Explanation of the Results of the Michelson Experiments Using Classical Mechanics
| Scientific Paper | |
|---|---|
| Title | Explanation of the Results of the Michelson Experiments Using Classical Mechanics |
| Read in full | Link to paper |
| Author(s) | Victor Nikolayevich Cochetkov |
| Keywords | Ether, the invariance of speed of light, the law of conservation of momentum, the special theory of relativity |
| Published | 2012 |
| No. of pages | 17 |
Read the full paper here
Abstract
The article is attempts to show that the results of A.A. Michelson experiments not conflict with classical mechanics, but rather confirm it. Using the laws of conservation of momentum and energy in the consideration of the Michelson interferometer allows us to conclude that the path difference of separated beams is independent of speed and direction of movement of the luminiferous medium.
Overview
The paper is a seventeen-page argument by V. N. Kochetkov — the byline on the PDF reads "Kochetkov Victor Nikolayevich", chief specialist at FSUE TSENKI, the Russian centre for the operation of space ground infrastructure; the wiki indexes him under the transliteration Victor Nikolayevich Cochetkov. Its thesis is that the null result of the Michelson experiments is not evidence against the aether at all, but a straightforward consequence of classical mechanics correctly applied — specifically, of applying conservation of momentum and energy to the interferometer and its light together, as a single closed system.
The departure from the standard account is located at a single point. The textbook derivation of the expected fringe shift, Kochetkov argues, rests on an assumption that is never stated as an assumption and is plainly false: that light travelling inside the interferometer does not interact with the interferometer's own components. "How can a beam of light reflected (to change the direction of its momentum) of the mirror and it does not have any influence on these mirrors? It is — it is unreal!" Once the mirrors and beam-splitter are allowed to recoil, the arm lengths in the moving frame are no longer the simple expressions of the textbook derivation, and — Kochetkov claims — the path difference ΔL comes out independent of the magnitude and direction of the aether velocity V. The interferometer therefore cannot detect an aether wind, and its null result licenses no conclusion about whether an aether exists. The paper is written in a somewhat rough English translation from Russian; several sentences are garbled, and one in particular (in section 3) states the opposite of what the accompanying formula shows.
The argument
The standard derivation restated
Sections 1 and 2 set out the conventional analysis for the arrangement of Fig. 1: source A, semi-silvered plate B, mirrors Z1 and Z2 at arm lengths l1 and l2, telescope D. For V parallel to the B–Z1 arm, the paths measured in the aether frame are
L1 = c t1 = l1c/(c − V) + l1c/(c + V) = 2l1/(1 − V2/c2)
for the longitudinal arm, and L2 = 2l2/√(1 − V2/c2) for the transverse one, giving ΔL = L1 − L2. The generalisation to arbitrary angle α between V and the B–Z1 direction is then worked out in full, yielding
ΔL = [2/(1 − V2/c2)] · [l1√(1 − (V2/c2)sin2α) − l2√(1 − (V2/c2)cos2α)]
which reduces to the α = 0 case as required. The point of carrying the angle through is that on this analysis ΔL varies with orientation, so rotating the apparatus should shift the fringes.
Kochetkov is unusually careful to enumerate what this derivation quietly assumes. His list runs to nine items: reflection at the mirrors and plate is instantaneous; there is no interaction between beam and plate while light traverses the plate; displacements of the optical components under light pressure are neglected; deformations of mirrors and plate under light pressure are neglected; frequency changes on interaction are neglected; "there are no changes in the values of the momentums of the light and the Michelson interferometer, as a whole, when the beams of light interact with the structural elements"; the aether's characteristics inside the beam volume do not change on interaction; and the arm lengths stay constant in time. It is the momentum assumption that the rest of the paper attacks.
The mechanical analogue
Section 3 replaces the interferometer with a closed mechanical system to make the point without optics. A rectangular parallelepiped has sides A, Z1, Z2, D and an internal plate B; two point bodies leave side A together with equal speeds, one taking the B–Z1–B route and the other the B–Z2–B route, both finally striking D. If the bodies are stipulated to bounce off the walls without transferring any momentum — the mechanical counterpart of the optical assumption — the path lengths come out as
L1 = 2l1/(1 − V2/v2), L2 = 2l2/√(1 − V2/v2)
with v the body speed, exactly parallel in form to the optical results (1) and (2). Kochetkov's verdict on this is blunt: "But it is impossible that the bodies to interact without changing their momentums."
