γDraconis αPersei ηUrsae Majoris αCassiopeiae αAurigae (errors)

6 4.5 3 2 2 2 2 1

Observed Movement 19” 25” 39” 39” 23” 36” 34” 16”

Major Axis length 40”.2 41”.0 40”.2 40”.4 40”.2 40”.4 40”.8 40”.0

Aberration angle 20”.1 20”.5 20”.1 20”.2 20”.1 20”.2 20”.4 20”.0

MEAN VALUE: 20”.2 LIMIT MEAN: 20”.25 GIVING A c VALUE OF 303,400 Km/s * in the Flamsteed Catalogue. Now in Auriga The mean of these results is again 20” .2, just as for γDraconis alone. However, Bradley took the extreme limits given by a τPersei estimate and the αAurigae (Capella) value that contained other errors, and taking the mean of these gave the final value as 20”.25 for the first period at Kew. Re-processing Bradley’s Results

Busch, Auwers and Newcomb re-processed the first γDraconis observations. Busch finally obtained, after some significant analysis, determination of mean errors and weighting procedures, a value of 20”.2495. Auwers criticized Busch’s treatment, made corrections, took into account collimation and screw errors and gave his final result at 20”.3851. Newcomb applied a further correction and obtained 20”.53 for the aberration constant. A similar procedure gave Busch a value of 20.2050 arc seconds for the second period results, while Auwers’ criticism and re-processing gave a result of 20”.460. The observations of the third period were treated by Bessel and Peters. Both rejected the observations of 20, 21, and 23 February, 1754, as they “disagree with the rest and give large remainders.”9 They respectively obtained K = 20”.475 and 20.522 arc seconds. The final average value, omitting both of Busch’s disputed re-workings, was 20”.437 for a mean date of 1740. A c value of 300,650 Km/s results. Table 3 lists the values.

Table 3 Results of Bradley’s Observations10

Location Kew Kew Kew Kew Wanstead Wanstead Greenwich Greenwich

Stars 8 stars γDraconis γDraconis γDraconis 23 stars 14 stars γDraconis γDraconis

Date 1726-27 1726-27 1726-27 1726-27 1727-47 1727-47 1750-54 1750-54

Authority Bradley Busch Auwers Newcomb Busch Auwers Bessel Peters

Aberration angle 20”.25 20”.2495 20”.3851 ± 0.0725 20”.53 ± 0.12 20”.205 20”.460 ± 0.063 20”.475 20”.522 ± 0.079

MEAN VALUE: 20”.437 FOR 1740 VALUE OF c = 300,650 Km/s From Bradley’s final observations in 1754 until the work of Struve at the Pulkova Observatory in 1840, there appears to be only one extant set of observations, namely that of Lindenau. He processed observations of Polaris between 1750 and 1816 to obtain a value for the aberration constant of 20”.45 ± 0.011 for a mean date of 1783.11 This gives a value for c of 300,480 Km/s in 1783. Between 1840 and 1842, Struve studied seven stars from Pulkova with Repsold’s transit instrument in the prime vertical position.12 His value for K, issued in 1845, though with a mean date of 1841, was 20”.445 ± 0.011. Folke re-processed Struve’s observations with five stars as Struve had remarked that “the observations of the two stars in Cassiopeia are less exact due to their great brilliancy which precluded accurate setting on them.”13 This gave a value of K = 20”.458 ± 0.008. In 1853, Struve re-processed his observations allowing for temperature and vibration effects and a zenith correction, issuing a final value of K = 20”.463 ± 0.017.14 This results in a c value of 300,270 ±250 Km/s against the mean date of 1841. Though the value Struve issued in 1845 was the generally quoted definitive value,15 this

1853 correction is to be preferred and will be taken as the best result against the 1841 data. Further work by Struve between 1842 and 1844, again using Repsold’s transit instrument in the prime vertical, gave a further determination of the aberration constant. From this set of observations, Struve set K = 20”.480.16 This results in a value for c of 300, 020 in 1843. After a series of observations using the Pulkova vertical circle, a meridian circle and the transit instrument in prime vertical, and comparing them with those of Struve, Nyren, in 1884 announced that the value of K must be increased to 20”.492 ± 0.006.17 This was set against the date of 1883. Newcomb announced this as the definitive value in 1886, superceding Struve’s value.18 The actual value from the weights applied to his observations was 20.4915 arc seconds. This results in a value for the speed of light in 1883 of 299,850 ± 90 Km/s. Other Aberration Values In addition to the results outlined above, there are some 58 further values obtained by this method. Table 4 supplies the complete listing.19 The constant value Kc = 6144402 has been adopted. However, many observations, and particularly those from Pulkova and Kazan give high values for K and suggest that their best value is K = 20”.511.20 If this result, also quoted by Whittaker, were used, then c would be above today’s value in nearly all cases in Table 4.14 Newcomb suggested the probably cause of the high value for K from Pulkova even in the days of Nyren.21 As many of the Pulkova observations need to be made in twilight, any star will appear fainter in transit across the eat vertical than when crossing the west vertical an hour or so later if they are evening observations. For morning observations the reverse situation holds. The observer would tend to note the passage of the fainter image systematically too late. Speaking of the effect this has on K, Newcomb commented, “we can not but have at least a suspicion that…values may be slightly too large from this cause.” It appears that all Pulkova observations were affected by this problem, and so as a class should illustrate any general trend shifted into a lower range of c values. The 63 aberration determinations from 1740 – 1930 listed in Table 4 were made with basically the same type of equipment, with essentially the same error margins and substantially the same observational methods. The results from Pulkova Observatory are illustrated in Figure I. A least squares linear fit to all data gives a decay of 5.04 Km/s per year with a confidence of 96.1% that c has not been constant at 299,792.458 Km/s for the period covered by these Bradley-type determinations. These results suggest that the possibility of a decay in c should be examined further. Table 4 – Bradley Method Values (Aberration) Pulkova observations (used in Fig. 1) indicated by *

Average Date of year observation 1740 1726-1754 1783 1750-1816 1841*

1840-1842

Value of K in Value of c in arc seconds Km/sec Bradley: Reworked avg. 20.437 300,650 Lindenau: ±from 20.450 ± 0.011 300,460 ± 170 weights Struve: corrected 1853 20.463 ± 0.017 300,270 ± 250 Observer

1841* 1843* 1843 1858 1864.5

1840-1842 1842-1844 1842-1844 1842-1873 1862-1867

1866.5 1868 1870 1873 1879.5 1880.5 1883*

1863-1870 1863-1873 1861-1879 1871-1875 1879-1880 1879-1882 1883-1883

1889.5 1889.5 1889.5 1890.5 1891.5 1891.5 1891.5 1891.5 1891.5 1892.5 1893 1894.5 1896 1896.5 1897 1898.5 1898.5 1899 1900.5 1901.5 1901.5 1903 1904.5 1905 1905 1906 1906.5 1907 1907 1907.5* 1907.5

1889-1890 1889-1890 1889-1890 1890-1891 1890-1893 1891-1892 1891-1892 1891-1892 1891-1892 1891-1894 1892-1894 1894-1895 1893-1899 1896-1897 1897-1897 1898-1899 1898-1899 1899-1899 1900-1901 1901-1902 1901-1902 1903-1903 1904-1905 1905-1905 1904-1906 1906-1906 1904-1909 1907-1907 1906-1908 1907-1908 1907-1908

Folks-Struve 20.458 ± 0.008 Struve 20.480 Lindhagen-Schweizer 20.498 ± 0.012 Nyren-Peters 20.495 ± 0.013 Newcomb: weighted 20.490 avg. Gylden 20.410 Nyren and Gulden 20.52 Nyren – Wagner 20.483 ± 0.003 Nyren 20.51 Nyren 20.52 Nyren 20.517 ± 0.009 Nyren: weighted 20.491 ± 0.006 average, all observations Kustner 20.490 ± 0.018 Marcuse 20.490 ± 0.012 Doolittle 20.450 ± 0.009 Comstock 20.443 ± 0.011 Becker 20.470 Preston 20.430 Batterman 20.507 ± 0.011 Marcuse 20.506 ± 0.009 Chandler 20.507 ± 0.011 Becker 20.475 ± 0.012 Davidson 20.480 Rhys-Davis 20.452 ± 0.013 Rhys-Jacobi-Davis 20.470 ± 0.010 Rhys-Davis 20.470 ± 0.011 Grachev-Kowalski 20.471 ± 0.007 Rhys-Davis 20.470 ± 0.011 Grachev 20.524 ± 0.007 Grachev 20.474 ± 0.007 Int’n’l Latitude Service 20.517 ± 0.004 Doolittle 20.513 ± 0.009 Int’n’l Latitude Service 20.520 ± 0.004 Doolittle 20.525 ± 0.009 Ogburn 20.464 ± 0.011 Doolittle: weighted avg. 20.476 ± 0.009 Bonsdorf 20.501 ± 0.007 Doolittle: weighted avg. 20.498 ± 0.009 Bonsdorf et.al. 20.505 ± 0.008 Doolittle 20.504 ± 0.009 Bayswater 20.512 ± 0.007 Orlov 20.491 ± 0.008 Int’n’l Latitude Service 20.525 ± 0.004

300,340 ± 120 300,020 299,760 ± 180 299,800 ± 190 299,870 301,050 299,440 299,980 ± 50 299,580 299,440 299,480 ± 130 299,850 ± 90 299,870 ± 260 299,870 ± 180 300,460 ± 130 300,560 ± 170 300,170 300,750 299,630 ± 170 299,640 ± 130 299,630 ± 170 300,090 ± 180 300,020 300,430 ± 190 300,170 ± 150 300,170 ± 170 300,150 ± 100 300,170 ± 170 299,380 ± 100 300,110 ± 100 299,480 ± 60 299,540 ± 130 299,440 ± 60 299,360 ± 130 300,250 ± 170 300,080 ± 130 299,710 ± 100 299,760 ± 130 299,650 ± 120 299,670 ± 130 299,550 ± 100 299,860 ±120 299,360 ± 60

1908 1908.5* 1908.5 1909 1909.5* 1909.5* 1910 1914* 1916* 1922* 1923.5 1926.5 1928 1930.5 1933 1935* 1935.5

1908-1908 1908-1909 1908-1909 1909-1909 1904-1915 1909-1910 1910-1910 1913-1915 1915-1917 1915-1929 1911-1936 1925-1928 1928-1928 1930-1931 1915-1951 1929-1941 1926-1945

Doolittle Semanov Int’n’l Latitude Service Doolittle Zemtsov Semenov Doolittle Numerov Tsimmerman Kulikov Spencer-Jones Berg Spencer-Jones Spencer-Jones Sollenberger Romanskaya Rabe (gravitational)

20.507 ± 0.012 20.518 ± 0.010 20.522 ± 0.004 20.520 ± 0.009 20.500 20.508 ± 0.013 20.501 ± 0.008 20.506 20.514 20.512 ± 0.003 20.498 ± 0.003 20.504 20.475 ± 0.010 20.507 ± 0.004 20.453 ± 0.003 20.511± 0.007 20.487 ± 0.003

299,630 ± 180 299,460 ± 150 299,410 ± 60 299,440 ± 130 299,730 299,610 ± 190 299,710 ± 120 299,640 299,520 299,550 ± 50 299,760 ± 50 299,670 300,090 ± 150 299,630 ± 60 300,420 ± 50 299,570 ± 100 299,920 ± 50

References 1 G. Sarton, “Discovery of the Aberration of Light”, Isis, Vol, 1931, 16, p.233 2 J.B.J. DeLambre, Histoire de L’Astronmie Modern, Vol. II, Paris, 1821, p. 616 3 Bradley’s letter to Halley in Philosophical Transactions, No. 408, vol 35, pp 639-40. One mss copy is dated Jan. 1, 1729, though it was in the Phil Trans. For December 1728. 4 J. Audouze and G. Israel, editors, Cambridge Atlas of Astronomy, Cambridge University Press, Dec. 1985, p. 413 5 The I.A.U. value in 1984 of K = 20”.496 ± 0.001. Now redefined as 20”.49552. With c defined as 299792.458 Km/s, this gives Kc = 6144402. This value is adopted here to be conservative. 6 Bradley’s letter to Halley in Philosophical Transactions, No. 408, vol 35, p.653 7 ibid 8 ibid, pp 653-655 9 K.A. Kulikov, Fundamental Constants of Astronomy, (translated from the Russian for NASA by the Israel Program for Scientific Translations), original version Moscow, 1955, pp 81-83 Note: If the observations of 20, 21, 23 February, 1754 are included, Bessel obtained K = 20”.797. 10 ibid

11 Kulikov, op. cit., Table III, No. 15. Errors obtained from a comparison of weights 12 S. Newcomb, Nature, May 13, 1886, p. 30. Also Kulikov, op.cit., p. 83, and Table III, No. 35 13 Kulikov, op.cit., p. 84 and Table III, no. 36 14 E.T. Whittaker, History of Theories of Aether and Electricity, Vo. 1, Dublin 1910, p. 95. also Kulikov, op.cit., p. 85 15 S. Newcomb, op.cit 16 Kulikov, op.cit., Table III, No. 5 17 Kulikov, op.cit., p. 85, and Table III, no. 41 18 S. Newcomb, op.cit. 19 Taken from Kulikov, op.cit., Table III, p. 191 – 195. Dated values only taken from Table and repeats from Table III Parts 1 and 2 that occur in Part 3 are omitted. Also four values from Table 10 not listed in Table III have been included. 20 See Kulikov, op.cit., pp 88, 92, 93. These values of K are systematically high when compared with the USA results. Nevertheless, as a class, they still exhibit the feature of c decay, though shifting the c values into a lower range. 21 S. Newcomb, “The Elements of the Four Inner Planets and the Fundamental Constants of Astronomy”, Supplement to the American Ephemeris and NauticalAlmanac for 1897, Washington, 1895, p. 136. Aberration values quoted here appear in Kulikov’s more comprehensive Table.

Part 3: Fizeau and the Toothed-Wheel Experiments H. L. Fizeau The results Enter Cornu Cornu’s Results The Young/Forbes Result Perrotin’s Procedures Perrotin and Prim’s Results Conclusions from Toothed-Wheel Experiments Table 5: Toothed Wheel Experimental Values

H. L. Fizeau The two methods of measuring the velocity of light, c, that have been considered to date have both been astronomical. However, back in 1638, in his ‘Discorsi’, Galileo suggested the basis of a terrestrial experiment over a number of miles using lanterns, shutters and

telescopes to timed flashes of light. The Florentine Academy in 1667 tried the idea over a distance of one mile without any observable delay. Just nine years later the reason became apparent: Roemer’s value for c was so great in comparison to human reaction times in operating the lantern shutters that there was no hope of observing the finite travel time delay for c over one mile (or 1609.344 meters). It was not until 1849 that the French physicist H. L. Fizeau overcame the problem in the following fashion. In the first place it was desirable to have as large a distance as practical involved, instead of just one mile. Fizeau used as his base-line the distance between two hills near Paris, Suresnes and Montmartre, measured as 8633 meters.1 As he had arranged to observe the returning beam of light, the total distance traveled was thus 17,266 meters. Though this distance was large in comparison with the single mile used with lanterns, it was the second shortest base-line ever used in this type of experiment. In place of the shutters on lanterns, Fizeau used a rotating wheel with 720 teeth and driven by clockwork made by Froment.2 Light from an intense source was focused on the rim of the wheel, then made into a parallel beam by a telescope, and traversed the 8633 meters. There it was received by another telescope which focused the beam onto a concave mirror, sending the light back along the same path that it had just traveled. The returned beam was viewed between the teeth in the wheel. The system was focused with the wheel at rest and with the light shining between the gap in the teeth. The wheel was then rotated, automatically chopping the beam into a series of flashes like the lantern shutters.

diagram courtesy of http://home.iprimus.com.au/longhair1/chap6.htm (this diagram is for the net article only. A more detailed original diagram will be in the book)

The results Initially, as the wheel’s rotation rate was increased from zero, the observed light intensity dropped, until the light flash that had passed between the teeth on the way out struck the next tooth on its return. The observed light intensity was then at its minimum. However, by increasing the wheel’s rotation rate, a situation arose where the returning flash went through the next gap to the one it passed through on the way out. This gave an observed maximum intensity. Fizeau found the first minimum occurred with the wheel rotating at 12.6 turns per second and the first maximum followed at 25.2 turns per second.3 The flash of light had thus traveled the 17,266 Km distance in 1/(25.2 x 720) seconds. Hence, in one second, the light traveled 25.2 x 720 x 17,266 Km. This gives Fizeau’s value for c as 313,300 Km/s. This is the usual figure given in textbooks.

