LIFE COMES FROM LIFE, PART IIIa: A Preliminary Discussion of the Author's Theory (of Quantum Reality, and Consciousness) in Relation to the Theories due to Bohr, Wheeler, Bohm, Everett, Finkelstein, Einstein, von Neumann, and Heisenberg. Jagdish N. Srivastava CNS Research Professor Colorado State University Fort Collins, CO 80523-1877 United States of America [email protected] higherReality.googlepages.com

[This paper appeared in Savijnaanam, Vol. 3-4, 2004/2005, pages 79-110, published by the Bhaktivedanta Institute, Kokata. The printed version of the paper has figures, illustrations, and the pictures of the scientists and of the author. The publishers may exercise copy right on the article.]

0. ABSTRACT This paper is one in a series of papers in this journal, under the general title of “LIFE COMES FROM LIFE”. Herein, we present a major theory (denoted by TK), concerning the Foundations of Reality, which includes Quantum Reality (denoted by QR), Consciousness, and Reality in general. This theory is meant to supersede the other wellknown theories in this area offered thus far. In parts I, and II, of the present series of articles, it was stated that TK rests on two basic axioms A1 and A2. Axiom A1 says that there does exist an intrinsic, deep, deterministic, ‘Reality’, which shall often be called ‘Nature’ (denoted by N). Furthermore, N consists of logical-mathematical objects alone, and all such objects are a part of N. Axiom II says that there is a basic presence in Reality, called ‘Consciousness’, that is akin to the presence of ‘Space’ in our customary notion of the physical universe in which we live. Also, in Reality (or Nature), there are two types of entities: ‘Inanimate’ and ‘Animate’, where the latter are endowed with ‘Consciousness’, and the former are not. Furthermore, the ‘consciousness’ of an animate entity gives to it the experience of certain portions of Nature as ‘physical objects’. (Of course, all such portions are logical-mathematical objects only. Thus, ‘matter’ and ‘material objects’ are only logical-mathematical objects, even though (to our senses) they seem to be physical objects.) In part II, it was heuristically shown that ‘total consciousness’ corresponds to V, the ‘Totally Empty Set’, that is a member of all possible ‘universes’ (or ‘classes’, ‘systems’, ‘spaces’, etc.) in N, and furthermore, that is a subset of the empty set of each such universe. (For example, if U is the universe of pens in a given bag, then V is a part of U, but V does not contain any pen from U. In other

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words, V is contained in the empty set of U.) The purpose of the part III sub-series of these papers is to concentrate on Axiom I. In this part (IIIa), we present a brief discussion of eight current theories (denoted by T1, T2,…,T8) of Quantum Reality, and compare and contrast them with the theory TK, attempting to establish the greater plausibility of the latter. 1. INTRODUCTION The Role of Mathematics. The subjects of Mathematics, Physics, and Statistics are more closely linked together than is normally realized. The role of Mathematics in the sciences, particularly in Physics is well appreciated. As will be discussed later, some people have gone to the extent of saying that Physics has a ‘probabilistic foundation’. Irrespective of how far such an assertion concerning the ‘foundation’ (i.e., the nature of, and the rules governing, the smallest particles) is justified, it is clear that at least at the gross physical level (i.e., at the level of (the so-called) Classical Physics), all phenomena are essentially stochastic phenomena in some sense. In this article, we shall try to lay the groundwork for establishing that, deep down, ‘Reality’ consists of ‘mathematical’ (and hence ‘statistical’, where collections of variables are involved) structures only, and that ‘Physics’ is the ‘experience’ by us of certain aspects of the same (called by us, the ‘physical’ aspect). 1.1 The Smallest Particles. As Stenger (1995) has pointed out, the word ‘quantum’ is now used even outside Physics, for a variety of meanings (in some cases, even as a fashion). Here, however, we shall refer to it to mean objects (and numbers associated with them), which are at the currently known smallest levels. The particles that are currently considered as indivisible will often be called ‘fundamental’. Following Herbert (1985), a single particle at the quantum level will often be called a ‘quon’. 1.2 Quantum Reality (QR). The phrase QR will be used here to broadly refer to the nature of, and the rules governing, the particles at the smallest levels, such as atoms, electrons, protons, neutrons, quarks, etc. [For an introduction to QM and QR, a suitable text reference is Griffith (1087, 1995). An interesting and readable discussion of QR from various angles will be found in Rothman and Sudarshan (1998).] In this series of articles, we shall put no arbitrary restriction on how ‘deep’ we wish to go into the nature of the quons. 1.3 The Knowledge Viewpoint. The reason for the lack of such restriction is the ‘Knowledge Viewpoint’ that says: “If something is not known now, then we can not necessarily say that it is ‘not knowable’ ”. Thus, as a fundamental principle, we take the optimistic (rather than the pessimistic) attitude, and assert that whatever knowledge we have now is incomplete, and that if we seek enough, and in the proper way and in appropriate directions, then we shall find further knowledge. 1.4 Incompleteness of the Knowledge of QR. Thus, in particular, our current knowledge of QR is incomplete; this is in agreement with Einstein (Theory T6) who came to this conclusion for other reasons (which may not be wholly correct). The purpose of this

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article is to provide some insight into how to broaden our current knowledge, i.e., make it more complete. 1.5 Theories of QR. Herbert (1985) has a given an excellent discussion of eight major theories; as mentioned above, these are numbered T1 to T8. To this we append T9. However, T9 is not a theory in the same sense as the others are. Indeed, it is a whole branch of Physics called ‘Quantum Field Theory’ (QFT). [See, for example, Kaku (1993). For a discussion of quantum electrodynamics, see Feynman (1985).] It also includes the famous works on certain ‘objects’ known as ‘strings’ (or, in general, ‘branes’) that are considered as the smallest known building blocks of matter. (These ‘objects’ are, to the author, essentially ‘mathematical objects’, though the scientists in the field seem to consider them as descriptions of ‘physical objects’.) To be precise, T9 is not a theory (like TK, or T1,…,T8) of the foundations of QR. However, T9 is a whole field of research, representing the current mathematical development of fundamental questions on the elementary particles. It is mentioned here because it is felt that the author’s theory TK would be closely aligned with it. 1.6 Comparison of Theories. Given several competing theories of QR, the question is how to compare them. We need to know whether any one of them is ‘correct’, and if so, how to determine which one is correct. Of course, each competing theory must satisfy the known observations; otherwise it would be rejected outright. Thus, the theories have to be compared and contrasted on the basis of their ‘lack of weirdness’, ‘scientific plausibility’ and ‘logical appeal’. (I have used single quotes (‘…’) on the criteria in the preceding sentence, because the precise meaning and the method of use of any of them may vary from one person to another.) 1.7 Objectivity. Criteria (like those in the last paragraph) have one requirement that is generally supported by everyone, namely, ‘objectivity’. In other words, we wish to know about things as they really are, uninfluenced by personal prejudice or bias. Opposed to this is ‘subjectivity’, where the view of things is influenced by personal factors. Many thinkers consider experimentation as a possible objective verification of facts. However, even here there is a basic difficulty that we now discuss. 1.8 Law of Intrinsic Confounding in Experimentation (LICE). As is well known, in the theory of Statistical Design of Scientific Experiments, ‘confounding’ arises quite often. Two quantities a and b are said to be confounded if we are able to know the value of only some function of a and b, but we do not know them separately. The simplest case is where we know the value of (a+b), but do not know a or b individually. 1.9 Now, let U be a (mathematical) universe. The physical universe in which we live would be an example of U. Let U1 denote a ‘site’, or a sub-universe inside U. Let S be a ‘study’ an ‘experiment’ that is performed at U1, and let k denote the ‘knowledge’ obtained from S or the ‘result’ of S (which could be the value of some observation made as a part of S). Then, the following fact, whose proof is obvious, would be referred to as ‘LICE’:

