Richard Feynman: "Another consequence of the [Maxwell's] equations is that if the source of the disturbance is moving, the light emitted goes through space at the same speed c. This is analogous to the case of sound, the speed of sound waves being likewise independent of the motion of the source. This independence of the motion of the source, in the case of light, brings up an interesting problem: Suppose we are riding in a car that is going at a speed u, and light from the rear is going past the car with speed c. Differentiating the first equation in (15.2) gives dx'/dt=dx/dt-u, which means that according to the Galilean transformation the apparent speed of the passing light, as we measure it in the car, should not be c but should be c-u. For instance, if the car is going 100,000 mi/sec, and the light is going 186,000 mi/sec, then apparently the light going past the car should go 86,000 mi/sec. In any case, by measuring the speed of the light going past the car (if the Galilean transformation is correct for light), one could determine the speed of the car. A number of experiments based on this general idea were performed to determine the velocity of the earth, but they all failed - they gave no velocity at all. We shall discuss one of these experiments in detail, to show exactly what was done and what was the matter; something was the matter, of course, something was wrong with the equations of physics. What could it be?...As mentioned above, attempts were made to determine the absolute velocity of the earth through the hypothetical "ether" that was supposed to pervade all space. The most famous of these experiments is one performed by Michelson and Morley in 1887." http://www.feynmanlectures.caltech.edu/I_15.html
The light-from-rear-going-past-car experiment and the Michelson-Morley experiment are by no means analogous. In the former, the light source is OUTSIDE the moving system. In the latter, the light source is INSIDE the moving system. So applying the principle of relativity to the light-from-rear-going-past-car experiment is incorrect and the result c'=c-u is true, as demonstrated here:
"When an observer moves away from a stationary source...the velocity of the wave relative to the observer is slower than that when it is still."
View: http://www.youtube.com/watch?v=SC0Q6-xt-Xs
Applying the principle of relativity to the Michelson-Morley experiment is correct because both source and observer are INSIDE the moving system. The measured speed of light will always be constant, c'=c, and the two perpendicular beams of light will always return simultaneously. This implies, however, that relative to a stationary observer OUTSIDE the moving system, the speed of light will be c'=c±v, as posited by Newton's theory (it is THIS scenario that is analogous to the light-from-rear-going-past-car experiment):
"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." http://philsci-archive.pitt.edu/12289/1/Einstein_Discover.pdf
"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)." https://en.wikipedia.org/wiki/Emission_theory
Banesh Hoffmann, Einstein's co-author, admits that, originally ("without recourse to contracting lengths, local time, or Lorentz transformations"), the Michelson-Morley experiment was compatible with Newton's variable speed of light, c'=c±v, and incompatible with the constant speed of light, c'=c:
"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." Banesh Hoffmann, Relativity and Its Roots, p.92 https://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768
The light-from-rear-going-past-car experiment and the Michelson-Morley experiment are by no means analogous. In the former, the light source is OUTSIDE the moving system. In the latter, the light source is INSIDE the moving system. So applying the principle of relativity to the light-from-rear-going-past-car experiment is incorrect and the result c'=c-u is true, as demonstrated here:
"When an observer moves away from a stationary source...the velocity of the wave relative to the observer is slower than that when it is still."
Applying the principle of relativity to the Michelson-Morley experiment is correct because both source and observer are INSIDE the moving system. The measured speed of light will always be constant, c'=c, and the two perpendicular beams of light will always return simultaneously. This implies, however, that relative to a stationary observer OUTSIDE the moving system, the speed of light will be c'=c±v, as posited by Newton's theory (it is THIS scenario that is analogous to the light-from-rear-going-past-car experiment):
"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." http://philsci-archive.pitt.edu/12289/1/Einstein_Discover.pdf
"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)." https://en.wikipedia.org/wiki/Emission_theory
Banesh Hoffmann, Einstein's co-author, admits that, originally ("without recourse to contracting lengths, local time, or Lorentz transformations"), the Michelson-Morley experiment was compatible with Newton's variable speed of light, c'=c±v, and incompatible with the constant speed of light, c'=c:
"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." Banesh Hoffmann, Relativity and Its Roots, p.92 https://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768
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