Although this value for Fizeau’s result is often quoted,4 the technical literature prefers another value for the following reason. Fizeau stated that his result was the mean of 28 measurements that gave c as 70,948 leagues of 25 to the degree per second (’70,948 lieues de 25 au degre’).5 As Dorsey points out, the meter was meant to be 1,10,000,000 part of the earth’s meridional quadrant and hence Fizeau’s league became equal to 40/9 Km. Multiplication of 40/9 by 70,948 gives the technically accepted result of 315,300 Km/s as Fizeau’s value for c, the speed of light.6 Fizeau’s experimental details were not given in his report, and one promised later after further work seems not to have been found. However, in a quote from the French journal ‘L/Astronomie’, with no exact reference given, two further values appear against an 1855 date that are presumably Fizeau’s.7 They give c as 305,650 Km/s and 298,000 Km/s, thought this latter value may be a bad citation for Foucault’s initial work in 1862. Enter Cornu In 1872, A. Cornu used Fizeau’s method to determine c over a base-line of 10,310 meters from the École Polytechinque to Mont Valerien.8 This was in the nature of a preliminary experiment, and was refined later. Of the 658 measurements made, 86 were determined using a weight driven motor and the remaining 572 using a clockwork spring drive. The results obtained were later rejected by Cornu9 as being “affected by serious systematic errors”.10 Dorsey states that “The apparatus was crude; the precision was low”.11 This preliminary result that Cornu rejected was 298,400 Km/s in air or 298,500 ± 300 Km/s in a vacuum.12 In 1874, the Council of the Paris Observatoire, headed by LeVerrier, who was the Observatory Director, and Fizeau, decided to ask Cornu to obtain a definitive value for c. The date was April 2, and the reason was that a transit of Venus was to occur on December 9th of that year. A value for c accurate to one part in a thousand would be needed by astronomers observing the event. Cornu complied with the request. The sending telescope was mounted on the Paris Observatory and the light flashes sent to the tower of Montlhery where the collimator lens returned the chopped beam. The base-line was 22,910 meters. Four smoked aluminum wheels of 1/10 to 1/15 mm thickness were used. Three had pointed teeth numbering 144, 150, and 200 respectively. The fourth wheel of 40 mm diameter has 180 square teeth. The wheels could be rotated in either direction, which eliminated a number of errors. The apparatus was powered by a weight-driven, friction-brake controlled device. An electric circuit automatically left a record of wheel rotation rates on a chronograph sheet advancing 1.85 cm/s. A 1/20 second oscillator was used to subdivide the one second intervals of the observatory clock. Times were estimated to 0.001 second were claimed. The main difficulty in observation was the determination of the exact moment of total eclipse of the returned flash as the background is always slightly luminous. The speed of the wheel corresponding to the disappearance of the beam was noted, as was the speed for its re-appearance and a mathematical averaging procedure was adopted.13 Cornu’s Results In his initial report of December 1874, Cornu announced that his preliminary reductions of

the data resulted in a value for c of 300,330 Km/s in air.14 Multiplied by a refractive index for air of 1.0003 gave the vacuum velocity of 300,400 ± 300 Km/s. After final reductions of the data gave a result of 300,170 Km/s for air, Cornu felt obliged to apply a correction for possible vibrations of the wheel which resulted in a value of 300,350 Km/s in air.15 The addition of the 82 Km/s to bring the value to that of a vacuum gave his final result again as 300,400 ± 300 Km/s to four figures. In all, he claimed to make 630 measurements of c for this toothed wheel determination. However, he records 624 sets of observations, of which he appears to have used 546 in the reduction process.16 Following the publication of the initial report, Helmert noticed that, for low speeds of the wheel, the c values were higher than the mean value, while for high wheel speeds, the values were lower than the mean.17 This suggested that a systematic error was affecting the result such that c* = c (H/q) where c* was the reported value of c, and H = 7.1. The q term was the order of the eclipse so that for higher rotation speeds q was also higher. Dorsey derived a similar function.18 Helmert’s correction was generally discussed, verified, and accepted, even as late as 1900, despite Cornu’s protestations at the treatment.19 The Cornu-Helmert value was 299,990 ± 200 Km/s. Dorsey, after considerable analysis, decided that “The best value one can derive from the observations seems, from these data, to be 299.8 metametres/sec. in air with a possible range of ± 0.2”.20 After applying a refractive index correction, the final Cornu-Dorsey vacuum c value was 299,900 ± 200 Km/s. The mean dates for Cornu’s experiments were 1872.0 for his preliminary work at the Ecole Polytechnique, and 1874.8 for those at the Paris Observatory. It should be noted that Newcomb gives incorrect dates for these determinations and also attributes the value of 299,900 to a re-discussion of Cornu’s results by Listing.21 Though Listing had just published a paper (Astron. Nachr., Vol. 93, p. 369, 1878) on solar parallax, Cornu’s results were accepted without discussion. This misinformation was transmitted by Michelson in his Tables22 and by Preston (‘The Theory of Light’, p. 511, 1901). Michelson furthermore quotes the value as Listing’s even when referencing a work that correctly attributes it to Helmert (Phil. Mag., 6th series, Vol. 3, 1902, p. 334). Later Michelson gave the result as 299,950 Km/s, different from Cornu, Helmert or Listing, leaving the origin of this figure lost in obscurity.23 The Young/Forbes Result One of the main problems facing the toothed wheel method was the estimation of the exact moment of eclipse of the light beam. Cornu overcame the problem by making pairs of observations on either side of the exact eclipse position and further pairing with reversed wheel rotation. Young and Forbes in England in 1991 used a different technique. From an observing station at Wemyss Bay, light was sent to two distant reflectors, instead of the normal one, in the hills behind Inellan. The reflectors were in the same line but the nearer one was 16,835.0 feet from the observation post, and the other was at 18,212.2 feet distance. The two images so formed were observed simultaneously. The position of the eclipses or the maximum was not needed. The speed of the cogwheel was measured instead at the time when both images appeared to be of equal intensity. The advantage of this method is that the eye is extremely sensitive to slight differences in the intensity of adjacent images. The extreme disadvantage of their arrangement consisted of the

short base-line. Even taking the most distant reflector, the base was only 5551.07 metres long. This was by far the shortest for this type of experiment being not quite two-thirds of Fizeau’s base-length. The problems of the short base asserted themselves, as did other experimental features that were not conducive to obtaining good results. This determination was severely criticized by both Newcomb24 and Cornu.25 It is omitted in the definitive list of best c determinations treated by Birge.26 Dorsey comments, “it is generally admitted that their work is seriously in error, and is reported unsatisfactorily.”27 This Young/Forbes result was given as 301,382 Km/s28 “with an unwarranted accuracy but they give no probable error.”29 Perrotin’s Procedures Joseph Perrotin was born in 1845 and was appointed as the Director of the Observatory at Nice in France during the late 1800’s. His assistant at the Observatory was Prim, who had the details of their determination of c by Fizeau’s method published in 1908.30 Cornu was still alive at the inception of the project in 1898, and gave his counsel throughout its duration. Cornu died in 1902, the year in which the experimental proceedings were finalized. Perrotin died shortly after, in 1904, before completing the discussion, leaving Prim to release the final calculations in 1908. In the initial work, centering about 1900.4, the base-line was from the Nice Observatory to the village of La Gaude, a distance of 11,862.2 metres. In the more extensive series, that centered around 1902.4, a longer path of 45,950.7 metres to Mont Vinaigre was employed. In the La Gaude series, a total of 1540 measurements of c were made, 607 by Perrotin and 933 by Prim. The Mont Vinaigre experiment totaled 2465 measurements with Perrotin making 1452 and Prim 1013. In all the complete exercise made 4005 measurements to come to the final value for the series.31 With Cornu as advisor, much of the equipment and procedure was the same. The illuminator and the powering apparatus were those Cornu used, as were the chronograph, pendulums, and 1/20 second oscillator. The microscope with variable magnification was also that used by Cornu in his determination.32 The only essentially different equipment items were the sending and collimator lenses and the toothed wheel itself. This latter was 35.5 mm. diameter, and comprised 150 triangular teeth. It differed from Cornu’s 150 toothed wheel only in the thickness of the aluminum, being 0.8 mm thick. The stage was thus set for an interesting comparison between Cornu’s results and those of Perrotin, using virtually the same items of equipment, but separated in time by about 28 years. Perrotin and Prim’s Results As soon as the necessary reductions had been carried out by Perrotin, it was announced that the La Gaude series gave a value of 299,900 ± 80 Km/s.33 The mean date was 1900.4. Under similar circumstances, Perrotin published the Mont Vinaigre result as 299,860 ± 80 Km/s for a mean date of 1902.4.34 On this occasion, he discussed both results and issued their average as 299,880 ± 50 Km/s, the mean date being 1901.4.35 This later figure was frequently quoted as Perrotin’s final definitive value. Perrotin began writing up all the details of the two series, but had not completed the task at the time of his death in 1904. Prim continued writing the discussion, issued in 1908, reworking the calculations in the process. Prim’s discussion makes no mention whatever of the

reports that were issued earlier. Instead, he derived a value for the La Gaude series of 300,032 ± 215 Km/s. However, he was unhappy with the method used to obtain the result. The other option that he considered was a least-squares treatment, but he felt that the number of observations over the La Gaude path was too few to justify this approach. Consequently, this La Gaude value was completely discarded as unsatisfactory.36 Prim then re-appraised the Mont Vinaigre experiments and treated them by the least-squares method to yield a final value of 299,901 ± 84 Km/s at the mean date of 1902.4.37 Although Dorsey criticized this value (he did not comment on the earlier reports), he did not derive a better one, despite extensive analysis. The issuing of this final discussion resulted in some confusion, particularly since Prim’s final declared value of 299,901 Km/s for the Mont Vinaigre path was so close to the Perrotin value for the La Gaude path of 299,900 Km/s. Many failed to realize that they were from a different series of experiments over a different base-line. Even Michelson fell into this trap, quoting this final declared value as having been obtained over the shorter La Gaude path.38 Conclusions from Toothed-Wheel Experiments Table 5 summarizes the above results by listing the fourteen values obtained by this method. A least squares linear fit to all these data points gives a light speed decline of 164 Km/s per year, while a fit to the most reliable values, marked [*], gives a decline of 2.17 Km/s per year. The confidence interval was 99.4% that c was not constant at its present value during the period covered by these experiments. The Fizeau values have been described as pioneering experiments that were “admittedly but rough approximations…intended to ascertain the possibilities of the method.”39 The remaining unstarred values were rejected by the experimenters themselves or have been severely criticized as outlined above. Nevertheless, when all the data points are included, the decrease in the speed of light is even more evident. The comparison between Cornu’s re-worked values and those obtained with substantially the same items of equipment by Perrotin is of great interest. The Cornu mean is 299,945 Km/s, while the Perrotin mean is 299,887 Km/s. The drop measured by this same equipment is thus 58 Km/s in 26.6 years. It is fascinating to note that both Perrotin and Prim, despite problems with the analysis, independently obtained results in which the earliest determination resulted in the higher value for c. If we ignore the bad citation of 1855, the only values that went against the decay trend in the entire of Table 5 were those rejected by the experiments themselves or those severely criticized by others. When combined with the results of the two astronomical type determinations, the decay trend now appears in three different methods of measuring c. These methods have involved about 30 different c measuring instruments, comprising at least six by the Roemer method, at least 21 for aberration, and at least three by the Fizeau method. A decay trend measured by 30 different instruments lengthens the odds against coincidence to roughly one in a billion.

Table 5 Toothed Wheel Experimental Values (NOED = number of experiments done)

starred values are generally considered the most reliable

Fizeau

1849.5

28

Base line in meters 8633

Fizeau

1849.5

28

8633

313,300

Fizeau

1855

8633

305,650

Fizeau

1855

8633

298,000

Cornu

1872

658

10,310

298,500 ± 300

Cornu

1874.8

624

22,910

300,400 ± 300

*Cornu/Helmert 1874.8

624

22,910

299,990 ± 200

*Cornu/Dorsey

1874.8

624

22,910

299,900 ± 200

Young/Forbes

1880

12

Perrotin/Prim

1900.4

1540

11,862.2

300,032 ± 215

*Perrotin

1900.4

1540

11,862.2

299,900 ± 80

Perrotin

1901.4

*Perrotin

1902.4

2465

45,950.7

299,860 ± 80

*Perrotin

1902.4

2465

45,950.7

299,901 ± 84

Experimenter

Date

NOED

5551.07

c value in Km/sec 315,300

301,382

299,880 ± 50

Comments Base too short (journals) Base too short (textbooks) No reference – usually omitted Bad date citation for Foucault? Rejected by Cornu – serious errors Flawed analysis – 4 figures only Reworked in 1876 – generally accepted Reworked by Dorsey in 1944 Usually severely criticized 1908 – discarded by Prim Perrotin’s published 1900 analysis Perrotin’s generally accepted mean Perrotin’s published 1902 analysis Prim’s final declared value

References 1 H. Fizeau, Comptus Rendus, 29:90-92, 132 (1849); also E.R. Cohen et.al., Reviews of Modern Physics, Vo. 27 No. 4, 1955, p. 363 2N.E. Dorsey, Transaction of the American Philosophical Society, New Series, Vol. XXXIV, Part 1, October, 1944, p. 13 3 K.D. Frooma and L. Essen, The Velocity of Light and Radio Waves, Academic Press, London, (1969), p. 4. Also Martin and Connor, Basic Physics, Whitcomb and Tombs, Melbourne, p. 1377

4 Froome and Essen, pp. cit., p. 4. Also Martin and Connor, op. cit., p. 1378. Also Science, 66, Supp. x, Sept. 30, 1927 in quoting an article from L’Astronomie, no exact reference given. 5 H. Fizeau, Comptus Rendus, 29:90-92, 132 (1849); Also, de Bray, Nature, Vol. 120, October 22, 1927, p. 603. Also N.E. Dorsey, Transaction of the American Philosophical Society, New Series, Vol. XXXIV, Part 1, October, 1944, p. 13 6 De Bray, Nature op. cit. Also Dorsey, op. cit. Note: W. Harkness, “Washington Observations for 1885 Appendix III” p. 29 lists this value erroneously as an in vacuo result. 7 Anon, Science, 66, Supp. x, Sept. 30, 1927. No exact reference quoted. 8 A. Cornu, Journal de L’Ecole Polytechnique, 27 [44]:133-180, (1874) 9 A. Cornu, Annales de L’Observatoire de Paris Vol. 13, (1876), p. A 298, footnote 10 de Bray, Nature, Vol. 120, October 22, 1927, p. 603 Note (3) 11 N.E. Dorsey, Transaction of the American Philosophical Society, New Series, Vol. XXXIV, Part 1, October, 1944, p. 15 12 Dorsey, ibid. p. 16. Also de Bray, op.cit., p. 603 13 A. Cornu, Annales de L’Observatoire de Paris Vol. 13, (1876), p. A 298, footnote. Also Cornu, Comptus Rendus, Vol 79, (1874), p. 1361. Also Dorsey, op. cit., pp 18, 19 14 Cornu, Comptus Rendus, Vol 79, (1874), p. 1363 15 A. Cornu, Annales de L’Observatoire de Paris Vol. 13, (1876), p. A 293. Also N.E. Dorsey, Transaction of the American Philosophical Society, New Series, Vol. XXXIV, Part 1, October, 1944, pp 34, 35 lists it as 300,340 Km/s. 16 A. Cornu, Annales de L’Observatoire de Paris Vol. 13, (1876), p. A266 17 Helmert, Astronomische Nachrichten, 87 (2072), (1876), pp 123-124 18 N.E. Dorsey, Transaction of the American Philosophical Society, New Series, Vol. XXXIV, Part 1, October, 1944, pp17 and 95, equation (103) 19Rapports presentes au Congres International de Physique de 1900, vol 2, pp225-227. The probable error was estimated by Todd, American Journal of Science, 3rd series, Vol. 19, (1880), p. 61 20 Dorsey, op.cit., p. 36 21 S. Newcomb, Astronomical Papers for American Ephemeris and Nautical Almanac, Vol. 2, part 3, (1891) p. 202. 22A.A. Michelson, Decennial Publications of the university of Chicago, Vo. 9, (1902) p. 6.

