On the Alternative Interpretation of Special Relativity
| Scientific Paper | |
|---|---|
| Title | On the Alternative Interpretation of Special Relativity |
| Read in full | Link to paper |
| Author(s) | Jozef Kajfosz |
| Keywords | Special Relativity, principle of relativity, Lorentz transformation, absolute motion, consistency of measurements, privileged frame |
| Published | 2013 |
| No. of pages | 24 |
Read the full paper here
Abstract
A short outline of the alternative, Lorentzian version of special relativity is presented. It is shown that a simple principle of consistency of measurements, familiar and obvious to every experimentalist, when applied in the interpretation of experimental evidence about inertial motion, leads straightforward to the Lorentzian formulation of relativity which involves both the principle of relativity and Lorentz transformation and also a privileged state of motion and effects related to absolute motion.
Overview
Kajfosz — a retired nuclear physicist of the institutes at Řež and Cracow — sets out to present the Lorentzian reading of relativity as a self-contained position rather than as an objection to Einstein's. His opening move is to insist on what is not in dispute: the principle of relativity is accepted, the Lorentz transformation is accepted, and the resulting scheme is "both empirically and mathematically indistinguishable from the standard, Einsteinian interpretation of SR." He states explicitly that citing experiments which supposedly refuted an aether is therefore beside the point, since such arguments target "short, temporary working hypotheses" from the road to the finished Lorentzian view, not the view itself. The disagreement he wants is about interpretation only.
The engine of the paper is a single elementary rule which he calls the principle of consistency of measurements: two numerical descriptions may only be compared if they were obtained under the same assumptions. Applied to inertial motion, this rule is supposed to force a distinction between the formal equivalence of inertial frames — which the paper affirms — and the physical equivalence of states of motion, which the paper denies. From that denial follows a privileged state of motion S0, real physical changes in bodies set into motion relative to it, and an explanation, rather than a postulate, of why those changes cannot be detected. The article began in Polish in 1983–84; Kajfosz reports that it was rejected by Postępy fizyki by a referee who then published his own piece on the same subject, and he notes wryly that the interpretive question is nowadays taken up "still less by physicists than by philosophers of science."
The argument
Properties versus descriptions
Two people each report a rod as "5 metres". Are the rods equally long? Only if "metre" means the same thing for both. From this schoolroom example Kajfosz draws his central distinction: a property of a physical object is "an objective element of reality, independent of the observer", while a description of that property contains both objective and conventional elements inherited from the assumptions used to measure it. "A formal equality of the descriptions of properties is not a sufficient condition for a physical equality of those properties." The converse consequence carries the later argument: if two descriptions of the same objective situation differ, the measurements were not consistent — they rested on different assumptions.
The missing quantity
Purely spatial or purely temporal properties need only a unit. Mixed quantities need something more. To time a ball travelling along a rod one must first synchronise clocks at its ends; to synchronise them one must know the speed of some signal; to measure any speed one must already have synchronised clocks. Kajfosz calls this "a vicious circle", not a technical nuisance but "a very fundamental feature of the construction of our world", removable "by no circumvention". The only resolution is to synchronise by convention — a stipulation which is simultaneously a definition of a velocity and of the simultaneity of distant events, and which must therefore be listed among the assumptions of every measurement.
SIMs, IFRs and identical objects
Two objects are in the same state of inertial motion (SIM) if they are at rest relative to each other; an inertial frame of reference (IFR) additionally carries coordinates, unit standards and a simultaneity convention. Objects are identical if, placed side by side in the same SIM, all their corresponding properties are equal. Changing the IFR is a change of convention only, and can act on nothing; changing the SIM of a body requires force and acceleration, so real change cannot be ruled out in advance. Kajfosz states the resulting question as "the primary issue of physics of inertial motion": do the properties of identical objects remain equal after transfer to different SIMs?
Two descriptions, one reality
He builds two identical light-clock crosses P and R — perpendicular arms of equal length with emitters, detectors and a clock — and lists seven properties: the two arm lengths, the four one-way light times, and the clock rate. In the home frame both give Lx = Ly = l, all four light times l/c, rate 1. Transfer R to a new SIM and describe it with the unchanged assumptions of the home frame: Lx = l/γ, Ly = l, Tx+ = l/[γ(c − v)], Tx− = l/[γ(c + v)], Ty± = γl/c, rate 1/γ, with γ = 1/√(1 − v2/c2). Since every conventional element is identical across the two descriptions and the descriptions differ, "the differences in those descriptions must be caused by some elements of objective reality."
Redoing the measurements with a second set of assumptions anchored to the moving SIM returns the tidy home-frame numbers for R and the γ-laden ones for P. Kajfosz reads the pattern twice over. The formal equality of the two "own-frame" descriptions is precisely the principle of relativity, which he restates as: the description of any property depends only on the described velocity of the object's SIM in the chosen IFR. But the inequality of descriptions of the same reality under the two assumption sets shows that those sets are mutually inconsistent — as one would expect, since they embed different simultaneity conventions. "Formally identical assumptions are thus not equal if they relate to different states of motion."
