The Origin of Michelson’s Experiment

The Origin of Michelson’s Experiment.
Difficulties and Solutions

To determine the relative movement of the luminiferous ether in relation to the Earth, the American physicist Albert Abraham Michelson intended to calculate the orbital speed of the Earth around the Sun by measuring the speed of light in different directions. This idea - suggested by James Clerk Maxwell (14) - used the law of addition of speeds: the speed of light between two stationary points being 300,000km/s and the speed of the Earth orbiting the Sun being 30km/s, the speed of light as measured on the Earth becomes:

a) when light rays head toward the Earth in the opposite direction from its movement:
300,000km/s + 30km/s
b) when the light rays head in the same direction:
300,000km/s - 30km/s

However, the accuracy of the measurements envisaged by Maxwell seemed inadequate. In 1881 Michelson imagined a far more accurate experiment using light interference (14). But he was disappointed. Not only did he not find the expected value, but he was unable to observe the smallest difference in speed between light rays from different directions. The speed of light was not influenced by the speed of the Earth.

He gave the following explanation: light behaves like sound, which travels at the same speed in all directions because the atmosphere that transports it is fixed to the Earth; similarly, light has the same speed in all directions, since the ether in the Earth’s vicinity is fixed to the Earth.

This was Michelson’s account of his results. However, it conflicted with the contemporary view of a stationary ether through which the Earth moves. This view stemmed from a famous hypothesis by Augustin Fresnel (10), later demonstrated in a famous article by Armand Fizeau (7, 8). The explanation by Michelson, a young assistant in Hermann von Helmholtz’s laboratory in Berlin, was given a cool reception. Two famous British physicists, Lord Kelvin (William Thomson) and Baron Rayleigh (Robert Strutt), whom he consulted (17), advised him “…to repeat his German interferometer experiment, but only after first checking Fizeau’s earlier result on the speed of light in moving water”).

This is what Michelson did. In 1886, in collaboration with Edward Morley, he repeated Fizeau’s experiment and confirmed his result (15). The hypothesis of a stationary ether was reinforced. Then, in 1887, they repeated Michelson’s first experiment, taking into account the criticism levelled at it (16). Here again they confirmed Michelson’s result and kept his explanation of an ether fixed to the Earth, which contradicted the earlier explanation.

One of two things was true: either Fizeau was right and it was necessary to retain the idea of a stationary ether; or Michelson and Morley were right and it was necessary to take on the opposite idea of an ether fixed to the Earth’s surface.

The idea of a stationary ether was retained, but the lack of effect of the speed of the Earth on the measurement of the speed of light entailed a contradiction of the law of addition of speeds.

This version of the origins of the experience of Michelson that is found in works of the history of science contains three mistakes:

1. The “demonstration” by Fizeau (7,8) of Fresnel’s hypothesis of a stationary ether (10) closes not with support but with condemnation of this hypothesis: Fizeau concludes the opposite of what he is made to say.

2. That contradiction in Fizeau’s and Michelson and Morley’s experimental results is only apparent. It is explained in Michelson and Morley’s article of 1887, but the explanation has been passed over in silence and this has resulted in the contradiction and preference for Fresnel’s hypothesis being maintained.

3. Fresnel’s hypothesis, which is the source of Fizeau’s article and had been much criticized until this “demonstration”, contains two opposing propositions that make it unacceptable.

Fizeau’s Condemnation of Fresnel’s Hypothesis of Stationary Ether

Fresnel’s hypothesis assumed:
that the ether was not fixed to the surface of the Earth but was stationary;
that it was present in all bodies, even opaque ones like the Earth, and that it was partially borne along inside them when they moved.

Like most of his contemporaries, Fizeau was not happy about this hypothesis. He felt that current knowledge of the ether was inadequate and set about clarifying its relationship to ponderable matter by seeking to establish whether the speed of light in transparent media was modified when such media were in motion. Fizeau’s experiment (7,8) was a technical feat. He obtained a modification of the speed of light with the movement of bodies moving at just a few metres per second. The result had an intermediate value between the value calculated according to whether the ether was stationary or fixed to the Earth, and this was quite close to the value obtained from Fresnel’s hypothesis. It therefore supported the hypothesis of a stationary ether.

And yet Fizeau’s conclusion read as follows:

“I believe the success of this experiment ought to entail the adoption of Fresnel’s hypothesis or at least of the law he has found [...] for, though it is very great evidence in its favour, [...] Fresnel’s conception will appear so extraordinary, and certain aspects of it so difficult to admit, that further proof will be required along with a detailed examination by geometers before adopting it as the expression of the reality of things (7, 8).”

Put another way, Fizeau rejected Fresnel’s hypothesis of a stationary ether because it was too extraordinary and not credible.

This conclusion was unexpected after the results of his experiment, but the article’s reception was even more unexpected:
- No attempt was made to explain what was difficult to admit in Fresnel’s hypothesis.
- No claim was made about Fizeau being mistaken. He was a famous physicist* whose honesty was proverbial.**
- The conclusion, which was an embarrassment, was forgotten.
- The results of the experiment remained such that the dilemma was biased in their favour, without comment!

But this oversight generated a misinterpretation: the author was made to say the opposite of what he had concluded.

This contradiction between the experimental result and the conclusion in Fizeau’s article was later explained by Michelson and Morley.

