The Overlooked Phenomena in the Michelson-Morley Experiment

Scientific Paper
Title	The Overlooked Phenomena in the Michelson-Morley Experiment
Read in full	Link to paper
Author(s)	Paul Marmet
Keywords	Michelson-Morley experiment, relativity theory, Classical Physics
Published	2006
Journal	Galilean Electrodynamics
Volume	17
Number	4
No. of pages	12
Pages	63-71

Read the full paper here

Abstract

We show here that Michelson and Morley used an over simplified description and failed to notice that their calculation is not compatible with their own hypothesis that light is traveling at a constant velocity with respect to a rest frame. During the last century, mathematicians uselessly solved the Michelson-Morley equations in numerous ways without realizing that two essential fundamental phenomena are missing in the Michelson-Morley equations. We see that the law of reflection of light on mirrors must be corrected when the mirror is moving. Also, due to the transverse direction of the moving frame, light does not enter in the instrument at 90^o as assumed in the Michelson-Morley experiment. We acknowledge that, the basic Michelson-Morley idea, to test for non-isotropy of space-time by comparing times taken by light to travel in parallel directions vs. transverse directions, is very attractive. However, we show here that this test is not valid, because of those two classical secondary phenomena, which have not been taken into account. When these overlooked phenomena are taken into account, we see that a null result, in the Michelson-Morley experiment, is the natural consequence resulting from the assumption of an absolute frame of reference and classical physics. On the contrary, a drift of the interference fringes must be observed in order to support Einstein's relativity. Therefore, for the last century, relativity theory has been based on a misleading experiment.

Overview

Paul Marmet's target here is not the Michelson-Morley measurement but its prediction. He accepts the experimental record — no fringe drift of the predicted amplitude has ever been seen — and accepts the experiment's own framework: an absolute rest frame in which light travels at c, with Galilean transformations and no relativistic corrections whatever. His claim is that within that framework Michelson and Morley made an arithmetic omission, and that when it is repaired the two arms of the interferometer take exactly the same time in every orientation. The null result then becomes the classical prediction rather than an anomaly.

The two omissions are (i) that the law of reflection at a 45° beam-splitter is altered when the mirror itself is moving through the rest frame, and (ii) that light from a source carried along with the apparatus does not enter the instrument along the geometric Y axis but at a small angle to it — a version of the aberration Bradley found in 1725. Marmet's provocative conclusion is the reverse of the textbook one: since classical physics with an absolute frame now predicts a null result, and since (on his reading) a fringe drift "would be required in order to support Einstein's relativity", the observed null result "invalidates Einstein's relativity". He is careful to add that this does not resurrect the ether either: "the presence of ether appears totally useless, when an appropriate model is used. Without matter nor radiation, space is nothing."

The argument

The paper's equations are set as images and do not extract from the PDF; what follows describes them from Marmet's own surrounding text.

The standard calculation restated

Marmet first reproduces the 1887 reasoning in the absolute frame. Along the arm parallel to the motion, light crosses at (c − v) outbound and (c + v) returning, giving a round-trip time t_v = t_o(1 + v²/c²) to second order, where t_o = 2L/c. Along the transverse arm the light path in the rest frame is an isosceles triangle, giving t = t_o(1 + v²/2c²) — "only half of the other value". The residual Δt = (t_o/2)(v²/c²), doubled by a 90° rotation that exchanges the arms, is the predicted fringe drift.

Reflection on a moving mirror

Marmet's first correction. Consider the 45° splitter M moving downward at v in the same direction as the incoming light. He first gives a pictorial argument: because the wavefront sweeps across the mirror face in a finite time while the mirror descends, the effective reflecting surface traced out is tilted with respect to the instantaneous 45° plane — the "effective moving mirror" of his figure 2, whose tilt is half the change in the reflection angle.

He then computes the angle directly by Huygens construction. Let P be the projected width of the wavefront on the mirror. Light descends at (c − v) relative to the moving mirror, so the time to sweep the face is T₁ = P/(c − v). During T₁ the already-reflected light from the near edge travels a horizontal distance D = cT₁ = P/(1 − v/c), so D − P = Pv/c and

tan α = (D − P)/P = v/c.

Light is therefore reflected at (90° + α) rather than 90°. Reversing the mirror's direction reverses the sign of α; an appendix repeats the construction for a mirror moving transversely and obtains the same magnitude.

Aberration of the entering beam

The second correction. The source travels with the interferometer, so the wavefront arriving at M was emitted from a position the source has since left. Light reaching M therefore makes an angle θ with the Y axis even though the source is instantaneously directly above M. Marmet insists this is a wholly classical statement about transit time, not an observational illusion: the light "either can be considered to move at velocity c at the angle θ in the rest coordinates, or at velocity c cos θ along the Y axis of the moving coordinates", so the transit time between M and M₂ is (L/cos θ)/c. He offers the analogy of two cars sounding horns while driving abreast in still air: each driver hears the other's horn from abeam, but the sound's transit time is lengthened by 1/cos θ.

The cancellation

With the frame moving parallel to the incoming light (his figure 4), the transverse arm's beam is not sent from A to C and back but from A to C′ and back, the path being longer by the factor 1/cos α. Expanding, t(A→C′→A) = t(A→C→A)(1 + α²/2). Since α = v/c and t(A→C→A) = t_o(1 + v²/2c²), the product is t_o(1 + v²/c²) — identical to the longitudinal arm. The missing half of v²/c² is exactly supplied.

