The Double Helix Theory of the Magnetic Field (An interpretation of Maxwell’s 1861 paper ‘On Physical Lines of Force’ parts I to III) Frederick David Tombe, Belfast, Northern Ireland, United Kingdom, Formerly a Physics Teacher at, College of Technology Belfast, and Royal Belfast Academical Institution, [email protected] 15th February 2006, Philippine Islands (9th April 2006 amendment)

Abstract. Maxwell’s 1861 paper ‘On Physical Lines of Force’ (parts I to III) is interpreted, and an improvement is proposed which involves replacing his vortex cells with rotating electron positron dipoles. The cause of magnetism is then explained in terms of a vortex sea of electron positron dipoles, in which magnetic field lines are comprised of helical springs created out these dipoles. The electron positron dipoles are bonded together in a double helix pattern and the resulting helical springs close on themselves in elliptical or circular solenoidal hoops. James Clerk-Maxwell published his paper 'On Physical Lines of Force' in 1861 in the Philosophical Magazine [1]. http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf

The Interpretation I. In part I of his 1861 paper ‘On Physical Lines of Force’ [1], Maxwell proposes that magnetism can be explained by the pressure differential between the axial and the equatorial planes of a vortex sea, in which the vortices are aligned along their axial plane, and all rotating in the same direction. He considers that a tension exists in the axial plane, and that a centrifugal pressure exists in the equatorial plane. He justifies his proposal by introducing the equations of mechanical equilibrium and combining them with his vortex theory of pressure differential, and showing that such an arrangement would explain the mathematics of some important aspects of magnetism. In doing so, equation (1) in Maxwell’s paper gives us the relationship between density and magnetic permeability, which proves to be of ultimate importance in the final conclusion of his work, when he carries this result forward into equation (132) of part III. Maxwell attempts to reconcile his mathematical results with his physical model, and he arrives at some interesting explanations. He explains the alignment of a bar magnet in a magnetic field in terms of differential axial tension in his vortex columns, giving rise to a torque. He discusses a very interesting aspect of magnetism that sheds light on the mystery of the phenomenon of diamagnetism, and which would appear to be the ‘Archimedes Principle of Magnetism’. It could be inferred from what he says, that ferromagnetic materials contain within them a vortex sea, which is denser than that which pervades outside of matter, whereas diamagnetic materials contain within them a vortex sea, which is less dense than that which pervades outside of matter. He explains the force on a current carrying wire in terms of a pressure in the equatorial plane of the vortices, pushing from behind. This explanation is of considerable interest, in that it may be adequate as far as a current in a wire is concerned, but it would fail to account for the extension of this concept to the motion of a charged particle in a magnetic field as per the Lorentz force,

E = vXB

(Lorentz Force)

(1)

(see Appendix A for a discussion on the format of equation (1)) Towards the end of part I, Maxwell deduces that the primary force involved in magnetism must obey an inverse square law, and he cites this fact as having already been shown by Coulomb. He finishes by deriving the equations for the force acting between two long straight current carrying wires, and showing that the force must be inversely proportional to the distance between the wires. In part II, Maxwell introduces electrical particles in order to drive the vortices, and to link them to the current in electric wires. His aim was to connect the phenomenon of magnetic attraction to the phenomenon of electromagnetic induction. Again we observe Maxwell’s method in which he first proposes a physical model, upon which he builds a mathematical model. The mathematical model (equation (77), see Appendix A) in turn leads to physical predictions that he then attempts to reconcile with his physical model. His mathematical model appears to explain Faraday's law of electromagnetic induction, although there appears to be a deficiency in his attempt to reconcile one aspect of Faraday’s law with his physical model. There are two aspects to electromagnetic induction. There is induction in a static wire in a time varying magnetic field, and there is induction in a moving wire in a static magnetic field. In relation to the latter, Maxwell’s explanation involves some of the principles that we might expect to be involved when attempting to explain velocity dependent air resistance. His explanation involves a pressure build up in front of the motion, which would inevitably lead to the conversion of kinetic energy into potential energy, which in turn would be dissipated into the vortex sea. This could explain the de Broglie wave nature of particle motion, and may become more noticeable at high speeds, but it is not a satisfactory basis for explaining the Lorentz force. The Lorentz force is indeed a velocity dependent force, but the solution to its motion is helical and it involves no energy transfer from kinetic to potential. The Lorentz force by its very nature would tend to defy any explanation in terms of elasticity, and so despite the mathematical success of Maxwell’s method, it does not physically account for the Lorentz force. Maxwell had failed to notice the connection between equation (77) and the Coriolis force. In part III, Maxwell considers the elasticity of the individual vortex cells in connection with displacement under the action of an electric field, and in doing so, he concludes that each vortex cell possesses the characteristics of transverse elasticity associated with a perfect solid. He derives Coulomb’s law of electrostatics and then combines the mechanical equilibrium conditions with the electric field force, and establishes an equation linking electric permittivity to transverse elasticity. Equation (132) is an equation from classical wave mechanics (see Appendix B) which links wave speed in an elastic medium with density and transverse elasticity. Maxwell substitutes these parameters with magnetic permeability and electrical permittivity, and using the experimental results obtained by Weber and Kohlrausch in 1856, in which they calculate the ratio between the electrostatic and the electromagnetic units of charge, he obtains a wave speed equal to the speed of light. This result should have left nobody in any doubt that light is a transverse electromagnetic wave in a vortex sea. On discovering this result, Maxwell stated “ - - - we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena --“