Also Dorsey, op.cit., pp 76-79 23 A.A. Michelson, Journal of the Franklin Institute, Nov. 1924, p. 627; and Nature, Dec. 6, 1924, p. 831. See also de Bray, Nature, Vol. 120, Oct. 22, 1927, p. 604 24 S. Newcomb, Astronomical Papers for American Ephemeris and Nautical Almanac, Vol. 2, part 3, (1891) p. 119, 25Rapports presentes au Congres International de Physique de 1900, vol 2, p. 229 26 R.T. Birge, Reports on Progress n Physics, Vo. 8, (1941) p. 99 27 Dorsey, op.cit., p. 4 28 Young/Forbes, Phil. Trans., vo. 173, Part 1, (1882) p. 231 29 DeBray, Nature, vol. 120, Oct. 22, 1927, p. 604 30 J. Perrotin and Prim, Annales de L’Observatoire Nice, vol. 11, (1908) pp A1-A98 31 Ibid. Tableau III, See also Dorsey, op.cit., pp 40-41 32 See Dorsey, op.cit., p. 37, for comparison of equipment 33Perrotin, Comptus Rendus, Vol. 131, (1900) p. 731 34Perrotin, Comptus Rendus, Vol. 135, (1902) p. 881 35 Ibid. p. 883 36 Dorsey, op.cit., p. 37. See also de Bray, Nature, vol. 120, Oct. 22, 1927, pp. 603-604 37J. Perrotin and Prim, Annales de L’Observatoire Nice, vol. 11, (1908) pp A1-A98 38A.A. Michelson, Journal of the Franklin Institute, Nov. 1924, p. 627; and Nature, Dec. 6, 1924, p. 831. See also de Bray, Nature, Vol. 120, Oct. 22, 1927, p. 604 39DeBray, Nature, vol. 120, Oct. 22, 1927, p. 603, quoting Fizeau, Comptus Rendus 29:90 (1949)

Part 4: Foucault and the Rotating Mirror Experiments English, French, and Americans in Rotation Foucault’s Rotating Mirror Foucault’s Problems Foucault’s Micrometer and c value Enter the Americans Newcomb’s Experiments Newcomb's Problems

Newcomb’s Results The Beginnings with Michelson Michelson’s New Apparatus Michelson’s Second Series Results Michelson’s Third Series Michelson’s Third Series Results Michelson Tries Again Details of the New Try Results from the New Try Michelson’s Series Five Results from Series Five Dorsey’s Comments Michelson’s Last Experiment Over to Pease and Pearson Conclusions From Rotating Mirrors Table 6: Rotating Mirror Experiments

English, French, and Americans in Rotation In 1834, at 32 years of age, Sir Charles Wheatstone of England (1802-1875), after whom the electrical circuitry known as the Wheatstone Bridge is named, entered the discussion on the speed of light. He was the first to suggest the method that incorporated a rotating mirror for the measurement of c.1 Unfortunately for the history of England in the debate about the value for c, Sir Charles’ suggestion was not taken up by his countrymen. Instead, the French again led the way in pioneer experimentation, following which the lead came under American control. Sir Charles’ suggestion regarding the rotating mirror was picked up four years later, in 1838, by the noted Parisian astronomer and physicist D.F.J. Arago (1786-1853). (Arago is mainly remembered today for his work on the interference of polarized light, which he investigated in 1811, and electromagnetism in which he worked with Ampere (1775-1836).2 He also conducted experiments confirming diffraction that resulted from Resnel’s development of the wave theory of light.3 Arago polished the suggestion,4 which was then examined in detail by his collaborating French fellow scientists, Fizeau and Foucault, between 1845 and 1849. Following a difference of opinion, Fizeau dropped out, leaving Foucault to pursue the issue independently.2a Jean Leon Foucault (1819-1868), who preferred the name Leon, is remembered by the Foucault pendulum, whereby he demonstrated the rotation of the earth. In optics, the Foucault knife-edge test bears his name, a test which many amateur astronomers use to try their concave mirrors for accuracy. His association with Fizeau led him into dealings with light, and his doctoral thesis in 1851 comprised his research into the velocity of light in water. One year prior to this, his study of the possibilities of the rotating mirror method led him to call attention to two inherent problems in 1850 and again in 1854.5 However, by 1862 he had overcome these difficulties sufficiently to obtain a pioneering result for c by the method that now bears his name. Encouraged by Foucault’s success, Michelson followed on in the U.S.A. in 1878 with a series of experiments until 1926 with the same method. His compatriot, Newcomb, also

performed several determinations from about 1880 to 1883. The final determination by a form of this method coupled with a toothed-wheel type of effect was performed by Pease and Pearson in California and reported in 1935. Foucault’s Rotating Mirror The basic principle involved in the method is as follows: a source of light passes through a semi-transparent plate of glass and is reflected from the rotating mirror. The reflected light is then focused through the lens onto a concave mirror, which returned the light to the rotating mirror. If the rotating mirror is stationary, light is reflected back to the semitransparent plate of glass, from which it is reflected to the observer. If the mirror is set rotating, the image appears at E’ instead of E as R has moved through a small angle in the time taken for light to travel from R through L to M and back. The distance EE’ depends on the rate of rotation of R, the distance RM, and also RGE. Measuring the values of these quantities allows the value for c to be determined. The basic equation is c = 2D ω/αwhere D is the distance RM, the angular velocity of the mirror is ω, and the angle αis that which the mirror has turned through to give the deflection EE’.6 Foucault used a plane glass disk that was silvered on one side and blackened on the other as his rotating mirror. It was just 14 mm in diameter and mounted in a ring that was part of the vertical axis of a 24 vane turbine driven by compressed air. The total air pressure was kept constant at 30 cm of water, to within 0.2 mm, and the air was delivered to the turbine by a regulated precision blower. A continuous flow of oil at constant pressure lubricated all bearings. A toothed disk performing two rotations per second under precision clockwork was used as a stroboscope for determining the speed of the mirror. Though Foucault rotated the mirror at 500 turns per second,7 he stated that the mirror and the disk would keep in step within one part in 10,000 for minutes at a time when the mirror was rotating at 400 turns per second.8 Foucault’s Problems One of the problems inherent in the method as mentioned above was diffraction. The smallness of the rotating mirror accentuated this and it resulted in a returned image whose sharpness was impaired and whose contours were altered. To overcome this problem, Foucault used at the light source a grid of ten equal and parallel lines to the millimeter. The resultant image thus was composed of a series of lines of maximum and minimum intensity. The distance apart of the maxima would be the same as that of the lines of light in the grid itself, and so also for the minima. The second problem in the technique that Foucault addressed was that the intensity of the returned image dropped off as the cube of the distance that the mirrors are apart. In terms of Figure III, the critical distance is RM. If that distance is too large, the returned image is too faint. He overcame this problem by a chain of five mirrors, although initially he suggested a series of convex lenses.5a This allowed him to have a folded light path of 20 meters within the confines of a room. It appears that Michelson failed to appreciate this light-saving technique.9 Later experimenters overcame these problems in another way that allowed for a much longer light-path and a vastly increased distance EE’ between images. In Michelson’s work, the lens, L, was of much longer focal length and such that R and M were virtually conjugate foci

of L.2b The source, S, was placed close to R, and with L of appropriate focus, the concave mirror, M, could be placed several miles away. When viewed through the micrometer eyepiece, there is the direct reflection from the revolving mirror and beside it the returned image at a distance dependant upon the rotation rate. For Foucault’s arrangement, the mirror reflected the light back to the eyepiece once every revolution, giving a flickering effect until a high enough rotation rate was achieved.10 Newcomb and Michelson used mirrors of four or more reflecting faces which also gave a brighter image. Foucault’s Micrometer and c value Measurement of the distance EE’ by micrometer is the vital part in the whole exercise. The larger is this displacement of the two images, the smaller is going to be the relative error in measurement and the more accurate the value of c. Obviously, with a larger distance for RM, the greater also will be the displacement EE’. It is at this point that Foucault’s measurement problems began. The short base-line of 20 meters allowed only a small displacement EE’ with the rate at which the mirror could reliably rotate. To get the optimum displacement he took the rotation rate to 500 turns per second rather than, as outlined above, the more desirable 400. This fixed rotation rate appears to have been used for all experiments.7a Foucault initially determined the displacement EE’ by means of the screw of the micrometer eyepiece. The calibration of the micrometer was performed by measurements from it of ten spaces of the grid on the light source. This grid had been accurately made with great care by Froment and served as the length standard for the micrometer, having ten spaces of the grid to the millimeter. However, Foucault discovered that the screw was not as good as he had expected, and discarded this method of using it.11 Instead he fixed the micrometer at a setting of seven divisions of the grid or 0.7mm., and adjusted the distance of the mirror axis of R from the source S (Figure III) to get that exact displacement. The distant SR was about one meter. In a sample set of twenty measurements, the distance variation in SR was 5 mm, with the micrometer fixed at 0.7 mm, and the mirror rotated at 500 turns per second.12 However, there are some further difficulties in using the micrometer in this fashion. We can only assume by what method the micrometer was set, as no record was left of this. In the best case, with the mirror at rest, setting on the seventh division from the center of the grid may involve some uncertainty. This arises from uncertainty in the accuracy of the original marking of the grid lines and from the breadth of the images from the grid, particularly under brilliant illumination. Be that as it may, a more important problem arises since it was admitted that the returned image was altered in contour by the very effects of diffraction that he was trying to avoid. Dorsey points out that the position of the displaced lines of maximum and minimum intensity were themselves probably changed by this effect with respect to their true position if the contours had not been altered.12a In other words, with the mirror rotating, the position of the image of the center of the grid was systematically changed by diffraction so that the 0.7 mm was not its true displacement after all. All Foucault’s c values would be systematically affected as a result of these micrometer/diffraction problems which give a large relative error due to the small value of the displacement. Foucault worked on his c observations from May 22 until September 21 of 1862, and quotes his final value in references 6 and 7 as 298,000 ± 500 Km/s.13 However Harkness states

that the final result from 80 observations made on September 16, 18 and 21 of 1862 is 298,574 ± 204 Km/s.14 As these seem to be the observations used by Foucault in his calculations, it is not immediately apparent how Harkness obtained his result. These values almost certainly result from the micrometer/diffraction problem mentioned above. This pioneer experiment could have been built on by the French, but it seems that the influence of Fizeau and Cornu concentrated attention on the toothed wheel method, as evidenced by the Perrotin series. This left the way open for others to take up the possibilities of the method. Enter the Americans These possibilities were taken up by two Americans independently, Michelson and Newcomb, in that order. Simon Newcomb (1835 – 1909) was a distinguished astronomer who was associated with both the United States Naval Observatory and John Hopkins University. Among many other feats, he formulated a precise theoretical expression for the changing tilt of the earth’s axis by taking into account the effects of the pull of the sun, moon and planets on the earth’s equatorial bulge. It is still known today as ‘Newcomb’s Formula.’ (However, more recent investigations by the late government astronomer from South Australia, George Dodwell, indicate an important observational anomaly in that formula which deserves further attention, and will be dealt with another time).15 Newcomb’s extensive report of his determinations of c during 1880-1882 appeared in 1891.16 It seems that he has been considering the project since 1867. However, it was not until March of 1879 that Congress gave him the necessary appropriation for the work. By then Michelson had already performed preliminary experiments and was working towards a more definitive value for c. Michelson’s results were published in 1878 and 1880 respectively. He had performed his experiments at the Naval Academy, Annapolis, where he was an instructor, and submitted his results to the Secretary of the Navy. As the protocol required, the Naval Secretary forwarded the manuscript to the Nautical Almanac Office, whose Superintendent was none other than Newcomb.17 Newcomb thereupon requested that Michelson be seconded to assist him with his determination. The required assistance was rendered during a portion of Newcomb’s first series, until September 13, 1880. By then, Michelson had accepted an appointment to the Case Institute and moved to Cleveland, Ohio, terminating his association with Newcomb. However, Newcomb encouraged Michelson to make an entirely new determination of c there at Cleveland, which was done in 1882, and wrote the introductory note to Michelson’s report in 1891. Michelson continued with a more extensive series of determinations of c which will be considered after Newcomb’s set. Newcomb’s Experiments Newcomb utilized a square steel prism as his rotating mirror, which was 85 mm. long and 37.5 m. square. All four faces were nickel-plated and polished. The prism was rotated about its long axis inside a metal housing that had two open windows opposite each other. Rotation of the prism was effected by a stream of air directed through the windows against the 12 vanes in each of the two fan wheels rigidly attached to either end of the prism. It seems from Newcomb’s Figure 5 of Plate VI that four of the vanes were pointing in the direction of the corners of the prism on the lower wheel. However, the prism corners were midway between vanes for the upper wheel. Dorsey suggested that wheels of 13 vanes may have been better for symmetry and to overcome any potential problems caused by its

absence.18 A stiff frame carrying the observing telescope swung about an axis coincident with that of the rotating prism. At its other end were a pair of microscopes for reading the deflection. The radius of the arc over which it swung was 2.4 meters. The sending telescope was placed immediately above the observing ‘scope and had as its light source an adjustable slit illuminated by sunlight reflected from the heliostat. Light from the slit was directed to the upper half of one of the rotating prism’s faces. Following its return from the distant concave mirror, the light beam was reflected from the lower half of the same face into the observing telescope. In his initial work, centering about 1880.9, the base-line was 2550.95 meters from Fort Meyer to the U.S. Naval Observatory. For this series he used mirror speeds ranging from 114 to 254 turns per second. In his second and third series, centered in 1881.7 and 1882.7 respectively, the base was lengthened to 3721.21 meters from Fort Meyer to the Washington Monument. The base-line was measured by the United States Coast and Geodetic Survey. Here, mirror speeds of 176 to 268 turns per second were employed. The mirror rotation rate was obtained from a chronograph record of every 28 turns of the mirror, the time being recorded by a rated chronometer. Newcomb placed the observing telescope in a suitable position and adjusted the rotation rate of the prism until the returned image was just on the cross hairs. The prism rotation rate was then held steady until a long enough chronograph record had been obtained. The observing ‘scope was then swung equally far on the other side of the zero deflection position, and the prism rotated in the opposite direction while the necessary quantities were noted. This method overcame the problem of getting an accurate setting on the undeflected beam due to its brilliance and the width of the slit. Additionally, the trouble suffered by Foucault with the lack of symmetry in the diffraction pattern was eliminated. The difficulty of Foucault’s miniscule deflection of 0.7 mm was well under control. The first series with the shortest base line gave double angles ranging from 10,500 arc seconds to 22,300” with an average of 15,000”. That is an average of 4.2 which translates into about 17.5 cm for the linear deflection, the range being roughly 12 cm to 26 cm for the double angle. This average is just 125 times the linear deflection of Foucault’s pioneer result if the single angle is taken. Newcomb’s Problems All told, there were three distinct series of experiments. Michelson assisted Newcomb for part of the first series from June 28 until September 13, 1880. The series continued until April 15, 1881, by which time 150 experiments had been performed. Of these, Michelson had been involved with 99. The second series went from August 8, 1881, until September 24, with 39 experiments performed. The third series, in which Newcomb was assisted by Holcombe, extended from July 24, 1882, to September 5 of that year for a total of 66 experiments. This made a grand total of 255 experiments. However, they were not all equally successful. The first series over the short path from Fort Meyer to the Naval Observatory seemed to go smoothly, but all was not as it seemed. The second series over the longer path from Fort Meyer to the Washington Monument showed up the problem. Newcomb had the pivots of the mirror examined and re-ground by the manufacturers at the beginning of each series.19 As the second series proceeded,

abnormalities were noticed. Different mirror faces appeared to give slightly different displacements of portions of the image. By the 12th of September, 1881, there was no doubt. The image was split into two pairs of parts. The arrangement indicated that an axial vibration of the mirror was responsible with its period being half the time of rotation. The vibration did not produce visible results below certain speeds.20 Newcomb sent the mirror to the maker on September 14th. There, two troubles were discovered by the maker. First, he reported the mirror to be sensibly out of balance, a condition that seems to have existed from the beginning, thereby affecting the first series. The second problem was that the pivot was not perfectly round. The problems were fixed and experimentation began again on the 19th, but by the 24th the pivot problem had reasserted itself. The pivot by then had “cohered to its conical cap, and the mirror was sent to the makers for another thorough overhauling of its pivots.”21 At the same time, Newcomb arranged for the sending and receiving telescopes to have their positions interchangeable. If the mirror was out of balance, or if there were torsional vibrations of the mirror in which the top was in a different position relative to the bottom, then interchanging the telescopes would change the sign of the systematic error. The problem would thus be picked up and estimated, or eliminated. Newcomb suspected that such torsional vibrations may have been present due to a static twist from the offset vanes in the fan wheels, as well as the mirror imbalance already noted. This allowed both problems to be corrected. However, after analysis, Dorsey decided that the magnitude of the force needed for such a static twist, whether from fan wheels or any other cause, was too high. Furthermore, in the third series that was conducted in 1882, the reversal procedure produced a difference “too small for taking account of.”22 Thus, the third series ran smoothly, with no mirror imbalance and no upsetting vibrations detected. The first series appeared to be affected by the presence of the vibration from the mirror imbalance. It could not have been detected without the telescope reversals unless its period happened to be some high multiple of the time for quarter of a revolution. This was only attained in some of the observations of series 2. Newcomb therefore based his value of c soley on the results of series 3. He stated, “The preceding investigations and discussions seem to show that our results should depend entirely on the measures of 1882.”23 Newcomb’s Results The result from Newcomb’s first series of 150 experiments centering on 1880.9 over the 2550.95 meter path was 299,627 Km/s. That from the second series of 39 experiments over the 3721.21 meters for a mean date of 1881.7 was 299,694 Km/s. Both of these values are for air. Newcomb did not even bother to reduce them to a vacuum or even mention their probable errors because of the problems associated with these two series. The result from the third series of 66 experiments over 3721.21 meters with a mean date of 1882.7 was 299,860 ± 30 Km/s for a vacuum. This was the result he favored.23a However, with some reluctance, and only in order to avoid criticism, he included the first two series in a mean value with the third as 299,810 Km/s for a vacuum.23b No probable error was given for this mean because of Newcomb’s dissatisfaction with it. The Beginnings with Michelson Albert A. Michelson was an American physicist born in 1852. Prior to his death in 1931, he

had been Professor of Physics at the University of Chicago where many famous experiments on the interference of light were done. He had been an instructor in physics and chemistry at the U.S. Naval Academy after he had graduated in 1873. His Superintendent questioned his “useless experiments” on light that were done while he was there. He continued his light velocity experiments during his ten years at the Case Institute of Technology, and his work was rewarded in 1907 with the Nobel Prize.24 Michelson’s first two determinations of c were performed entirely independently of Newcomb and were personally initiated by him and privately funded. His initial aim in the first series in 1878 was to prove that a much larger displacement was possible than Foucault obtained with his apparatus.25 His base line was 500 feet, or 152.4 meters. The rotating mirror was thirty feet from the slit and eyepiece and achieved 130 turns per second. Given the final result, it appears that the displacement was about ten times greater than Foucault’s, being around 7.58 mm. Michelson had achieved his initial purpose in showing that the procedure worked. Because of his funding situation, Michelson’s equipment was simple for the first series. The circular mirror was silvered on one side and about one inch in diameter. The drive comprised a blast of air that was directed against the mirror itself. The rotation rate was measured stroboscopically. This initial apparatus was used to obtain ten measurements of c for 1878.0, the result being 186,500 ± 300 miles/s or 300,140 ± 480 Km/s. Note that de Bray retains the probable error of ±300 miles/s as ± 300 Km/s (no conversion) and gives the base line the same as the second series.13a Dorsey refers to this result as “merely an exploratory determination”,26 while Michelson himself discarded it owing to its large probable error. Michelson’s 1880 paper dealing with both this exploratory determination and the second, more sophisticated series, commented on the limitations of the initial equipment. Referring to the mirror drive, he states “This crude piece of apparatus is now supplanted by a turbine wheel which insures a steadier and more uniform motion.”27 All told, then, this initial series is not held to be definitive by anyone. Michelson’s New Apparatus By mid-1878, Michelson had received a contribution of $2000 from Mr. A.G. Hemingway of New York, to be used towards another determination of c.27a This allowed new instruments to be constructed during the remainder of that year and into the first half of 1879. A much longer path was envisaged. As it eventuated, the path was 1986.23 feet between mirrors, or 605.40 meters, at the U.S. Naval Academy.28 A new mirror was made of a disk of glass 1.25 inches in diameter, 0.2 inches thick, and silvered on one side only. It was mounted in a metal ring that was part of a spinning axle having six outlets exhausting air as a form of air turbine with constant thrust. This system overcame any erratic motion arising from Newcomb’s type of drive. However, the disadvantage was that it could not rotate in both directions. The mirror speed was stroboscopically determined by an electrically driven tuning fork compared with a freely vibrating standard Koenig fork on a resonator. Comparison was made via the beat phenomenon. The arrangement was carefully studied by Professor A. M. Mayer of Stevens Institute, Hoboken, on July 4, 1879, after the series was completed on the 2nd of July. Two series of measurements were made averaging 256.072 and 256.068 vibrations per second at 18.3 degrees centigrade. Originally, the fork was armed with a tip