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Theorem 1.1 The result k depends, in general, upon both S and U1. For example, if S denotes ‘looking for birds’, and U1 denotes Antarctica, then k may often be a penguin. But, if we take U2 (Sahara Desert) in place of U1, the result k would drastically change, for we may never see a penguin there. 1.10 Forced Subjectivity. In the above, it is clear that if we are looking for birds, the site has an important bearing on the result. However, suppose we decide to live in U2 alone, and we know nothing about the rest of U. Then, there is no chance that we would ever see penguins. Here, we are locked into the situation where our result k is influenced by our decision to be in U2. Thus, subjectivity has crept into S and k. If we are forced to be in U2, then it is a ‘forced subjectivity’. If the decision of choosing an experimental site out of sub-universes U1, U2, . . , is left to us, then whatever choice we make will influence the k that we shall obtain. But, since our choice has a subjective element in it, k too shall have a subjective element. We shall have to cope with this subjective aspect of k. Note that if there are a large number of sub-universes U1, U2, …, involved, and only one of them is to be chosen for the experiment, then we will be forced to have a k that is influenced by our subjectivity. 1.11 Deep Reality and LICE. Now, suppose that U is known very little, and we are in some U1 that is only vaguely known. In this case, it would be very hard to cope with the subjective element, and generalizations from U1 to U could be quite misleading. This remark is obviously very true of ‘Deep Reality’. Thus, in research in this field, including in particular QR, one would have to reckon with LICE at every step. This indicates that in QR and deeper levels, pressing for ‘objectivity’ by doing experiments is not too meaningful. This does not mean that experimentation has no value any more; it is quite the contrary. However, we cannot afford any more not to look at the physical and foundational implications of what we do (as has been the situation in many quarters in the Physics establishment for some time). Furthermore, the above also does not give us a license for being subjective, divorcing ourselves deliberately from objectivity. Thus, there is no implication against experimentation or objectivity. However, it does ask us to guard against unwarranted generalization and philosophization, including particularly the kind that ignores the intrinsic confounding in experimentation or considers the ‘notknown’ as the ’not-knowable’. 1.12 Contents of the article. As mentioned in the abstract, keeping the above in mind, we proceed with a discussion of fundamental issues. We present a simple description of some experiments, which will form a focal point of our discussion. Next, we present QR theories partly using this context. There are many excellent books that discuss fundamental issues in QR. In this paper, we shall follow the numbering of the theories (#1 to #8) by Herbert (1985). ( I call them T1 to T8 for ease of reference.) Herbert has not only presented the issues elaborately, he has gone into an in depth discussion of the various subtle questions that arise. It is said that asking the proper questions is half of the research. Herbert’s in depth questioning has certainly been very helpful to the author in his research in this field.

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2 FOUR IMPORTANT EXPERIMENTS 2.1a. Four Experiments in Physics We now describe four experiments, each of which shall play an important role in the discussions in this paper. These experiments are simple to understand. However, their results are extremely profound and lead us to the large dilemmas that arise in the field of Quantum Reality. Many of these have been debated for about three quarters of a century. 2.1b. In passing, it will be useful to record here two ‘general assertions’ (denoted by, ga1, and ga2, say) concerning electrons which are commonly made. Now, ga1 is: “An electron is a ‘point-particle’, i.e., it’s length, breadth, and thickness is almost zero (i.e., it is smaller than every positive number)”. Also, ga2 is: “An electron has ‘spin’, which is an ‘internal’ property of the electrons. The spin creates a spin-angular-momentum, which is measurable in any single direction in our 3-dimensional space.” It is interesting to note that if the spin of an electron is probed in any given direction in our 3-dimensional space, then the spin-axis of the electron is always found to be tilted at the angle of 54.7 degrees to the direction that is being probed. [See, for example. Schäfer (1997; p. 193).] 2.2. The Double-Slit Experiment 2.2a. The experiment is illustrated in Fig.1a, with some explanations in Fig.1b.

Fig.1a Here, we have a source S that emanates light. In front of S, there is a barrier A, which has two slits g and h, through which light can pass. At a further distance after A, there is a screen B that is sensitive to light. Now, we consider two cases, I and II. Under case I, we suppose that one of the slits is closed. Thus, suppose that h is closed, and only g is open. Then, on the screen B, a pattern is formed which corresponds to the frequency with which light particles (photons) arrive there. This frequency roughly corresponds to a bell shaped distribution, and looks like the curve cg in case I in the Fig. 1(b). Similarly, when g is closed and h is open, we get the curve ch .

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Fig.1b 2.2b. Now, consider the Case II when both slits g and h in A are open. In this case, under the assertion ga3 (“Each photon goes through one and only one slit”), one would expect that the pattern on B would correspond to a frequency curve which would be the ‘sum’ of the frequencies represented by curves cg and ch in figure I(a). However, the pattern actually noticed in Case II corresponds to the curve shown for Case II in Figure 1(b). The curve for Case II is much different from the curve that would correspond to the ‘sum’ of the curve g and h in Case I. 2.2c. Indeed, the observed curve for Case II corresponds to what we would expect under the assertion ga4 (“Light behaves as a wave, and when there are two open slits, interference of light occurs”). Indeed, under ga4, the waves of light passing through g and h (in A) interact with each other on the screen B, where they reinforce each other in areas where both waves have crests or both have troughs, and cancel each other in areas where one of them has a crest and the other has trough. 2.2d. Now, suppose a (detector) dg is put behind the slit g (i.e., between A and B), and a detector dh is put behind h. Suppose the intensity of the light at the source is reduced so that only one photon passes at a time. (This can be done.) Then, it is found that either dg registers the photon, or dh registers, but never both. Of course, this is what we would expect if light is only a particle. 2.2e. Thus, it appears that when light ‘exits’ at the source S to ‘move’ towards A and B, it “knows” whether one or both slits are open, so that if only one slit is open it may go as a particle. Also, if both slits are open it may go as (i) a wave, if there is a screen ahead where the two parts of the wave could meet (and interference could occur), and (ii) as a particle, if there is no screen where they could meet. 2.3 Stern-Gerlach Experiment 2.3a. Here, as in Fig. 2a, we have a source O that is an oven where silver is heated, and its atoms boil off. These atoms are passed through a collimator C, which produces s straight beam of atoms. Next this beam is passed through an inhomogeneous magnetic field. Without loss of generality, we shall assume that the beam is traveling in the y-direction, and the magnetic field is in the z-direction, it being inhomogeneous in the z direction. After the bean goes through the above-mentioned magnetic field, it is found that it splits into two beams (which are formed ‘up’ and ‘down’ in the z-direction.) [See, for example, Sakurai (1994).]

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Fig. 2a.

2.3b. Briefly speaking, the ‘theory’ behind the above is this. Each silver atom carries 47 electrons, 46 of which are ‘paired’, so that their ‘spin’ and ‘spin-angular momentum’ cancel out. However, one electron is free, and if its spin is ‘up’, it goes into the ‘up’ part of the beam (after it is split), and if its spin is ‘down’, then the atom goes into the ‘down’ beam. Since the chance is ½ that an electron will have spin ‘up’ or ‘down’, the original beam splits into two roughly equal parts. 2.3c. Suppose now that the original beam B (going in the y-direction) passes through the Stern-Gerlach’ Apparatus (SGA) with magnetic field in the z-direction (SGAz). Then, it splits into two beams (say, Bz+ and Bz-), with respect to the z-direction. The free electron in each atom gets oriented in the z-direction to either z+ or to z-. Thus the beam Bz+ consists of such atoms where electrons have the orientation z+. Similar situation exists with Bz-. 2.3d. Next, suppose we take the beam Bz+, and again pass it through a SGAz. This time only one beam comes out, namely the beam Bz+. (See Fig. 2b) This is what one would expect under the assertion ga5: [“If any beam, say B`, is passed through SGAz, then either one or two beams shall come out. If B` itself is a beam that is coming out of SGAz, then by passing it again through SGAz, the same beam B` will be obtained. If B` is not a beam that has come out of SGAz, then B` will split into two beams B`z+ and B`z-.]