Displacement Current II. An interesting side issue in part III of Maxwell's 1861 paper is his mention of ‘electric current due to displacement’. From his equation for displacement in the vortex cell under the action of an electric field, we can easily deduce the modern day equation, J = −dE/dt

(Current Density)

(2)

which, as with all the equations below, includes a constant of proportionality depending on choice of units. Equation (2) can be corroborated if we take the divergence of both sides and apply the equation of continuity of charge, div J = −dρ/dt

(Equation of Continuity of Charge)

(3)

and Coulomb's law of electrostatics, div E = ρ

(Coulomb’s Law of Electrostatics)

(4)

Maxwell goes on to develop the idea of ‘Displacement Current’ in his 1864 paper [2], and the involvement of Coulomb’s law in current density becomes a factor of major significance. Maxwell believed that in the dielectric medium between the plates of a charging capacitor, a polarization is occurring which must give rise to a displacement current in order to maintain the solenoidal nature of the circuit current , and in order to avoid having a discontinuity of the magnetic field between the capacitor plates. Between the plates of a charging capacitor in an electrical circuit, E will be equal to Eo − Ei, where Eo is the steady electric field driving the circuit current, and Ei is the induced electric field that opposes the displacement process in the capacitor dielectric (Lenz’s law). It therefore follows that −dE/dt will equal +dEi/dt. Displacement current is a form of magnetism, and to prove this we can use the equation, curl B = +dEi/dt

(Ampère’s Circuital Law-Time Varying)

(5)

to derive a wave equation, by combining it with Faraday's law of electromagnetic induction, curl Ei = −dB/dt

(Faraday’s Law of Electromagnetic Induction)

(6)

The result is a wave equation with a propagation speed equal to the speed of light, d²Ei/dx² = 1/c².d²Ei/dt²

( Electromagnetic Wave Equation )

(7)

In part III of his 1861 paper, between equations (132) and (136), Maxwell shows that electromagnetic waves are transverse elastic disturbances in the vortex sea. We have now also seen from the above proceedings that the concept of displacement current can demonstrate exactly this same fact, yet neither of these two Maxwellian approaches get taught in the universities today. The former approach, which conceals E=mc² in equation (132) (see Appendix B) has been totally swept under the carpet, despite the fact that it is the jewel in the crown of Maxwell’s entire career. The latter approach has been modified in such a way as to conceal the need to have a dielectric medium pervading throughout space, yet it is arrant nonsense to try to suggest that displacement current can occur in the absence of a dielectric medium. Kirchhoff, the father of cable telegraphy, derived what was essentially equation (7) in 1857 [3], without consciously using the concept of displacement current. Kirchhoff believed himself to be working inside the electric wire, but the subsequent extension of his telegraphy equation to coaxial cable suggests that he was actually working outside the wire without realizing it. In taking the telegraphy equation into the wider space beyond the wire, it is imperative that space be filled with a dielectric medium, and it is Maxwell’s concept of displacement current which makes Maxwell the father of wireless telegraphy. The dielectric medium is necessary, not only to give physical meaning to displacement current, but also to account for the relationship between Coulomb’s law of electrostatics and Faraday’s law of electromagnetic induction. Coulomb’s law of electrostatics is involved in displacement current, and hence also in Faraday’s law of electromagnetic induction, because it is the primary force acting at femtoscopic level between the particles of the dielectric, whereas the actual Faraday’s law itself covers macroscopic phenomena associated with elastic stresses in the dielectric medium as a whole. If Coulomb’s law were not the root cause of Faraday’s law at femtoscopic level, then we would not be permitted to amalgamate equations (5) and (6) to derive the electromagnetic wave equation (7), because the Ei terms in each equation would have different meanings, and hence could

