"To state that the speed of light is independent of the velocity of the observer is very counterintuitive. Some people even refuse to accept this as a logically consistent possibility, but in 1905 Einstein was able to show that it is perfectly consistent
if you are prepared to give up assumptions about the absolute nature of space and time."
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html
So Einstein vandalized space and time and the counterintuitive nonsense became "perfectly consistent" with the preposterous "spacetime". Yet the constancy of the speed of light remained obvious nonsense in the Doppler effect scenario. The motion of the
observer cannot change the wavelength of the incoming light:
"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
"The wavelength is staying the same in this case."
https://www.youtube.com/watch?v=MHepfIIsKcE
"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
Accordingly, if the speed of the observer relative to the light source is Vo, the speed of the light relative to the observer is c+Vo.
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Pentcho Valev
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