of copper foil which was lost and a platinum one of 4.6 mgm used as its replacement. The copper tip seems to have given 256.180 vibrations per second. All work prior to the platinum tip replacement on June 4th, 1879, was discarded.29 This comprised 30 sets of observations while the equipment was being set up and adjusted from April 2nd until June 5th. In the actual series itself, from June 5th, the electric fork was compared by beats with the standard two or three times before every set of observations and the temperature read concurrently. The speed of the mirror was usually 257.3 turns per second, but four sets of experiments were made on July 2nd at speeds of about 193, 128.6, 96.5, and 64.3 turns per second. This test indicated no untoward effects or systematic errors. However, Dorsey points out that they are harmonics of one-eighth the usual speed and any error in that harmonic could not be found.30 Because Michelson used a single lens of 45.7 meters focal length between the two mirrors instead of two telescopes, the mirror rotation axis had to be very slightly inclined to the vertical to avoid the mirror flashing light into the eyes of the observer. The effect of this change in azimuth was tested by Michelson to see if there was any variation in speed in the mirror on that account. His testing procedure was designed to pick up any variation due to the frame holding the mirror, friction from the pivots, or the sockets. The azimuth angle was varied both ways and the mirror was inverted on its bearings. These tests were carried out on June 7 and 9 for the frame inclined at various angles (ten sets of experiments), an June 30 and July 1 for the mirror inversion (8 sets). He reported “The results were unchanged, showing that any such variation was too small to affect the result.”31 It was only possible to conduct experiments for an hour after sunrise and an hour before sunset, as an electric lamp illumination of the source slit was found unsuitable after the first experimental set, and so the sun had to be employed. The source slit was firmly clamped to the frame of the micrometer screw that moved the eyepiece. The distance from the micrometer and source slit to the rotating mirror was either of two values: 8.60 or 10.15 meters. The average displacement from each was about 112.6 or 133.2 mm respectively. The micrometer screw calibration was checked by the aforementioned Professor Mayer. Each ‘set’ of observations consisted of the mean of ten consecutive settings of the micrometer, along with other relevant values. Michelson invited other observers to make the micrometer readings on a number of occasions. There were three sets on both of the evenings of June 14th and 17th made by other observers. Their values were in close agreement with Michelson’s final mean of all observations. The test indicates a lack of bias in the micrometer settings. Michelson’s Second Series Results In setting up and testing his apparatus from April 2 to June 5 of 1879, Michelson made 30 observations which were not considered in his final analysis and were not even recorded in any of his reports. His series proper began on June 5, and concluded on July 2 that same year, and comprised precisely 100 sets of experiments. Each set consisted of a group of ten readings as mentioned above. Initially, Michelson gave his result as 299,944 ± 51 Km/s and then rounded to 299,940 ± 50 Km/s.31a This value was then revised for both a false temperature correction and a

trigonometrical misinterpretation of the micrometer readings. When this was done, the final corrected value for c was given as 299,910 ± 50 Km/s for a vacuum.32 Dorsey felt that a value of 299,900 might be justifiable.33 When Newcomb mentioned the correction, he misquoted the value as 299,942 Km/s.34 Todd’s discussion refers to this value as given in the ‘corrected slip’ but quotes 299,930 Km/s.35 Some of this confusion may be traced to Michelson’s report to the American Association for the Advancement of Science.36 The report itself was published accurately. However, an Abstract of Michelson’s report was then circulated. The Table of values that appeared in the Abstract, and those in the ‘corrected slip’ associated with the Abstract were erroneous.37 Todd’s discussion was based on these incorrect values and so is of little worth. Michelson’s Third Series After moving to the Case Institute, Michelson was prompted by Newcomb to continue his investigation into the value of c. This was carried out in 1882, essentially concurrent with Newcomb’s final series. Michelson used virtually the same equipment as that in his second series.38 The same micrometer, the same rotating mirror, lens, and air drive were used both times. The general optical arrangements were the same. The main differences were the path length of 624.546 meters (the old one was 605.4 meters) and the distant fixed mirror was slightly concave and fifteen inches in diameter compared with seven inches for the old. The same tape was used for measuring as was the previous calibration of the micrometer screw. The new cross-checks and comparisons indicated that all was satisfactory, even for Dorsey. The other main difference was the stroboscopic speed measurement. The electrically driven fork made 128 vibrations per second (the old was 256), and compared by beats with the freely vibrating standard. A clock comparison was made with the standard. It was thus determined that the standard had 128 vibrations per second from 71 degrees F down to a low of 54 degrees F. Everything else was the same as the previous series. Dorsey admits that “One would expect the result to be essentially the same for each.”38a Accordingly, the state was set for an interesting comparison of results, as this new series virtually differed only in location. Michelson’s Third Series Results Michelson conducted 563 experiments in his determination of c between October 12 and November 14, 1883. The mirror was rotated at speeds ranging from 128.927 turns per second up to 258.754 with the usual speed being close to 258 turns per second. These speeds resulted in deflections from 68.907 mm. up to 138.233 mm with the average being close to 138 mm. The distance from the rotating mirror to the micrometer was 10.15 meters, the same as the largest separation in the second series. Michelson’s definitive value for a vacuum in this series was 299,853 ± 60 Km/s. As Dorsey notes, no reason is given why the probable error for this series is 10 Km/s larger than for the previous one. Dorsey also admits that a value of 299,850 Km/s might be justifiable. Thus, taking either the values issued by Michelson, or Dorsey’’s approximation to them, resulted in a lower value for c at the later date. Michelson Tries Again A few people among us do enjoy exploring new fields once they have turned 70. Michelson

was one of those. He may have been somewhat influenced by the fact that his earlier determinations of c had been privately funded. This time the Carnegie Institute of Washington offered to back the enterprise. Accordingly, an improved method, a longer path and fewer financial restrictions saw Michelson rising to the challenge and conducting a new series of experiments in August of 1924, when he was 72. The new method, which has been described as a special case of the rotating mirror experiment, actually combined features of both the old toothed wheel system and the Foucault arrangement. It is illustrated on Figure IV. The source of light, S, was a Sperry arc focused on a slit. This light then passes to one face of the octagonal rotating mirror, R, and via a system of small optically flat mirrors, B and F, to the large concave mirror, D. This sent a parallel beam of light to its twin mirror, E, some 22 miles away. From there it was reflected by mirror G back via E to D. From there it went into the eyes of the observer, O, by the optical flats and the opposite face of the octagonal mirror. The system was adjusted with the octagonal mirror at rest and the image of the slit adjusted on the micrometer. The octagon was then rotated, displacing the image. However, at a certain critical speed, the next face of the octagon was in the position of the first face and as a consequence, the image was again undeflected. This situation was basically similar to the undimmed image from the toothed wheel. This system also allowed two types of measurement. The speed of the octagon can be measured for the undisplaced image, or, alternatively, fixing the speed at some convenient value, the image displacement can be measured by the micrometer. Additionally, Michelson arranged for a number of rotating mirrors to be used, some of 8, 12, or 16 sides, and comparisons made. This beautiful experiment was first suggested by Cornu,39 though Michelson did not appreciate Cornu’s view of it as harmonizing both the Foucault as well as the Fizeau methods.40 Newcomb also made the helpful suggestion that a multifaceted prismatic mirror be used in which the returned beam be reflected from the opposite face to the outgoing one.41 Details of the New Try The twin concave mirrors each had a 30 foot focus (9.14 meters) and two foot aperture (61 centimeters). Light was sent from Mt. Wilson Observatory in California some 22 miles to San Antonio Peak. The measurement between the two mountain bench marks was 35,385.53 meters, with a probable error of one part in two million.42 When the distance from the markers to the mirrors is added, the final distance became 35,426.23 meters.43 The reports indicate that the glass octagonal prism was used exclusively as the rotating mirror for this determination of 1924.44 It was driven by two nozzles directing a blast of air at 40 cm mercury pressure against the six (or 8?) vanes of an open fan wheel. Mirror speeds were about 528 turns per second and regulated by a control valve issuing a counter-blast to the fan wheel. The distance of the micrometer from the rotating mirror was 25 centimeters and the unshifted position of the image was utilized. The item that had to be established was the rate of mirror rotation for the unshifted position of the image. Again, stroboscopic means were employed. This time it was an electrically driven tuning fork of 132.25 vibrations per second. It was compared with a free auxiliary pendulum that was itself checked against an invar gravity pendulum rated and loaned by the U.S. Coast and Geodetic Survey. Experiments were conducted at night between August 4

and 10, 1924, and comprised ten series of observations conducted on eight occasions, giving a total of eighty experiments. Results from the New Try Michelson initially published a result of 2999,820 ± 30 Km/s.44a However, it was then realized that the vacuum correction was faulty due to the altitude of the experiments and further examination of this issue resulted in a correction being issued later, giving the final value for this fourth series as 299,802 ± 30 Km/s.45 Dorsey conceded a value of 299,800 Km/s, but later points out that a further correction to the group refractive index is more appropriate than the ordinary index, and this adds another 2 Km/s to the value, leaving it as it stands.46 Because he planned to continue with further experiments using other mirrors but the same equipment, Michelson called this result ‘preliminary.’ However, the series was complete in itself and deemed of sufficient accuracy to be published at once. Michelson’s Series Five The arrangements for series five were virtually unchanged form the initial series four experiments.47 The main differences were occasioned by the use of a variety of mirrors. In addition to the 8-sided glass prism used earlier, there were four new mirrors. One was an 8faced prism of nickel-steel which was rotated at approximately 528 revolutions per second, as the old glass octagon was. There was a 12-faced nickel-steel mirror and a 12-faced glass mirror, the latter being 6.25 cm. in diameter, and both rotating at about 352 revolutions per second. For the glass mirrors the drive was as before. The steel mirrors had four air nozzles at 90 degrees that impinged upon 24 recessed buckets cut into a wheel attached to the axle. In each case the air drive was reversible, the steel mirrors having a second bucket wheel for the occasion. The other improvement was the use of a tuning fork of 528 vibrations per second that was driven by a vacuum-tube circuit. This was compared directly with the same standard C.G.S. invar gravity pendulum used before. Comparisons were made between this standard pendulum and the observatory clock on July 1 and August 15 of 1926, the agreement being to about 1 part in 100,000. Thus, with basically the same equipment, the scene was again set for an interesting comparison of the values obtained for c. Results from Series Five Michelson states that “the definitive measurements were begun in June 1926 and continued until the middle of September.”47a This is just two years after the first run with the equipment. The mean date is 1926.5 for reasons seen shortly. An interesting result emerged after usual appropriate weighting of the values from the five separate prismatic mirrors. If the correct reduction to the vacuum is applies to them, they read as follows: Glass octagon – 299.799 Km/s Steel octagon – 299.797 Km/s 12-faced glass prism – 299,798 Km/s 12-faced steel prism – 299,798 Km/s 16-faced glass prism – 299,798 Km/s 47b

In other words, they are in agreement to within ± 1 Km/s. It should be pointed out, however, that in the case of the glass octagon the values obtained earlier from 1924 and 1925 were lumped up with the 1926 results to get the final quote. All told, the final result came from eight values of c, each comprising around 200 individual experiments. The eight values derive from the above quoted five as there were two separate sets for the 16-faced glass prism and 3 separate sets for the glass octagon, including the 1924 results. Thus, about 1600 individual experiments were performed to obtain the final value for the fifth series. Michelson then quoted a final value of 299,796 ± 4 Km/s in his report. However, as Birge pointed out, the final value had to be revised upwards 2 Km/s due to Michelson’s failure to take account of the group velocity correction.48 Additionally, despite the close agreement of the above results, Birge felt that the variety of temperatures and pressures that would have been encountered introduced an element of uncertainty. Consequently, he and Dorsey put the corrected value at 299,798 ± 15 Km/s. Michelson’s statements in Studies in Optics (1927: 136-137) and those in Encyclopedia Britannica (23:34-38, 1929) give misleading impressions about the values obtained from this series and should be ignored. Following this series, Michelson endeavored to try with the same equipment a series of experiments over a path from Mt. Wilson Observatory to Mt. San Jacinto, a distance of about 82 miles, or roughly 131 Km. However, because of bad atmospheric conditions, the experiments were abandon and the initial results obtained were not considered reliable enough for publication.49 With essentially the same equipment, therefore, Michelson obtained 299,802 Km/s for his results in 1925.6, and 299,798 Km/s for his results in 1926.5. This was the second time that two series by Michelson have shown a lower value for c on the second occasion with the same equipment. However, that is not all. Comparison between those two sets of series also shows a drop with time. In other words, four determinations, in two sets of two, show a consistent drop with time through the four, within each of the two related sets, and between the two sets. As noted previously, Michelson’s results alone indicate, on a least squares analysis, a decay of 1.86 Km/s per year over the 47 years of his c experimentation. These last two series suggest about 2 Km/s per year for the decay rate.

Dorsey’s Comments Dorsey noted for Michelson’s work that “Although each series of determinations has yielded a value that differs from each of the others, Michelson has made no attempt in his reports, or elsewhere, so far as I know, to account for these differences.”50 This statement still holds even if Dorsey’s modified values for Michelson’s work are used. With a persistent drop in values for c by a single experimenter, as well as for all values by any particular method, one would imagine that the simplest explanation that Michelson or Dorsey could offer is that the physical quantity itself is dropping with time. De Brey suggested this, but Dorsey preferred to have his problem unsolved rather than accept that explanation. Indeed, Dorsey tried to overcome the problem by invoking the action of vibrations. However, this was tested for each time. The single mirrors were able to be inverted or have their azimuth changed to cross-check that possibility while the multi-faceted mirrors could be rotated both ways to check. No vibrations were discovered by these processes. Dorsey suggested, however, that this meant vibrations were at a maximum! It is an argument from silence as no evidence of such anomalous motion was discovered, whether it be blurred, split, or multiple images or asymmetric broadening such as Newcomb found with his work which genuinely did have vibration troubles. On the basis of this evidence from silence, Dorsey then claims that all series had vibrations that would give rise to the lower value for c in the 1924-26 determinations compared with the 1878-80 series. He does not elucidate why a drop in c would result from vibrations being present in BOTH cases. Furthermore, he ignores the small drop in c that was picked up within both the 1878-80 series and the 1924-26 determinations. Indeed, since the same equipment was being used, Dorsey’s proposed vibrations would be equally present within the 1879-80 series or the 1924-26 series, and all measurements then equally affected. The drop in c within each of the series is not the result of this proposed systematic error, then, but despite it. It would be picked up whether or not the systematic error was there. All any systematic error (real or imaginary) does is to shift the effect into another range of values, and Newcomb’s experience suggests that Dorsey’s proposed vibrations would give a measured value of c below its true value. Accordingly, as all Michelson’s results are above the present value of c, and vibrations would seem to lower the result, then all these values should be corrected upwards if Dorsey’s vibration idea is accepted, thus accentuating the already observed trend. Michelson’s Last Experiment Because of the increasing accuracy and necessity for precise vacuum correction, Michelson decided tin 1929 to initiate what was to be his last final experiment. His collaborators were Pease and Pearson.51 The idea was that a one mile long pipe would be exhausted of its air and by repeated reflections from mirrors at either end a path length of some ten miles could be achieved in a fair vacuum. Pressure in the pipe varied from 0.5 to 5.5 millimeters of mercury. The arrangement was essentially that shown in Figure V. A carbon arc source was at S focused on an adjustable slit 0.075 mm wide and was reflected from a 32-faced rotating mirror, R. The mirror was a glass prism 0.25 inches long and 1.5 inches along the diagonals of its cross-section. All its angles were correct to one arc second and its surfaces to 0.1 wave. Light was reflected from the upper half of face ‘a’ of the mirror through a glass window, W,