not be equated to each other during the amalgamation procedure. It is clear that we are dealing with a neutral sea of particles on a scale many orders of magnitude smaller than atomic and molecular matter. The obvious choice for what these particles ought to be is electrons and positrons, as these are the only stable pairs of particles on that scale which are known to exist. The very distinct de Broglie waves which are associated with beams of electrons, would give strong evidence that these electrons are reacting with particles in a medium on their own scale, and Maxwell said in part II of his 1861 paper, in the paragraph following equation (34), “It appears therefore that, according to our hypothesis, an electric current is represented by the transference of the moveable particles interposed between the neighbouring vortices - -“. There can be no other way in which to account for the relationship between Coulomb’s law and Faraday’s law, other than by a sea of electrons and positrons. Even years before Oersted discovered electromagnetism, he had suspected that electricity lay at the root of magnetism, and the subsequent use of the quantity electric charge in all electromagnetic equations indicates that this is so, without even concerning ourselves with all the above considerations about displacement current. Oersted’s discovery in 1820 when combined with the discoveries of Benjamin Franklin, relating to lightning and the fact that two kinds of electric charge exist, should have been sufficient evidence for us to have been able to deduce that a dielectric medium pervades throughout space, and indeed in 1839 such a medium of positive and negative particles was already being discussed. The Rev. Samuel Earnshaw produced a paper [4] entitled ‘On the nature of the molecular forces which regulate the constitution of the luminiferous ether’, which contains a theorem demonstrating that any such arrangement involving only the Coulomb force could not exist as a static lattice. They were nearly there! All they had to do was rotate the unlike particles into pairs of orbiting dipoles. More recently Dr. Menahem Simhony has proved beyond any doubt that a physical medium of electrons and positrons pervades what we customarily accept to be the vacuum, and his theory comes from within the discipline of solid state physics, and is totally independent of the discipline of electromagnetism. You can read more about Dr. Simhony’s theory in this web link, http://web.archive.org/web/20040606235138/www.word1.co.il/physics/mass.htm Dr. Simhony has essentially shown that the equation E=mc² is an equation from classical wave mechanics (see Appendix B) and that it applies to ion pair production in a salt crystal, with E representing ion binding energy and c being equal to bulk wave velocity. Simhony applies this equation to the 1932 Carl Anderson electron pair production experiment and shows that the Gamma rays are merely liberating electrons and positrons from their bonds and that as such, a background electron positron medium is a very real physical thing.

The Dipole and the Vortex Sea III. I am proposing that Maxwell's vortex cell is a rotating electron positron dipole driving a vortex inside it. I am proposing that if a randomly arranged sea of electrons and positrons is created, it will eventually settle into an equilibrium state dictated by Coulomb’s law of electrostatics. This equilibrium state will take the form of a sea of mutually orbiting electron positron dipoles whose average diameter will be determined by the initial energy conditions. I have used Dr. Simhony’s application of E=mc² and applied it to orbital kinetic energy theory (see Appendix C) and I estimate that these dipoles will have a diameter in the order of femtometers with tangential speeds of the order of the speed of light. When a magnetic field exists, these dipoles will be aligned along their axial plane and rotating in the same direction as each other. In the axial direction, the Coulomb force will create tension, and the reason why the columns of dipoles will not collapse under this axial tension is because they are solenoidal and will form closed elliptical or circular hoops, and because the bonds between neighbouring dipole columns will be repulsive, due to centrifugal pressure in the equatorial plane. When the like particles of dipoles of adjacent vortex columns come close together, we will experience repulsion. When the unlike particles of neighbouring vortex columns come together, we will have an attraction, but due to the mutual tangential velocities, the particles will not be linearly accelerated together along their lines of connection. This is a fundamental fact of classical central force orbital mechanics, and it is the reason why the Moon doesn’t fall to the Earth. The Moon is centripetally accelerated towards the Earth, but it is not linearly accelerated along its line of contact with the

