Physical Essence of Michelson-Morley Experiment

Scientific Paper
Title	Physical Essence of Michelson-Morley Experiment
Read in full	Link to paper
Author(s)	Qing Zeng
Keywords	interference experiment, hypothesis of constancy of light velocity, Galilean principle, vector of light velocity
Published	2010
No. of pages	11

Read the full paper here

Abstract

This article restudies physical essence of Michelson-Morley experiment, and the result is: 1.Use Einstein's special relativity to calculate interference experiment, but the result is not consistent with experiment conclusion. 2. Use Galilean principle of relativity to calculate interference experiment, and the result is totally consistent with experiment conclusion. This means that Einstein's principle of constancy of light velocity loses the evidence. This article challenges relativity, it deserves the readers to read and it has significant physical significance.

Overview

Zeng Qingping, of the Air Force Radar Academy of the Chinese People's Liberation Army, argues that the Michelson–Morley experiment does not support Einstein's second postulate at all, and that it is instead a direct confirmation of the Galilean principle of relativity applied to light. His complaint is methodological: relativity, he says, "uses text language to state that light velocity is constant", and in words this appears to explain the null result, "but the situation is quite bad if mathematical language is used to calculate". When the relativistic velocity-addition formulae are applied to the two arms of the interferometer, he claims a residual optical path difference of β²d survives — the same difference the classical aether analysis predicts — so that relativity fails the very experiment it is said to explain.

His positive proposal is an emission account: light in vacuum has no oscillating medium and "the mass of light field is zero, the movement of light field need not any force, so light movement is a kind of radiation", constant at c₀ relative to its source. Since in the interferometer the source, the beam splitter and both mirrors are mutually at rest, the one-way optical path is d = c₀Δt in every arm and every orientation, and the null result follows immediately with no contraction, no time dilation and no aether. The paper is one of a long series by the author attacking Maxwell's field theory and the Lorentz transformation; its reference list closes with forthcoming titles including "Einstein's Lorentz Transformation Is a Math Game".

The argument

The classical aether calculation

Zeng first restates the textbook aether analysis, taking the interferometer at rest and the aether streaming past it at v. For the longitudinal beam b₁ the speeds are c₀−v and c₀+v, so

t₁ = d/(c₀−v) + d/(c₀+v) = (2d/c₀)·1/(1−β²)

For the transverse beam b₂ the effective speed is √(c₀²−v²) each way, so

t₂ = (2d/c₀)·1/√(1−β²)

giving a relative optical path difference of β²d where none is observed.

The claimed failure of special relativity

Zeng then repeats the calculation using the relativistic velocity transformation, taking the aether coordinate system as the moving (primed) frame and the interferometer as the rest frame. For the horizontal beam he sets u′_x = c₀, u′_y = u′_z = 0 and obtains

u_x = (c₀ + v)/(1 + v/c₀) = c₀

He is explicit about how pleased this made him: "It is amazing! Hypothesis of constancy of light velocity gets the mathematic prove in the calculation of horizontal wave velocity. We once cheered for it!" The round-trip time is then 2d/c₀ regardless of direction.

For the vertical beam he sets u′_x = 0, u′_y = c₀, u′_z = 0, and applies the transverse formula:

u_y = c₀√(1−β²)/(1 + 0) = c₀√(1−β²)

"The problem is revealed," he writes. "The motto of relativity is 'Physical essence which is vertical to the direction of movement is unchangeable'. But now there happens a problem: light velocity which is vertical to the direction of movement changes to c₀√(1−β²)." The transverse round trip therefore takes 2d/(c₀√(1−β²)), and equation (8) gives a residual difference, which he converts to an optical path difference of β²d — the same non-zero prediction as the aether theory. He addresses Einstein directly: "you said that light velocities detected by either two inertial systems were c₀, but you did not mention the static system."

The Galilean/emission resolution

Sections 4 and 5 rebuild the experiment on the premise that c₀ is a velocity relative to the emitter. Four exploded figures treat the cases of a source moving against, with, and transverse to the emission direction. In each case the absolute speed seen by the hypothetical "Ether person" differs — c₁ = c₀ − v, c₂ = c₀ + v, or by the parallelogram rule c = √(c₀² + v²) for transverse emission — but the mirror moves with the source by the same vΔt, so the separation actually traversed is always d = c₀Δt. Zeng's homely illustration is that "the time that a bullet fired at the stem hit the stern target is equal to the time that a bullet fired at the stern hit the stem target".

