APPENDIX 7: Varying c, Maxwells Equations & Special Relativity
Those who were taught to derive Maxwell’s equations from Relativity may object that (4) is obtained on the assumption that c is a constant. But, as shown in Bleany & Bleany [196], (4) can be readily derived without any initial assumptions about the behavior of c, ε, or μ, just as Maxwell himself did. This is done by obtaining a set of four simultaneous partial differential equations based on (a) Gauss’s theorem applied to electrostatics; (b) Gauss’s theorem applied to magnetic fields; (c) Faraday’s and Lenz’s law of electromagnetic induction; and (d) Ampere’s law for magnetomotive force. The equations from (a) and (b) become ε div E = 0and μ div H = 0 for a vacuum, and so are independent of any variations in ε and μ. The equations from (c) and (d) eventually become curl E = -μ(∂H/∂t) and curl H = ε(∂E/∂t). Provided that μ varies slowly with respect to H, and that ε varies slowly with respect to E, this formulation is still valid. The general wave equation which (a), (b), (c), & (d) reduce to has the form [del]2A = (1/v2)(∂2A/∂t2)where v2 = 1/(με) = c2 and A is some scalar or vector quantity. Again, this equation is valid for describing wave motion provided that v2 varies slowly with respect to A. But this condition is always maintained with a varying ZPE since a ZPE change manifests as a change in ε, μ, and c, as well as proportional changes in atomic clock rates which govern atomic processes. In addition, another derivation of Maxwell’s equations shows an almost infinite variation in ε, μ, and c is permitted in the system of units that Maxwell himself was using [49]. The analysis here therefore indicates that Maxwell’s equations can be satisfied with a varying ZPE, ε, μ, and c. (ii) Special Relativity (SR) & Some Problems If the physical properties of the ZPE and hence the vacuum are indeed changing, giving a changing c, this is not so different from the change that occurs in c when light goes from air into glass or water. SR is not called into question because the speed of light is slower in glass or water than it is in air. Similarly, on the approach used in this paper, the changing speed of light should not call SR into question because there was still an upper limit to what the speed of light was initially in the primordial vacuum. This upper limit value for c comes through from the redshift data as being around 6 x 1011 c now. What has happened to the vacuum is effectively the same as its optical density increasing uniformly on a cosmological scale from its initial low value. Therefore the speed of light has dropped from its upper limit velocity down to its present speed. The same situation would apply if the optical density of an infinitely long cylinder of water was smoothly increasing as light traveled along it. SR would not be called into question in that case. Therefore, because the upper limit velocity still exists (even though it is significantly higher than the currently accepted limit velocity), then simultaneity is maintained and SR is valid on that basis. But this topic embraces other issues so we explore further. Originally, the whole necessity for relativity in one form or another arose because of the Michelson-Morley experiment which was conducted in 1887. In this experiment, each half of a split light beam travels along one of two equally long but perpendicular arms of a special optical device, and then bounces off mirrors back to an observer. The optical device was an interferometer which will produce interference fringes when the combined light waves of the split beams are out of step. At the time, fringe-shifts had been expected because it was thought that the vacuum was a light-carrying medium or aether, and that light moving through the aether would take longer in one direction than another as it moved against the aether “current”, rather like a canoe on a river. An aether current was expected because of the motion of the earth through the aether. In other words, it was expected that the aether would provide an absolute frame of reference against which all other velocities could be measured. As it turned out, no significant fringe shifts were observed, even when the device was rotated to other positions. Observation showed that the round-trip times for light going in any direction were the same. This result drove Lorentz [197] in 1904 and Einstein in 1905 to formulate their respective theories of relativity. Einstein explained the result in Special Relativity (SR) by proposing that (1) There was no absolute frame of reference anywhere in the universe. Lorentz did not have that restriction. (2) That the speed of light was an absolute constant. Lorentz did not need that. (3) Einstein proposed that mathematical transformations had to be applied to time, space, and mass and had to be applied both ways when comparing two objects in motion. By contrast, Lorentz Relativity (LR) says that such transformations only apply one way and that is only to clocks, meter sticks and momentum, not time, space and matter. There is an important distinction in this latter point. For example, SR requires time itself to be affected by velocity or gravitational potential. By contrast, in LR nothing ever happens to time itself, just to certain types of clock attempting to keep time. In a somewhat similar way, an increase in temperature may lengthen the pendulum of some clocks and affect their