Earth. This argument can be isolated for the special case of two particles acting under a mutually attractive inverse square law, in circumstances in which they have exceeded their mutual escape velocity. In this situation, the prescribed orbit will be hyperbolic, and if we resolve their mutual linear acceleration along the line of connection between the two particles, we will actually obtain a centrifugal repulsion, even though the two particles are being attracted together in the Galilean reference frame. This leaves us in no doubt that the vortex columns will repel each other, and that stability and equilibrium within the magnetized vortex sea will be maintained by a balancing of the axial tension within the vortex hoops, and the equatorial pressure between the vortex hoops. In part I of Maxwell’s 1861 paper he discusses how lines of axial tension link directly between the north and the south poles of a bar magnetic, whereas when two like poles are brought together, the lines of force will spread away from each other. Maxwell took this to indicate that magnetic force of attraction between two bar magnets is caused by a tension in the axial lines of force, and he therefore suggested that magnetic repulsion arises from a pressure. That repulsion pressure will inevitably arise from the equatorial centrifugal pressure acting between the dipole columns. The sea will be a liquid, but it will adopt a fixed structure when under the influence of a magnetic source, which means that electromagnetic waves will be able to enforce their own alignment. We are dealing with a liquid that becomes a solid when it is in a magnetic field. The axial tension within a column (hoop) can be regulated by the relative orbital phase of immediately neighbouring dipoles. The situation of maximum attraction within a column (hoop) will occur when the dipoles are aligned anti-parallel to each other, with every electron having a positron immediately below and above it. This tension can be reduced if a relative angular displacement occurs between the phases of neighbouring dipoles, such as to render the column into a double helix pattern. This would suggest that the physical interpretation of a magnetic line of force is a narrow tubular vortex driven by electrons and positrons arranged in a double helix pattern closed on itself, and that axial tension can be regulated by the number of turns per unit length within the double helix. We will call the number of turns per unit length the 'Helix Angle'. We might say that a magnetic field line is a double helical hoop. The equatorial pressure can be regulated by increasing or by decreasing the vorticity of the cells. If we increase the vorticity, the repulsion between the helical columns will increase, and to balance this, the axial tension will increase by virtue of the helical columns tending to straighten out, by reducing their helix angle, as like in the stretching of a helical spring. In fact it would seem that a magnetic field line of force actually is a helical spring. When such a degree of similarity exists, it is usually an indication that the exact same principle is in operation. In this case, when the helical spring becomes totally relaxed, it will disintegrate into an amorphous sea. The actual geometrical lines of magnetic force when analysed at femtoscopic level will be the Coulomb lines of force within the double helix vortex column. These lines of force will exhibit two major trends. One trend will be a helical axial trend connecting the actual dipoles in the column. As it is a tension, it will have no resultant average direction, but it will approximate to the position of the macroscopic magnetic lines of force. The other trend will be that of the rotating lines of force passing across the equatorial plane between the electrons and positrons within each dipole. This rotational aspect takes us directly to the ultimate question of what exactly the vortex consists of. Whatever the physical interpretation is, we have a rotating field within the dipoles, and we will now return to the earlier question regarding the fact that it seems to be impossible to physically account for the Lorentz force by elasticity theory. The Lorentz force is velocity dependent, and the velocity is undoubtedly measured relative to the vortex sea, but no amount of reasoning relating to dielectric elasticity seems to be able to explain how this force only comes into effect when a particle is moving, and such as not to involve a transfer of energy from kinetic to potential. The only parallel in nature to the Lorentz force is the Coriolis force, which requires a rotating frame of reference. The Coriolis force is a fictitious force like the centrifugal force, but nevertheless Maxwell has already successfully used the centrifugal force in his analysis of magnetism. Let us now take a closer look at the Coriolis force.

The Coriolis Force

IV. The Coriolis force is a force that only exists in a rotating frame of reference. It is identical in its operation to the Lorentz force. It is a velocity dependent force and it acts at right angles to the direction of motion. It takes the form, F = v X 2mω

(Coriolis Force)

(8)

with v referring to the velocity of a particle relative to the rotating frame of reference, m referring to its inertial mass, and ω referring to the angular velocity of the rotating frame of reference. Many scientists would argue that the Coriolis force is only an illusion that occurs when we view a situation from a rotating frame of reference. The extension of this illusionist perspective is that we are living on a planet that is a rotating frame of reference, and as such we have all seen the patterns of the cyclones on the weather maps, which are dictated by the Coriolis force. We might then say that when a cyclone causes a natural disaster, that it was all only an illusion. These illusionists are overlooking the fact that the very concept of rotation implies the existence of a very definite frame of reference. In the case of gravity, this special frame of reference appears to be fixed relative to the background stars, and I am not referring to Maxwell’s vortex sea. We have something that sits stationary relative to the background stars, even though the background stars are not actually fixed, and only appear to be fixed in our time scale. That something must therefore occupy a kind of average universal rest position from which we measure the concept of rotation. It has not been my objective to penetrate the mysteries of gravity or electrostatics, but the mystery of the Lorentz force dictates that we seriously have to consider that the very space itself inside the rotating dipole is in a state of rotation. It’s not simply a matter of geometrical lines of force rotating. Something very real must be there, and in a state of rotation such as to generate an electrostatic equivalent of the Coriolis force. Whatever it is, Maxwell acknowledged its existence, and in part I of his 1861 paper he used fluid dynamics and vorticity to successfully calculate the precise mathematical theory of magnetism. Just as Maxwell’s concept of displacement current means that we cannot deny the existence of an electron positron dielectric, so also does his vortex theory mean that we cannot deny that a very real medium of some kind exists in the space between the electrons and positrons and connects them with each other. It sounds like I am advocating an aether within an aether, but I believe that only the vortex fluid, whatever it is, is an aether. We shall refer to the sea of electron positron dipoles as ‘The Electric Sea’, and consider it not to be aethereal, but rather to be just another physical medium, on a much smaller scale than atomic and molecular matter. Both the aether and the electric sea are missing from modern day physics textbooks, yet they combine and interact with each other to cause the entire theory of electromagnetism. The interaction of the aether with the electric sea leads to Maxwell’s vortex sea. The difficulty in finding a physical link between Coulomb’s law of electrostatics and Newton’s law of gravitation would further suggest that there may even be separate aethers for electrostatics and gravity. I have never made any serious attempt to try and explain electrostatics or gravity, but I have long suspected that their cause lies in aethereal media. I cannot even begin to imagine what these two aethers are made of, but the evidence of the Coriolis force suggests that they really do exist. The radial field lines of gravity and electrostatics, as depicted in static situations, bear a striking similarity to that of irrotational fluid flow, with the elementary particles behaving like sources and sinks. Ian Montgomery and Prof. RT Cahill [5] in Australia have independently advocated theories of gravity, in which gravity is caused by an inflowing medium. During a recent debate with Ian Montgomery, he convinced me of the merits of a velocity field centred on the escape velocity. I personally can’t think of any way to complete such a theory, and neither do I agree with either Ian Montgomery or Prof. RT Cahill regarding the substance of what would be inflowing. Ian Montgomery believes, somewhat ironically in my opinion, that the inflowing medium comprises of electron positron couplets, which are not specified to be rotating. This would conflict with my own idea that any such inflow medium would have to be flowing between the electrons and positrons themselves, and could therefore hardly actually be electrons and positrons. I do however believe that there is considerable merit to the inflow concept, and that it may become of importance if we should ever detect a lag between the angular velocity of the electron positron dipoles, and that of the vortex which they are driving within them.

