General Transformations of Space and Time according to Aether Theory
| Scientific Paper | |
|---|---|
| Title | General Transformations of Space and Time according to Aether Theory |
| Read in full | Link to paper |
| Author(s) | Joseph Levy |
| Keywords | aether, space, time, speed of light, length contraction, synchronism discrepancy, hidden variables |
| Published | 2010 |
| Journal | ArXiv |
| No. of pages | 24 |
Read the full paper here
Abstract
Assuming the existence of a preferred aether frame and the anisotropy of the one-way speed of light in platforms different from the aether frame, we derive the space and time transformations relative to bodies moving in any direction of space and not only in the direction of the common x-axis of the co-ordinate systems under consideration. Taking for granted length contraction and clock retardation, we show that the experimental space-time transformations result from measurement distortions due to the fact that the length of the rods and the frequency of the clocks, used for the measure, do not have a constant value as a result of their motion through the aether, and because the standard synchronization procedures are affected by a synchronism discrepancy effect. When the motion of bodies is aligned along the common x-axis, the transformations assume the same mathematical form as the conventional transformations. However, their meaning is quite different because they have been derived on the basis of very different assumptions, and they arise from the measurement distortions mentioned above. Therefore they conceal hidden variables which are the true transformations.
Overview
The paper (arXiv:1003.1953, v1 9 March 2010, v2 18 November 2010) is a derivation exercise carried out entirely inside the Lorentzian programme. Levy takes as given the four assumptions he attributes to Lorentz: a fundamental aether frame in which light speed is isotropic; anisotropy of the one-way light speed in every other frame; contraction of rods along the direction of absolute motion; and retardation of clocks moving relative to the preferred frame. From these he asks what an observer riding a moving platform will actually *measure* for the distance and elapsed time of a journey, given that his metre-stick is short, his clock is slow, and his two distant clocks have been set by a procedure that assumed a symmetry the aether does not permit.
What is new relative to the standard textbook treatment — and relative to Levy's own earlier work — is the generalisation off the common x-axis. Previous derivations, he notes, considered only motion along the shared axis of the two coordinate systems. Here the moving body travels along a rigid path making an arbitrary angle α with the axis, and a second stage connects any two moving systems S1 and S2 that both recede from the aether frame S0. The pay-off Levy claims is theoretical discrimination: at α = 0 the derived transformations collapse onto the familiar Lorentz form, but at other angles they need not, so the generalisation "would permit to distinguish theoretically the two theories and give criteria for experimental testing." The interpretive thesis running through the paper is that the measured coordinates are systematically distorted, and that behind them lie hidden variables which are "the Galilean transformations" (see Galilean transformation).
The argument
Contraction of a slanted rigid path
A rigid path of rest length l0 lying at angle α in the moving frame has its x-projection contracted while its y-projection is untouched. Combining the two by the Pythagorean relation gives Levy's equation (1), the anisotropic-contraction formula that all subsequent results depend on: the real length is l0 multiplied by (1 − v012/C2)1/2 and divided by (1 − (v012/C2)sin2α)1/2. Crucially, Levy insists this real shortening is invisible from inside: the measuring standards contract in exactly the same ratio, so the *apparent* length of the path in S1 comes out as l0 again. Only an observer at rest in the aether frame reads the length correctly.
One-way light speed at an angle
Appendix 1 rederives, following Prokhovnik, the directional light speed used throughout. For a rod at angle α on a platform moving at v, requiring that the resultant velocity vector have magnitude C in the aether frame gives the quadratic C12 + 2vC1cosα − (C2 − v2) = 0, whose physical root is C1 = −vcosα + (C2 − v2sin2α)1/2, with the sign of the cosine term reversed for the return trip. Levy stresses that the equation "implies that the three speeds have been measured with the help of the same clock", one not slowed by motion.
The synchronism discrepancy
Because the outward and return light speeds differ, half the two-way transit time is not the one-way transit time, so the Einstein–Poincaré procedure (and, equivalently, slow clock transport) mis-sets the distant clock by an amount Δ. Levy computes Δ for arbitrary α and checks two limits: for α = 0 it reduces to v01l0/C2, and for α = π/2 it vanishes. He identifies the first with the term appearing in the numerator of the conventional time transformation, and claims this as an explanatory advantage: aether theory "provides a rational explanation of the meaning of this term, that has no equivalent in special relativity."