time-keeping, but not the actual time itself. LR thus accepts that other types of clock exist for measuring time that may be unaffected by speed or potential. But SR requires time itself to be actually affected by velocity or potential, and the same applies to mass and length. Just recently, an entirely new approach to the problem was attempted and the results suggest that Lorentz was basically correct and that Einsteinian physics is deficient [219]. Einstein made use of his required length transformation of space to overcome the problem of the lack of fringe shifts. He claimed that the contraction of the arms of the interferometer in the direction of travel made the interferometer arms shorter by just the amount needed to compensate for what was expected to be a longer travel time for light through the moving aether. Note that in his lectures even as late as 1929, Einstein claimed that the aether existed, but that his SR overcame the problems with the observations in an aether-filled universe. But there is another, perfectly logical, explanation for the lack of fringe shifts in the Michelson-Morely experiment. The absence of the fringes may primarily mean that the earth apparently has no motion relative to the aether or light carrying medium. This was a problem in 1905. But if we now exchange the old aether concept for the now known Zero Point Energy (ZPE) that fills the cosmos, and through which light propagates, we can obtain a perfectly satisfactory answer to the problem caused by the lack of fringe shifts. The local gravitational field of the earth can be shown to be an augmentation of the ZPE in our vicinity brought about by the presence of oscillating point charges [198]. This local field of the (augmented) ZPE has no motion with respect to the earth’s center of mass since it originates with the presence of the earth’s mass. Thus, the Michelson-Morely experiment will show no fringe shifts. But the Earth does rotate with respect to its own gravitational field, and hence with respect to the augmented ZPE. Importantly, this does produce fringe-shifts, known as the Sagnac effect, that were first seen in 1913 when a rotating platform was used for the experiment. It was replicated in the Michelson-Gale experiment of 1925 using the earth’s own rotation. The ZPE approach is thereby shown to be a far simpler explanation for the lack of fringe-shifts than the complication of SR. This, then, calls into question the necessity for SR at all. But if the necessity for SR is called into question, it will then be objected that SR produced Einstein’s famous equation of mass-energy equivalence using the speed of light. Nevertheless, O’Rahilly has shown that this equation can be deduced without the necessity of SR at all [201]. Again, it may be pointed out that the later General Theory of Relativity (GR) was based on SR and has many successes to its credit. In answer to this two points need be noted. First, GR was built on SR by using only one-way mathematical transformations (not both ways as SR requires), and those transformations were relative to the local gravitational field, which became a preferred reference frame, namely the centre-of-mass [202]. This means that GR is in line with LR [203] but is not really consistent with SR. The second and key point that must be noted is that all the predictions of GR, including the bending of light in a gravitational field, and the advance of the perihelion of Mercury, can be reproduced using the ZPE and classical electrodynamics without the necessity for any kind of relativity at all [see reference 204 and references therein]. This, too, suggests that relativity may be redundant with a ZPE whose existence and effects answers questions relating to a large number of physical phenomena. If the original reason why relativity was introduced has thereby been negated, one may be forgiven for questioning other aspects of SR. Take the claim that the speed of light is (1) an absolute constant and (2) that c is the universal speed limit with nothing going faster. In order to achieve point (2), the SR position requires mass to increase as velocity increases. It is certainly true that this is the observed behavior of particles in accelerators since the particles have not reached, let alone exceeded, the speed of light. There are two points to note here. First and foremost, it should be emphasized that ZPE theory gives some good reasons why mass should increase with velocity quite apart from anything to do with relativity. Second, Van Flandern has pointed out that a similar situation existed for propeller driven aircraft in level flight trying to exceed the speed of sound. The air molecules cannot be driven faster than sound no matter how fast the propellers spin, so the aircraft itself cannot go any faster. However, if there was a force propagating faster than the speed of sound, or a continuous acceleration, such as in a jet engine capable of exceeding that limit, then higher velocities are potentially achievable. As for the claim that nothing can exceed this universal speed limit, science has been living with the existence of tachyons for some time, and these particles certainly travel faster than light. But that is not all. There is some, currently contentious, evidence that the speed of gravity may in fact be very significantly faster than light [205, 206]. If this is in any way correct, it would establish that the postulates on which SR is