Why the changes hide
Physical non-equivalence and undetectability are reconciled by a self-measurement argument: "If when transferred to a new SIM the length of an object changes, then the length of a transferred standard length unit will change in the same way as well. The changed length measured by a changed length unit will give an unchanged result." The same holds for clock rates. He offers a second, independent demonstration: were properties genuinely unchanged by transfer, distant clocks could be synchronised by sliding rods past one another or by importing a moving clock, and no convention would be needed — but such procedures famously give velocity-dependent, inconsistent results.
A dynamical account of formal relativity
Because c is the propagation speed not only of signals but of the electromagnetic interactions binding a body together, transferring a body to a new SIM without changing it would leave each element out of equilibrium in a now-anisotropic field of delayed forces. Instead the parts shift until equilibrium is restored, and the reconfigured body is one in which "each element ... remains in a state of equilibrium which cannot be distinguished from the previous one." Formal relativity is thus a consequence of dynamics, not of geometry. Kajfosz notes a bonus: contraction, slowing of processes and mass increase cease to be independent postulates — in an optical clock, dilation follows automatically from contraction, and contraction of charge distributions yields the mass increase.
Decomposing the Lorentz transformation
The Lorentz transformation x′ = γ(x − vt), y′ = y, z′ = z, t′ = γ(t − vx/c2) is split into a Galilean part, which changes only the frame, and a remainder which changes only the units and the simultaneity convention. The intermediate description — the object at rest in the new IFR but still carrying the old assumptions — retains all the "relativistic" effects, which for Kajfosz "clearly" shows that those effects "are not associated with the motion of the object relative to the observer, but with the accepted assumption about how light propagates". The time equation's two pieces are labelled a "dilational" and a "synchronisational" part.
The velocity-space picture
Plotting SIMs as points in a velocity space, subluminal bodies fill a sphere C of radius c, light lives on its surface, and the hypothetical superluminal class lies outside; effects grow with distance from the centre. Since c = c′, the Lorentz transformation maps the sphere onto itself and merely shifts which point sits at the centre, leaving the three-class division invariant. Kajfosz's summary image is that "since there exists a sphere, there must exist also its center" — and that reading Einstein's second postulate as a statement about speeds rather than descriptions "would be equivalent to the statement that each point inside the sphere C is its center." He closes by dispelling a hope of his own side: clocks flown out and returned cannot locate S0, because the outbound and inbound legs almost cancel, leaving only the familiar direction-independent effect in which "the returning object is always 'younger'."
Assessment
The paper is unusually disciplined for its genre. Kajfosz concedes the principle of relativity, concedes the Lorentz transformation, concedes that no experiment can distinguish his view, and states these concessions at the outset instead of letting them emerge under pressure. The property/description distinction is a real philosophical point and is deployed consistently: the notation D(R, SB, FA, IA, UA), cumbersome as it is, does useful work by making explicit which assumption set produced which number — something standard treatments leave tacit. The observation that a measurement using standards subject to the same change as the object measured cannot register that change is correct and worth stating plainly. The dynamical account of contraction as restored equilibrium is a recognisable and respectable line, close to the constructive reading that Lorentz himself favoured; and Kajfosz's remark that dilation follows from contraction in an optical clock, rather than being separately postulated, is a genuine economy.
The difficulties are of principle. The step that carries the whole argument — from "descriptions under one assumption set differ" to "the properties themselves differ" — is asserted, not derived. It goes through only if one has already granted that a description made with a single fixed assumption set is the privileged window on reality, which is exactly the point at issue; the standard reading answers that the mismatch reflects the geometry of space-time rather than a change in bodies, and Kajfosz does not engage that answer beyond calling it a "mixing-up [of] the physical concepts with the geometric ones" in his summary list. The sphere argument is rhetoric doing the work of proof: velocity space is not a Euclidean ball with a metrically distinguished centre in any frame-independent sense, and "since there exists a sphere, there must exist also its center" is a metaphor, not a derivation.
Nor is the account free of assumption where it claims not to be. The claim that one and only one SIM can have isotropic light speed presupposes the very structure it means to establish; in the standard reading, isotropy under each frame's own conventions is the situation, not a contradiction. And the paper's central concession cuts both ways: an interpretation that is by construction indistinguishable from the received one cannot be preferred on evidence, so the argument reduces to a claim of superior intelligibility. That is a legitimate claim — but the paper does not weigh it against the costs, notably that the privileged frame is in principle unobservable, that the compensating changes must be exact to all orders for every kind of matter and every interaction, and that this exactness is asserted from the equilibrium argument rather than shown. Modern high-precision tests bear directly on this: rotating optical-resonator experiments constrain anisotropy in the one-way light speed to parts in 1017, so the required conspiracy is now a very tight one. Kajfosz's own example of muon lifetimes extended "even hundreds of times" in storage rings is accurate as a fact, but it is equally a prediction of both accounts, and so illustrates rather than resolves the impasse he describes.
Where the paper is at its weakest is in explaining that impasse. Kajfosz attributes the century-long failure of dialogue largely to imprecision on the standard side — its alleged conflation of descriptions with properties, of frames with states of motion, of formal with physical equivalence. Those four charges are stated in the summary as a list, without any worked example of a mainstream text committing them. Given how carefully the rest of the article argues, that omission is conspicuous, and it leaves the concluding section reading as complaint where the body of the paper reads as analysis.