Recovering Lorentz-form transformations at α = 0
Assembling clock retardation and the discrepancy gives the apparent time Tapp = T0(1 − v012/C2)1/2 − Δ. For α = 0 this rearranges into equation (3), T0 = (Tapp + v01Xapp/C2)/(1 − v012/C2)1/2, and the corresponding space relation (5) — algebraically the Lorentz transformations, with the reciprocal pair (6) and (7). Levy immediately qualifies the resemblance: the barred quantities are "apparent" coordinates produced by contracted standards and arbitrarily synchronised clocks; C is the light speed in the aether frame alone, not in every inertial frame; and because the relativity principle was never assumed, the complete symmetry of the conventional transformations — "the cause of most of the difficulties encountered by SR" — is absent. He adds that real speeds compose Galileanly, with the mass increase limiting any body to V < C relative to the aether, so that a body B moving away from A is limited to vB < C − vA.
The perpendicular direction as a discriminator
At α = π/2 the results differ in character rather than in form. The time relation reduces to Tapp = T0(1 − v012/C2)1/2, with the v01Xapp/C2 term simply absent because there is no synchronism discrepancy transverse to the drift, and the space relation (8) involves the one-way speed CO'A explicitly. Levy remarks that "special relativity has no rational explanation for this result", since with no preferred frame T0 means nothing.
Two moving systems
The second half repeats the construction for three systems S0, S1, S2, with the vehicle on a path rigidly attached to S2. Ratios of real distances are set equal to ratios of real speeds, contraction (1) is applied twice, and the composite result (11) is specialised. For α = 0 the pair of relative speeds collapses into the single quantity v12,app = (v02 − v01)/(1 − v01v02/C2), and expressions (14) and (20) then have exactly the conventional Lorentz form in v12,app. Levy's reading is that the relativistic velocity-addition rule is a statement about *apparent* speeds only: "real speeds obey the Galilean law of composition of velocities... only apparent speeds obey the relativistic law." As a consistency check he notes that setting v01 = 0 makes S1 coincide with the aether frame and returns the expected Tr = T2,app/(1 − v022/C2)1/2.
Assessment
The paper's genuine merit is bookkeeping discipline. Levy is careful, at every step, to distinguish the real length l from the apparent length l0, the universal time T0 from the clock reading Tapp, and the aether-frame light speed C from the directional speeds C1 and C2. That discipline is what makes the central observation land: the same measurement distortions that hide the aether also guarantee that the observer recovers the Lorentz algebra, so the empirical adequacy of the Lorentz transformations is not by itself evidence for the relativity principle. The treatment of clock synchronisation is the strongest part — the demonstration that the v01Xapp/C2 term is precisely the synchronism discrepancy is clean, and it is a real interpretive gain over presentations in which that term is simply postulated. The angular generalisation is also a legitimate extension rather than a restatement; equation (1) is a non-trivial result about slanted rods that many aether treatments never write down.
The difficulties, however, are structural. Length contraction and clock retardation are "taken for granted" — Levy says so explicitly — rather than derived from any dynamics of matter in the aether. Since these two effects are exactly what is needed to make the aether unobservable, the theory purchases its agreement with experiment by assumption, and the "hidden variables" it recovers are hidden by fiat. Nothing in the paper explains why rods contract by precisely (1 − v2/C2)1/2; the Michelson–Morley null result is accommodated, not predicted.
The promised experimental discriminator is also weaker than advertised. The stated aim is to "give criteria for experimental testing", but the two special cases actually computed both reproduce standard predictions: at α = 0 the transformations are algebraically identical to the conventional ones, and at α = π/2 the difference is that a term absent in both accounts is absent for a stated reason. No numerical prediction differing from special relativity at any attainable v01 is derived, and no bound on the Earth's absolute velocity is extracted. Since the whole scheme requires a definite v01, the natural candidate is the Earth's motion with respect to the CMB dipole, roughly 370 km/s — but the paper never mentions it, and never says which frame the aether frame is supposed to be. That omission matters, because modern one-way anisotropy searches (resonator and Ives–Stilwell-type experiments) already constrain direction-dependent light-speed variation to parts in 1017, and a reader cannot tell from the text whether Levy's scheme is compatible with them or merely silent about them.
Finally, the argument that recovering Galilean transformations as the "true" ones is a gain rests on a philosophical preference Levy states rather than defends: that a universal time exists and that the symmetry of the Lorentz transformations is a defect ("the cause of most of the difficulties encountered by SR") rather than a feature. Readers who do not share that starting point will find the derivation internally consistent — it is — while denying that it establishes anything the standard account does not. On its own terms the paper does what it sets out to do; whether that constitutes evidence for the aether is precisely the question it does not address.