Fig. 2b 2.3e. Now, suppose we take the beam Bz+, and pass it through an SGAx. We now find that the beam Bz+ splits into two beams (say, Bz+x+ and Bz+x-). (Fig. 2b) This is in consonance with ga5. 2.3f. Next, suppose we pass the Bz+x+ beam again through SGAz. We now find that the beam Bz+x+ splits into two beams, which we shall denote by Bz+x+z+ and Bz+x+z-. (See Fig. 3c.) This seems to suggest that something like assumption ga6 may also be valid along with ga5, where ga6 is: “When a beam B1 (going in the y-direction) passes

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through a SGAz, it orients electrons to either z+ or z-, and randomizes them with respect to the direction x. Similarly, when this beam is passed through a SGAx, it orients electrons to either x+ or x-, and randomizes them with respect to the z-direction. These assertions are true for any beam B1.” Notice that ga6 is in consonance with ga5, for when B1= Bz+, the electrons are not randomized in the z-direction; rather, all electrons remain oriented towards z+, which results in our getting only one beam when Bz+ passes through SGAz.

2.4 The Three Polarizer Experiment 2.4a Let S denote a square sheet of plastic with corners A,B,C,D as shown in Fig. 3a.

Fig. 3a. Fig. 3b.

Fig. 3c.

Fig. 3d.

Suppose that S has the property that it polarizes light vertically. This means that if an ‘ordinary’ (i.e., ‘un-polarized’) beam of light strikes S from one side, it is broken into two beams (one vertical, and the other horizontal), and only the vertical beam (i.e., a beam in the (y,z) plane) emerges from the other side of S. (The horizontal beam is absorbed by S.) Of course, here we are assuming that S is as shown in Fig. 3b, i.e., it is standing vertical in (x,z) plane with the side DC on the bottom; to emphasize the fact that S is in this position, we shall denote it by Sv. 2.4b Similarly, if S stands (in the (x,z) plane) with CB on the bottom (as in Fig. 3c), then we shall denote it by Sh. If un-polarized light is passed through Sh, then its vertical component (i.e., the one in the (y,z)-plane) is absorbed, and it’s horizontal component (i.e., the one in the (x,y) plane) passes through. 2.4c Now, suppose that Sv and Sh are put parallel to each other (both in the (x,z) plane), and un-polarized light is sent from a source O as shown in Fig. 3e. Then, Sv will allow the vertical beam to pass through which will then be absorbed by Sh, so that no light will emerge.

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Fig. 3e. 2.4d Notice that in figure 3e, the bottom sides of Sv and Sh are parallel to the x-axis. Now, suppose S is made to stand on its vertex C (as in Fig. 3d) so that the diagonal DB is parallel to the x-axis; in this position S will be denoted by Sd. (Note that Sv, Sh and Sd correspond to clockwise rotation of S respectively by 0°, 90°, and 45°). 2.4e Now, with the arrangement as in Fig. 3e, suppose Sd is put before Sv (i.e., between O and Sv), or it is put after Sh. Then, as one would expect, no light comes out at the end. However, consider the arrangement as in Fig. 3f, where Sd is put in between Sv and Sh. Now light does emerge at the end (i.e., out of Sh)! This runs counter to ordinary intuition, because the screens Sv and Sh together do block all light, and the addition of one more screen in between should only block some light rather than allow any light to pass.

Fig. 3f. 2.4f Interestingly, the above- mentioned experiment can be easily done by using sunglasses whose lenses are polarized. Get three of them. Hold one horizontal (like in glasses); light will pass through it, i.e. you can see through it. Now hold a lens in front of it and parallel to it, but in the vertical position. Now, no light will pass, and you will see almost nothing. Next, hold another lens in between these two at about 45 degree angle, and you will see through all the three of them, showing that now the light does pass.

2.5 THE EINSTEIN-PODOLSKY-ROSEN (EPR) AND RELATED EXPERIMENTS. 2.5a The foundation of Quantum Mechanics (QM) has been debated, often heatedly, ever since its inception in the mid-1920’s. As will be discussed later, Bohr and Heisenberg had certain philosophies that were contradicted by the philosophies of Einstein and Schroedinger. In particular, the former claimed that QM is complete, while Einstein felt that it is incomplete, a feeling that is also shared by the author. 2.5b Einstein’s thoughts culminated in the EPR (1935) paper, which is an important milestone in the further development of the subject. This EPR paper contains a ‘imaginary’ or ‘thought’ experiment, which leads to what is called the ‘EPR paradox’. The EPR thought experiment was later rendered a more concrete physical form by Bohm in the 1950’s. This triggered investigations by Bell (1964), leading to Bell’s Theorem,

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which in turn made the Einstein paradox testable in a sense. In Berkeley, in 1972, Clauser devised an experiment along the lines of Bohm’s ideas. But, this experiment contained some seeming loopholes, which were removed in an important revision of Clauser’s experiment by Arpect etal (1982) in Paris. A further modification, the “delayed choice experiment” was suggested by Wheeler. 2.5c The original EPR thought experiment considered two quons (say, A and B) that interact with each other in some way, and separate out. Let qA, qB and pA, pB respectively denote the position and the momentum of the two quons. It can be checked that, considered as operators, (qA-qB) and (pA + pB) commute with each other. Under the rules of QM, this means that the two quantities (qA -qB) and (pA + pB) have a simultaneous existence (i.e., they are simultaneously well defined), and can be simultaneously observed. As will be elaborated later, this means that knowing qA or pA, we could know qB or pB (without doing anything to B, and irrespective of how far B is from A). From this, EPR deduced that each of qB and pB have a definite value (simultaneously), and thus, that there is a ‘reality’ associated with these values. This is a conclusion that contradicts the opinion of Bohr and Heisenberg. 2.5d Although, EPR argued in terms of position and momentum, Bohm pointed out that a similar ‘paradox’ might arise using polarization of light. Now, light can be “unpolarized”, “linearly polarized”, or “circularly polarized”. As in the last section, here too we shall restrict ourselves only to the first two. Consider a source (say, O) (see Fig. 4) of light, which produces pairs of photons, each pair being in the so-called ‘twin-state’ (which we explain below). The two photons (of each pair) are made to travel in opposite directions.

Figure 4 Consider the photons from a given pair; call them A and B. Then, A travels to the left from S where it meets a light detector D1. Similarly, B travels to the right, where it meets a detector D2. The detectors D1 and D2 check the state of linear polarization of any photon that comes to them. To put it in a simplistic way, each detector acts like a linearly polarizing lens, and is comparable to S in Figure 3a. Let Sq denote S where S is rotated clockwise by an angle q while standing on the vertex C. Thus, Sv, Sh, and Sd correspond respectively to q = 0, 90, and 45 degrees. 2.5e The statement “a pair of photons in the twin state” means the following. Suppose we stand at the far right in Fig. 4 at the observer position “OBS”, so that “OBS”, D1, O, and D2 are in a straight line. Suppose that D1 and D2 are rotated so that looking at them from the OBS position we find both to be Sq, where q is arbitrary. Suppose a pair of photons is sent out of O. Then, the pair is in the ‘twin-state’ would imply that either light will pass through both detectors, or light will not pass through any detector. In other works, looking from the OBS position, if both detectors are in Sq position (where q is arbitrary) and the pair of photons A and B is in the ‘twin-state’, then it can not happen that A passes