that was 2 cm. thick, into the pipe and via the mirrors Q and N, onto the large optically flat mirrors M and p, 55.9 cm. in diameter. N was essentially a concave mirror 101.6 cm in diameter and of 15.02 m. focus that gave a parallel beam forming and image of the slit on M. After repeated reflections from M and P, the beam was returned through the window to strike the lower half of face ‘b’ of the rotating mirror, if it were at rest, and into the eye of the observer E. The distance from the rotating mirror to the eyepiece micrometer was 30 cm. In operation, the mirror was rotated at such a speed that face ‘a’ would move into the position occupied by face ‘b’ in the time that the light took to be reflected along the pipe and return. Depending on the adjustment of the four fixed mirrors, light could travel eight or ten miles before being returned to R. The two distances required different rotation rates of the prism. For a distance of 7,999.87 meters, the rotation rate was about 585 revolutions per second, while 6,405.59 meters required about 730 revolutions per second. This rotation rate was again controlled and determined stroboscopically with a tuning fork compared with a free pendulum swinging in a heavy bronze box of constant temperature and low pressure. The pendulum was itself compared with a time-piece that was checked against time signals from Arlington, Virginia. In practice, the speed of the mirror was held at some convenient value close to the position where the returned beam was undeflected. The difference from the precise 1/32 of a revolution was determined by measuring the deflection with the micrometer. The mirror was, in fact, reversed at the same convenient speed and the double displacement measured. The drive was a compressed air turbine. Also capable of reversal we the arrangement whereby light from the slit hit the top of face ‘a’ while the returned hit the bottom of face ‘b’. In this it was similar to Newcomb’s arrangement to check for any vibrational errors. Correction for residual air in the pipe was done for each experiment. Over to Pease and Pearson Michelson made preparation for this c determination from 1929 until February 19, 1931, when the experiments actually began. The work was sponsored by the University of Chicago, the Mount Wilson Observatory, the Carnegie Corporation and the Rockefeller Foundation. The evacuated pipe was constructed of Armco-iron steel sheets and was one meter in diameter. It was situated by Laguna Beach, in California, on the Irvine Ranch close to Santa Ana. Michelson began his measurements on February 19, 1931, when he was 79, and was ably assisted by Pease and Pearson. The work continued on until February 27, 1933, with a total of 233 series of observations comprising 1110 sets, making 2885 experiments all told for the full determination. However, after spending a lifetime measuring c and studying the behavior and properties of light, Michelson died on May 9, 1931, after completing only 36 of the 233 series. Even while they were working, Pease and Pearson noticed a peculiar circumstance. Irregular as well as regular variations in the value of c obtained occurred hourly and daily, as well as over longer periods – up to a year. Deviations of 10 Km/s over a period of a week or so were common, and occasionally they went as high as 30 Km/s.52 Within the 233 series conducted, the average deviation from the mean value of a series is about 10.5 Km/s. As Cohen points out, “The base line was on very unstable alluvial soil. A correlation between fluctuations in the results and the tides on the sea coast was reported.”53 For good measure, the base-line was discovered to be fluctuating from other causes as well. As Birge noted, Pease and Pearson “found their carefully measured mile-long base line showed for two years

a steady increase in length of 6.5 mm. per year…and then a sudden decrease of 8mm after a mild earthquake in the vicinity.”54 As the base line was only measured on those three occasions, one wonders what else it was doing in the meantime, being not only by the sea coast, but also right by the main fault line, as well as considering the fact that the pipe was joined by many seals. Dorsey notes something else that may be relevant. Though he continues on about possible vibrations that Pease and Pearson established as negligible, he points out that the micrometer only read directly to 0.001 inches.55 This corresponds to a velocity of 32 Km/s. Yet this was used to establish the displacement from the central position and the mean deviation of the sample five readings from their mean is about 0.00025 inches. It is for these reasons that Pease and Pearson’s final quoted value of 299,744 ± 10 Km/s is regarded today as unacceptably low due to systematic errors in the micrometer readings and problems with an unstable base line. The plot of distribution frequency of all 2885 values compared with the mean value is enlightening. There were 1095 values that lay in the range of 299,770 to 299,780 Km/s and 1790 values outside it. Of this latter number, 1025 values were below 299,770 and only 765 above 299,780. The distribution is plainly unsymmetrical and thus differs appreciably from the normal error curve, there being an excess of low values. Conclusions From Rotating Mirrors The results of the rotating mirror experiments are summarized in Table 6. If the results rejected by the experimenters themselves are omitted along with Fourcault’s admittedly pioneer experiment which was “intended to ascertain the possibilities of the method,”13b then a least squares linear fit to the six data points gives a decay of 1.85 Km/s per year. The value of the correlation coefficient, r, equals -0.932, with a confidence interval of 99.6% in this decay correlation. Omitting Pease and Pearson’s result gives a decay of 1.74 Km/s per year, with r = 0.905, this correlation being significant at the 98.2% level. There is also a 95.6% confidence interval that c was not constant at its present value during the years of these experiments. A comparison between Michelson’s four definitive values strongly suggests a decay in c. The fact that the first two values, obtained with the same equipment show a decay, and the last two values, also obtained under similar conditions, show a decay, is important. The fact that Newcomb independently obtained a value practically identical with Michelson in mid 1882 virtually simultaneously is also worthy of remark. It suggests that their error limits may even be narrowed somewhat, rather than increased, as Dorsey would like. The persistent downward trend in the measured value of c was noted by de Bray after Michelson’s 1924 series results became available. As a result, he wrote to the Editor of Nature on the 20th December, 1924, and to l’Astronomie in France on January 23rd, 1925, calling attention to the trend.56 In the latter case, he predicted a lower value for Michelson’s next determination, which was in the process of being prepared. In the event his prediction was justified. As a result of that circumstance, the Editor of Nature, having ignored his earlier calls, decided to publish de Bray’s next offering, which opened up the discussion in the scientific literature throughout the late twenties, the thirties and into the early forties. Again, as de Bray himself noted, the only values that go against this trend in Table 6 are those that the experimenters themselves have rejected. If the polygonal mirror technique is counted separately, there are now five methods that have demonstrated a decay in the speed

of light over time.

Table 6 Rotating Mirror Experiments (NOED = number of experiments done) Experimenter

Date

NOED Faces

Base Rev/sec (meters) 20.0 500

1. Focault

1882.8

80

1

2. Michelson

1878.0

10

1

152.4

3. Michelson

1879.5*

100

1

605.4

4. Newcomb (mean)

1881.8

255

4

2550.95

66 5. Newcomb 6. Michelson

1882.7* 1882.8*

7. Michelson

1924.6*

8. Michelson 9. Pease/ Pearson

3721.21

563

4 1

624.645

80

8

35,426.23

1926.5* 1600

8-16

35,426.23

1932.5* 2885

32

1,610.4

c value in Km/s 0.7 mm 298,000 ± 500 130 7.58 mm 300,140 ± 480 257.3 133.20 mm 299,910 ± 50 114-268 18 cm av. 299,810 Deflection

18 cm av.

299,860 ± 30

176-268 129-259 138 mm av. 299,853 ± 60 528 Nil 299,802 ± 30 264-528 Nil 299,798 ± 15 585-730 0.01 mm 299,774 av. ± 10

Comments 1. Foucault: Micrometer and diffraction problems coupled with miniscule deflection. 2. Michelson: Value discarded by Michelson – large probable error and crude equipment. 3. Michelson: Number of experiments listed as 100, but there were ten sets per experiment. 4. Newcomb: This mean resulted from the inclusion of two series whose results Newcomb rejected as unreliable due to systematic errors (mirror imbalance and vibration). These results were 299,627 Km/s in 1880.9 and 299,694 Km/s in 1881.7, both for air. They were included with the final reliable value to get a vacuum mean only in order to avoid criticism. These figures give the average displacement and range of rotation rates and the total number of experiments conducted. The smaller path is quoted. 5. Newcomb: Definitive value. He insisted that his results “should depend entirely on the measures of 1882.” 6. Michelson: This 1882.8 result was obtained with the same equipment as his 1879.5

result. This value is lower. 7. Michelson: Essentially a new method. An octagonal glass prism with a rotation rate giving no deflection. 8. Michelson: Polygonal mirrors of 8, 12, and 16 faces. Result corrected for group velocity. Equipment the same as for 1924.6. This new method registered a decay in c over two years approximately equal to 2 Km/s per year. 9. Pease/Pearson: Unstable baseline and minute deflection giving micrometer problems. Generally disregarded today.

References: 1 C. Wheatstone, Philosophical Transactions, 583 (1834) 2 2a 2bF.A. Jenkins and H.E. White, Fundamentals of Optics, McGraw-Hill, New York, 3rd Edition, (1957) pp 387, 388, 554 3 S.G. Starling and A.J. Woodall, Physics, Longmans (1958), p. 691 4 D.F.J. Arago, Comptus Rendus, 7:954 (1838) and 30:489 (1839). Also Pogg. Ann., 46:28 (1839) 5 5aL. Foucault, Comptus Rendus, 30:551-560 (1850), also Annales de Chmie et Physique, Ser. 3, 41:129-164 (1854) 6 N.E. Dorsey, Transactions of the American Philosophical Society, Vol XXXIV, Part 1, (1944) pp 1-108 7 7aL. Foucalt, Recueil des travaux scientifiques de Leon Foucalut, Paris (1878), pp 219226. Numerical data, drawings and detailed description of apparatus: pp 173-226, 517-518, 546-548 8 L. Foucault, Comptus Rendus, 55:501-503, 792-798 (1862) 9 A.A. Michelson, Studies in Optics, Chicago (1927) pp 120-138 10 Starling and Woodall, op. cit., p. 448 11 L. Foucalt, Recueil des travaux scientifiques de Leon Foucalut, Paris (1878), pp 792-796 12 12aSee also Dorsey, op.cit., pp 13-14 for other details 13 13a 13bM.E.J. Gheury de Bray, Nature, Vol. 120, October 22, 1927, p. 603 14 W. Harkness, Washington Observations for 1885, Appendix III, p. 29

15 Bulletin of the Astronomical Society of South Australia, Sept. 1967 16 S. Newcomb, Astronomical Papers for the American Ephemeris, Vo. 2, (1891), pp 107230 17 Dorsey, op.cit., p. 55 18 Ibid. p. 53 19 S. Newcomb, op.cit., p. 192 20 ibid. pp 168, 185 21 ibid. Also see Dorsey, op.cit., p. 49 22 Dorsey op.cit. p. 51 23 23a 23b S. Newcomb op.cit., pp 201-202; also M.E.J. Gheury de Bray, op.cit., p. 604 24 Jenkins and White, op.cit., pp 244-245 25 A.A. Michelson, Procedures of the American Association for the Advancement of Science, 27:71-77 (1878). Also American Journal of Science, Ser. 3, 15:394-395 (1878) 26 Dorsey, op. cit. p. 55 27 27aA.A. Michelson, Astronomical Papers of the American Ephemeris Nautical Almanac, Vol. 1 Part 3 (1880), pp 115-116 28 Ibid. p. 128 29 Ibid, comparison of pp 116, 124, 128, 132 30 Dorsey op.cit., p. 62 31 31aA.A. Michelson, Astronomical Papers of the American Ephemeris Nautical Almanac, Vol. 1 Part 3 (1880), pp 141,144 32 A.A. Michelson, Astronomical Papers of the American Ephemeris Nautical Almanac, Vol. 2, Part 4 (1881) p. 244 33 Dorsey, op.cit. p. 63 34 Newcomb, Astronomical Papers of the American Ephemeris Nautical Almanac, Vol. 2, Part 3 (1891) p. 119, footnote 35 D.P. Todd, American Journal of Science, series 3, 19:61 (1880) 36 A.A. Michelson, Procedures of the American Association for the Advancement of

Science, 28:124-160 (1879) 37 American Journal of Science, series 3, 18:390-393 (1879) 38 38aA.A. Michelson, Astronomical Papers of the American Ephemeris Nautical Almanac, Vol. 2, Part 4, pp 231-258. See also Dorsey, op.cit., pp 64-66 39 A. Cornu, Rapp. Cong. Internat. De Physique (Paris), 2:225-246 (1900) 40 A.A. Michelson, astrophysical Journal, 60:256-261 (1924), especially p. 259 41 Newcomb, Astronomical Papers of the American Ephemeris Nautical Almanac, 2:107230 (1891), especially Chapter VIII 42 A. A. Michelson, Astrophysical Journal, 65:1-22 (1927), quoting Major W. Bowie’s report, p. 14 43 Michelson called 144 feet 44 meters instead of 43.9 meters, and Dorsey somehow gets 35,426.18 meters out of these figures, which does not compute. De Bray (see ref. #13), quotes survey distance only. 44 44aA.A. Michelson, Astrophysical Journal, 60:256-261 (1924). Also Journal of the Franklin Institute, 198:6270628 (1924). Also Nature, 114:831 (1924). Also information from Astrophysical Journal, 65:1-22 (1927). See also Dorsey, op.cit., pp 66-69 45 A.A. Michelson, Astrophysical Journal, 65:2 (1927) 46 Dorsey, op.cit., P. 69 c.f. 70 47 47a 47bDescription in Astrophysical Journal, 65:1-22 (1927) 48 R.T. Birge, Reports on Progress in Physics, vol. 8, (1941) p. 94 49 Jenkins and White, op. cit., p. 389; and de Bray, op.cit., p. 603 50 Dorsey, op.cit., p. 79 51 Michelson, Pease, Pearson, Astrophysical Journal, 82:26-61 (1935) 52 R.T. Birge, op,cit., p. 95 53 E.R. Cohen, et. al., The Fundamental Constants of Physics, (1957) p. 108 54 Birge, op. cit., p. 93 55 Dorsey, op. cit. p. 74 56 M.E.J. Gheury de Bray, Isis, vol. 25, (1936), pp 437-448, especially, p. 442

The History of Light Speed Research

Before 1941 Setterfield's Work The minimum value of the speed of light Why is c not measured as changing now? addition September 5, 2003 On the Measurement of Time, and the Velocity of Light Work on light speed by others Moffat Albrecht and Magueijo Davies Responses to critical webpages Supportive and Explanatory Essays by others Lambert Dolphin's page of collected relevant links and abstracts

For a basic history of the light speed work and measurements through time, first please read A Brief History of c (Barry Setterfield, 1987) and Helen Setterfield’s article as originally published in Chuck Missler's "Update". The work with the data was originally published by Trevor Norman and Barry Setterfield in their 1987 Report, "Atomic Constants, Light and Time," requested by Lambert Dolphin, a senior physicist at Stanford Research Institute International, as an internal document, or white paper, for their discussion. The paper was reviewed by professors in related fields at Flinders University in South Australia, where the two men were working, and Flinders itself published the paper in 1987.

Before 1941 Question: Was this material about the speed of light changing talked about before? Setterfield: Between 1880 and 1941 there were over 50 articles in the journal Nature alone addressing the topic of the decline in the actual measured values of lightspeed ( c). For example in 1931, after listing the four most recent determinations of c, De Bray commented in Nature "If the velocity of light is constant, how is it that, invariably, new determinations give values which are lower than the last one obtained ...? There are twenty-two coincidences in

favour of a decrease of the velocity of light, while there is not a single one against it" (his emphasis). The interest was world-wide, and included the French, English, American, German and Russians. In addition, these discussions included some consideration of the fate of the newly developing concept of relativity if c were not a constant. The whole discussion was brought to a close in August of 1941 by Professor R. T. Birge in an article dealing with the changing values of the atomic constants "With special reference to the speed of light" as the title stated. Birge's first paragraph raised many questions. In part it read: "This article is being written upon request, and at this time upon request.... Any belief in a change in the physical constants of nature is contrary to the spirit of science" (his emphasis) [Reports on Progress in Physics (Vol. 8, pp.90-100, 1941)]. Although this article effectively closed the whole discussion, the data trend continued. This was documented in our 1987 Report. Please see Table A in the 1987 Report. These statistics were illustrating the fact that, in a situation where c was measured as changing, it was nonetheless true that at a given date (1882), three different methods of measuring c obtained the same result to within 5 km/s. In other words, these methods were giving consistent results. This is an important point. It was picked up by Newcomb in 1886 when he stated in Nature that the results obtained around 1740 by the two methods employed then gave consistent results, but those results gave a value for c that was about 1% higher than in his own day. Later, in 1941, history repeated itself. In that year Birge commented on the results that were obtained in the mid-1800’s by the variety of methods employed then. He acknowledged that "these older results are entirely consistent among themselves, but their average is nearly 100 km/s greater than that given by the eight more recent results." What cannot be denied is that there was a systematic drop in the values of c obtained by all methods. Even Dorsey, who was totally opposed to any variation in c was forced to concede this point. He stated "As is well known to those acquainted with the several determinations of the velocity of light, the definitive values successively reported…have, in general, decreased monotonously from Cornu’s 300.4 megametres per second in 1874 to Anderson’s 299.776 in 1940…"

Comment: Perhaps he [Birge] had in mind the idea that c was varying, just by itself, without being given a dynamics from its own term in the physical action S. That idea would violate the time-translation invariance, and likely the space translation invariance also, of physical law. In addition to blaspheming the uniformity of natural (which could evoke the "contrary to the spirit of science" remark), it would destroy the conservation of energy and momentum. That is one reason why I so strongly urge that any such theory be presented formally as a relativistic classical field theory, in which Noether's theorem(s) ensure energy and momentum and angular momentum conservation. Setterfield: First of all, you will note in the 1987 Report that there is a consistent trend in seven atomic quantities on the basis of conservation of energy, as shown in Table 24. The issue of relativity is discussed in the report in the section entitled The Speed of Light and Relativity. Here is the point. All methods of measuring c have given consistent results at any given time, but the values of c have dropped with time. This can be illustrated by the results from Pulkova

Observatory alone where the value of c was obtained from the aberration method first used by Bradley. The Pulkova Observatory results were obtained using the same equipment on the same location by experienced observers over a long period of time. The observational errors remained unchanged, as did the inherent accuracy of the equipment. Nevertheless, from 1750 to 1935 the value of c obtained from this observatory dropped by more than 750 km/s. When all the results are in, each method individually revealed the drop in c, as did all methods lumped together. These results are backed up by changes in other atomic constants that are associated with c through the conservation of energy. One reviewer of the 1987 Report, who had a preference for the constancy of atomic quantities, noted that instrumental resolution "may in part explain the trend in the figures, but I admit that such an explanation does not appear to be quantitatively adequate." The Pulkova results prove that this is not the cause of the trend. Indeed, when the professor of statistics at Flinders University examined the data in the Report, he felt that a prima facie case existed for c decay and asked us to prepare a seminar for the Maths Department. In all the subsequent discussion and turmoil that the 1987 Report engendered, he stood by this assessment.

