Kip Thorne: "If you move toward the [light] source, you see the wavelength shortened but you don't see the speed changed"
https://youtu.be/mvdlN4H4T54?t=296
No the moving observer does not see the wavelength shortened:
"Thus, the moving observer sees a wave possessing the same wavelength [...] but a different frequency [...] to that seen by the stationary observer."
http://farside.ph.utexas.edu/teaching/315/Waveshtml/node41.html
"Vo is the velocity of an observer moving towards the source. This velocity is independent of the motion of the source. Hence, the velocity of waves relative to the observer is c + Vo. [...] The motion of an observer does not alter the wavelength. The
increase in frequency is a result of the observer encountering more wavelengths in a given time."
http://a-levelphysicstutor.com/wav-doppler.php
And since the moving observer does not see the wavelength shortened, he sees the speed of light changed (c'=c+Vo).
Einstein's 1905 falsehood turned out to be highly malignant:
"He opened by explaining how Einstein's theory of relativity is the foundation of every other theory in modern physics and that the assumption that the speed of light is constant is the foundation of that theory. Thus a constant speed of light is
embedded in all of modern physics and to propose a varying speed of light (VSL) is worse than swearing! It is like proposing a language without vowels."
http://www.thegreatdebate.org.uk/VSLRevPrnt.html
"If there's one thing every schoolboy knows about Einstein and his theory of relativity, it is that the speed of light in vacuum is constant. No matter what the circumstances, light in vacuum travels at the same speed... The speed of light is the very
keystone of physics, the seemingly sure foundation upon which every modern cosmological theory is built, the yardstick by which everything in the universe is measured. [...] The only aspect of the universe that didn't change was the speed of light. And
ever since, the constancy of the speed of light has been woven into the very fabric of physics, into the way physics equations are written, even into the notation used. Nowadays, to "vary" the speed of light is not even a swear word: It is simply not
present in the vocabulary of physics."
https://www.amazon.com/Faster-Than-Speed-Light-Speculation/dp/0738205257
"The whole of physics is predicated on the constancy of the speed of light," Joao Magueijo, a cosmologist at Imperial College London and pioneer of the theory of variable light speed, told Motherboard. "So we had to find ways to change the speed of light
without wrecking the whole thing too much."
https://motherboard.vice.com/en_us/article/8q87gk/light-speed-slowed
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