He then redoes the calculation allowing recoil. Each bounce now carries its own bookkeeping — Vz11 is the velocity the box acquires toward Z1 when body 1 leaves side A, v12 the body's speed after leaving Z1, and so on through nine such quantities for the two routes. Because the box plus bodies is a closed mechanical system, all nine are fixed by conservation of momentum and energy. The claimed result: ΔL "does not depend on the magnitude and direction of the velocity V of the motion of the moving inertial system of axes relative the parallelepiped".
Transfer to the interferometer
Section 4 carries the conclusion back to optics. The revised assumption list is the original one with a single item reversed: light does interact with the mirrors, plate and telescope. To close the system, Kochetkov adds that the light exists only in a limited volume around the interferometer — "light is not propagate any source beyond of the interferometer the outside" — so that the instrument together with the surrounding aether "can be regarded as conventionally closed system", within which momentum and energy must be conserved because neither is exported. He acknowledges a disanalogy with the mechanical model: light acts on the optics not like a discrete body but "more like a stream of ether, which has a periodically varying characteristics".
The concluding inference is that "a similar result should lead", namely that ΔL is constant, independent of the speed and direction of the aether, so that reorienting the apparatus produces no fringe shift. The paper's final sentence states the whole claim: the Michelson experiments "may not serve as confirmation of the lack of the ether, as using the Michelson interferometer can not register the ether wind."
Assessment
The instinct behind the paper is a legitimate one, and it is stated more sharply here than in most aether-retaining accounts. Radiation pressure is real; mirrors do recoil when they reflect light; and the standard fringe-shift derivation genuinely does treat the interferometer as a rigid, inert scaffold whose components neither move nor absorb momentum. Kochetkov deserves credit for setting out that assumption explicitly, as a numbered item alongside eight others, rather than leaving it implicit as textbooks do. The mechanical analogue is a well-chosen device: it isolates the question of momentum bookkeeping from any dispute about the nature of light, and the α-dependent form of ΔL in equation (6) is correctly derived and correctly reduces to the α = 0 case.
The difficulties are serious, and three are decisive. The first is that the central result is asserted, not derived. The claim that conservation of momentum and energy makes ΔL independent of V is stated twice — once for the mechanical model at the end of section 3, once for the interferometer in section 4 — and in neither place is the calculation performed. Equations (9) and (10) define the nine recoil velocities and then stop; the reader is told they "can be determined by using the laws of conservation of momentum and energy" and that this "leads to the conclusion", but no solution, no algebra and no numerical example appears. For a paper whose whole force depends on that cancellation, this is the step that most needed to be shown.
The second is one of magnitude. Radiation pressure on the mirrors of an interferometer is of order P/c for beam power P — for a laboratory source, on the order of 10−9 N or less against a several-hundred-kilogram sandstone-and-mercury float in Michelson and Morley's 1887 apparatus. The predicted classical fringe shift, by contrast, is of order v2/c2 times the arm length in wavelengths — about 0.4 fringe for the 1887 arms. Nothing in the paper estimates either quantity, so nothing establishes that recoil effects are anywhere near the size needed to cancel the expected shift; and the two scale differently with beam power, so the cancellation would have to be an accident that happened to hold at every intensity Michelson, Morley and Miller used.
The third is the closure step. Treating "the interferometer and the surrounding ether" as a closed system requires the stipulation that light does not propagate outside the instrument, which is simply false — the beam reaching the telescope leaves it, and the source radiates in all directions. More fundamentally, the aether the paper posits is one that "do not interact with structural elements of the Michelson interferometer", so it is unclear what work the aether can do inside the conservation argument.
Finally, the argument, even if granted, is an argument about one instrument. The isotropy of light propagation is now constrained by methods that share no mechanism with the Michelson interferometer — resonant optical and cryogenic microwave cavity experiments of Michelson–Morley type, Kennedy–Thorndike and Ives–Stilwell configurations, and modern rotating-cavity tests reaching parts in 1017. A recoil argument specific to a beam-splitter and two mirrors does not touch these. The paper's conclusion — that the interferometer cannot register an aether wind — would need to be extended to every one of those geometries before it could support the broader claim that the aether survives untested.
The translation should also be noted for readers: the English is rough throughout, and the sentence opening section 3 ("difference of length ΔL must be independent of the angle α, ie difference of length ΔL is dependent on the direction of vector velocity V") contradicts itself and contradicts equation (6), which plainly depends on α. The intended sense is evidently that the classical analysis predicts an orientation dependence, which the experiments did not find.