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(through D1), but B does not pass (through D2), or that A does not pass and B does pass. 2.5f The above is the scenario of Bohm’s version of the EPR thought experiment. We shall later discuss the conclusion drawn from this, by various people, concerning the nature of QR. We first consider the main experiment. Suppose that D1 corresponds to Sq1 and D2 is set at Sq2, where q1 and q2 are unequal. (For simplicity, we shall assume that both the angles q1 and q2 have a value between (-90) degrees and (90) degrees. Now, it can happen that A passes (through D1) but B does not pass (through D2), and vice versa. We shall say that the ‘error’ (denoted by e) equals 0, when A and B both pass, or when A and B both do not pass. Also, we define e = 1, when one of A or B passes while the other does not pass. For each photon pair, the value of e is a binomial random variable with a constant probability r of “success” (i.e., of obtaining e = 0). The theory of QM predicts that r is function only of |q| (i.e., r = r(q)=r(-q)), where q = (q1 - q2). Bell (1964) argued that if this is true, then we must accept certain drastic conclusions in the foundations of QR. 2.5g Clauser (see, for example, Clauser and Shimony (1978)) set out to check if QM’s prediction is right, doing an experiment of the sort described above. (Of course, the actual experiment was far more complex and sophisticated then the skeleton described here.) In 1972, he announced that the results of his experiments confirm the predictions of QM. To elaborate the nature of this experiment, first let q = 0, i.e., q1= q2; in this case it is found that r = 1, i.e. e = 0 irrespective of the value of q1, and irrespective of the values of d1 and d2, where d1, d2 are respectively the distances between O and D1, and O and D2. Let P1, P2 … be a sequence of pairs of photons emitted by O, where Pi (i = 1,2, …) consists of photons Ai (=Pi1), and Bi (= Pi2) in the twin state. Let q be fixed, and let q1i and q2i (i = 1, 2, ….) be a sequence of values of q1 and q2, such that q1i = q2i + q. The experiment is as follows. For ( i= 1, 2, …), choose a value of q2i, and fix D2 in the position Sq2i. Let uhi (h=1, 2; i = 1,2….) be a variable which takes the value 0 or 1 only, such that uhi = 0, if the photon Phi passes through the detector Dh, and uhi =0, otherwise. Thus, (for any i), set D2 in position Sq2i and D1 in position Sq1i (where q1i = q2i + q), and measure u2i and u1i. Obtain ei = |u1i - u2i|. Then (e1 + ….+en)/(n), is the proportion of errors in the first n trials. The QM theory predicts that as n increases, this ratio converges to r(q); this fact was found to be true in Clauser’s experiment. 2.5h The question is, for any fixed i, how does the choice of q2i influence the behavior of P1i giving rise to the value u1i? Is there some hidden mechanism by which information in the value of q2i gets conveyed to P1i so that it behaves accordingly? Clauser’s experiment was not refined enough so as to remove the suspicion that after D2 is set to Sq2i, there is no subtle message going from P2i (or D2) to P1i so as to influence the latter’s behavior. Now, according to Einstein’s theory of relativity, no message can travel at a speed faster than that of light. So, in order to remove the above suspicion, Aspect et al (1982) devised a revised experiment. Here, a fast system was developed where a different polarization measurement could be at intervals of 10 nanoseconds. With such a system, it is impossible that a light signal from D2 (carrying information on the value of U2i) can reach D1 before P1i reaches D1. In other words, the possibility that there is some hidden physical mechanism by which the value of u1i is influenced by the value of

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u2i, is eliminated by this very sophisticated experiment. 2.5i Although I have put the above discussion in the context of a sequence q2i (i = 1,2, …) of values, this does not mean that in the actual experiments, all the values of q2i (for different i) were distinct. This is not so at all. Indeed, in an actual experiment, all the q2i may be identical, or may take only a few distinct values. The experiments were conducted apparently to check whether the value of u2i is somehow getting communicated to P1i, thus causing an influence on u1i. The author believes that the experiments were not concerned with the effect of q2i on the value of u1i; indeed, as stated above, all the q2i could be equal. 2.5j Both experiments (particularly, Aspect et al) were very sophisticated, and used excited calcium atoms. For some further details see, for example, Baggott (1992). 2.5k As mentioned in 2.4f, Bell’s (1964) theorem has an important impact on the fact that these experiments give results that coincide with the prediction of QM. What is Bell’s theorem about? Well, firstly, Bell assumed the reality of the quons (in this case, photons) in the sense that they exist and have real static attributes. Next, under a particular assumption he obtained an inequality that r(q) must satisfy if those assumptions are valid in the experiment. 2.5l The main assumption was of ‘locality’ that says that no object or influence can move faster than light. Now, in the Aspect experiment, the photons are moving in opposite directions at the speed of light. Thus, there is no possibility of any communication between them in the sense that (for every i) the value of u2i cannot influence u1i. Thus, for each i, under the assumption of locality, it follows that q2i influences only u2i, and similarly, q1i can influence only u1i, and this happens irrespective of how large the values of d2 and d1 are, i.e., irrespective of how far the two detectors are from the source O, the calcite crystal. 2.5m It was found that the experiments confirmed the predictions of QM that, in turn, violates the inequality. Now, it seemed obvious to the various theorists that all assumptions in Bell’s theorem were obviously satisfied. So, the majority in the physics community concluded (though many did so reluctantly) that the locality assumption of Bell’s theorem is not being satisfied, and somehow u2i is influencing u1i, and vice versa. In other words, we cannot say that (for any i) the realities associated with P1i and P2i are separate. Now, Einstein had said that there is a separate reality associated with the two photons in any pair. But, from the arguments given above, one concludes that Einstein was not correct on this issue, and furthermore, that there is some faster-than-light communication going on. 2.6 THE DELAYED CHOICE EXPERIMENT In the two-slit experiment (sec. 2.2), one finds that when we place detectors dg or dh, light seems to behave as a particle, but when there are no detectors (and both slits are open) we observe interference effects showing that light is a wave. Thus, it seems that the

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type of measurement we make influences the behavior of photons. The question arises as to when the photon ‘makes up it’s mind’ about whether it will follow only one path or it will take both paths. John Wheeler (for a more elaborate discussion, see, for example, Baggott (1992)) proposed in 1978, that a ‘delayed choice’ (DC) experiment be conducted, whose purpose would be to decide on ‘the type of measurement to be made’ after the photon ‘had decided as to whether it shall follow one or both paths’. Thus, the choice of the type of measurement is delayed until after the photon has ‘made its decision’ as to whether it will pursue two paths or just one. An experiment of this type was conducted in Maryland and in Munich. We shall not describe this experiment in further detail. However, we wish to record that here too, the result was the same as in the Aspect experiment. The following two results were observed. The first result (DC1) is: If both paths were open all the way up to the place (say P) in the overall apparatus where the interference measurement is observed, then the interference is (always) observed, showing that in this case, the photon (always) takes both paths. The second result (DC2) is: If, before the two photons can reach the place P, at least one of the two paths is closed, so that the condition in DC1 is not satisfied, then the photon is detected only in one of the paths. 3. THE VARIOUS THEORIES In this section, we begin to discuss the theory TK by itself, and also in the context of other theories. This will be continued through the rest of this paper. It will be further continued in part IIIb, and other parts in this series of papers. As we discuss various questions, many assertions will arise which are likely to come up again and again. For the sake of compactness (i.e., to avoid repetition of phrases and sentences, and thus to save journal space), we shall suitably symbolize them. Assertions that are very specific to a particular theory shall have a reference to the same in their symbol. Other general assertions will be included in the ‘ga’ series already introduced (viz., ga1,…ga6). Statements which constitute conclusions reached by various arguments and discussions shall be classified by c1, c2,.., etc. Remarks will be denoted by R1, R2,…., etc. 3.1 We start with TK; some of the assertions that it upholds are as follows. (tka1) Nature (denoted by N) consists of logical-mathematical (log-mat) objects only. ALL log-mat objects are members of N. (tka2) Reality consists of two kinds of entities: Animate and Inanimate. (tka3) One fundamental property of Reality is ‘Consciousness’. Inanimate entities have no consciousness. Animate entities perceive certain objects in N as ‘physical’ objects; their perception of the ‘physicality’ of an object depends on the nature of consciousness that they possess. (tka4) The so-called ‘elementary particles’ (quons) are log-mat objects only, and are properties of what is commonly known as the ‘Wave Function’ (WF).

