Michelson-Morley Experiments Revisited: Systematic Errors, Consistency Among Different Experiments, and Compatibility with Absolute Space

Scientific Paper
Title	Michelson-Morley Experiments Revisited: Systematic Errors, Consistency Among Different Experiments, and Compatibility with Absolute Space
Read in full	Link to paper
Author(s)	Hector A Munera
Keywords	Michelson and Morley, systematic error, preferred frame
Published	1998
Journal	Apeiron
Volume	5
Number	1-2
Pages	38-54

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Abstract

Despite the null interpretation of their experiment by Michelson and Morley, it is quantitatively shown that the outcomes of the original experiment, and all subsequent repetitions, never were null. Additionally, due to an incorrect inter-session averaging, the non-null results are even larger than reported. Contrary to the received view, Illingworth's and other repetitions of the experiment were consistent with Miller's positive results. On the theoretical side, a new systematic error is uncovered: the angle between the projection of earth's velocity on the plane of the interferometer and the reference arm of the apparatus has been practically ignored. This phase angle produces a noticeable change in the position of the peaks from one turn to the next of the interferometer. Hence, the data analysis cannot be based on the average of fringe shifts during a session, but rather on the calculation of individual speed for each turn. This procedure was applied to the only two sessions reported in detail in the literature: Miller's September 23, 1925 at 03:02 in Mount Wilson and Illingworth's July 9, 1927 at 11:00 in Pasadena. Surprisingly, it was found that in both cases the measured speeds exactly correspond to the projection of earth's orbital velocity only. As a result, the evidence against a preferred frame completely disappears.

Overview

Héctor A. Múnera, writing from the Centro Internacional de Física in Bogotá, returns to the primary literature of the Michelson-Morley Experiment and its repetitions between 1887 and 1930 and asks a narrow, checkable question: what did the experimenters actually measure, as distinct from what they concluded? His answer is that every experiment in the class — Michelson and Morley 1887, Morley and Miller 1904-05, Miller's long series at Cleveland and Mount Wilson, Piccard and Stahel in a balloon and at Mount Rigi, Kennedy, Illingworth, Michelson-Pease-Pearson, and Joos at Jena — reported a non-zero drift speed, and that in every case but Miller's the authors interpreted their own non-zero number as null.

The paper's departure from the textbook account is therefore not a new experiment but a re-reduction of the old data. Múnera identifies two systematic errors in the standard analysis and a third in the reading of statistics. The first, SE1, is the century-old objection of W. M. Hicks: the observed fringe displacement belongs to one of two calibration families with opposite sign, so averaging sessions taken on different days drives the mean toward zero. The second, SE2, is his own contribution: the phase angle between the projection of the Earth's velocity onto the plane of the interferometer and the reference arm has been treated as constant when it is not. His conclusion is that "the evidence against a preferred frame completely disappears" — not that a preferred frame has been demonstrated, but that the experimental case against absolute space rests on a data-reduction artifact.

The argument

Theory of the experiment, with the phase angle restored

Múnera works in right-handed horizon coordinates S(φ) at latitude φ, with the interferometer lying in the X-Y plane. The relevant velocity is not V itself but V_I, the projection of the Earth's velocity onto the plane of the instrument, where V = V_s + V_o + V_r (solar, orbital and rotational contributions). The time difference over the two arms is

ΔT = (2L/c) β² cos w cos(Δw − w_N),

with β = V_I/c, Δw the angular position of the reference arm relative to local north, and w_N the counterclockwise angle from north to V_I. Following Hicks, the band displacement contains a small calibration angle Δθ ≈ ±10⁻⁵ radians set during adjustment of the mirrors; because β² < Δθ, the denominator is controlled by Δθ and the displacement reduces to z ≈ Kβ²cos²w with K = P₀/2Δθ. Since the sign of Δθ may be either positive or negative, there are two families of displacement, z⁺ and z⁻. This is the origin of SE1. Múnera quotes Hicks directly: "the adjustment of the mirrors can easily change from one type to the other on consecutive days... If this is not attended to, the average displacement may be expected to come out zero."

SE2 follows from the same equations. A rotation of the reference arm through π/2 gives a shift whose magnitude depends on w_N, so that |D| < 2A except when w_N = 0. Michelson and Morley knew of diurnal variation but assumed w_N = 0 throughout. Computing V_I and w_N from the orbital motion alone (a circular orbit, obliquity ε = 23.45°, a spherical rotating Earth), Múnera plots both over 24 hours for Cleveland, Pasadena, Mount Wilson, Mount Rigi and Jena. The variation within a single session is large: at Cleveland on 9 July between 12:00 and 13:00, V_I falls from 18.1 to 16.8 km/s while w_N swings from −151.5° to −176.4°. From this he draws five remarks, of which the operative one is that readings taken at the same Δw on different turns are not repeated trials of the same observable, so their average is necessarily smaller than the maximum.