Michelson and Morley’s Explanation of the Apparent Contradiction between their Results and Fizeau’s

After checking the results of Fizeau’s experiments in 1886, results that leant apparently towards the hypothesis of a stationary ether, Michelson and Morley pointed out at the start of their 1887 article (16):

1- that Fresnel’s hypothesis comprised not one but two postulates:

a) the ether through which the Earth travels remains stationary;
b) the ether in moving transparent media travels more slowly than these media;

2- that Fizeau’s experiment only confirmed the second assumption and
3- that they themselves planned to verify the former.

The two assumptions work in parallel towards a single demonstration but are independent. The verification of Fizeau’s second postulate does not, as Fizeau’s contemporaries believed, imply the accuracy of the first. There is then no contradiction between the results of Fizeau’s experiments, which support the second postulate regarding the ether movement in transparent bodies, and those of Michelson and Morley, which are hostile to the first postulate of a stationary ether.

Yet this explanation has been passed over in silence and the opposition between Fizeau’s and Michelson and Morley’s experiments has consequently been maintained, as has the contradiction between the hypothesis of a stationary ether and the law of addition of speeds.

Fresnel’s Questionable Hypothesis of a Stationary Ether

François Arago (10) had observed that the refraction of light rays from the stars was the same for all stars. Refraction is due to the different speed of light when it passes from one medium to another. Arago had expected it to be faster for light from stars the Earth was moving towards than for light from stars from which it was moving away, as the speed of light ought to have been greater in the first case (300,000km/sec + 30km/sec) than in the second (300,000km/sec- 30km/sec). This was the same as Maxwell’s reasoning over Michelson’s experiment.

The refraction was the same and provoked the same surprise: the movement of the Earth had no effect on the speed of light. Arago was unable to explain this result using the corpuscular theory of light and invited Fresnel to see if he could do so using wave theory.

In his reply, Fresnel (10) first pointed out that a wave theory explanation would be simple if one supposed that the ether was fixed to the Earth in its immediate vicinity. Thus it would be like the atmosphere, which is fixed to the Earth and transports sound at the same speed in all directions. But he added, “it then appears impossible to explain the aberration of stars*** “, which he contented, needed a stationnary ether. As Arago’s observation entailed the contrary idea of an earthbound ether, Fresnel sought a compromise between an earthbound and stationnary ether.

The proof was laborious, with Fresnel introducing a new hypothesis at every turn: Arago (2, 1) was not convinced. Stockes, Martinus Hoek, Wilhelm Veltmann, Kettler, Doppler, Klinkerfuess, Airy, Challis, Lorenz, Fizeau and Michelson (7, 11, 14) did nothing to conceal their scepticism. But, more than anything, this proof raised a contradiction:

- On the one hand, the density of the ether in ponderable bodies had to be higher than that in space, since “the delay of light in transparent media was the sole result (9) of a greater density of the ether.”
- On the other, “the ether passed freely through the globe” (9) which has a coercitive effect: the density of the ether had to be equal in ponderable bodies and in space because, if it had been lower, this would have hampered the ether from penetrating and, if higher, from escaping.

The density of the ether inside the Earth being simultaneously equal to and higher than the density of the ether in space, according to Fresnel’s assumptions, constitutes a nonsense that renders the hypothesis untenable.

Conclusion

Fresnel’s demonstration of the immobility of the ether contains an error that leads to meaningless nonsense and renders this assumption null and void.

This error explains Fizeau’s difficulties, when after an experiment supporting Fresnel’s assumption against his better judgment, he rejected the conclusion, while being unable to explain it.

It also explains Michelson’s difficulties, when he contributed the explanation that Fizeau was missing, but could not turn around the opinion still attached to Fizeau’s experimental results.

On the contrary, Michelson’s assumption of an ether related to the Earth makes it possible to explain the result of Michelson and Morley’s experiment where the light rays’ path is confined entirely to the surface of the Earth and where the law of addition of speeds does not apply.

The latter hypothesis could still be confirmed by another experiment using light rays from the stars, whose path is located almost completely beyond that part of the ether bound to the Earth, in the stationary ether where the law of addition of the speeds does apply. This experiment could be performed using spectrometry. The spectral shift of stars, due to their speed in relation to the Earth, depends not only on the movement of the stars but on the movement of the Earth. The detection of periodic variation in this shift in phase with the Earth’s orbital movement should enable its speed to be calculated as Michelson wished.

---

* Fizeau was the first to measure the speed of light at the surface of the Earth. He had independently rediscovered the Doppler Effect six years after Doppler and had shown how to use it to measure the speed of stars (by spectral shift), whereas Doppler, who predicted a change in their colour, had been wrong. This is why discerning physicists call this effect the “Doppler-Fizeau effect”.

** Fizeau relinquished his teaching post at the Polytechnic School to a younger, less fortunate colleague. He did not set about measuring the speed of light in the laboratory until he had obtained authorization from Arago, whose idea it had been. This meant he did not publish the measurement until a few days after Foucault.

*** The aberration is a slight apparent shift of the stars due to the Earth orbiting the Sun: a star’s position does not lie in the direction where it is seen because the Earth moves between the moment the light rays were emitted by the star and the moment they hit the Earth. This phenomenon discovered by James Bradley in 1727 (3) was dubbed “aberration” * by E. Manfredo (1, 13) in 1731. (An incomplete bibliography led me to wrongly attribute (4) to Euler rather than Manfredo the origin of the word “aberration”, referring to Bradley’s phenomenon, as well as a confusion he was not guilty of.) Fresnel first professed not to have understood it, then devoted a monograph to it entitled Rêveries, which he eventually abandoned the idea of publishing (9). But he did answer Arago, his friend and protector at the Academy. His answer was brief, occupying just nine of the 2,493 pages of his complete works, and he never returned to the subject during the remaining nine years of his life.