The Coriolis force is an integral part of Coulomb's law of electrostatics just as it is an integral part of Newton’s law of gravity. The aether vortices in the dipoles are to all intents and purposes rotating space, whether or not we accept that that space is flowing up out of one dipole particle and down into the other. A magnetic field is therefore a region of rotating space, and one might say that a magnetic field is a rotating frame of reference for electrically charged particles. It is a true rotational field in the fluid dynamical sense. A charged particle moving in a magnetic field will experience a Coriolis force. The Coriolis force lies at the root of the Lorentz force.

The Helical Spring Theory of Magnetism V. It is now clear that Coulomb’s law of electrostatics involves two aspects. The static situation is a special case in which the field lines are radial and irrotational. Earnshaw’s theorem [4] tells us that a dielectric medium cannot be sustained by a static irrotational Coulomb field acting alone, and so we cannot have a lattice of static particles unless we introduce an additional force. We do not wish to introduce an additional force as it would corrupt Faraday’s law of electromagnetic induction, and so we must look to the rotational aspect of Coulomb’s law. We must look to central force orbital theory, which is in fact what Coulomb’s law is all about in its more general sense. Maxwell has given us a vortex sea that is rotational, so we must blend this vortex sea with orbital dynamics, so that magnetic effects can be accounted for using both the irrotational and the rotational aspects of Coulomb’s law. The axial tension in the helical columns arises out of pure irrotational electrostatics, whereas the equatorial pressure between the helical columns is a rotational centrifugal effect, and the Lorentz force is a rotational Coriolis effect. Magnetic field strength is a product of both helix angle and helix vorticity. As vorticity increases, so also does the magnetic field strength increase, and so also does the Coriolis Lorentz force increase. We will once again examine the different manifestations of magnetism in order to take a closer look at which effects are coming into play. Consider the situation in which the vortices are randomly aligned in an amorphous sea, and imagine a single rotating dipole adjacent to a current carrying wire. At certain orientations of the dipole, the current in the wire will experience a Coriolis force due to the aether vortex. As the current is constrained to move in the wire, and as the dipole is free to move, the reaction will be that the dipole will reorientate itself to the position of minimum Coriolis force. This will be such that the wire will lie in the equatorial plane of the dipole. In a sea of such dipoles, the axes of the vortex columns will form closed hoops around the wire. If the current in the wire is increasing, it will yield some of its kinetic energy to the dipoles in the surrounding sea, and this will have the initial tendency of making their orbits expand. This in turn will put them out of equilibrium within the sea, and the equilibrium restoring pressure of the sea will transmit this excess energy throughout the sea as transverse electromagnetic waves. The expanding dipole orbits will be constrained by the equilibrium pressure in the equatorial plane, and as such, a continuing increase in energy will be directed into increasing the tangential kinetic energy, and hence the vorticity of the dipoles. As the vorticity increases, the centrifugal force will increase. The increasing centrifugal force will increase the repulsion between the helical columns. In order to maintain equilibrium, this in turn will lead to axial tension increasing, by virtue of the helix angle decreasing, as like in the stretching of a helical spring. We might say that in a magnetic field, space is filled with miniature femtoscopic helical springs that close on themselves in elliptical or circular solenoidal hoops. A current carrying wire will be surrounded by these vortex hoops, and when the current increases, the vortices will spin faster, and the hoops will stretch and tighten up. The dipoles outside the wire will store this extra rotational kinetic energy like flywheels, and when the current is switched off, these flywheels will yield their excess rotational kinetic energy back into the current again, giving the current a final surge forwards. This final surge is usually interpreted in terms of back E.M.F. and Lenz’s law. When a bar magnet aligns itself in a magnetic field, we can see that it is being pulled into line by axial tension in the lines of force. The axial tension will be unevenly distributed as a result of the superimposition of the two magnetic fields, and this will create a torque on the bar magnet, whereas when an electric current loop aligns itself in a magnetic field, we can clearly see the action of the Lorentz force. In all likelihood, both the Lorentz force and axial tension will be occurring in both situations, and it will simply be a question of degrees.