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(tka5) Quantum Mechanics (QM) is incomplete. Also, QM is deterministic. (tka6) What is commonly known as the WF is in reality a ‘multi-dimensional’ object; here the word “multidimensional” means “of 0, 1, 2, 3, 4,5, or higher dimensions”. The commonly used WF is only a marginal property of the ‘real’ WF (which will be denoted by ‘RWF’). The RWF will be considered to have a dimension equal to or larger than the corresponding WF. The word ‘Quantum Cloud’ (QC) will often be used to refer to the RWF of one or more particles, depending on the context. (tka7) The RWF or the QC depends upon the ‘space-time’ in which it is defined; any change in this space-time instantaneously changes the RWF as a whole. In nonrelativistic situations, this will refer only to ‘space’. (tka8) ‘Inside’ N, various logical mathematical objects ‘interact’ with each other (under the applicable rules of logic and mathematics in the universe in which they exist) according to what they actually are, and the relationship they have with each other. This ‘interaction’ is deterministic. Stochastic situations also arise commonly, but their base is a mathematical, deterministic, field. (tka9) Reality consists of N and the ‘experience’ given to the animate entities by their consciousness; this experience may include consciousness of parts of both animate and inanimate entities in N, and of various relationships among these. Sometimes, loosely speaking, the words ‘Nature’ and ‘Reality’ will be used synonymously. 3.2 Some of the conclusions reached under TK in part II are recorded below for ease of reference. (c1) If E is an animate entity in N, then E has the abstract mathematical form given by E= E (V, W, X), where W is ‘a class of “restrictions” on the consciousness of E, and X is the definition of E in the universe (say, U) in which it exists. (In layman’s terms, in the context of humans, W and X may respectively be called the ‘body of psychic involvements’ of E, and the ‘physical body’ of E. W acts as a class of restrictions on the consciousness of E.) (c2) Both W and X are subject to change with time, and do interact with each other. X changes in accordance with the rules of U and the definition of X. W changes because of the experience that E accumulates. (c3) As W becomes more and more empty, the “consciousness of E” (denoted by “C(E)”) increases more and more. 3.3 Remark R1: We make this remark in order to clarify the nature of consciousness. Consider an animate entity E. Imagine E to be a reservoir of infinite size. Imagine that there are rocks or other stuff in the reservoir because of which the capacity of the reservoir is decreased. Then, “Consciousness’ corresponds to the capacity of the

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reservoir. Also, the class of psychic restrictions W corresponds to the rocks etc. The larger the W is, the less is the capacity (i.e., the ‘consciousness’ of E). V corresponds to ‘total consciousness’; E approaches V, as W becomes totally empty. 3.4 Theory T1 This is adhered to by most physicists. It was proposed by Bohr and Heisenberg, and is often referred to as the ‘Copenhagen interpretation’. Below, we list certain assertions of this theory, and discuss them under the paradigm of TK. The TK viewpoint is presented in assertions marked by symbols of the form (tk:---). (t1a1) There is no deep ‘Reality’. (tk:t1a1) TK disagrees, and maintains that Reality consists of log-mat objects, Consciousness, and their interactions. (t1a2) Before the measurement, the quons have no dynamic attributes. (tk:t1a2) The TK paradigm is different. Exhibiting itself as a particle or a wave (to an observer) is itself an attribute of the Quantum Cloud (QC). So, TK goes in the same ‘direction’ as T1 (but a step beyond T1), and asserts that it is imprecise to talk about quons the way we have been doing. TK asks us to accept Einstein’s statement that Quantum Mechanics (QM) is incomplete. TK requires us to explore the QC. TK says that when we try to measure, say, the momentum of a quon, we are, in the first place, forcing the QC to exhibit the particle attribute. T1 says: “A quon does not have a definite dynamic attribute”; TK makes a stronger statement: “A QC does not have a definite attribute of being a particle or a wave or (possibly) something else, and the measurementact (M-act) forces it to take a stand. If the M-act is going after a dynamic attribute of a particle, then the QC exhibits the particle attribute, and the value of the dynamic attribute (of the exhibited particle attribute of the QC) is the deterministic consequence of the nature of the QC and the M-act, all of which are log-mat objects and therefore interact under the log-mat rules. If the details of the parameters of the QC are known, it should be possible to predict the value of the dynamic attribute; however, until then, a situation like at present (where the said value looks random) will continue. (t1a3) The value of a dynamical attribute (of a quon) depends upon “the entire experimental situation”, and is affected by the relationship between the quon and the Mdevice. (tk:t1a3) Again, as stated above, the TK paradigm is different. But, generally, TK agrees with this. According to TK, the ‘entire experimental situation (where we wish to measure a dynamical attribute of a quon)’ does, indeed, force the QC to exhibit the particle attribute, and the observed dynamical attribute is thus affected by it. However, instead of talking about the relation between an M-device and a quon, we should consider the relation between the M-device and the QC. (t1a4) Before measurement, a quon does not possess a definite value of a dynamic attribute (such as position and momentum), but it does have well defined static attributes.

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(tk:t1a4) Well, TK generally agrees, but goes a bit further. TK says that before an Mdevice ‘interferes with’ (or ‘acts upon’, or ‘goes after’) a QC (say, to measure a dynamic attribute of a quon), the QC is probably in a ‘general’ state that may or may not be in the mode to ‘produce’ (or ‘exhibit’) a quon, on its own. On the other hand, it is clear that if there is no quon before the M-act, then before the M-act there is no dynamic or static attribute either. Thus, TK agrees with T1 on dynamic attributes, but goes further on static attributes. TK says that even a static attribute (like the existence of the particle itself) is a result of the presence of an appropriate environment for the QC. Also, such an environment, though producible by us (by the processes by which we produce conditions to observe a quon), may also get produced on its own by purely ‘log-mat’ (in common language, ‘physical’) processes, i.e., without the involvement of a conscious observer. The author believes that the environments under which a QC takes on a particle attribute occur in relative abundance, and that is why one tends to assume that quons with static attribute exist. Similarly, there is an abundance of situations where the QC may give rise to the wave attribute. (t1a5) Heisenberg has remarked: “Atoms are not ‘things’.” In other words, like a rainbow, they are an illusion. Bohr agrees with the remark.

(tk:t1a5) Well, TK also agrees, but in a different sense, and with a different consequence. Indeed, this remark appears to be more supportive of TK, than of any other theory. TK agrees because it maintains that the experience of the seeming ‘physicality’ of an object is caused by our consciousness, the object itself being only a log-mat structure. Since logic and mathematics belong to the realm of ‘ideas’, a log-mat object is on par with an ‘idea’. Since, in common language, a ‘thing’ is more like a ‘physical object’ rather than an ‘idea’, TK would say that ‘an atom is not a thing’. On the other hand, we know from textbooks in physics and chemistry that molecules are made out of atoms, and since all ‘ day to day things’ are made out of the molecules and atoms, one would conclude that all things are made out of objects that are not ‘things’. The question would then arise as to how an accumulation of objects that are not ‘things’ generates an object that is a ‘thing’. TK rescues Physics from such absurdities. (t1a6) M-devices are like the ordinary objects in classical physics. M-devices and M-acts are beyond the rules of QM, and are not analyzable. (tk:t1a6) TK disagrees strongly. Under TK, no special status is accorded to any object or group of objects. Under TK, the difficulties that T1 faces due to the above assertion are avoided. 3.5 Theory T2 This is primarily due to Professor John Wheeler, who accepts T1 but adds certain new elements. We consider some assertions below. In connection with T2, he also discussed the ‘galactic lens’. But, that will be discussed in section 4.

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(t2a1) ’Reality’ is created by the act of observation. (tk:t2a1) The comment will be in several parts. Part I. TK says ‘yes’ and ‘no’. Suppose an observer has two rooms in his house, one of which has a chessboard and no other game, and the other has a deck of cards and nothing else. He selects a room and plays a game. Then, he will ‘create’ one of two realities: either play chess or play cards. Thus, in this sense, the experimenter does create ‘Reality’, in agreement with T2. Part II. However, under TK, a deeper situation exists. ‘Reality’ is already there in the Nature N in the form of log-mat objects. Given an animate entity E, the consciousness of E (i.e., C(E)) reveals to E a few of these objects, which then constitute his ‘observation’. In this sense, in agreement with T2, one can loosely say: “The consciousness of the observer creates his ‘Reality’”. But, such expression would be ‘loose’ and not ‘precise’, since the ‘Reality’ is already there in the form of log-mat objects, and the C(E) merely reveals some of it to E, giving to E an ‘observation’. The difference between T2 and TK is that the latter says that ‘Reality’ is not ‘created’ by the observer; rather, it is ‘perceived’ or ‘experienced’ by him or her. (t2a2) Wheeler often stated: “No phenomenon is a real phenomenon, unless it is an observed phenomenon”. (tk:t2a2) TK says ‘yes’ or ‘no’ depending on what we mean by the words ‘real’ and ‘phenomenon’. Under TK, the Nature N is full of log-mat objects, which interact with each other (without any necessary interception of an observer), causing (log-mat) ‘phenomena’ to arise; in this sense, TK disagrees with Wheeler. But, if we say that a phenomenon cannot be called ‘real’ unless it has been perceived by some one, then TK agrees. It should be emphasized here that the log-mat world, though it certainly exists and constitutes the deep Reality, is not perceptible to inanimate entities. Observers are, of course, animate entities, and their consciousness gives them the perception of the existence of some objects of the log-mat world; however, that perception converts the log-mat object into some form of physical reality. But, this perception is not unique for different entities, because it is dependent on the W and X of the observing entity E(V,W,X). For example, the same electromagnetic wave may be seen as green by a human and a shade of gray by an animal. The same sound wave may be audible to an insect but not to a man. The same cheese may be likable to one person but disagreeable to another. In this sense, TK supports Wheeler even more than what perhaps he himself imagined, because the reality of being green to one observer and gray to another, is obviously ‘created’ by something in the observer. (t2a3) Only elementary phenomena are not real until they are observed. [Herbert (1985) stated (p.167) that Wheeler emphasized this remark, but many others (like, for example, Mermin) disagreed, and applied T2 to all phenomena.]

