﻿ 8.MMX

# Michelson-Morley Experiment

It has been highlighted that the failure of this experiment to detect a wave medium has been cited as empirical evidence that contradicts the possibility of any WSE model. Therefore, it is important that we first understand the technical assumptions underpinning this experiment and then try to see whether any alternative explanation can be offered up for the negative result.

So, to begin, this experiment proceeds on the initial assumption that the reference frame of the equipment is moving with velocity [v] through a wave media, i.e. the aether. Therefore, if the propagation velocity of light [c] is always relative to the wave media, then any velocity [v] of the equipment must affect the propagation times relative to the equipment in motion with velocity [v]. However, the propagation times in question will be different depending on the horizontal or transverse paths taken through an interferometer, which will then cause wave interference at the final destination. For ease of comparison, the mirrors on the horizontal and transverse paths are positioned at the same distance [L=LH=LT], such that [L] can be used as a common term. The analysis of the Michelson-Morley experiment is usually based on the propagation time of a light-beam with velocity [c]. The light-beam is first transmitted from a source [S], where on route it passes through a half-silvered mirror at an origin, defined as [t=0], and continues on until it is reflected by a horizontal mirror positioned at distance [L], which is moving with velocity [v]. The beam hits the mirror at time [t1] having propagated a distance [ct1], while the mirror has moved a distance [vt1], such that:

[1]

Where the roundtrip propagation time [tH] is:

[2]

Again, in the vertical direction, the beam is emitted from the same source having velocity [ c] towards the half-silvered mirror, but now hits the vertical mirror at time [t 3 ] having propagated the distance [ ct3] , while the mirror has moved a distance [ vt3] along the [ x] direction. However, in order to hit the mirror, the propagation path of the beam is [L] in the [y] direction and [ vt3] in the [x] direction. The propagation path [LP] can be calculated using the Pythagorean theorem:

[3]

However, in order to have some equivalence with the form in [2], we really want to know the propagation time [t3] in terms of the distance [L].

[4]

In the transverse case, the forward and backward paths are the same, such that the total propagation time on the transverse path simply doubles the result in [3].

[5]

So, based on the times in [2] and [5], we can calculate the propagation time difference between the two paths taken.

[6]

Based on [6], the initial path difference is simply defined by the propagation velocity [c], such that [LD=ctD]:

[7]

This path difference after a 90° rotation simply reverses the order of the terms shown in the brackets:

[8]

By dividing [ LD1−LD2] by the wavelength [λ] of light used, the fractional wavelength shift [n] can be calculated as a function of the velocity [v].

[9]

The equipment used in the Michelson-Morley experiment had an arm length [L=11m] and used light with a wavelength [λ=500nm], while the velocity [v] was initially approximated to the Earth’s velocity around the Sun, i.e. [v=30km/s]. On this basis, a fractional wavelength shift [n=0.44] can be calculated, which it was assumed would produce an interference shift that could be detected. However, the negative result of the experiment led to the conclusion that there is no measurable aether drift and therefore no aether.

Note: Today, it is recognised that the velocity [v] of the Earth through some absolute aether might have to be interpreted on a much larger scale than the local solar system. By analysing the data collected by astronomical observation, the local group of galaxies, which includes the Milky Way, is moving at ~627 km/s relative to the reference frame of the CMB. However, the solar system within this larger system, which includes the Earth-frame, is only moving at ~360km/s with respect to the CMB frame. On this basis, the larger value of [v=360km/s] would suggest an even greater interference shift, such that any WSE model would have to proposed some other causal mechanism to explain the negative results of the Michelson experiment.

Historically, the idea of length contraction was proposed as a possible explanation of the negative results in which all objects, i.e. including the interferometer, physically contract by [g L ] along the axis, where [g] is simply another form of the Lorentz factor [g] defined by the Lorentz transforms.

[10]

If length contraction of [ L=gL] is inserted into the formula for [ TH] given in [2], then the light propagation time equals the formula for [ TT] given in [5].

[11]

However, while this solution may appear to resolve the mathematical anomaly, it was never clear that this solution provided a causal explanation as to how length contraction physically took place within a localised moving reference frame. This said, the subsequent publishing of special relativity in 1905, based on the Lorentz transformation, which appear to rationalise the need for both time dilation and length contraction anchored in the constancy and invariant velocity [c]. As such, it began to be accepted that a stationary aether no longer had any role played in the kinematic description of a unified spacetime, which we might characterised in Einstein’s own words:

Although the estimated difference between these two times is exceedingly small, Michelson and Morley performed an experiment involving interference in which this difference should have been clearly detectable. But the experiment gave a negative result, a fact very perplexing to physicists. Lorentz and FitzGerald rescued the theory from this difficulty by assuming that the motion of the body relative to the æther produces a contraction of the body in the direction of motion, the amount of contraction being just sufficient to compensate for the difference in time mentioned above. Comparison with the discussion in Section 11 shows that also from the standpoint of the theory of relativity this solution of the difficulty was the right one. But on the basis of the theory of relativity the method of interpretation is incomparably more satisfactory. According to this theory there is no such thing as a ‘specially favoured’ (unique) co-ordinate system to occasion the introduction of the æther-idea, and hence there can be no æther-drift, nor any experiment with which to demonstrate it. Here the contraction of moving bodies follows from the two fundamental principles of the theory, without the introduction of particular hypotheses; and as the prime factor involved in this contraction we find, not the motion in itself, to which we cannot attach any meaning, but the motion with respect to the body of reference chosen in the particular case in point. Thus for a co-ordinate system moving with the earth the mirror system of Michelson and Morley is not shortened, but it is shortened for a co-ordinate system which is at rest relatively to the sun.

In 1932, Kennedy and Thorndike modified the Michelson–Morley experiment by making the path lengths of the split beam unequal, with one arm being very short. The Kennedy–Thorndike experiment took place for many months as the Earth moved around the sun. Their negative result showed that the speed of light [c] to be independent of the velocity [v] of the apparatus in different inertial frames. It also appeared to highlight that the individual values of length contraction and time dilation must assume their exact relativistic form. Therefore, over the years, additional empirical evidence has simply added to the consensus that sp ecial relativity provides the solution to the Michelson–Morley null result, although many remain sceptical on the basis that the solution appears to rest on a mathematical conjecture, i.e. the Lorentz transforms, rather than some physically understood cause and effect. However, the following papers are provided as examples of potential counter-arguments that might explain the null result of the Michelson-Morley (MMX) experiment:

The issue of the null outcome of the MMX will also be reviewed further in the next discussion in terms of a number of different relative and relativistic frames of reference, which may help to explain how the asymmetry of the interferometer paths is compensated by a physical length contract in the direction of motion and time dilation.