Question: How small are the differences in the speed of light that we are talking about, since instrumentation became accurate? Setterfield: The differences in the speed of light that we are talking about since instrumentation became accurate (about 1700) is about 3000 + kilometers per second. That is, about 1% higher compared to today's value. Some comments from the journals may help here: From 1882 to 1883, Professor Simon Newcomb measured the speed of light in a series of definitive experiments. At this same time Albert Michelson had independently performed a series of experiments to determine the speed of light as well. In that same year, Nyren had determined the speed of light by the aberration method. The value obtained by these three experiments was 299854 +/-5 kilometers per second. In other words, they were in agreement to within 5 km/s. In 1886, Professor Simon Newcomb admitted that the definitive values accepted in the early 1700's were 1% higher than in his own day. [Nature, 13 May, 1886, pp 29-32] Interestingly, history repeated itself. In 1941, Professor R.T. Birge, in looking over the most recently obtained values for the speed of light, commented that the measured values of c from the 1880's "are entirely consistent among themselves, but their average is nearly 100 km/s greater than the eight most recent values." [Report on Progress in Physics, vol. 8. pp 90-101, 1941] So the difference was noticeable. However, you raise the validity of the early measured values of lightspeed by Roemer and Bradley. Let us take Bradley's abberation measurements first. The same method using the same equipment was being employed at Pulkova observatory from about 1780 until about 1940. The data collected by this abberation method from Pulkova using the same equipment showed a consistent decline which amounted to 890 km/s over a period of 160 years. This is far larger than the error in measurement at Pulkova which averaged around 150 km/s. As far as Bradley's measurements themselves were concerned, I have listed the measurements he made on 24 stars over a period of 28 years, along with the reworkings of 5 different authorities. These are discussed in detail in the 1987 Report "The Atomic Constants, Light and Time" and the associated Tables 2 and 3. The result was 300,650 km/s, just 858 km/s

above the present value. This final result omitted the re-workings of Busch which would have increased the mean value to 1632 km/s above the present value, but all that detail is documented in the Report. Before the critics say that the figures are hopelessly wrong, it is respectfully suggested that they check the original data for themselves and point out where the experts that re-worked the data have gone wrong. As far as Roemer is concerned, some misleading statements by one recent authority have led to conflicting claims. Observations by Cassini gave the earth orbit radius delay for light travel as 7 minutes 5 seconds. Roemer gave it as 11 minutes from a selection of data. Halley noted that Roemer's figure for the delay was too large, while Cassini's was too small. Newton listed the delay as being between 7 and 8 minutes in 1704. Since then, observations using Roemer's method all gave results higher than today's value. Delambre, from 1000 observations around 1700 gave the delay as 493.2 seconds which gives a value of 303,320 km/s. Martin in 1759 gave the value as 493.0 seconds. Glasenapp in 1861 gave it as 498.57 seconds, Sampson in 1876.5 gave it as 498.64 seconds and Harvard gave it as 498.79 +/- 0.02 seconds which translates into 299,921 km/s +/- 13 km/s. Accordingly, while Roemer's exact value is debatable, the other documented values by this method all indicate that c was higher then. The details about all of this are available in the Report.

Setterfield's Work Setterfield was pressured into some early publication of some of his material in progress in the early 1980’s. Please disregard this material as everything there has been either finalized or updated in subsequent material. The first important paper was Atomic Constants, Light and Time, written in 1987 in response to a request from a senior physicist at Stanford Research Institute International. It was attacked on primarily statistical bases, and defended by Alan Montgomery, a professional statistician and Lambert Dolphin, the physicist who had originally requested the paper. A more complete and sophisticated analysis of the Setterfield work was done by Montgomery himself. Malcolm Bowden also took the time to deal with some of the challenges. Other challenges were responded to in published materials and private correspondence for five years following that work, at which time Setterfield resumed his research. The 1990’s Tifft’s work on the redshift and the challenges and extra research concerning it were being debated. This material turned out to have strong implications for the Setterfield research. One of the results of putting all of this together was Atomic Quantum States, Light and the Redshift, a paper which was never published, but which is currently being divided into a series of other papers with fuller explanations. Two of them are Is the Universe Static or Expanding? And Exploring the Vacuum. Gradually a model has been emerging from all of this: a model not expected, not originally looked for, and one that disagrees with both the evolutionary/long ages ideas and the standard creationist and young earth ideas. This model is roughly outlined in A Brief Earth History and A Brief Stellar History.

Upon request, two essays were also written to deal with the material in a general and basic way. The first was written by Barry with an anticipated audience of those having some small background in physics. It is The Vacuum, Lightspeed, and the Redshift. Then a second, much more basic paper aimed toward the general lay audience was written by Helen Fryman (Setterfield), entitled A Simplified Explanation of the Setterfield Hypothesis. Currently, Setterfield is researching into a field which he has been repeatedly questioned about: mass. This has been a field of much speculation and study in physics especially recently in terms of what mass actually is. When one considers that Einstein’s famous equation, E = mc2, combines mass with energy and the speed of light, it is clear that there are properties of both mass and energy which must be both defined and understood in order to make sure this emerging model is cohesive. Regarding a number of the papers listed above, many questions have come in through the years. Immediately following is discussion explicitly pertaining to the methodologies followed by Barry. Discussion and questions regarding the various areas of research will be on the associated pages and may be found by returning to the Discussion Index.

Other Physical Processes if the Velocity of Light is not Constant. (Barry Setterfield) SEVEN RELEVANT BASIC FEATURES OF THE NEW THEORY: 1. Photon energies are proportional to [l / c 2)]. 2. Photon fluxes from emitters are directly proportional to c. 3. Photons travel at the speed of c. 4. From 1 to 3 this means that the total energy flux from any emitter is invariant with decreasing c, that is, [ 1 / c 2 x c x c ]. This includes stars and the radioactive decay of elements etc. 5. Atomic particles will travel at a rate proportional to c. 6. There is an additional quantisation of atomic phenomena brought about by a full quantum ± of energy available to the atom. This occurs every time there is a change in light-speed by ± 60 times its present value. 7. A harmonisation of the situation with regards to both atomic and macroscopic masses results from the new theory, and a quantisation factor is involved. RESULTS FROM THOSE SEVEN FEATURES: A). From 2, as photosynthesis depends upon the number of photons received, it inevitably means that photosynthetic processes were more efficient with higher c values. This leads to the conclusions stated originally.

B). As radiation rates are proportional to c from 2, it inevitably follows that magma pools, e.g., on the moon, will cool more quickly. Note that A and B are built-in features of the theory that need no other maths or physics. C). From 6 and 7, the coefficient of diffusion will vary up to 60 times its current value within a full quantum interval. In other words there is an upper maximum to diffusion efficiencies. Otherwise the original conclusions still stand. D). In a similar way to C, and following on from 6 and 7, the coefficient of viscosity will vary down to 1/60 times it current value within the full quantum interval. This implies a lower minimum value for viscosities. Within that constraint, the original conclusions hold. E). In a way similar to C and D, and again resulting from 6 and 7, critical velocities for laminar flow will vary up to 60 times that pertaining now, within the full quantum interval. The original conclusions then hold within that constraint. F). As the cyclic time for each quantum interval was extremely short initially, it follows that it is appropriate to use an average value in C, D, and E, instead of the maximum: that is, about 30. As c tapered down to its present value, a long time has been spent on the lower portion of a quantum change with near-minimum values for C, and E, and near maximum values for D. These facts result in the effects originally elucidated.

Dear Mr. Setterfield, Today I came across the variable speed of light on the internet. I decided to investigate it. In that investigation I found your original paper on the variable speed of light and read it. I realized from the assumptions that the paper was flawed so I am motivated to point out that mistake in the paper with this email. In the assumptions you state that all methodologies of measurement were lumped together. This is a mistake to lump methodologies and the conclusions are to be discounted because of this mistake. I'll explain. Measurement is fickle. No two methodologies can be averaged for a conclusion, methodologies can be compared for usefulness, but not lumped together. I developed aerospace materials for 18 years and learned this lesson the hard way. NASA uses the ASTM methodologies, rigorously defined for reproducibility anywhere. Different methods were not accepted, only the method NASA concluded would produce good enough results to get the job done so the spacecraft would behave as predicted. The reason for this heavy-handedness by NASA is that in general, once a spacecraft goes up, no one can repair it, and the spacecraft must be engineered to work right the first time, so measurement must be defined, reproduceable, and standardized in the ASTM when appropriate to the customer specifications and then entered into the contract as quality control methodologies. Indeed, contracts with NASA are a lot of paperwork. Because all data was lumped together, the next step was to subject the data to a curve fit. After that step, you are indeed destined to be drawn to your paper's conclusions. The assumption to lump the data is a mistake, the next two steps, curve fitting and drawing

conclusions, do not hold, but they do logically follow. Many people will accept the logic and thus accept the conclusion. In my experience, few people examine assumptions. Many papers which use data can be analized in this way and found to fall down. The subject is not wrong, the methodology is not wrong, only the assumptions, and when the assumptions are wrong, the methodology cannot justify the conclusion, so the conclusion is wrong. This is a brutal truth, but I can explain more. If you examine each methodology by itself, for instance, the laser, you will see a sociological effect, the improvement of the methodology and the technology over time, reflected in the data. The data reported in your paper for the methodology of laser demonstrates that the methodology has settled down into reproducibility and is producing a constant value for 'c'. Several other methods show the measurement result 'settling down' as the method 'improves' over years or decades. Because of this settling effect the earlier data is discounted and the moste recent reproducable results are trusted. We used this technique to make aerospace materials and it works. What matters in engineering is not conclusions but only if you do what works. So, good engineers who understand measurement are then allowed to engineer again. The bad engineers look for another job to engineer again. Measurement is a very subtile and difficult part of scientific thinking. Indeed the data demontrates to me in an intuitive fashion the socialogical effect of history upon the resulting measurement. Scientific thinking is difficult, it is based upon assumptions, conventions, and agreement. It is never right, it only approximates. It is in constant upheaval. Science will never know the truth, it will only know what works in the world today. There is nothing wrong with science, its paradox is that it is not absolute yet it provides the base of knowledge for the engineers of technology to create the machines we employ today, such as the internet and this email. When science is political, such as the current philosophical conflict between science and creationists, well, it is only politics. The email still goes through because of the engineers. All that matters is what works, good science works, bad science does not work. Science is not theology and cannot be such. Science will never tread the path of theology. I discounted the theological conclusions on creationist web sites once I saw the assumption in the paper of lumping the data together. That paper was flawed, as my experience in making spacecraft parts has demonstrated. Assumptions are fundamental to success. If you want VSL badly enough you will change your assumptions. I assume the intent of the paper was honest, but methodology was flawed. If the intent of the paper was to push a theological agenda then the paper would be dishonest and you would have to face God about that at some point. I do not know your motivation. It does not matter if the speed of light is variable or not. I am not against VSL therory, I am against poor methodologies. Indeed, Magueijo is attempting to exploit VSL, http://theory.ic.ac.uk/~magueijo/. Perhaps VSL will be proven, much the same way that Einstein upset the world with the notion of variable time and how it eventually was proven. My 'scientific' guess from the data you presented is that if variability exists, the actual variability would be a very very small number. VSL would then be true, but, an unusable concept to the creationist web sites which exploit it to prove the date of creation at about 10,000 years ago. The whole notion of proving this date seems to me no different than counting the angels on the head of a pin, more politics than truth searching.

Good science is like good theology, it is what lasts over time, it is what people find usable, it is what gets written into history. Indeed, we no longer hold all of the ancient beliefs, times change, some beliefs change, and indeed, our beliefs of today will not all be present in the future, only those beliefs which are usable will endure in those of the future. I hope my voice provides illumination, I do not intend consternation. God has created a world which is here for us to discover. Let's keep at it. Setterfield: Thank you for your important letter. Your time and effort are appreciated. However, I think that if you had read my 1987 Report in more detail, it might have become apparent that I had indeed treated each measurement method individually and had drawn the correct conclusions as a result. The Report was built up one Table at a time where all the measured values by a particular method were listed. In that process, it was shown statistically that each measurement method registered a decline in the value of c over time. For example, Table 3 (scroll down a bit) lists only the aberration method results. In fact, I go further. The first Figure in the Report is a graph of the aberration measurements exclusively from the Pulkova Observatory where the same equipment had been used for over a century. The result was a clear decline in the value of c so obtained. I could go further still. For example, I point out in the Report, that on a number of occasions, apart from Pulkova, the same equipment was used by experimenters at a later date. In each case a lower value for c was recorded on the second occasion. Finally, when all methods are put together, there is still a resultant decline in c. In this matter, I am intrigued by the fanfare with which it was announced recently that astronomical observations might have indicated a change by one part in 100,000 in the finestructure constant. However, the more obvious measured changes in c seem to be treated rather dismissively by comparison. I might be rather perverse, but the situation does appeal to my sense of humour! Under these circumstances, I suggest that a closer reading of the Report would nullify much of your well-intentioned criticism. I trust this answers your concerns.

Questions: What does this mean in plain English? "Time after creation, in orbital years is approximately, D = 1499 t2". You state later that the age of the cosmos is approximately 8000 years (6000 BC + 2000 AD). How is this derived from the formula? Setterfield: This formula only applies on a small part of the curve as it drops towards its minimum. Note that "D" is atomic time. Furthermore, 't' or orbital time, must be added to 2800 BC to give the actual BC date. The reason for this is that 2800 BC is approximately the time of the light speed minimum. The more general formula, but still very approximate, is D = 1905t2 + 63,000,000. In this formula, "D" is atomic time. And once the value for "t" has been found it is added to 3005 BC to give the actual BC date. This is done because the main part of the curve starts about 3005 BC when the atomic clock is already registering 63 million years. Working in the reverse, therefore, if we take a date of 5790 BC, we must first subtract 3005. This gives a value for "t" of 2785 orbital years. When 2785 is squared, this gives 7.756 million. This is

then multiplied by 1905 to obtain 14.775 billion. From this figure is then subtracted 63 million to give a final figure of 14.71 billion. This is the age in years that would have been registered on the atomic clock of an object formed in 5790 BC.

The minimum value of the speed of light Two questions were originally posed to Malcolm Bowden in the U.K. Dear Professor Bowden, I am presently writing a book entitled, Origin of the Human Species. In one of the later chapters, I am dealing with dating problems, comparing the apparent biblical time frame to that of the standard theory of evolution. I have been aware of Norman and Setterfield's work for some time now and have included a section on c decay and its implications. I just came across your article supporting c decay on the web. Personally, I am sympathetic to c decay as a solution to my own predilections supporting Adam and Eve! But good science must stand on its own feet. I had included a line citing M.E.J. Gheury de Bray's 1934 findings: I cite particularly his reference to two bits of data: c in 1926 was 299,796 k/s plus or minus 4 k/s and in 1933 was 299,774 k/s plus or minus 1 or 2 k/s. I have deleted the above line because I discovered the present established speed of light to be 299,792.458 k/s. How can de Bray get a reading in 1933 some 18 k/s below TODAY's reading? Can you help me with this? Dennis Bonnette, Ph.D. Chairman, Philosophy Department Niagara University, NY 14109

Dear Professor Bowden, I just came across the following website which I bring to your attention: (URL was garbled) What I found disturbing was a claimed refutation of c decay very near the bottom of this extensive document. It was based on the effect of elevated light speeds in distant celestial objects with respect to our observation here on Earth. The author claims that we would see the objects in "slow motion" because of the c decay as the light rays approached Earth. He claims this is refuted by the consistency of motion of pulsars and other regular objects at great distances. (I hope I have described the issue well enough for you to know what I am talking about or for you to be able to find the text in question on the website.) How would you respond to this claim against c decay? I was most impressed in your own website by the "common sense" argument about the expected distribution of errors as science refines the constant value of a true constant. But I grasp just enough of the abovementioned author's argument to be concerned about it. Your comment would be much appreciated.

Sincerely, Dennis Bonnette

Response from Malcolm Bowden: Dear Dr. Bonnette, Thank you for your email with CDK queries. May I say that I am not a professor! I am a qualified Engineer - Civil and Structural. I regret that I am not a physicist and therefore can have great difficulty in answering technical questions such as you have posed. I have, however, forwarded your queries on to Lambert Dolphin and Barry Setterfield for their far better input. I have given your email address to them so they might reply direct. Lambert Dolphin has a huge website whch has much on CDK on it. You will find it at http://ldolphin.org or via my website. You may find your answer there anyway, but it might take some finding in this large site. Regarding the de Bray quote, one of the difficulties is what the shape of the curve is. Barry often refers to the Bible verse of "the heavens being stretched out" and one curve is a close fit to a damped oscisllation curve as it decreased. This means is may have overshot the present speed, rose above it and then decreased to the present level. Looking at the graph in my book "True Science Agrees with the Bible" which should be the same as the website one, I see that there are a cluster of readings that are lower than the present speed between 1930 and 1940 and all have very short error bars. None, however, are as much as 18 k/s lower. I am wondering what this reading might be. It is probably one on my graph that has been corrected in some way. This suggests to me that there was another "overshoot" at that time before it settled down to the presen speed. I am forwarding this to Barry and Lambert to see if they have a better explanation than this. Regarding the pulses from quasars, this is techinical but I agree that there seems to be a problem here. If c is fast, then pulses sent out at 1 sec intervals would travel through space and their speed would gradually slow down. This means that they would arrive at the earth at very long intervals between them. I do not know if there is any easy answer to this so am appealing to the others experts again. On aspect is that on looking into the ways of measuring distance in astronomy, I am very surprised at how much assumptions play a part. It is far from being an exact science! The question is can we be sure that they at vast distances? If they are closer than we think, the light would reach us quite quickly and the problem would be solved because there would not have been vast time periods for the light to slow down. Certainly, it is the fall in the general readings that is very convincing to me, but there are many ramifications. I may say, that whenever I have a technical query like these two, Barry has always answerd it to my satisfaction - so I have great confidence in his reply to this also. Sorry that I cannot be of greater help but I am awaiting the replies of the greater experts! Yours in anticipation, Malcolm Bowden. PS. I think you will be very inrterested in my latest book "True Science agrees with the Bible". Berean Call in USA hold ALL my four books. Tel: 541 382 6210. There is more

information about them on my website. In "True" I have set out my own version of the dating periods since creation about 4178 BC.