In part I of the 1861 paper, Maxwell showed how the force acting on a current carrying wire could be accounted for in terms of a pressure in the equatorial plane of the vortices. The above considerations have shown us how such an equatorial pressure will be accompanied by an axial tension in the lines of force. When we extend this principle to the force acting between two electrical current circuits, we get picture of Ampère’s force law in terms of closed hoops of helical springs, wrapped around two closed loops of current, and pulling them together with a combination of axial tension, equatorial pressure, and the Coriolis Lorentz force. Faraday’s law of electromagnetic induction arises when a static wire is placed in a time varying magnetic field. In this situation, current electrons in the primary wire are yielding some of their kinetic energy to the dipoles (flywheels) in the surrounding sea. The tendency for dipole orbits to expand is being resisted by rotational centrifugal repulsion in the equatorial plane. While the driving current is varying in time, the vortex sea will be continually seeking to establish a new equilibrium. The centrifugal pressure will be transmitted onwards through the sea as electromagnetic waves, but if we introduce a closed loop of secondary wire into the vicinity, it will act as a pressure outlet, and a current will be driven in it. Faraday’s law of electromagnetic induction can also arise from the rotational Coriolis aspect, as when a moving wire is placed in a static magnetic field. The Lorentz force drives a current in the wire at right angles to the direction of motion of the wire.

The Gyroscope VI. Maxwell used a method in which he introduced vorticity to account for elastic tension. He combined this with fluid dynamical equilibrium conditions, and he arose at the correct mathematical theory of magnetism. Despite this very ingenious approach, Maxwell was unable to predict all the underlying physical causes of magnetism. He was inspired by the centrifugal force, and his equations led to the correct mathematical result, but they did not explicitly expose the Coriolis effect. Likewise in gyroscopic theory we use equilibrium conditions and apply a torque to establish the motion, in what we believe is in line with experimental observation. Despite this apparent agreement with the mathematics, a spinning and precessing gyroscope behaves in a manner that totally defies our expectations. In terms of our experience of gravity, there seems to be no explanation that is good enough to explain why the gyroscope doesn’t fall over. When we hold a spinning gyroscope in our hands and try to move it, we can feel resistance acting at right angles to the direction in which we try to move it. This again seems to contradict the fact that there is no other force acting on it apart from gravity, and therefore why should it behave any differently from a static gyroscope? In part II of the 1861 paper, Maxwell attempts a physical explanation for the induction of a current in a moving wire. His mathematical model correctly predicts this effect, but his physical explanation does not account for the Lorentz force. Gyroscopes are analysed using a set of equations known as Euler’s equations. These equations bear at least a superficial resemblance to the Coriolis based equation (77) (see Appendix A). It would be a matter of interest as a topic of future research, to carry out a detailed analytical comparison between Maxwell’s equation (77) and the equations for gyroscopic motion. Let us suppose that when a gyroscope rotates, it causes the gravitational aether within it to rotate as well. Let us suppose that a rigid body entrains the gravitational aether in its rotational motion, but not in its translational motion, such as that a spinning rigid body drives a gravitational vortex, just as a rotating dipole drives an electrostatic vortex. This would mean that when a spinning gyroscope undergoes translational motion, it will move a part of itself into its own rotating Coriolis field, and as such experience a force at right angles to its motion. This Coriolis force will change the downward motion of the gyroscope into a sideways motion, and then into an upward motion. The cycle will repeat leading to precession and nutation. If we subject a gyroscope to forced precession, it will move upwards and we will get a drop in its weight. Professor Eric Laithwaite demonstrated this fact on television during the 1974 Royal Institution Christmas lectures. You can read more in the web link, http://www.bbc.co.uk/history/historic_figures/laithwaite_eric.shtml In May 1983, I personally visited Prof. Laithwaite at the Imperial College of Science and Technology, London, in order to watch a demonstration of this phenomenon. In the engineering laboratories in the

basement of this university, I watched as Prof. Laithwaite lifted a heavy precessing gyroscope above his head, with what appeared to be the greatest of ease. I had only his word for it that he couldn’t have done the same thing if the gyroscope were not precessing. I was certainly not able to lift that gyroscope above my head with one hand when it was not spinning. However for safety reasons, Prof. Laithwaite would not allow me to pick up the spinning gyroscope as it was quite obviously a very dangerous object, and could have crashed out the window and rolled across Exhibition Road, if it had been accidentally dropped.