For the frame moving transverse to the incoming light (his figure 5) the two corrections trade places: light strikes the splitter at (45° − θ), and the moving-mirror correction α restores the reflected beam to the X axis, so that arm is the ordinary longitudinal case; while the transmitted beam travels A→B′→A at angle θ, picking up the same 1/cos factor. Reversing the direction of motion changes only signs. Marmet concludes that "the time taken by light to travel between mirrors is always the same", in every orientation, so "the rotation of the Michelson-Morley apparatus in space should never show any drift of interference lines."

Extensions

He notes the same overlooked effects should be carried into other tests: he claims the derivation of length contraction from the Lorentz transformation is affected, and that in the Brillet and Hall experiment a corresponding change of the light path inside the Fabry-Pérot etalon means the observed null frequency shift again corresponds to an absolute frame. Fourth-order terms, the Fizeau drag and mirror misalignment are all judged negligible by comparison, though he remarks that transverse Fizeau drag "seems to be totally unknown".

Assessment

What is genuinely valuable here is the discipline of the exercise. Marmet does not import relativistic corrections and then complain about them; he stays inside the 1887 framework and asks whether its own geometry was carried through consistently. The two effects he raises are real physical effects — reflection from a mirror in motion relative to the medium is modified, and aberration between a co-moving source and detector is present — and it is a fair question whether the original paper handled them. The car-horn analogy is a clean way to make the point that the transit time can be lengthened even though each observer sees the signal arriving from abeam. He is also unusually consistent for this literature in refusing to conclude that an ether exists.

The decisive difficulty is that the correction appears to be the same effect counted twice. The transverse-arm formula he starts from, t = 2L/√(c² − v²), is derived from the isosceles-triangle path — and that triangle's half-angle satisfies tan = v/c, with each leg longer than L by precisely the factor 1/cos of that angle, i.e. by (1 + v²/2c²). Marmet's α is the same v/c, and his correction multiplies by the same 1/cos α. In other words the tilt of the light path relative to the arm, and the second-order path lengthening it causes, are already the entire content of the standard transverse result; applying them again as a separate "law of reflection" correction doubles a quantity that has been counted once. That the two happen to be numerically identical is not a coincidence but the reason his cancellation comes out exact.

Two further points tell against the derivation on its own terms. First, the reflection calculation mixes frames: the sweep time is computed with the light descending at (c − v) relative to the moving mirror, while the horizontal run of the already-reflected light is taken at c in the rest frame, with the frame's own downward v not carried along. In a strictly Galilean absolute-frame treatment both legs must be referred to the same frame, and doing so removes the asymmetry that generates α. Second, the geometry assumes the beam returns to A. A tilt of α ≈ v/c ≈ 10⁻⁴ rad is not a small perturbation of the path shape: over the 11 m effective arm of the 1887 apparatus it displaces the beam at the end mirror by about 1 mm, and a plane end mirror sends a beam arriving at α back at α, landing roughly 2 mm from A rather than at A. Marmet writes the path as A→C′→A and takes its length as 2L/cos α, which presumes the very return the tilt would prevent. In the standard treatment the closure condition — that the light must actually strike the fixed end mirror and come back to the splitter — is what fixes the ray direction; it is not free to be adjusted afterwards.

The interpretive claim is also mis-stated. Special relativity does not predict a fringe drift in this experiment: the interferometer is at rest in its own inertial frame, the two arms are 2L/c each, and the null result is the theory's straightforward prediction. Marmet's sentence that "a positive shift of interference fringes with the amplitude compatible with the Michelson-Morley predictions is required in order to be compatible with Einstein's relativity" appears to identify relativity with the Lorentz-ether reading in which the contraction is invoked to hide a real anisotropy; on that reading a shift is indeed cancelled by contraction rather than absent, but that is not what the sentence says. The section 6 remark about "the non-zero result observed in the Michelson-Morley experiment" also sits oddly against the rest of the paper, which everywhere treats the result as null.

Finally, the empirical target has moved a long way since 1887, and a mechanism that works by cancelling a mechanical path difference in a two-arm rotating interferometer has to be re-examined for each newer geometry. Modern isotropy tests use cryogenic optical resonators and clock comparisons rather than beam-splitter path lengths, and constrain a direction-dependent variation in c at the level of a few parts in 10¹⁸; the Kennedy-Thorndike class of experiments, with deliberately unequal arms, tests the velocity dependence that a pure geometric cancellation of this kind does not address; and the time dilation of the Ives-Stilwell transverse Doppler measurement is not a path-length effect at all. Marmet addresses Brillet and Hall by referring to a companion analysis, but the general burden — showing that the same cancellation reappears in every one of these different geometries — is acknowledged rather than discharged. The paper is best judged as a sharp and legitimate question about the 1887 derivation whose proposed answer rests on double-counting the aberration angle.

See also

• Paul Marmet
• Michelson-Morley Experiment
• Albert A. Michelson
• Dayton C Miller
• Stellar Aberration
• Aether
• Length Contraction
• Lorentz Transformation
• Speed of Light
• Special Relativity