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(tk:t2a3) Again, as explained above, under TK, the basic Reality is of log-mat nature, and exists by itself, independently of observers. However, only an observer can perceive this basic Reality, and any observer perceives it only as physical reality. But, as we elaborated above, this physical perception itself depends on the observer. Under the TK paradigm, obviously, all phenomena are included, and we need not worry about what constitutes ‘elementary’. 3.6 Theory T3 The chief architect of this theory is Bohm. (t3a1) ‘Reality’ should be looked upon as a Whole, not necessarily divided into parts. (tk:t3a1) In general terms, TK agrees with this. TK regards Nature N as having emanated out of V; this is in the spirit of Goedel’s remark that “Mathematics is the study of subsets of the empty set”. (Wang (1988)). Under TK, V, N, and Consciousness, constitute the ‘Whole’. But, Consciousness is a property of V, and N emanates from V. Thus, in a sense, ‘Reality’ (which is also the Whole) is contained in V. Because of this, the Whole is contained in every part of Itself. If the Whole is taken out from the Whole, then the Whole still remains. Thus, readers who are familiar with Bohm’s ideas on the ‘implicate order’ etc. will find them echoed in TK. However, Bohm had the theory of ‘pilot waves’ in this connection. The author considers this theory to be premature. Under TK, it is expected that the theory of the QC will be developed from the base of the current Quantum Field Theory. (t3a2) Consider two quons. As they come close, their proxy waves come together, and also their phases get entangled. When they separate out, the waves go apart, but the phase entanglement continues. In this way, in a sense, every thing in the universe is entangled together. (tk:t3a2) As Schroedinger said, the above is a very important fact. This fact should be looked into more closely. It turns up in the Aspect experiment as well. It is expected to play an important role in the development of the theory of the QC. Many believers of theories T1 and T2 play down this fact; the author disagrees with them on this matter. 3.7 Theory T4 Everett proposed this theory as a part of his Ph.D. thesis at Princeton in 1957. (t4a1) Consider an experiment that is such that if it is actually done, then it would lead to k different outcomes. Now, suppose this experiment is actually done. Then, our universe (in which we exist) will generate (k-1) copies of itself, so that there will be k universes in all. These universes will be alike in all respects. In one of them, the experimenter will be present; in the remaining identical copies of the experimenter will appear. The universes will differ in only one respect, namely, that in the different universes, different outcomes of the experiment will appear.

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(tk:t4a1) The theory T4 does not tell wherefrom the (k-1) new universes, with all the matter in their galaxies and black holes, shall spring. Apparently, all this matter in the new universes shall spring out of nothing. The same is true even more of living beings in the universes. Without belaboring the point further, it should be clear that if all these universes are getting created out of nothing, then they should be universes of ideas only, like what TK postulates. Without leaning on TK, the theory appears to be extremely farfetched and untenable. But, even under TK, the author believes that the theory probably involves basic logical contradictions, and so may not be supportable without appropriate modifications. (t4a2) Theory T1 gives a special status to an M-device. But, T5 solves that problem by not requiring such status. (tk:t4a2) Theory T1 is erroneous on this issue. In any case, the ‘solution’ offered by T4 is too extravagant. 3.8 Theory T5 This was professed by Finkelstein. (t5a1)There are many sectors of Reality, where the Boolean logic needs to be replaced by other systems of logic. Quons belong to such a sector. (tk:t5a1) It is true that in many universes, a different logic-system may rule. TK shows the existence of infinite number of universes, and it is easy to come up with a universe that is based on a mathematical system where a non-Boolean logic is the rule. However, the phenomena in Nature including the elementary particles are too profound to be resolved just by using a different logic. On the other hand, since TK asserts that Nature consists of log-mat objects only, the role of logic in the development of TK cannot be exaggerated. Thus, for example, the developments that have been inspired by T5 in logical realms where the distributive law does not hold should prove useful. (t5a2) In the 3-polarizer experiment, the phenomenon can be explained by saying that the photons obey a non-distributive logic. (tk:t5a2) Part I. This is true. However, the field of QR abounds in complex questions where such assumptions do not help much. Moreover, the statement under consideration is an observation as much as an explanation. It gives rise to a new question: Why do photons obey a different logic? Part II. Under TK, the 3-polarizer phenomenon is explained in a simple manner. Consider the space available for the QC. When only two screens, Sv and Sh, are used, the polarization is in two consecutive directions at right angles to each other. Thus, in this case, the ‘space for the QC’ (i.e., the space that is available to the photons for passing through) has one particular structure. On the other hand, if a screen Sd is placed in

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between Sv and Sh, the structure of the ‘space for the QC’ is changed drastically. In the first case the space available for the definition of the QC is of one kind (that blocks photons), in the second case it is of a different kind (that allows photons to pass). It is this ‘space for the QC’ that Quantum Mechanics is correctly taking into account in its explanation of the phenomenon. 3.9 Theory T6 Often called ‘realism’, this theory contains the ideas of Einstein, Schroedinger, and others. Generally, this theory is at variance with T1. (t6a1) As in Herbert (1985), let us call an object to be a ‘ordinary object’ if it has attributes of its own, independently of whether it has been observed or not. Then, T6 says that a deep Reality does exist, that it is full of ordinary objects only, and, furthermore that it is deterministic. As Einstein said : ”God does not play dice.” (tk:t6a1) Part I. TK agrees that a deep Reality does exist, but it insists that the physical world that our senses experience is only seemingly so, and that in Reality, objects are log-mat objects. Because, all objects are log-mat objects, they interact in a deterministic fashion. However, this can and does create situations that look random (particularly when the situation is influenced by a lot of factors, and we are ignorant either of the factors, or the paradigm under which they interact, or both). Part II. Theorists of T1 consider two particles (say, electrons) that appear to be totally ‘identical’; they point out that if you measure some attribute on two such electrons that are in ‘identical’ situations, then you may find that the values of the attribute are different for the two particles. From this, they conclude that there is an inherent randomness present in the Nature. Einstein disagreed with this, saying that ‘The Lord does not play dice’. TK agrees with Einstein on this. Under TK, the electrons are themselves attributes of QC’s, and the values of the attribute turn out to be different for the two electrons because the other parameters of the two QC’s are probably not the same. The current confusion is further enhanced because the paradigm under which the QC’s exhibit electrons is also not known. Part III. On the question of the world being populated by ‘ordinary objects’, TK says ‘yes’ and ‘no’. If it is understood that all objects in Nature are log-mat objects alone, then TK says a strong ‘yes’, because these log-mat objects are independent of observers, and exist on their own. However, on the question whether an electron possesses definite dynamic attributes (as T6 suggests), TK disagrees. This is because, even under the TK paradigm, the measured value of an attribute of an electron is, as Bohr said, dependent on the entire M-situation. Indeed, under TK, the electron itself is only an attribute of the QC, and since the QC does not exhibit that attribute except under appropriate conditions, the electron cannot even be said to exist all the time. However, as remarked earlier, it seems that appropriate conditions for a QC to exhibit the particle attribute exist relatively quite often, and that probably is the reason why it appears as if the particle exists (all the time).