Michelson-Morley and the Entrained Electric Sea VII. The Earth’s gravity will entrain the electric sea in its orbital motion around the sun. There are no special properties possessed by the electric sea that would give it immunity to Newton’s law of gravitation. The entrainment should gradually taper off as we move out into space, unless for whatever reason the situation is interfered with at some distinct boundary such as the magnetosheath. Magnetospheric charts indicate that the Earth’s magnetic field is enclosed within a distinct boundary, and the late Dr. Carl Zapffe wrote extensively on this topic [6]. The solar wind interacts with the Earth’s magnetosphere in a manner that is more than just a reaction to the Earth’s magnetic field. The Solar wind actually plays a major role in shaping the Earth’s magnetosphere. This would suggest that the solar wind and the electric sea are one and the same medium. The commonly accepted view that the solar wind comprises of protons and electrons is a primitive idea that dates back to the early days following its discovery, at a time when positrons hadn’t yet been discovered. It may well be that protons are indeed carried with the solar wind, but in order for the solar wind to interact with the Earth’s magnetosphere in the fluid dynamical manner in which it does, it would need to comprise of particles on a similar scale and density to the electric sea. Protons would react to the Earth’s magnetic field, but they would not distort it, and further evidence that the solar wind comprises of electrons and positrons lies in the fact that it carries magnetic fields along with it. A plasma of protons and electrons couldn’t possibly bring along magnetic fields. No fluid medium other than the medium responsible for the very existence of magnetic fields could possibly carry magnetic fields along with it, in the manner in which the solar wind does. The electric sea, in the form of the solar wind passes by the Earth at an average speed of 450 Km/sec, and the Earth’s gravity acts so as to shield the Earth inside a tent, which has a long tail pointing away from the Sun. The magnetosphere tail points away from the Sun because the Earth’s orbital speed of 30Km/sec is on average only about one fifteenth of the solar wind speed. The entrainment principle, without the Zapffe amendment, was first advocated by George Stokes in 1845. Stokes aether drag theory was discounted on the grounds that the situation at the boundary would make a solid ‘aether’ unsuitable, and that a liquid ‘aether’ couldn’t support transverse waves. The argument ensued, that whatever this mysterious ‘aether’ was comprised of, it would have to possess both solid and liquid characteristics. The electric sea is a liquid that becomes a loosely bonded solid in a magnetic field, and so it would overcome these objections to the Stokes aether drag model. Maxwell shows us in part III of his paper that the necessary transverse elastic properties are contained within the individual vortex cells. The individual rotating electron positron dipoles would also contain perfect self restoring transverse elasticity under the action of an electric field, and as such, a liquid electric sea is quite capable of supporting transverse electromagnetic waves. Another objection to the Stokes aether drag model relates to the phenomenon of stellar aberration. It is said that stellar aberration could not occur in the Stokes model. I am not convinced of this fact, and neither am I convinced about Lorentz’s objections concerning the velocity field that would be associated with the Stokes model. However, both of these concerns are overcome if we adopt the Zapffe model. In the Zapffe model, we simply carry Bradley’s explanation for stellar aberration up to the magnetosheath. The Earth’s magnetic field is undoubtedly somehow caused by the Earth’s rotation. It is probably due to the electrically charged particles within the Earth itself, that are rotating with the Earth, and interacting with the electric sea in a manner similar to that of an electric current in a wire, as opposed to the manner in which a bar magnet interacts with the electric sea. There could be an excess of free electrons, or there might be superconducting material inside the Earth.

All the above considerations are perfectly in line with the Michelson-Morley experiment of 1887. Additionally we might expect a physical vortex in the electric sea in the polar regions of the Earth. This would be due to a partial lag between the electric sea and the Earth, arising during the Earth’s diurnal motion and possibly detected by the Michelson-Gale experiment of 1925.

References [1] Clerk-Maxwell, J., “On Physical Lines of Force”, Philosophical Magazine, Volume 21, (1861) [2] Clerk-Maxwell, J., "A dynamical theory of the electromagnetic field", Philos. Trans. Roy. Soc. 155, pp 459-512 (1865). Abstract: Proceedings of the Royal Society of London 13, pp. 531--536 (1864) [3] Kirchhoff, G., “On the motion of electricity in wires”, Philosophical Magazine, Volume 13, pp. 393 412 (1857) An interesting interpretation of Kirchhoff’s 1857 paper can be viewed on this web link, http://www.ifi.unicamp.br/~assis/Apeiron-V19-p19-25(1994).pdf [4] Earnshaw, S., “On the nature of the molecular forces which regulate the constitution of the luminiferous ether”, Trans. Camb. Phil. Soc., 7, pp 97-112. (1842) [5] Cahill, R., “Gravity as Quantum In-Flow’, Apeiron Vol. 11, No.1 (2004) http://redshift.vif.com/JournalFiles/V11NO1PDF/V11N1CA1.pdf [6]Zapffe, Dr. Carl.A., “The fivefold hypothetical structure underlying time dilation and the special theory of relativity”, Indian Journal of Theoretical Physics, Volume 26, No.2, pp.103-122 (1978) [7] Wilhelm Eduard Weber (1804-1891) and Arden Barker ([email protected]) have both independently advocated a sea of electric dipoles. Arden Barker has specifically advocated an electron positron medium for the purposes of the propagation of electromagnetic radiation.

