Special Relativity Postulates
| Scientific Paper | |
|---|---|
| Title | Special Relativity Postulates |
| Read in full | Link to paper |
| Author(s) | Yuri N Keilman |
| Keywords | special relativity, Lorentz metric, time dilation, length contraction, 4-d ether |
| Published | 2009 |
| No. of pages | 19 |
Read the full paper here
Abstract
This text is towards the discussion that will be held on 8-8-09. I like the interested people to know my direction beforehand. This particular version was uploaded on 8-7-09.
Overview
The document is Keilman's position paper for a debate held on 8 August 2009, headed "Debate: Einstein's Special Relativity Postulates: True or False?" It is written as a sequence of numbered slides rather than as continuous prose, and its target is not the relativists but Keilman's fellow critics of relativity. His answer to the debate question is neither "true" nor "false" but "misposed": the postulates are consequences that Einstein promoted to starting points, and arguing about their truth is arguing about the wrong thing.
Keilman's own position is unusual within the dissident literature. He accepts Special Relativity as "a classical theory and a big discovery" and defends its mathematics as "not disputable," while charging Einstein with a "phenomenal" misrepresentation in the way he presented it. What he denies is that time dilation and length contraction are physical at all — against Lorentz, who thought they were real changes caused by motion through the Aether, and against those relativists who treat them as real effects on physical systems. And he ends by reinstating an aether of his own: a four-dimensional one, absolute, and immune to the influence of matter, which is an explicit denial of general relativity.
The argument
Step one: coordinates require a metric
The paper opens with pure mathematics. A coordinate system is introduced by naming coordinates, giving their span, and — the point Keilman keeps returning to — giving a metric tensor, "we need one to know the norm of a vector." A POINT is a mathematical object carrying identity, definite once its coordinates are given, whose identity survives an arbitrary coordinate transformation provided a unique inverse exists. The set of all points constitutes a SPACE, which therefore "has objective meaning (remains the same does not matter what coordinate system is used)." Vectors and tensors are defined the same way, by the transformation laws their components obey.
He then works the Lorentz and Galilean transformations through the tensor transformation law g′ik = (∂xa/∂x′i)(∂xb/∂x′k)gab, starting from the Lorentz Metric in covariant components g00 = 1, g01 = g10 = 0, g11 = −1. Under the Lorentz transformation the components come back unchanged; under the Galilean transformation they do not, acquiring V-dependent terms. The moral is stated as an injunction: "no coordinate system exist without Metrics Tensor."
Step two: the correct order of derivation
Keilman then sets out what he calls "the normal introduction of SR," in four steps:
- Maxwell's Equations are written in four independent coordinates t, x, y, z, and therefore require a 4-dimensional coordinate system.
- The Lorentz Metric follows from Maxwell's equations.
- The Lorentz Transformations provide invariance of the Lorentz Metric — so every moving coordinate system obtained by an LT has the same metric tensor. "It is the consequence but Einstein turned it to the 1st postulate."
- The 4-vector of velocity of any object is a unit vector; for light all its components are infinite while the norm stays unity, and this makes the coordinate speed dx/dt equal to 1 in every such system. "This consequence Einstein used as a 2nd postulate."
On Maxwell's equations themselves he makes a point that separates him from most aether theorists: the system is a partial differential system in four independent variables whose characteristics are wave fronts moving at c, and "the constancy of the speed of light does not require 3-d ether (as thought Maxwell, Lorentz and many up to the present day) because it can have another explanation (demonstrated by Einstein)."
His charge against Einstein is then specific. Einstein discovered that Lorentz was wrong to claim physical time dilation and length contraction — "instead of saying truth, he confirmed Lorentz." To convert a mathematical improvement into a new physical theory he "hid LM as much as possible, turned the consequences into the starting points (postulates), endowed the coordinate systems with frames and observers... and used LT wherever normally LM is needed." Keilman adds that to describe any physical situation, or the whole world, "only one coordinate system (with LM) is needed" — observers and frames are decoration.
Step three: why dilation and contraction are not physical
The physical claim rests on a single argument repeated in three forms. Since a coordinate transformation is performed "without ever disturbing the physical object," the object's physical properties cannot differ between coordinate systems; therefore "'time dilation' and 'length contraction' have no physical meaning," the physical content being carried instead by proper time and proper length. Separate coordinates of a point carry no identity — only the full set does — and "the physical system can be physically changed only by interaction with another physical system."