Applying this to both arms, and noting that "reflection is the second radiation launched by light source (hit the reflector), so the light source of reflecting light is reflector", he obtains t₁ = t₂ = 2d/c₀, hence Δt = 0 and zero path difference: "No matter which season is and how the interferometer rotates, because Δt = 0, the optical path difference is always zero and interference fringes do not exist."

He draws two further conclusions from the transverse arm. That beam b₂ hits the centre of M₂ at all "proves that light radiation has lateral stiffness"; and it "proves that light wave is not dragged by Ether, which means Ether does not exist."

Assessment

The paper's virtue is that it does not hide behind words: it writes the transformation down and computes. Its emission-theoretic resolution of the null result is also correct as far as it goes, and worth stating plainly — if light travels at c₀ relative to its source, and source and mirrors are rigidly attached, then both arms give 2d/c₀ and the Michelson–Morley null result is trivial. Zeng's classical aether arithmetic in equations (1) and (2) is also correct: t₁ = (2d/c₀)/(1−β²), t₂ = (2d/c₀)/√(1−β²), and to leading order c₀(t₁−t₂) ≈ dβ², exactly as printed.

The central claim, however, rests on a single algebraic omission, and it is checkable in one line. Zeng transforms u′ = (0, c₀, 0) into the interferometer frame and reports only the y component. But the same transformation he quotes as equation (3) gives, for the x component,

u_x = (u′_x + v)/(1 + u′_xv/c₀²) = (0 + v)/(1 + 0) = v

He writes u_x = 0 in equation (7). Restoring the term, the speed of the light in the interferometer frame is

|u| = √(u_x² + u_y²) = √(v² + c₀²(1−v²/c₀²)) = √(v² + c₀² − v²) = c₀

exactly, with no approximation. The relativistic velocity transformation is in fact constructed so that the light cone is invariant; a light ray transforms to a light ray in every frame, which is what the identity above expresses. What changes is the direction — the beam that runs straight up the arm in the interferometer frame is aberrated in the aether frame, which is precisely the classical aberration triangle — not the speed. Zeng's reduced value c₀√(1−β²) is the y-component alone, and it is smaller than c₀ only because the missing x-component v has been discarded. So the paper's headline result, that relativity predicts an unobserved fringe shift of β²d, does not follow from the formula it invokes. Relativity in fact predicts t₁ = t₂ = 2d/c₀ in the instrument frame, hence exactly the observed null.

There is a related conceptual slip. Zeng repeatedly says relativity's "motto" is that quantities transverse to the motion are unchanged. What is unchanged transversely is length, not velocity: transverse velocities do transform, by the factor √(1−β²), for exactly the reason that the time interval transforms. This is standard textbook content, not an inconsistency uncovered in the theory.

The positive half of the paper is a rediscovery rather than a discovery, and this should be said clearly rather than as a criticism of the author's reasoning. That the ballistic or emission hypothesis explains Michelson–Morley without contraction has been known since Ritz put it forward in 1908, and is the reason the experiment alone was never taken as sufficient evidence for the second postulate. Emission theory fails on other evidence, and the paper does not engage with any of it. De Sitter's 1913 binary-star argument shows that source-dependent light speed would make the orbits of spectroscopic binaries appear grossly non-Keplerian; Brecher's 1977 analysis of X-ray binaries — where the extinction loophole Fox raised against de Sitter does not apply, because the X-rays travel through effectively transparent space — bounds any source-velocity dependence at k < 2×10⁻⁹. Alväger and colleagues at CERN in 1964 measured the speed of 6 GeV gamma rays emitted by neutral pions moving at 0.99975c and found c to within about one part in 10⁴, where the emission hypothesis predicts nearly 2c. The Kennedy–Thorndike experiment with unequal arms, and modern resonator versions of it, constrain the velocity dependence of clock rates to parts in 10¹⁷; and the Sagnac effect, on which the operation of ring-laser gyroscopes and the GPS depends, requires the one-way light-travel asymmetry that a purely source-relative speed would eliminate. The claim that light has "lateral stiffness" is asserted without argument, and the inference that a centred transverse spot "proves Ether does not exist" would follow equally from ordinary aberration.

Finally, a point of historical detail: the 1881 experiment described in section 2 was Michelson's alone in Potsdam; the definitive experiment with Morley, with the arm length increased tenfold by multiple reflection, was 1887. Nothing in the argument turns on it.

In summary, the paper is clearly written and its emission-theory calculation is internally correct, but the refutation it advertises is an arithmetic slip — one dropped velocity component — and the alternative it offers was excluded by observation decades before the paper was written.