based are probably fallacious. But we can go further by considering point (1), namely that c is an absolute constant. This paper has shown that the speed of light is dependent upon the physical properties of the vacuum, and the evidence is that these properties are changing. The speed of light has also been experimentally measured as consistently changing over a 350 year period [61, 25]. It is true that these experimental results have been criticized as being out of step with SR, but are we going to follow the data trail as a more correct description of reality, or support a theory that may need some surgery? It is true that c was declared a universal constant in 1983 as a result of using atomic clocks from 1972 to 1983 to measure c. As shown above, atomic clocks tick at a rate proportional to c, so that if atomic time intervals are t, then ct is a constant as shown in (18A). Thus the speed of light measured by atomic clocks will always be a constant. A comment by Van Flandern emphasizes this. He had measured the atomic clock as slowing compared with orbital time and stated, “Assumptions such as the constancy of the velocity of light … may be true only in one set of units (atomic or [orbital]), but not the other” [75]. So measurements of c using atomic clocks for macroscopic measurements will also maintain this requirement of SR, and c will always be a constant in the atomic frame of reference. Thus the integrity of the relativistic equations with the term c2t2 is retained if atomic time, t, is used. For an example, see reference [207]. Associated with these equations is the matter of length contraction originally claimed by Einstein. Incredibly for a theory that is so widely accepted, it seems that length contraction has never been seen directly in any experiment, but has only been inferred. For a discussion about this and the constancy of lengths in SR see [208]. That article concludes “…the clear implication of our considerations here is that length contraction is not a physical shortening, but is merely an observational consequence of time desynchronization. In SR, physical bodies do not actually change dimensions.” The whole idea of length-contraction, and the necessity for relativity in one form or another, originally arose because of the Michelson-Morley experiment. This development brings into question the relevance of SR particularly since the ZPE explanation is far simpler. On this matter, Harwit states: “Current observations indicate that the universe is bathed by an isotropic bath of microwave radiation. It is interesting that the presence of such a radiation field should allow us to determine an absolute rest frame on the basis of local measurement.” He then goes on to salvage what is left for SR by saying, “Such a frame would in no way violate the validity of special relativity which, as stated earlier, does not distinguish between different inertial frames. Rather the establishment of an absolute rest frame would emphasize the fact that special relativity is really only meant to deal with small-scale phenomena and that phenomena on larger scales allow us to determine a preferred frame of reference in which cosmic processes look isotropic.” [210]. So two spacecraft traveling in different directions can determine their individual absolute velocity relative to the microwave background radiation and each other since an absolute frame of reference does exist macroscopically. Harwitt then concludes that SR can only apply to small-scale or atomic phenomena. By contrast, ZPE formalism covers a broad area in which SR is not holding up well. Thus Magueijo pointed out that “…the urge to reconcile VSL [variable speed of light] to relativity is motivating much ongoing work… It now appears that the constancy of c is not so essential to relativity after all; the theory can be based on other postulates.” [211]. But conclusions from Cahill’s work at Flinders University go further. His experimental results mean “that the Einstein postulate regarding the invariance of the speed of light was incorrect – in disagreement with experiment, and had been so from the beginning. This meant that the Special Relativity effects required a different explanation, and indeed Lorentz had supplied that some 100 years ago: in this it is the absolute motion of systems through the dynamical 3-space that causes SR effects, and which is diametrically opposite to the Einstein formalism”[219]. References [25] B. Setterfield, D. Dzimano, ‘The Redshift and the Zero Point Energy’ Journal of Theoretics, (Dec. 2003). Available online at http://www.journaloftheoretics.com/Links/Papers/Setter.pdf [49] K. Wanser, Fullerton University, private communication about his article in press (July 5, 2004). [61] T. Norman and B. Setterfield, ‘The Atomic Constants, Light, and Time,’ Research Report, Stanford Research Institute (SRI) International & Flinders University, South Australia, August (1987); available online at http://www.setterfield.org/report/report.html [75] T.C. Van Flandern, Precision Measurements and Fundamental Constants II, B.N. Taylor and W. D. Phillips, (Eds.), National Bureau of Standards (U.S.) Special Publication 617, (1984) 625-627. [196] B.I. Bleany and B. Bleany, op. cit., pp.236-239. [201] A. O’Rahilly, “Electromagnetic Theory”, pp.304-323, Dover Publications (1965). [219] R.T. Cahill, Progress in Physics, 4 (2006), pp.73-92
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