Appendix A (The Lorentz Force) It is generally unknown that equation (77) in Maxwell’s 1861 paper, is in fact the Lorentz force. Maxwell derived this equation long before Lorentz did. It is customary to write the Lorentz force in the form, F = q(E + vXB)

(1A)

The qE term is referred to as the ‘local aspect’, and it represents that aspect of Faraday’s law of electromagnetic induction which is generated by a time varying magnetic field on a static charge, and covered by the equation, curl E = −∂B/dt

(2A)

The part of equation (1A) that is actually attributed to Lorentz is the convective aspect, F = qvXB

(3A)

I am disregarding the local aspect of equation (1A) as it bears no significance to the physical aspect that I am considering when I refer to the Lorentz force. When I refer to the Lorentz force, I am referring to the force on a moving charged particle in a static magnetic field, and it was Lorentz who supplied the formula for this situation. As such I divide equation (3A) by q and bring it into a field theory format that is more in line with how Lorentz first presented it,

E = vXB

(4A)

If we divide equation (1A) by q we get, Etotal = Elocal + vXB

(5A)

Taking the curl we get, curl Etotal = −∂B/dt − (v.grad)B = −dB/dt

(6A)

Equation (6A) corresponds to equation (6) in the main article. We see how it is the Lorentz force that justifies the use of total time derivatives in the electromagnetic equations, as opposed to the more commonly used partial time derivatives.

Appendix B (E=mc²) Dr. Menahem Simhony has brought to our attention the fact that E=mc² is an equation which arises out of classical wave mechanics and relates wave propagation speed in an elastic medium to tension in the medium. In part III of Maxwell’s 1861 paper, equation (132) is one such version of this classical wave speed equation. The density term in equation (132) gives us the mass, and the transverse elasticity gives us the tension and leads us to the energy. I can perhaps demonstrate this more clearly using the similar equation for wave speed in a vibrating string, http://www.soton.ac.uk/~jhr/MA274/node3.html Wave speed is given by the equation, (1B)

c² = T/ρ

in which T is tension per unit length, c is wave speed, and ρ is equal to mass per unit length. This multiplies across to become, mc² = Force x Distance = Energy

(2B)

In electromagnetic theory, the velocity c in E=mc² is a function of the vortex sea itself. It is a macroscopic phenomenon, whereas the E term is a femtoscopic phenomenon that refers to bonding energy between the electrons and positrons in the sea. I will now try to jump between the macroscopic scale and the femtoscopic scale to see if I can extract the equation E=mc² from the electromagnetic wave equation, d²Ei/dx² = 1/c².d²Ei/dt²

( Electromagnetic Wave Equation )

(3B)

Ei is a second derivative of displacement y multiplied by mass and divided by charge. The sinusoidal solution for Ei tells us that the displacement y will also therefore have the same form of equation, d²y/dx² = 1/c ².d²y/dt²

(4B)

Now let us consider femtoscopic level in which we are examining a disturbance due to a Gamma ray that is ejecting an electron from its orbit with a positron. Let’s multiply across by m, for the mass of the electron. We get, mc². d²y/dx² = md²y/dt² = Coulomb Force

(5B)

Integrating with respect to x we get, (6B)

mc². dy/dx = Energy + Constant of Integration

dy/dx will be unity since position and displacement are the same thing in this femtoscopic scenario. Hence, E=mc² + Constant of Integration

(7B)

The constant of integration is a consequence of trying to simplify a multi-particle problem into a two particle problem. We have just carried out a qualitative treatment which cannot yield the correct numerical value, but it does tell us that the famous expression E=mc² is rooted in Maxwell’s vortex sea.

Appendix C When a body is in a circular orbit under an inverse square law, it is a fact that in order to escape from its bound orbit, it will require an additional amount of kinetic energy equal to the amount that it already possesses. If a Gamma ray of 1.02 MeV is required to separate an electron positron pair, it follows empirically that we need energy of 0.511 MeV to eject an electron from a vortex dipole. This will equal both its kinetic energy in orbit 1/2mv², and also the value mc². It follows that, (1C)

1/2mv² = mc²

therefore v will equal √2 c. We can substitute this into mv²/r and equate it to the electrostatic force given by Coulomb’s law. This will give the dipole an orbital diameter of about one femtometer. However if the electron is to escape from the sea altogether, it will have to escape from the bonds of the positrons in the neighbouring dipoles, above and below it in the helical column. This is not so easy to calculate, but if we estimate that at the very most we might need about three orbital energies to get the electron liberated from the sea altogether, then the diameter could increase to about ten femtometers and the tangential speed will reduce to about half the speed of light. I am inclined to believe that the liberation energy will be predominantly centred on the individual dipole, as the energy associated with the axial tension may indeed cancel out with the repulsion in the equatorial plane. I would estimate the dipole diameter to be no more than two femtometers. This means that we are on a scale of about one millionth the size of an atom, and as such, the electric sea should have absolutely no problem in passing between the nuclei of atomic and molecular matter. The electric sea should be able to pass through atomic and molecular matter just as water passes through a basket. We should now note three different scales of magnitude, (a) Air (b) Electric Sea (c) Aether

(sound) (light/magnetism) (gravity/electrostatics)

relative scale one relative scale one millionth relative scale infinitesimal

(nanoscopic) (femtoscopic)