The light clock is worked through: with mirrors separated by d, a clock moving at v has t1 = (d/c)/√(1 − v2/c2), so the moving clock ticks slower in coordinate time. Lorentz read this as a physical slowing caused by motion relative to the resting aether. Einstein, on Keilman's telling, asked instead for the 4-dimensional extension of Pythagoras' theorem, Δτ2 = Δt2 − Δx2/c2, which is the Lorentz Metric — and with Δτ = 1 the physical time of the moving clock has not changed at all. The twin case is different in kind, Keilman notes, because there the physical times really do differ: "the straight way between two events is the longest way in LM (in EM the straight way is the shortest)."
The simplification he offers is a drawing on paper. A physical line AB of unit length is laid on a Euclidean plane; choosing the coordinate angle φ = 0 aligns x with the line and gives x2 = 1, while any other φ gives x2 = cos φ < 1 — "if we turn our attention only to x-axis and forget about y-axis then it looks like our physical line 'contracted' — but actually it is not." Repeating the construction in the (t, x) plane with the Lorentz Metric, x2/c = sinh ψ and t2 = cosh ψ, gives a "dilated" t2 > 1 for ψ ≠ 0 — "but we did not touched the clock!" He adds, pointedly, "Notice also that I disconnected observer (myself) from the coordinate system."
Step four: the 4-d ether and the paradigm
From Einstein's approach, Keilman concludes, "it follows that 4-d space is absolute." Einstein denied the 3-d aether and thought no aether existed at all, using "space-time" and allowing matter and fields to influence it. Keilman's counter-proposal: 4-d space "can be called 4-d ether," a physical category that is not a substance and is not perishable, absolute, described by the Lorentz Metric and by all the points of 4-d space, and — the crucial clause — one that "can not be influenced by the presence or absence of matter (this is the denial of GR)."
The closing PARADIGM section generalises the complaint. Mathematics and theoretical physics have "definitely gotten astray" and have intermixed over the last hundred years. Mathematics and linguistics alike are "products of human society — they did not exist in nature before humans came"; both work by inventing unique constructions used to describe physical reality, and both must be kept separate from the objects they describe.
Assessment
The distinctive move here is worth stating plainly, because it is rarer than it looks: Keilman turns the standard dissident objection inside out. Most critics on this wiki argue that time dilation and length contraction are absurd and therefore relativity is false. Keilman argues that they are not physical claims at all, and that the absurdity belongs to the presentation rather than to the mathematics. His derivation order — Maxwell → Lorentz Metric → Lorentz Transformations → the two postulates as theorems — is defensible and has the pedagogical merit of showing where the constancy of c actually comes from. The insistence that no coordinate system exists without a metric tensor is elementary but is exactly the point at which many popular anti-relativity arguments go wrong, and the paper's quiet detachment of the observer from the coordinate system removes a great deal of the mystification that surrounds "what the observer sees." The rotated-line analogy is the clearest thing in the paper.
The difficulties are real. The most important is that the argument proves less than Keilman needs. It is true that relabelling coordinates cannot alter a physical system; it does not follow that dilation and contraction are merely relabelling. The muon lifetime measured at rest and in flight, and the transverse Doppler shift confirmed in the Ives–Stilwell experiment, involve comparisons of physically distinct world lines — precisely the twin situation Keilman himself concedes is a genuine difference of proper time. He does not explain where the line falls between the cases he dismisses and the case he admits, and the whole weight of the paper's positive claim rests on that line.
Second, several steps are asserted rather than derived. "Lorentz Metric follows from Maxwell's Equations" is stated but never shown — what is shown is that the LM is invariant under LT and not under GT, which is a different proposition. The claim that "the 4-vector of light velocity has all its components infinite (but still unit norm/speed)" is a formal contortion; the standard treatment is simply that a null vector admits no proper-time parameterisation, and calling its components infinite invites the confusion Keilman elsewhere wants to remove.
Third, the "4-d ether" is a name, not a theory. Keilman calls it a physical category that is not a substance and cannot be affected by matter, and offers nothing that would distinguish it from Minkowski spacetime under a different label; no equation, prediction or measurement follows from the renaming. Its only work in the paper is to license the rejection of general relativity, and that rejection is not argued at all — it is asserted in a parenthesis, without engaging the light deflection, gravitational redshift, Shapiro delay or the observed orbital decay of binary pulsars, all of which any theory holding the metric immune to matter must account for by other means.
Finally, this is a debate handout, not a finished paper: it is fragmentary, its notation is inconsistent in places, and its rhetoric ("This misrepresentation is phenomenal") sometimes stands in for the argument. Read for what it is — a statement of direction addressed to fellow critics — it is a clear and unusually self-consistent one.