Review of the experiments

Applied case by case, the reinterpretation is consistent. Miller's harmonic analysis of the original Michelson-Morley curves gave 8.8 km/s at noon and 8.0 km/s in the evening — larger than Michelson and Morley's own bound because the cancelling error had been removed. Morley and Miller's 1904 repetition gave about 7.5 km/s once corrected. Miller's Mount Wilson results are tabulated at 10.1, 11.2, 9.6 and 9.3 km/s for April, August, September and February, with a probable error of ±0.33 km/s, which Múnera converts to 95% confidence bounds. Piccard and Stahel's balloon result, 6.9 ± 7.0 km/s, he reads as meaning only that the true speed lies between 0 and 13.9 km/s at 50% confidence — compatible with Miller, not contradictory to him; their Brussels figure of 0.0002 ± 0.0007 fringes becomes 1.7 ± 3.1 km/s. Their Mount Rigi curve corresponds, on their own statement, to a 1.45 km/s ether wind. Michelson, Pease and Pearson's "one-fifteenth of the expected" implies 77.5 km/s of solar motion. Joos reported "an ether wind smaller than 1.5 km/s" after discarding his large-amplitude sessions as error — which, on Múnera's account, is SE2 in action, since the amplitude is expected to vary from hour to hour.

The treatment of Shankland et al. (1955) is the sharpest section. Shankland's team argued that Miller's four seasonal curves should share a common maximum at Δw = 0 and differ only in amplitude. Múnera's Figure 1 shows that w_N is epoch-dependent, so no common maximum is expected; the objection is itself an instance of SE2. He also notes that Shankland's own statistics conceded that "statistical fluctuations alone cannot account for the periodic fringe-shifts observed by Miller."

Re-reduction of Illingworth and Miller

The quantitative core is the re-analysis of the only two sessions reported turn by turn. Illingworth's statistic y averaged over sessions with sign retained gives velocities scattered about zero, some of them imaginary (Illingworth reported these as negative speeds). Taking |y| instead, as the magnitude of a velocity requires, Múnera obtains 1.46 to 2.23 km/s across the eight sessions, with the lower 95% bound above zero in over half of them, and derives V_I in the narrow band 2.05 to 2.42 km/s.

For the intra-session analysis he computes a speed for each individual turn. In Illingworth's session 2A of 9 July 1927 the sign of y changes repeatedly within the session, supporting the conjecture that the calibration family changed between turns; the per-turn average speed is 3.13 km/s against Illingworth's own 0.87 km/s. In Miller's 20-turn session of 23 September 1925 at 03:02 the per-turn average is 8.22 km/s (8.72 km/s via |y|). The predicted projection V_A of the orbital velocity over the corresponding observing windows is 2.44 to 6.68 km/s at Pasadena and 8.00 to 11.88 km/s at Mount Wilson. Múnera's conclusion is that in both cases "the measured speeds exactly correspond to the projection of earth's orbital velocity only," and that it would be an extraordinary coincidence for two independent experimenters to produce that agreement by artifact.

Assessment

What is genuinely valuable here is the archival work. Múnera does not paraphrase secondary accounts; he goes to Michelson and Morley 1887, Hicks 1902, Miller 1933, Kennedy 1926, Illingworth 1927, Piccard and Stahel's three Comptes rendus notes, and Joos 1930, and quotes each author's own words against each author's own conclusion. The observation that a reported result of the form 6.9 ± 7.0 km/s is not a null result but an uninformative one is elementary and correct, and it is applied consistently. The identification of SE2 — that the phase angle drifts within a session on the same timescale as the measurement — is a real point about the design of the analysis, and the demonstration that Shankland's "common maximum" criterion presupposes a constant phase angle is a fair hit. The recovery of Hicks's calibration-family objection, which vanished from the literature for a century, is a service.

The difficulties are equally real. First, the central result is asserted from two sessions. Múnera says as much — these are the only two reported turn by turn — but a coincidence between per-turn averages and the orbital projection, established at n = 2, cannot bear the weight the concluding section puts on it, and he offers no error analysis of the predicted V_A against which the agreement is called exact. Second, the paper deliberately restricts the predicted velocity to the orbital component, setting solar motion aside "to be fair to M-M." But the ether hypothesis under test does not permit that restriction: if a preferred frame exists, the solar motion of roughly 370 km/s inferred from the Cosmic Microwave Background dipole should dominate the orbital 30 km/s entirely, and an apparatus responding to V_o alone is as much a puzzle for absolute space as for relativity. Múnera notes the amplitude discrepancy — Miller's observed curves run at about 30% of the predicted scale — and leaves it "an open question." Third, the argument sits uncomfortably beside the Kennedy-Thorndike class of experiments, which he explicitly excludes from consideration, and beside the modern optical-cavity isotropy tests that descend from them; those bound any anisotropy in the Speed of Light far below the few km/s recovered here. A demonstration that the 1887-1930 data were mis-reduced does not by itself answer them, and the paper does not attempt to.

Finally, the statistical re-reading cuts both ways. Replacing y by |y| removes a cancellation, but taking absolute values of a noise-dominated quantity produces a positive mean even when the true signal is zero — a bias Múnera does not discuss. His own Table 3 shows lower bounds of exactly zero in three of eight sessions. The paper is at its strongest as a critique of how the historical data were averaged, and at its weakest where it converts that critique into positive evidence for a preferred frame.

See also

• Hector A Munera
• Michelson-Morley Experiment
• Dayton C Miller
• Aether
• Speed of Light
• Length Contraction
• Jean-Pierre Vigier
• Apeiron