Paradoxe Relativität
| Scientific Paper | |
|---|---|
| Title | Paradoxe Relativit |
| Read in full | Link to paper |
| Author(s) | Erich Wanek |
| Keywords | special relativity, light velocity |
| Published | 2005 |
| No. of pages | 14 |
| Pages | 406-418 |
Read the full paper here
Abstract
In this (German) paper the following topics are dealt with
- Michelson's experiment may be interpreted in another way.
- When the velocity c = x/t is computed according to Lorentz's formula, it comes out that the contraction of length, equal 1 / (1 - v2/c2)1/2, and and the dilation of time, equal 1 / (1 - v2/c2)1/2, cancel each other out.
- The transformation of time is dependent on the direction of motion. This is to mean that clock time varies with the direction of motion with respect to the source of light.
- The clock paradox and relative motion.
- Space is not curved, but light rays are bent by gravity.
The velocity of escape from the universe exceeds, given its size and mass, the velocity of light. Therefore, the universe as a whole behaves like a black hole with all types of galaxies revolving around its center.
Overview
The paper is written in German; its full title is Paradoxe Relativität (the wiki page title is truncated). It is a chapter of Erich Wanek's Was von moderner Physik bleibt und fällt, Band I: Relativitätstheorie (Verlag Kritische Wissenschaft, Windeck/Sieg, 2005), occupying pages 406–418. Wanek notes in an opening footnote that it continues arguments he had published as early as 1959 in Wissen im Werden ("Lichtgeschwindigkeit und Bezugssystem") and in the 1962 Graz collection Kritik und Fortbildung der Relativitätstheorie edited by Karl Sapper, and he points readers to his Physics Essays 21/4 article "The particlewave" for the particle-wave model that underlies his view of light.
Wanek's thesis is that the Michelson–Morley experiment does not require Einstein's postulate at all. It shows only that light propagates isotropically for an observer at rest with respect to the apparatus, and that fact, he argues, is explained just as well by supposing that light is carried along by whatever field predominates at the place of the experiment — the Earth's gravitational or magnetic field — or alternatively by a ballistic emission of light quanta. On this reading the constancy of c is a local, field-bound constancy, not a universal one. Special relativity, he says, ignores these possibilities and instead postulates that any arbitrarily moving observer always measures c0; the paradoxes of the theory follow from that postulate rather than from nature. His conclusion is blunt: length and time do not really change, they only appear to change because the moving observer computes them differently — "die Zeit ist absolut und verändert sich nicht".
The argument
Two readings of the Michelson experiment
Wanek begins with the picture an outside observer would have of a light flash emitted on the moving Earth. He offers the homely image of a child inflating a balloon in a moving car: the observer standing in the street sees the expanding spherical surface travel along with the car, its centre staying with the source. If light is likewise "taken along" by the Earth's predominant field, then the outside observer measures c+v in one direction and c−v in the other, while the co-moving observer measures c in all directions, and nothing is paradoxical. He stresses that the demand of the principle of relativity that no experiment reveal a system's motion is already restricted in practice, because the field conditions of each reference frame — "die überwiegende Feldstärke" — must be taken into account, up to and including a superordinate field of the universe.
Relativity instead insists that the outside observer must also see a uniform sphere, which would put the same sphere in two different places; to avoid this it makes the two observers use different rulers (Length Contraction) and different clocks (Time Dilation) so that both obtain c = x/t. Wanek remarks that in principle either device alone would suffice: one could change only the rulers, or only the clocks.
The Lorentz transformation re-read
He then works through the transformation itself. Setting x = ct and x′ = ct′ in x′ = (x+vt)/√(1−v2/c2) and t′ = (t+vx/c2)/√(1−v2/c2), he obtains t′ = t(1+v/c)/√(1−v2/c2) — and in the opposite direction the same expression with (1−v/c). Forming c′ = x′/t′ the two radicals cancel and c′ = c identically. This is the abstract's second point: contraction and dilation simply annul one another.