Response from Barry Setterfield: Dear Dr. Bonnette, Yes! There is a "low point" in the measured values of the speed of light, c, in the period 19281940. This comprised five different determinations of c by four different experimenters. By 1947 the "low point" was over. The standard establishment view on the problem was that there was a systematic error in the apparatus used. In view of the fact that 4 out of the five values were obtained by Kerr Cells, that explanation MAY have some validity as it involved light going through a polarising liquid. However, the later versions of Kerr Cells were called Geodimeters, and when they were introduced the "low point" was no longer in evidence. But there is another possible explanation. Malcolm Bowden is absolutely correct when he says that an oscillation is involved in the cDK curve. Take the illustration of a child on a swing. When the swing is pushed, it is responding to a forcing function which may have any period. When the pushes cease, the swing settles down and finally oscillates at its own natural frequency. The complete behaviour of the swing is described mathematically by the two functions, namely the forcing function and the natural oscillation. The same thing is happening with the speed of light. Recent work undergoing peer review at the moment indicates that the general overall function is an exponential decay with a natural period of oscillation imposed upon it. The oscillation has in fact bottomed out in the recent past because evidence from associated constants suggests that c is on the increase again. The oscillation reached its peak around 700 AD. As for the pulsar problem, most pulsars that have been found are in our own galaxy or within our Local Group of galaxies where the change in c is small. The resultant slow motion effect is therefore going to be minimal, particularly as there is such a wide range in pulsar spin rates. What you described as the potential problem was the expected CHANGE in pulsar spin rates due to dropping values of c in transit. When the calculations are done, the effect is certainly minuscule for Local Group objects. If I can be of further assistance do not hesitate to let me know. (May 15, 1999).

Comment: It has been suggested that what may have been discovered is not a change in the value of c over the past 100 years, but rather "a secular change in the index of refraction of the atmosphere" due to the industrial revolution. Setterfield: This issue was discussed in the literature when c was actually measured as varying. In Nature, page 892 for June 13, 1931, V. S. Vrkljan answered this question in some detail. The kernel of what he had to say is this: "...a simple calculation shows that within the last fifty years the index of refraction [of the atmosphere] should have increased by some [6.7 x10-4] in order to produce the observed decrease [in c] of 200 km/sec. According to LandoltBornstein (Physikalisch-chemische Tabellen, vol.ii, 1923, p.959, I Erganzungsband,

"Tracking or intellectual phase locking and cDK." In another newsgroup postings on this topic, was suggested that the decay in c might be due merely to "tracking" or intellectual phase locking. This process is described as one in which the values of a physical constant become locked around a canonical value obtained by some expert in the field. Because of the high regard for the expert, other lesser experimenters will tailor their results to be in agreement with the value obtained by the expert. As a result, other experiments to determine the value of the constant will only slowly converge to the correct value. Although this charge may be levelled at some high school and first year university students, it is an accusation of intellectual dishonesty when brought into the arena of the cDK measurements. First, there was a continuing discussion in the scientific literature as to why the measured values of c were decreasing with time. It was a recognised phenomena. In October of 1944, N. E. Dorsey summarised the situation. He admitted that the idea of c decay had "called forth many papers." He went on to state that "As is well-known to those acquainted with the several determinations of the velocity of light, the definitive values successively reported ... have, in general, decreased monotonously from Cornu's 300.4 megametres per second in 1874 to Anderson's 299.776 in 1940 ..." Dorsey strenuously searched for an explanation from the journals that the various experimenters had kept of their determinations. All he could do was to extend the error limits and hope that this covered the problem. In Nature for April 4, 1931, Gheury de Bray commented: "If the velocity of light is constant, how is it that, INVARIABLY, new determinations give values which are lower than the last one obtained. ... There are twenty-two coincidences in favour of a decrease of the velocity of light, while there is not a single one against it." (his emphasis). In order to show the true situation, one only has to look at the three different experiments that were running concurrently in 1882. There was no collusion between the experimenters either during the experiments or prior to publication of their results. What happened? In 1882.7 Newcomb produced a value of 299,860 km/s. In 1882.8 Michelson produced a value of 299,853 km/s. Finally in 1883, Nyren obtained a value of 299,850 km/s. These three independent authorities produced results that were consistent to within 10 km/sec. This is not intellectual phase locking or tracking; these are consistent yet independent results from three different recognised authorities. Nor is this a unique phenomenon. Newcomb himself noted that those working independently around 1740 obtained results that were broadly in agreement, but reluctantly concluded that they indicated c was about 1% higher than in his own time. In 1941 history repeated itself when Birge made a parallel statement while writing about the c values obtained by Newcomb, Michelson and others around 1880. Birge was forced to concede that "...these older results are entirely consistent among themselves, but their average is nearly 100 km/s greater than that given by the eight more recent results." In view of the fact that these experimenters were not lesser scientists, but were themselves the big names in the field, they had no canonical value to uphold. They were themselves the authorities trying to determine what was happening to a capricious "constant". The figures from Michelson tell the story here. His first determination in 1879 gave a value of 299,910 km/s. His second in 1883 gave a result of 299,853 km/s. In 1924 he obtained a value of 299,802 km/s while in 1927 it was 299,798 km/s. This is not intellectual phase locking. Nor is it typical of a normal distribution about a fixed value. What usually happens when a fixed constant is measured is that the variety of experiments give results that are scattered about a fixed point. Instead, when all the c results are in, there is indeed a scatter; yet that scatter is not about a fixed point, but about a declining curve. It is a phenomenon that intellectual phase locking cannot adequately explain. If Dorsey, Birge or Newcomb could have explained it that

way, we would certainly have heard about it in the scientific literature of the time. (May 20, 1999)

Why is c not measured as changing now? Question: Since about 1960 the speed of light has been measured with tremendous precision with no observed change. Proponents of cDK usually reply that we have redefined units of measurement in such a way that when the modern methods of measurement are used the change in c disappears because of cancellation. Has anyone attempted to remeasure c by "old fashioned" methods? It would seem to me that redoing the classic measurements could settle this issue, at least to my satisfaction. This would provide a new baseline of at least four decades, and probably much more. Setterfield: The problem with current methods of light-speed measurements (mainly laser) is that both wavelengths [W] and frequency [F] are measured to give c as the equation reads [c = FW]. If you have followed the discussion well, you will be aware that, within a quantum interval, wavelengths are invariant with any change in c. This means that it is the frequency of light that varies lock-step with c. Unfortunately, atomic frequencies also vary lock-step with c, so that when laser frequencies are measured with atomic clocks no difference will be found. The way out of this is to use some experimental method where this problem is avoided. It has been suggested that the Roemer method may be used. This method uses eclipse times of Jupiter's inner satellite Io. Indeed it has been investigated by Eugene Chaffin. Although many things can be said about his investigation (and they may be appropriate at a later date), there are a couple of outstanding problems which confronts all investigators using that method. Chaffin pointed out that perturbations by Saturn, and resonance between Io, Europa, and Ganymede are definitely affecting the result, and a large number of parameters therefore need investigation. Even after that has been done, there remains inherent within the observations themselves a standard deviation ranging from about 30 to 40 seconds. This means the results will have an intrinsic error of up to 24,000 km/s. Upon reflection, all that can be said is that this method is too inaccurate to give anything more than a ball-park figure for c, which Roemer to his credit did, despite the opposition. It therefore seems unwise to dismiss the cDK proposition on the basis of one of the least precise methods of c measurement as the notice proposes that was brought to our attention. This leaves a variety of other methods to investigate. However, that is not the only way of determining what is happening to c. There are a number of other physical constants which are c-dependent that overcome the problem with the use of atomic clocks. One of these is quantised Hall Resistance now called the von Klitzing constant. Another might be the gyromagnetic ratio. A further method is to compare dynamical intervals (for example, using Lunar radar or laser ranging) with atomic intervals. These and other similar quantities give an indication that c may have bottomed out around 1980 and is slowly increasing again. Indeed, atomic clock comparisons with historical data can be used to determine the behaviour of c way back beyond 1675 AD when Roemer made the first determination. These data seem to indicate that c reached a maximum around 700 AD (very approximately). The data from the redshift paper implies that this oscillation is superimposed on an exponential decline in the value of c from the early days of the cosmos.

A more complete discussion appears in the Redshift paper. In other words, whole new sets of data are becoming available from additional sources that allow the original proposition to be refined. I trust that you find this helpful. (May 20, 1999).

Comment: I was thinking more in terms of a Fizzeau device, which is what I assumed was used by Newcomb and the others mentioned in your earlier comments. Setterfield: Your suggestion is a good one. Either the toothed wheel or the rotating mirror experiments should give a value for c that is free from the problems associated with the atomic clock/frequency blockage of modern methods, and the shortcomings of the Roemer method. The toothed wheel requires a rather long base-line to get accurate results as shown by the experiments themselves. However, given that limitation, an interesting feature may be commented upon. Cornu in 1874.8 and Perrotin in 1901.4 essentially used the same equipment. The Cornu mean is 299,945 km/s while the Perrotin mean is 299,887 km/s. This is a drop of 58 km/s in 26.6 years measured by the same equipment. The rotating mirror experiments also required a long base-line, but the light path could be folded in various ways. Michelson in 1924 chose a method that combined the best features of both the rotating mirror and toothed wheel: it was the polygonal mirror. In the 1924 series, Michelson used an octagonal mirror. Just over two years later, in 1926.5 he decided to use a variety of polygons in a second series of experiments. The glass octagon gave 299,799 km/s; the steel octagon 299,797 km/s; a 12 faced prism had 299,798 km/s; a 12 faced steel prism gave 299,798 km/s; and a 16 faced glass prism resulted in a value of 299,798 km/s. In other words all the polygons were in agreement to within +/-- 1 km/s and about 1,600 individual experiments had been performed. That is a rather impressive result. However, despite the internal accuracy to within 1 km/s, these results are still nearly 6.5 km/s above the currently accepted value. To my way of thinking, this polygonal mirror method would probably be the best option for a new determination of c. On the other hand, perhaps Newcomb's or Michelson's apparatus from earlier determinations may still be held in a museum display somewhere. Modern results from such apparatus would certainly arouse interest. Thanks for the helpful suggestion.

Questions: Are you saying that 'c' is no longer decaying? (assuming the velocity of light has decreased exponentially to nearly zero at the present time.) Do you mean "nearly zero" compared to what it may have been at the time of creation? Setterfield: The exponential decay has an oscillation superimposed upon it. The oscillation only became prominent as the exponential declined. The oscillation appears to have bottomed out about 1980 or thereabouts. If that is the case (and we need more data to determine this exactly) then light-speed should be starting to increase again. The minimum value for lightspeed was about 0.6 times its present value. This is as close to 'zero' as it came. addition September 5, 2003:

Question: I have been thinking about the speed of light's exponential decrease, and it seems to me that soon there will be a point in time when the speed of light will stop decreasing altogether, and either become a constant or maybe it will bounce back a little bit, like the recoil of a rubber band as it's let go. What do you think of this idea? And can you work out what year the speed of light would reach a zero point of deceleration, based on your deceleration curve? Setterfield: First of all, the decrease in the speed of light is not strictly exponential, although it does follow a well-defined mathematical curve. There is an extremely fast drop at first, which then tapers off similar to a Lorentzian curve. Will it ever cease decreasing? Yes, possibly. But, as you mention, there is a recoil effect which we have picked up in the redshift measurements and which has also been picked up in recent light speed measurements. The minimum light speed appeared to be reached, actually, around 1980, and there is evidence of a slight increase since then. You can see evidence of this in the last two graphs here. When you check the dates for both Planck’s Constant and the mass graph, you will see a slight change about 1980. Although the speed of light graph does not go this far in time, as I was just showing Birge’s accepted values, it would show the same slight change in direction at this time as well. The change you do see in the light speed graph around 1940 appears to be somewhat anomalous, as this same ‘burp’ can be seen during the same years in the lower two graphs as well.

On the Measurement of Time, and the Velocity of Light Setterfield: Several questions have been raised which deserve a reply. First, the matter of timing and clocks. In 1820 a committee of French scientists recommended that day-lengths throughout the year be averaged, to what is called the mean solar day. The second was then defined as 1/86,400 of this mean solar day. This definition was accepted by most countries and supplied science with an internationally accepted standard of time. This definition was used right up until 1956. In that year it was decided that the dynamical definition of a second be changed to become 1/31,556,925.97474 of the earth's orbital period that began at noon on the 1st January 1900. Note that this definition of the second ensured that the second remained the same length of time as it had always been right from its earlier definition in 1820. This definition continued until 1967 when atomic time became standard. The point to note is that in 1967 one second on the atomic clock was DEFINED as being equal to the length of the dynamical second, even though the atomic clock is based on electron transitions. Interestingly, the vast majority of c measurements were made in the period 1820 to 1967 when the actual length of the second had not changed. Therefore, the decline in c during that period cannot be attributed to changes in the definition of a second. However, changes in atomic clock rates affecting the measured value for c will certainly occur post 1967. In actual fact, the phasing-in period for this new system was not complete until January 1, 1972. It is important to note that dynamical or orbital time is still used by astronomers. However, the atomic clock which astronomers now use to measure this has leapseconds added periodically to synchronise the two clocks. The International Earth Rotation Service (IERS) regulates this procedure. Since January 1st, 1972, until January 1st, 1999

exactly 32 leap seconds have been added to keep the two clocks synchronised. There are a number of explanations as to why this one-sided procedure has been necessary. Most have to do with changes in the earth's rotational period. However, a contributory cause MAY be the change in light-speed, and the consequent change in run-rate of the atomic clock. If it is accepted that it is the run-rate of the atomic clock which has changed by these 32 seconds in 27 years, then this corresponds to a change in light-speed of exactly [32/(8.52032 x 108) c = (3.7557 x 10-8 c ] or close to 11.26 metres/second. The question then becomes, "Is this a likely possibility?" Many scientists would probably say no. However, Lunar and planetary orbital periods which comprise the dynamical clock, have been compared with atomic clocks from 1955 to 1981 by Van Flandern and others. Assessing the evidence in 1981 Van Flandern noted that "the number of atomic seconds in a dynamical interval is becoming fewer. Presumably, if the result has any generality to it, this means that atomic phenomena are slowing down with respect to dynamical phenomena." (Precision Measurements and Fundamental Constants II, pp. 625-627, National Bureau of Standards (US) Special Publication 617, 1984. Even if these results are controversial, Van Flandern's research at least establishes the principle on which the former comments were made. Note here that, given the relationship between c and the atomic clock, it can be said that the atomic clock is extraordinarily PRECISE as it can measure down to less than one part in 10 billion. However, even if it is precise, it may not be ACCURATE as its run-rate will vary with c. Thus a distinction has to be made between precision and accuracy when talking about atomic clocks. Finally, there were some concerns about timing devices used on any future experiments to determine c by the older methods. Basically, all that is needed is an accurate counter that can measure the number of revolutions of a toothed wheel or a polygonal prism precisely enough in a one second period while light travels over a measured distance. Obviously the higher the number of teeth or mirror faces the more accurate the result. Fizeau in 1849 had a wheel with 720 teeth that rotated at 25.2 turns per second. In 1924, Michelson rotated an octagonal mirror at 528 turns per second. We should be able to do better than both of those now and minimise any errors. The measurement of the second could be done with accurate clocks from the mid50's or early 60's. This procedure would probably overcome most of the problems that John foresees in such an experiment. If John has continuing problems, please let us know. Further Comments on Time Measurements and c: In 1820 a committee of French scientists recommended that day lengths throughout the year be averaged, to what is called the Mean Solar Day. The second was then defined as 1/86,400 of this mean solar day. This supplied science with an internationally accepted standard of time. This definition was used right up to 1956. In that year it was decided that the definition of the second be changed to become 1/31,556,925.97474 of the earth's orbital period that began at noon on 1st January 1900. This definition continued until 1967 when atomic time became standard. In 1883 clocks in each town and city were set to their local mean solar noon, so every individual city had its own local time. It was the vast American railroad system that caused a change in that. On 11th October 1883, a General Time Convention of the railways divided the United States into four time zones, each of which would observe uniform time, with a difference of precisely one hour from one zone to another. Later in 1883, an international conference in Washington extended this system to cover the whole earth.

