2017-08-08 07:47:36 UTC
The Michelson-Morley experiment was not based "on this general idea", that is, on the assumption that "the Galilean transformation is correct for light". Rather, it was based on the opposite assumption - that the Galilean transformation is wrong for light and the speed of light is independent of the motion of the source. It was this opposite assumption that was refuted by the null result of the experiment.
If the calculations are made on the assumption that the speed of light does depend on the motion of the source, as predicted by the Galilean transformation, then the null result of the experiment confirms the assumption. Consider Feynman's further analysis:
Richard Feynman: "First, let us calculate the time required for the light to go from B to E and back. Let us say that the time for light to go from plate B to mirror E is t_1, and the time for the return is t_2. Now, while the light is on its way from B to the mirror, the apparatus moves a distance ut_1, so the light must traverse a distance L + ut_1, at the speed c."
Feynman's last phrase,
"at the speed c",
is an abridged version of the assumption "The speed of light is independent of the motion of the source". If, instead of "at the speed c", we have a new premise,
"at the speed c + u",
taken from the Galilean transformation, the calculation (based on the new premise) will give a new prediction,
t_1 + t_2 = 2t_3 = 2L/c,
which exactly matches the null result of the Michelson-Morley experiment.
In 1887 (prior to FitzGerald and Lorentz advancing the ad hoc length contraction hypothesis) the Michelson-Morley experiment UNEQUIVOCALLY confirmed the variable speed of light posited by the Galilean transformation (Newton's emission theory of light) and refuted the constant (independent of the speed of the motion of the source) speed of light posited by the ether theory and later adopted by Einstein as his 1905 second ("light") postulate:
"To it, we should add that the null result of the Michelson-Morley experiment was unhelpful and possibly counter-productive in Einstein's investigations of an emission theory of light, for the null result is predicted by an emission theory."
"Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887. [...] The name most often associated with emission theory is Isaac Newton. In his corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)."
"The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."
Albert Einstein: "...I introduced the principle of the constancy of the velocity of light, which I borrowed from H. A. Lorentz's theory of the stationary luminiferous ether..."
Banesh Hoffmann, Relativity and Its Roots, p.92: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether. If it was so obvious, though, why did he need to state it as a principle? Because, having taken from the idea of light waves in the ether the one aspect that he needed, he declared early in his paper, to quote his own words, that "the introduction of a 'luminiferous ether' will prove to be superfluous."
Richard Feynman: "I want to emphasize that light comes in this form - particles. It is very important to know that light behaves like particles, especially for those of you who have gone to school, where you probably learned something about light behaving like waves. I'm telling you the way it does behave - like particles. You might say that it's just the photomultiplier that detects light as particles, but no, every instrument that has been designed to be sensitive enough to detect weak light has always ended up discovering the same thing: light is made of particles." QED: The Strange Theory of Light and Matter p. 15