What Wanek finds "bemerkenswert" is the residue. The classical factor (1+v/c) has to be cancelled by a time factor (1+v/c), which in his reading means nothing other than that the clocks must be synchronised differently according to the direction of motion relative to the light source. He rewrites the time factor as √((1+v/c)/(1−v/c)) = √((c+v)/(c−v)), and in the reverse direction √((c−v)/(c+v)), and observes that the quantities c+v and c−v therefore reappear inside the Lorentz Transformation itself.
Direction-dependence: three examples
A train passes a stationary light source. Its clocks were synchronised at rest and, on starting, can only have changed uniformly. Approaching, the observers must measure c rather than c+v; after passing, with the same rulers and clocks, they cannot suddenly measure c rather than c−v. Wanek computes the correction actually required at the moment of passage: a factor ((1−v/c)/√(1−v2/c2))2, which turns t′ into t″ = t(1−v/c)/√(1−v2/c2). An observer moving between two light sources, measuring both at once, would have to change his single clock by both factors simultaneously.
An observer at the equator measuring sunlight at sunrise and at sunset would classically get c+v and c−v with v the rotation speed; relativity requires c both times, which Wanek says presupposes that our clocks run slower at sunrise than at sunset. His third example is a long rotatable drum behind a slit, carrying a time scale — a row of synchronous clocks. Because the transformation desynchronises them for a moving observer, the drum would have to appear twisted, that is, deformed. He rejects the Simultaneity paradox that is offered in defence: it is a fallacy, he holds, to infer different times from a different signal speed, since precisely by knowing the signal speed one can synchronise clocks to equal times — and atomic clocks need no signals for comparison at all.
The clock paradox
If every moving clock runs slow, and either of two mutually moving systems may be called the resting one, the returning clocks must disagree in a way incompatible with the relativity principle. Wanek sharpens this with three systems: S1 and S2 moving at v1 < v2 relative to S3. An observer in S2, treating his frame as at rest, finds S1's clocks slow; an observer in S3 finds S2's slow — flatly contradictory verdicts, and "ein heftiger Streit" if the two could compare notes. His resolution is that when the relative motion ceases and the frames are again mutually at rest, all clocks read the same, so they cannot have changed rate in the interval; the twins therefore return the same age.
He adds a check on length contraction. The solar system moves at 275 km/s towards Cygnus; with an Earth radius of about 6×103 km the contraction in that direction would amount to a few metres, so every point near 40°–45° north latitude would have to rise and fall by metres daily, with "ungeheure Erdbeben und Flutwellen" as the consequence. Since nothing of the kind happens, the contraction is at most apparent — but a merely fictitious contraction and dilation cannot explain the Michelson result either.
Bent light, and the universe as a black hole
The last section attacks the Equivalence Principle's corollary of curved space. If space really were curved to the degree claimed, Wanek argues, we should see the starlight arriving in a straight line; the very fact that we observe a deflection shows that the ray is bent, not the space (Gravitational Lensing).
He then computes an escape velocity for the universe as a whole, treating it exactly as one treats an Earth satellite. Taking a radius of 5×1027 cm (the quoted range is 1027–1028 cm, about 5 billion light years) and a mass of 5×1055 g (quoted range 1055–1056 g), with f = 6.67×10−8 cm3g−1s−2:
- √(2fM/R) = √(13.34×1020 cm2s−2) = 3.65×1010 cm s−1
which exceeds the Speed of Light. Light quanta therefore cannot leave the universe but circle it as a satellite circles the Earth; the universe behaves like a Black Hole with the spiral nebulae orbiting its centre. The corresponding circular-orbit speed is
- √(fM/R) = √(6.67×1020 cm2s−2) = 2.58×1010 cm s−1
"also nahezu Lichtgeschwindigkeit" — and Wanek notes that computing the same speed from the Hubble constant, α = 0.5×10−17 s−1, as v = αr at r = 5×1027 cm gives the nearly identical 2.5×1010 cm s−1 (Hubble Constant).
