Stephen Hawking, "A Brief History of Time", Chapter 3: "Now imagine a source of light at a constant distance from us, such as a star, emitting waves of light at a constant wavelength. Obviously the wavelength of the waves we receive will be the same as the wavelength at which they are emitted (the gravitational field of the galaxy will not be large enough to have a significant effect). Suppose now that the source starts moving toward us. When the source emits the next wave crest it will be nearer to us, so the distance between wave crests will be smaller than when the star was stationary." http://www.fisica.net/relatividade/s...ry_of_time.pdf

Hawking's argument

"When the source emits the next wave crest it will be nearer to us, so the distance between wave crests will be smaller than when the star was stationary"

is invalid. The fact that the source "will be nearer to us" tells us nothing about "the distance between wave crests". The wavelength of light, unlike the wavelength of sound, is constant (for a given emitter).

Variable wavelength of light

https://youtube.com/watch?v=xsVxC_NR64M

contradicts the principle of relativity - by measuring the wavelength, inside his spaceship, the emitter would know his speed without looking outside.

Constant wavelength (the truth) entails, and is a corollary of, Newton's variable speed of light:

"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

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