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So, an electron (or, indeed, any quon) is only an appearance, which occurs rather quite often, and acts with rules that are quite precise. Part IV. In maintaining that Nature is full of ‘ordinary objects’, the theory T6 is asserting in particular that the quons have definite attributes, i.e., there is an element of reality associated with them. This is often referred to as ‘realism’ or ‘neo-realism’. TK does not agree with this basis for ‘realism’. However, TK posits another kind of realism, namely, the world of mathematical objects, and their experience by different animate entities. (t6a2) Let us refer to sec. 2.4 of this paper, and recall the discussion and the notation from there. Einstein, Podolsky, and Rosen (EPR) (1935) had put forward a thought experiment, a different version of which was looked into by Bohm, which eventually culminated in the experiment by Clauser, and then by Aspect. These experiments closely confirmed the predictions of QM, as summarized in sec.2.4. How does TK stand with respect to these? (tk:t6a2) Part I. In sec. 2.4 m, we saw that the majority of people in the physics community have reached the conclusion that Einstein was incorrect in assuming that there is a separate reality associated with each photon inside a pair, and that there is some faster than light communication going on. Part II. Now, TK has a different paradigm. Under TK, it is not meaningful to talk about ‘two photons of a pair are coming out from the calcite crystal, and moving in opposite directions towards D1 and D2’. According to TK, this last statement (in single quotes), even though seemingly quite obvious, is still incorrect. Because it is not valid, it removes the base using which Bell’s theorem is applied to the Aspect experiment. Thus, TK says that the Bell’s theorem is not applicable since the paradigm is different. Part III. Then, what is the TK paradigm? It is this. From the polarization detector D2 through the source O to the detector D1, there is a space which varies as we change the distances d2 and d1 and the angles q2i and q1i (for the ith ‘pair’). [Note that the word ‘pair’ is in quotes because, under the TK paradigm, the usage of this word has to be understood in a different way. The statement: “The crystal at the source O is birefringent, and there are two detectors D1 and D2 respectively at distances d1 and d2 , and at angles q1i and q2i” translates into the following under TK: “A QC is arising that shall exhibit two photons respectively at the two points where the two detectors are. This QC is dependent on the entire space between D1 and O and D2, including the distances d1 and d2, and also the angles q1i and q2i. The QC depends upon the difference (q1i-q2i). Since d1 can have any value, and the time of detection shows that detection occurred at D1 at a time when a particle starting from O and moving at the speed of light would have reached D1, it appears as if all along a particle started at O and moved towards D1 at the speed of light. The same is true of D2.” Part IV. The TK paradigm continues: “Now, it is not precisely true that ‘a particle moved out of O and was detected at D1’; hence, we shall instead use the phrase ‘An act of making a QC was done at O, and a ‘detection-event’ occurred at D1’. “

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Part V. TK says: ”What actually happens is that the QC starts forming ‘when the act of making the QC is done at O’. Next, the QC remains in its general state until the detection-events at D1 and D2. While in the general state, the QC keeps adjusting its form, if necessary, maintaining, in particular its dependence on (q1i-q2i). If, suddenly, d1 is changed to d10 and/or q1i is change to q1i0, the whole QC changes instantaneously, irrespective of the values of d1 and d2, i.e., irrespective of how big it is. Because, inside Reality, this happens, we can say that there are superluminal (faster than light) influences going on. However, all of Reality is really a logical-mathematical world, and TK says that there are spatial (more precisely, space-time) universes defined inside this over-all world. Part VI. “To elaborate this, we can compare the overall Reality to a computer program, which is a bunch of logically connected statements. To fix ideas, let us take an example, and assume that the purpose of the program is to depict the play ‘Macbeth’ on a screen. The way the programs are written, for this program too, various variables (representing various things) will be introduced. All these variables can be instantly made to act upon each other. The same is true of Reality. On the other hand, inside the overall program, consider the problem of creating a battlefield with fighters who fight each other. For this, assuming that the battlefield is going to be rectangular, we create a rectangular region. Inside this region, we set a suitable limit to how fast an icon representing a fighter can walk or run or do other things, Such a speed limit corresponds to the speed limit for our universe, postulated by Einstein. This also explains how a spatial universe may arise out of a logical-mathematical realm. Part VII. “Inside any space-time universe, there is a speed limit. So, TK maintains that Einstein’s speed limit is correct in a spatial sense, but it does not hold in the logical realm. Because Reality is really a log-mat world, inside which spatial universes exist, there are instantaneous influences in the overall realm, and speed limits in spatial universes inside it. The last remark that “The spatial universe (which the astronomers study) is a part of the overall logical-mathematical world of Reality” should be emphasized. ‘Outside’ the spatial universe, there is the main realm of ideas, and ‘spooky action at a distance’ can and does occur. The so-called psychic phenomena are possible. Anything is knowable to an animate entity E(V,W,X), if E is ‘pure’ enough, i.e., if the associated W is ‘small’ enough.” Part VIII. What about Bell’s theorem? TK says this: “Since the TK paradigm is different, the computations of Bell’s theorem are not applicable to the Aspect experiment. The theory of QM works because it correctly posits a property of the QC, namely, the Wave Function (WF). But, as stated earlier, the real WF (RWF) (called QC herein) is a bigger mathematical object, of which the WF is a marginal projection. Our ignorance about the RWF shows one direction in which QM is incomplete. 3.10 Theory T7

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The seed of this theory was sown by the great mathematician von Neumann, and friend Wigner. Stapp (1993), Goswami (1990), and Kafatos and Nadeau (1993) have authored books supporting this position. Some very strong arguments that ‘consciousness’ transcends ‘computation’, will be found in the book by Penrose (1994). (t7a1) We believe in theory T1, but add one postulate. It is that when we measure a quon’s dynamic attributes, the value that we obtain for the attribute is created by our consciousness. This also resolves the measurement problem under T1 because , unlike in T1, we do not need to assign a special status to an M-device. (tk:t7a1) Part I. In a way, the theory T7 is the closest to TK, because ‘Consciousness’ does play a very large role in it. Two questions need to be investigated under T7 first, before others can be taken up. The first question is : “What is ‘Consciousness’?”, and the second is: “How does ‘Consciousness’ pick the value of the attribute?” Under TK, the author has shown in Part II (of this series of papers) that ‘Consciousness’ is intimately connected to the totally empty set V, and for any animate entity E(V,W,X), the C(E) depends on W and X. But, what is the nature of this dependence needs to be thoroughly studied. Under TK, we live in Reality that is populated by log-mat objects, and the question is how are the attributes of the QC revealed to ‘Consciousness’. Thus, the questions are similar under T7 and TK, and a combined study may be useful. Part II. The main difference between T7 and TK is that, like the other theories, T7 also does not tell how ‘physicality’ arises. TK is able to address questions outside the realm of physics, and shows that there is an underlying unity in all the realms. T7 has to contend with the burden of much of T1 that it still carries. 3.11 Theory T8 This theory is due to Heisenberg as an add-on to T1. (t8a1) We consider the question of the state in which a quon exists when it is not being put to any measurement, and what happens during measurement. It is postulated that a quon normally exists in a state that we shall call ‘potentia’, but when it is subjected to an M-device then one of the potential choices becomes an actuality. For each attribute, the potentia represents a mixture of possible values that an attribute can take. (tk:t8a1) The author believes that the phrase ‘a mixture of the possible values that an attribute can take’ does not imply a mixture in the ordinary physical sense. Such a mixture is in the realm of possibilities. But, a ‘possibility’ is a ‘idea’. Thus, it appears that the potentia are in the realm of ideas. So, Heisenberg is unknowingly standing in the domain of TK. He does not tell how a ‘possibility’ (which is an idea) turns into an actuality (which corresponds to a physical object). Obviously, TK gives a clear-cut answer. The fact that Heisenberg propounded T8 is very supportive of TK. 4.CONCLUDING DISCUSSION