Two consequences are drawn. Light from galaxies would reach us along a semicircle πr rather than a straight line, so for a diameter of 9–10 billion light years the path is 14–15 billion; and antipodal galaxies should be visible twice, in opposite directions, like a mirror image. Wanek claims that galaxies at equal distance in one half of the sky show a stronger Redshift than those in the other, which could depend on whether their light travels with or against the rotation of the universe. The redshift itself he would rather explain, instead of by a motional Doppler Effect, as a loss of energy and hence frequency suffered over the longer travel time in the universal gravitational or magnetic field (Tired Light). Whether the "Weltall" is finite or infinite he declines to say: outside our "universe" there may be countless similar structures each circling a centre of its own.
Assessment
The strongest part of the paper is its insistence on a question that popular expositions do dodge: what, physically, is doing the work when two observers are said to measure the same light sphere. Wanek's field-entrainment proposal is a genuine alternative hypothesis rather than a mere complaint, and it has a respectable ancestry in the entrained-Aether tradition and in Emission Theory. His algebraic observation is also correct as algebra: with x = ct the Lorentz factors do cancel and c′ = c identically, and the Doppler-like combinations √((c+v)/(c−v)) do fall out of the transformation. The section-3 examples are a clear and honest way of putting the point that the transformation's time shift is direction-dependent.
The difficulties are equally clear. The argument treats the t′ obtained by substituting x = ct — that is, the Doppler formula for a particular light signal — as though it were the general clock-rate relation, and then finds it "paradoxical" that it depends on direction. It does, but so does the classical Doppler shift; the rate relation of relativity, t′ = t/√(1−v2/c2), is direction-independent, and the direction-dependence Wanek isolates is precisely the relativity of simultaneity he dismisses in the same breath. His dismissal is asserted, not derived: the claim that atomic clocks "need no signals for comparison" overlooks that comparing two spatially separated clocks is exactly the operation that requires a synchronisation convention. The three-system S1/S2/S3 contradiction likewise assumes that "runs slow" is a frame-independent relation, which is the assumption at issue.
Two empirical points weigh against the conclusions. The claim that clocks do not really change rate is contradicted by measurements the paper does not address: the Hafele–Keating flying-clock comparison, the muon lifetime dilation in storage rings, and the Ives–Stilwell transverse Doppler shift, all of which give the √(1−v2/c2) factor directly. His length-contraction reductio — earthquakes from a daily change in Earth radius — mistakes a coordinate description in a frame in which the Earth moves for a physical deformation felt in the Earth's own frame; nothing in the theory predicts stresses in the co-moving frame.
The cosmological section is arithmetically sound but rests on a Newtonian formula applied outside its range. Escape velocity √(2fM/R) presumes a finite mass in otherwise empty space, which is not what the quoted radius and mass describe; the numerical coincidence that √(fM/R) comes out near c, and near the Hubble velocity at the same radius, is a restatement of the well-known near-equality GM/Rc2 ≈ 1 for the observable universe rather than an independent discovery. The predicted mirror images of antipodal galaxies are a real, testable consequence — and searches for matched-pair or matched-circle images have not found them. The asserted hemispheric asymmetry in redshift at equal distance is stated without data or citation and does not correspond to any established survey result. Nor does the paper address the (1+z) stretching of Type Ia supernova light curves, which is a direct measurement of cosmological time dilation and is difficult for any static or purely energy-loss redshift account.
Read as what it is — a critical chapter in a book of criticism, not a fully worked alternative theory — the paper is candid about its own limits. Wanek explicitly leaves open whether the world is finite or infinite, and offers the field-entrainment picture as an "Erklärungsmöglichkeit" rather than a finished mechanism.