The key point to note here is that the vast majority of c measurements were made during the period 1820 to 1956. During that period there was a measured change in the value of c from about 299,990 km/s down to 299,792 km/s, a drop of the order of 200 km/s in 136 years. The question is what component of that may be attributable to changes in the length of the second since the rate of rotation of the earth is involved in the existing definition. It is here that the International Earth Rotation Service (IERS) comes into the picture. Since 1st January 1972 until 1st January 1999, exactly 32 leap seconds have been added to keep Co-ordinated Universal Time (UTC) synchronised with International Atomic Time (TAI) as a result of changes in the earth's rotation rate. Let us assume that these 32 leap seconds in 27 years represent a good average rate for the changes over the whole period of 136 years from 1820 to 1956. This rate corresponds to an average change in measured light-speed of [32/(8.52023 x 108) c = (3.7557 x 10-8) c] or close to 11.26 metres per second in one year. As 136 years are involved at this rate we find that [11.26 x 136 = 1531] metres per second or 1.53 km/s over the full 136 years. This is less than 1/100th of the observed change in that period. As a result it can be stated (as I think Froome and Essen did in their book "The Velocity of Light and Radio Waves") that limitations on the definition of the second did not impair the measurement of c during that period ending in 1956. Therefore, if measurements of c were done with modern equivalents of rotating mirrors, toothed wheels or polygonal prisms, and the measurements of seconds were done with accurate equipment from the 1950's, a good comparison of c values should be obtained. Note, however, that the distance that the light beam travels over should be measured by equipment made prior to October 1983. At that time c was declared a universal constant (299,792.458 km/s) and, as such, was used to re-define the metre in those terms. As a result of the new definitions from 1983, a change in c would also mean a change in the length of the new metre compared with the old. However, this process will only give the variation in c from the change-over date of 1983. By contrast, use of some of the old experimental techniques measuring c will allow direct comparisons back to at least the early 1900's and perhaps earlier. In a similar way, comparisons between orbital and atomic clocks should pick up variations in c. As pointed out before, this latter technique has in fact been demonstrated to register changes in the run-rate of the atomic clock compared with the orbital clock by Van Flandern in the period 1955 to 1981. By way of further information, the metre was originally introduced into France on the 22nd of June, 1799, and enforced by law on the 22nd of December 1799. This "Metre of the Archives" was the distance between the end faces of a platinum bar. In September 1889 up till 1960 the metre was defined as the distance between two engraved lines on a platinum-iridium bar held at the International Bureau of Weights and Measures in Sevres, France. This more recent platinum-iridium standard of 1889 is specifically stated to have reproduced the old metre within the accuracy then possible, namely about one part in a million. Then in 1960, the metre was re-defined in terms of the wavelength of a krypton 86 transition. The accuracy of lasers had rendered a new definition necessary in 1983. It can therefore be stated that from about 1800 up to 1960 there was no essential change in the length of the metre. It was during that time that c was measured as varying. As a consequence, the observed variation in c can have nothing to do with variations in the standard metre. (May 29, 1999)

Question: Barry points out that for obvious reasons no change in the speed of light has been noticed since the redefinition of time in terms of the speed of light a few decades ago. However, the new definition of time should cause a noticeable drift from ephermis time due to the alleged changing speed of light. I'm not aware of any such drift. Ephemeris time should be independent of the speed of light. Before atomic standards were adopted, crystal clocks had documented the irregular difference between ephemeris time and time defined by the rotation of the earth. Has Barry investigated this? Setterfield: On the thesis being presented here, the run-rate of atomic clocks is proportional to 'c'. In other words, when 'c' was higher, atomic clocks ticked more rapidly. By contrast, it can be shown that dynamical, orbital or ephemeris time is independent of 'c' and so is not affected by the 'c' decay process. Kovalevsky has pointed out that if the two clock rates were different, "then Planck's constant as well as atomic frequencies would drift" [J. Kovalevsky, Metrologia 1:4 (1965), 169]. Such changes have been noted. At the same time as 'c' was measured as decreasing, there was a steady increase in the measured value of Planck's constant, 'h', as outlined in the 1987 Report by Norman and Setterfield. However, the measured value of 'hc' has been shown to be constant throughout astronomical time. Therefore it must be concluded from these measurements that 'h' is proportional to 1/c precisely. As far as different clock rates is concerned, the data is also important. During the interval 1955 to 1981 Van Flandern examined data from lunar laser ranging using atomic clocks and compared them with dynamical data. He concluded that: "the number of atomic seconds in a dynamical interval is becoming fewer. Presumably, if the result has any generality to it, this means that atomic phenomena are slowing down with respect to dynamical phenomena" [T. C. Van Flandern, in 'Precision Measurements and Fundamental Constants II,' (B. N. Taylor and W. D. Phillips, Eds.), NBS (US), Special Publication 617 (1984), 625]. These results establish the general principle being outlined here. Van Flandern also made one further point as a consequence of these results. He stated that "Assumptions such as the constancy of the velocity of light · may be true only in one set of units (atomic or dynamical), but not the other" [op. cit.]. This is the kernel of what has already been said above. Since the run-rate of the atomic clock is proportional to 'c', it becomes apparent that 'c' will always be a constant in terms of atomic time. Van Flandern's measurements, coupled with the measured behaviour of 'c', and other associated 'constants', indicate that the decay rate of 'c' was flattening out to a minimum which seemed to be attained around 1980. Whether or not this is the final minimum is a matter for decision by future measurements. But let me explain the situation this way. The astronomical, geological, and archaeological data indicate that there is a ripple or oscillation associated with the main decay pattern for 'c'. In many physical systems, the complete response to the processes acting comprises two parts: the particular or forced response, and the complimentary, free, or natural response. The forced response gives the main decay pattern, while the free response often gives an oscillation or ripple superimposed on the main pattern. The decay in 'c' is behaving in a very similar way to these classical systems. There are three scenarios currently undergoing analysis. One is similar to that depicted by E. A. Karlow in American Journal of Physics 62:7 (1994), 634, where there is a ripple on the decay pattern that results in "flat points", following which the drop is resumed. The second and third scenarios are both presented by J. J. D'Azzo and C. H. Houpis "Feedback Control System Analysis and Synthesis" International Student Edition, p.258, McGraw-Hill Kogakusha, 1966. In Fig. 8-5 one option is that the decay with its ripple may bottom out abruptly and stay constant thereafter. The other is that oscillation may continue with a slight

rise in the value of the quantity after each of the minima. Note that for 'c' behaviour, the inverse of the curves in Fig. 8-5 is required. All three options describe the behaviour of 'c' rather well up to this juncture. However, further observations are needed to finally settle which sort of curve is being followed. (March 26, 2001).

Work on light speed by others Light Speed and the Early Cosmos (Barry Setterfield, January 24, 2002) The issue of light-speed in the early cosmos is one which has received some attention recently in several peer-reviewed journals. Starting in December 1987, the Russian physicist V. S. Troitskii from the Radiophysical Research Institute in Gorky published a twenty-two page analysis in Astrophysics and Space Science regarding the problems cosmologists faced with the early universe. He looked at a possible solution if it was accepted that light-speed continuously decreased over the lifetime of the cosmos, and the associated atomic constants varied synchronously. He suggested that, at the origin of the cosmos, light may have traveled at 1010 times its current speed. He concluded that the cosmos was static and not expanding. In 1993, J. W. Moffat of the University of Toronto, Canada, had two articles published in the International Journal of Modern Physics D. He suggested that there was a high value for 'c' during the earliest moments of the formation of the cosmos, following which it rapidly dropped to its present value. Then, in January 1999, a paper in Physical Review D by Andreas Albrecht and Joao Magueijo, entitled "A Time Varying Speed Of Light As A Solution To Cosmological Puzzles" received a great deal of attention. These authors demonstrated that a number of serious problems facing cosmologists could be solved by a very high initial speed of light. Like Moffat before them, Albrecht and Magueijo isolated their high initial light-speed and its proposed dramatic drop to the current speed to a very limited time during the formation of the cosmos. However, in the same issue of Physical Review D there appeared a paper by John D. Barrow, Professor of Mathematical Sciences at the University of Cambridge. He took this concept one step further by proposing that the speed of light has dropped from the value proposed by Albrecht and Magueijo down to its current value over the lifetime of the universe. An article in New Scientist for July 24, 1999, summarised these proposals in the first sentence. "Call it heresy, but all the big cosmological problems will simply melt away, if you break one rule, says John D. Barrow - the rule that says the speed of light never varies." Interestingly, the initial speed of light proposed by Albrecht, Magueijo and Barrow is 10 60 times its current speed. In contrast, the redshift data give a far less dramatic result. The most distant object seen in the Hubble Space Telescope has a redshift, 'z', of 14 (see note). This indicates lightspeed was about 9 x 108 greater than now. At the origin of the cosmos this rises to about 2.5 x 1010 times the current value of c, more in line with Troitskii's proposal, and considerably more conservative than the Barrow, Albrecht and Magueijo estimate. This lower, more conservative estimate is also in line with the 1987 Norman-Setterfield Report. note: April 2, 2003. Shortly after these high redshifts were announced, further analysis was done and it was found that data had been misinterpreted: what had happened was that these

objects being noted with this redshift were actually very red objects which were much closer to us than had been expected. The current most distant redshift is below z=7.

Moffat http://www.sciencedaily.com/releases/1999/10/991005114024.htm Published: 10-6-1999 Author: Bruce Rolston Speed Of Light May Not Be Constant, Physicist Suggests A University of Toronto professor believes that one of the most sacrosanct rules of 20thcentury science -- that the speed of light has always been the same - is wrong. Ever since Einstein proposed his special theory of relativity in 1905, physicists have accepted as fundamental principle that the speed of light -- 300 million metres per second -- is a constant and that nothing has, or can, travel faster. John Moffat of the physics department disagrees light once travelled much faster than it does today, he believes. Recent theory and observations about the origins of the universe would appear to back up his belief. For instance, theories of the origin of the universe -- the "Big Bang"- suggest that very early in the universe's development, its edges were farther apart than light, moving at a constant speed, could possibly have travelled in that time. To explain this, scientists have focused on strange, unknown and as-yet-undiscovered forms of matter that produce gravity that repulses objects. Moffat's theory - that the speed of light at the beginning of time was much faster than it is now - provides an answer to some of these cosmology problems. "It is easier for me to question Einstein's theory than it is to assume there is some kind of strange, exotic matter around me in my kitchen." His theory could also help explain astronomers' discovery last year that the universe's expansion is accelerating. Moffat's paper, co-authored with former U of T researcher Michael Clayton, appeared in a recent edition of the journal Physics Letters.

Albrecht and Magueijo Questions: I'm not a scientist, although I have some math and science background, and I am only just beginning to look into this discussion and may be asking a stupid question. Apology stated. I am a fellow believer and view Genesis as the ultimate "Theory" for which we need to find proof (not that we need to defend God, but it seems a reasonable part of our witness). That said, I want to review the emerging theories somewhat objectively. I noticed in Setterfield's paper there was reference to conservation of energy E=MC2. I found it interesting that VSL theory put forth by Magueijo doesn't require that, but seems to say energy will not be conserved with time. Have Setterfield (or yourself) reviewed the work of Magueijo? Perhaps he has discovered something important. Ultimately any theory has to make since on an earth populated by humans to be of any use to us. Does this consideration require conservation of energy in the Setterfield theory? Or, is it possible that energy may not be conserved over the history of the universe?

Setterfield: Yes, we certainly have considered Albrecht and Magueijo's paper and are aware of what he is proposing. His paper is basically theoretical and has very little observational backing for it. By contrast, my papers are strictly based on observational evidence. This requires that there is conservation of energy. The observational basis for these proposals also reveals that there is a series of energy jumps occurring at discrete intervals throughout time as more energy becomes available to the atom. Importantly, it should be noted that this energy was initially invested in the vacuum during its expansion, and has become progressively available as the tension in the fabric of space has relaxed over time thus converting potential energy into the kinetic energy utilised by the atom. The atom can only access this energy once a certain threshold has been reached, and hence it occurs in a series of jumps. This has given rise to the quantised redshift that occurs in space. Thus observational evidence agrees with the conservation approach rather than Mageuijo's approach. (1/31/01) see also Einstein's Biggest Blunder -- transcript of an interview with Albrecht and Magueijo

Davies in Nature, August 2002 Setterfield: On Thursday 8th August 2002, a burst of Press publicity accompanied the publication of a paper in the prestigious scientific journal Nature. That article was authored by Professor Paul Davies, of Sydney's Macquarie University, and by two astrophysicists from the University of New South Wales, Dr. Charles Lineweaver, and graduate student Tamara Davis. The paper suggested that the speed of light was much higher in the past and had dropped over the lifetime of the universe. These conclusions were reached as a result of the observations of University of New South Wales astronomer Dr. John Webb made in 1999 and the more recent observations of one of his PhD students, Michael Murphy. These observations indicated a slight shift in the position of the dark lines that appear in the rainbow spectrum of metallic atoms deep in space when compared with their expected position. Because there are a number of factors to disentangle statistically, and because the effect is small (about 1 part in 100,000), there remains some doubt as to the validity of the primary conclusion, let alone the suspected causes of the effect. The actual physical quantity that the observations are targeting is the fine structure constant. This constant links together four other atomic quantities, namely the speed of light, the electronic charge, Planck's constant and the electric property of free space called the permittivity. It is possible that any one of these quantities may be varying, or that there is synchronous variation between some or all of the components that make up the fine structure constant. Thus, one possible explanation for the observed effect is that the speed of light was higher the further back in time we look. But it is not the only explanation. Other possible explanations include a change in the value of the charge on the electron. However, the paper by Davies et al. rejects this possibility on the basis of what was expected to occur with black holes at the frontiers of the cosmos. Until I have seen a copy of the paper by Davies et al. I do not know if they have eliminated all other options. However, since a major paper by Andreas Albrecht and Jao Magueijo in 1999, and another one by John Barrow in the same issue of Physical Review D, the speed of light has come under increasing scrutiny as a physical quantity that may be varying. These scientists are

saying that if lightspeed was significantly higher at the inception of the cosmos (about 10 60 higher) then a number of astronomical problems can be readily resolved. Paul Davies statements echo that and he, like Barrow, considers that lightspeed has declined over the history of the universe. By contrast, Albrecht and Magueijo contained the lightspeed change to the earliest moments of the Big Bang and had it drop to its present value immediately afterwards. In that sense, this recent work is consolidating the belief that the drop in lightspeed has extended over the whole history of the universe. This is the position that the variable lightspeed (Vc) research has advocated since the early 1980's. The cause of the change in the speed of light has still to be determined, but according to Lineweaver, one of the prime suspects is that the structure of the vacuum has been changing uniformly across the cosmos. This is also the position that the Vc research has advocated since the early to mid- 1990's and was formalised in Atomic Quantum States, Light and the Redshift. It is also the key subject of "Exploring the Vacuum." Because there is an intrinsic energy in every cubic centimetre of the vacuum, this energy may manifest as virtual particle pairs like electron/positron pairs that flit in and out of existence. As a photon of light travels through the vacuum, it hits a virtual particle, is absorbed, and then shortly after is re-emitted. This process, while fast, still takes a finite time to occur. Thus, a photon of light is like a runner going over hurdles. The more hurdles over a set distance on the track the longer it takes for runners to reach their destination. Thus, if the energy content of space increased with time, more virtual particles would manifest per unit distance, and so the longer light would take to reach its destination. Much was made of the potential problems that lightspeed changes would cause to Einstein's theory of Relativity. This matter has been discussed ever since Albrecht and Magueijo's paper in 1999. However, the Vc work examined this issue back in the 1980's and decided that Einstein's work will basically remain valid provided that energy is conserved in the process. This necessarily involves changes in a number of other constants as Trevor Norman and I outlined in the 1987 Report, The Atomic Constants, Light and Time, from SRI International and Flinders University. These matters are also discussed in further detail in the 2001 paper. I also had the opportunity to briefly pursue the issue of observed changes to other atomic constants with Prof. Albrecht in March 2002. He admitted that his proposal had problems with the observations of some constants. I mentioned that these problems could be overcome if energy was conserved in the process. He stated that they had looked at that but decided that they could not achieve all the effects they wanted to if energy was conserved, and so abandoned that position. Albrecht and Magueijo attempted to largely avoid these problems by isolating lightspeed changes to the earliest moments of the Big Bang. However, these more recent results are tending to confirm that the change has been occurring over the lifetime of the universe. Consequently, the issue of changing atomic constants must be opened again, and the validity of Einstein's equations linked in with it. In summary, the scientific community is coming to believe that a drop in lightspeed has occurred over the lifetime of the cosmos from some initial value near 1060 times its current speed. The Vc research has indicated that lightspeed has been dropping over the life of the universe from a maximum value around 1011 times now. This is a more conservative estimate than others are proposing. The actual cause of the change in lightspeed is suspected by both secular scientists and those involved in the Vc research as being related to changes in the structure of the vacuum. Finally, Einstein's equations have been called into question. However, they can be shown to be basically correct provided that energy is conserved in the process of c variation, but some other atomic constants will vary synchronously in this case.

Those other constants, which have been shown to be varying in this way from observational data, were examined in the 1987 Report and the 2001 paper and support the Vc position. 10th August 2002. Related reference: Speed of Light Slowing Down After All? by Carl Wieland, 8/9/02.

Responses to critical webpages There are a number of pages on the web critical of the Setterfield work. As time permits, responses to these will be posted below. See also General Objections Response to Robert Day of Talk.origins A Response to Joseph Meert (Helen Setterfield)

Supportive and Explanatory Essays by others Speed of Light Slowing Down? by Chuck Missler Expanded explanation and implications regarding a changing c by Lambert Dolphin Reports of the Death of Speed of Light Decay are Premature, by Malcolm Bowden The Decrease in the Speed of Light -- an Update on Developments, by Malcolm Bowden The Decay of the Speed of Light, by James P. Dawson