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The purpose of this section is to integrate the previous discussion, bringing in new elements not touched upon thus far. This discussion will be continued in later papers in the part III sub-series of this series of papers. Many other authors (only a few of whom have been included in the references below) have produced profound works, and TK will be discussed in the light of those questions as well. Besides, various other independent sectors shall be opened showing that TK appears to be not only the most plausible theory, but also the theory that can bring together the different viewpoints. 4.1 Recall the discussion on QC in the last section. In [tk: t5a2II], the QC was explained under the three- polarizer experiment (sec. 2.4). The Aspect experiment (sec.2.5) was similarly covered in [tk:t6a2III,V]. One of the main points therein is that the QC depends on the available space (under a non-relativistic setting). It is to be emphasized that “available space” refers not only to size, or the overall dimensions, but the entire shape in all its details. This is confirmed by DC1 and DC2 of sec.2.6. 4.2a Thus, consider the double–slit experiment (sec. 2.2). We explain the TK viewpoint in a suggestive, intuitive, language. When both slits g and h are open, and there are no detectors dg and dh, then the ‘available space’ is the space between the source S up to the barrier A, and through the two slits to the screen B. This situation is not forcing the Quantum ‘Cloud’ to create the ‘drop’ (i.e., a ‘particle’); rather, it gives the QC the freedom to be in a ‘defused state’ (like a ‘fog’). It would remain diffused, but the screen B causes the ‘fog’ to interact with itself, resulting in what we see as interference. 4.2b On the other hand, suppose dg and dh are both present. Now, obviously, the shape of the space is much changed. The fact that dg is a detector causes the QC to ‘condense’ into a drop, same being the case for dh. When both dh and dg are present, two drops are not produced, because it is a QC which can produce only one drop. When only one detector (say, dg) is present, the QC ‘condenses’ in it, because through the other slit (h) the space is too open which avoids ‘condensation’. 4.3a Consider now the Stern- Gerlach (SG) experiment which is already discussed to some extent in sec. 2.3. Recall assertion ga6. Suppose, we pass an electron beam B` through SGAz. Then, two cases arise, depending upon whether B` itself is coming out of the SGAz or not. If B` is coming out of SGAz, then by making it go through SGAz again, only B` will come out. If B` is not coming out of SGAz, then B` shall split into two beams B`z+ and B`z-. This is true of any direction z that we choose in our 3-dimensional space. 4.3b Thus, in particular, we could have B`= Bx+, for some beam B, which shows that when B is passed through SGAx, it produces a beam in the direction x+ and/or x-, but SGAx causes a randomization in the directions such as z. Again, x and z represent any two mutually orthogonal directions in our 3-d space. It is clear that there is a lot of mechanism and structure associated with an electron. But, recall assertions a1 and a2 from sec. 2.1, which talk about the electron being a point particle that, nevertheless, has spin angular momentum. Also, recall that the spinning axis makes an angle of 54.7 degrees with the direction in which we wish to measure the spin.

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4.3c It is clear that we are in the ‘elephant and blind men’ situation, where the electron corresponds to the elephant, and the experience of the blind men to the different properties that we come across. However, unlike T1, TK does not end here saying that we have reached the limits of what can be known. Indeed, all the facts that we recalled in sec. 4.3b throw light on the nature of the QC. An accumulation of such facts shall lead to various hypotheses on the QC, some of which may suggest some further experiments, leading to advancement. 4.4a Herbert (1985, p. 142) presents several aspects of what he calls the ‘quantum measurement problem’ (qmp). We now consider some issues of the qmp along with a few other questions arising out of the discussion in the previous sections. More complicated issues will be considered in the future papers. 4.4b One aspect of the qmp concerns the question: ‘Where lies the boundary between the world of classical objects and the world of quantum objects?’ TK answers this by saying that under its paradigm, all objects are log-mat objects only, and the problem of the said boundary does not arise. However, as in all of Science, there is the boundary between what is ‘clearly’ known, and what is known with various degrees of fuzziness, and what is totally unknown. But, this boundary keeps changing as knowledge advances. 4.4c Another aspect is: “T1 says that QM is complete, but under QM we find that two quons that look identical in all respects end up giving different values of a given attribute, when measured. At what point do identical quons start to produce differences?” Well, according to TK, this production of differences is not because of some inherent randomness that is present at the deeper level. Under TK, the quons themselves are attributes of the QC, and although identical quons are produced by the QC (whenever it produces them), the rest of the ‘environment’ within the QC is not necessarily identical for the two quons. However this environment does influence the measured value of the attribute in a deterministic fashion, though details of the fashion are yet unknown to us. 4.4d Consider a photon of unpolarized light. Suppose it is passed through the screen Sd. Next, suppose it is passed through Sv; now, it will either come out as a v-polarized photon or be absorbed. Under T1, the d-polarized photon lives in a mixed state of the ‘possibility’ of being either v-polarized or h-polarized. But, when it hits Sv, an ‘actuality’ occurs: either nothing comes out or a v-polarized photon comes out. Herbert asks as to how the transition from ‘possibility’ to ‘actuality’ occurs. From the previous discussion in this paper, it is clear that under TK we do not talk about the photon moving here and there and being in this state or that. We talk in terms of the QC. At the screen Sv, the QC is either absorbed or changed into a form that ‘corresponds’ more to a v-polarized photon. How the QC ‘partly condenses’ into a quon is an important topic of study. 4.4e Continuing, suppose after Sd, we create two directions where the output from Sd could go, namely a screen Sv and also a Sh. According to T1, ‘the photon takes both paths’; yet, at the end we find that the photon is detected either at Sv or at Sh. The question is how the two paths become one. However, under TK, the situation is simple.

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There is the QC all the time, and it occupies all the available space. But, if the QC corresponds to one particle only, then it ‘partly condenses’ only at one place. Thus, the above kinds of questions do not arise. 4.4f Under what conditions does the wave function (WF) collapse? Recall that, under TK, the QC is the RWF. How it transforms and how it produces quons or wave interference are topics for further study. 4.5 We conclude this paper by saying that TK tends to unite the insights in different theories, while at the same time bypassing the dilemmas. 5. REFERENCES Baggott, J. (1992) The Meaning of Quantum Theory. Oxford University Press, New York, NY. Feynman, R. (1985) QED. Princeton University Press, Princeton, NJ. Goswami, A. (1993) The Self Aware Universe. Tarcher/Putnam, New York, NY. Griffiths, D. J. (1987) Introduction to Elementary Particles. John Wiley, New York, NY. Griffiths, D. J. (1995) Introduction to Quantum Mechanics. Prentice Hall, Upper Saddle River, NJ. Herbert, N. (1985) Quantum Reality. Double Day, New York, NY Kafatos, M., and Nadeau, R. (1990) The Conscious Universe. Springer Verlag, New York, NY. Kaku, M. (1993) Quantum Field Theory. Oxford University Press, New York, NY. Penrose, R. (1994) Shadows of the Mind. Oxford University Press, New York, NY. Rothman, T., and Sudarshan, G. (1998) Doubt and Certainty. Perseus Books. Reading, MA. Sakurai, J. J. (1994) Modern Quantum Mechanics, Addison Wesley, New York, NY. Schäfer, L. (1997) In Search of Divine Reality. The University of Arkansas Press, Fayetteville, AK. Srivastava, J. N. (2001b) Effect of Space and Environment on the Wave Function in Quantum Mechanics. (Abstract) Bulletin of the American Physical Society, Four Corners Meeting, Las Cruces, New Mexico, November 2001.

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Srivastava, J. N. (2001c) Foundations of Reality. Proceedings of The International Association on New Science, 11th Forum, pp75-78. Srivastava, J. N. (2002a) On the Falsity of Certain Conclusions Commonly Drawn from Applying Bell’s theorem to Physics Experiments. (Abstract) Bulletin of the American Physical Society, Annual Meeting, Albuquerque, New Mexico, April 2002. Srivastava, J.N. (2002b) Life Comes from Life, Part I: An Overview. Savijnaanam (Scientific Exploration for a Spiritual Paradigm) vol.1, pp 21-30. Bhaktivedanta Institute, Kolkata. Srivastava, J.N. (2003) Life Comes from Life, Part II: Consciousness, Life, and the Validity of the Bhagvad Geetaa Ontology. Savijnaanam (Scientific Exploration for a Spiritual Paradigm) vol.2, pp 19-42. Bhaktivedanta Institute, Kolkata. Stapp, H. P. (1993) Mind, Matter, and Quantum Mechanics. Springer Verlag, New York. Stenger, V. J. (1995) The Unconscious Quantum, Prometheus Books, Anherst, NY. Wang, Hao (1988) Reflections on Kurt Goedel. MIT Press, Cambridge, MA, USA. THE END ………….. JSK

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