Doppler effect in light (moving observer):

https://www.youtube.com/watch?v=bg7O4rtlwEE

The speed of the light pulses as measured by the stationary observer is

c = df

where d is the distance between the pulses and f is the frequency measured by the stationary observer. The speed of the pulses as measured by the moving observer is

c'= df' c

where f' f is the frequency measured by the moving observer.

Banesh Hoffmann, Einstein's collaborator, admits that, originally ("without recourse to contracting lengths, local time, or Lorentz transformations"), the Michelson-Morley experiment directly proved Newton's variable speed of light and disproved the constant (independent of the motion of the emitter) speed of light posited by the theory of the nonexistent ether and "borrowed" by Einstein in 1905:

"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-It.../dp/0486406768

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..." https://en.wikipedia.org/wiki/Lorentz_ether_theory

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