http://physics.ucsd.edu/students/courses/fall2008/managed/physics11/documents/Lecture5-11.pdf
"Doppler Shift. As long as the velocity of the observer, v, is much smaller than the speed of light, c, (for the case of sound waves much smaller than the speed of sound) then the expression that we derived is a very good approximation. Taking into account v may be in the opposite direction: f'=f(1±v/c). At this point you might ask why the shift in direction from the discussion of the equivalence principle. Soon, as we shall see, we can put this together with the equivalence principle to derive the gravitational redshift of light! In 1960 Pound and Rebka and later, 1965, with an improved version Pound and Snider measured the gravitational redshift of light using the Harvard tower, h=22.6m. From the equivalence principle, at the instant the light is emitted from the transmitter, only a freely falling observer will measure the same value of f that was emitted by the transmitter. But the stationary receiver is not free falling. During the time it takes light to travel to the top of the tower, t=h/c, the receiver is traveling at a velocity, v=gt, away from a free falling receiver. Hence the measured frequency is: f'=f(1-v/c)=f(1-gh/c^2)."
The receiver travelling at a velocity v=gt measures frequency f'=f(1-v/c)=f(1-gh/c^2), speed of light c' and wavelength L'. These are related by the equation f'=c'/L' which means that only two formulas, c'=c-v and c'=c, can be true insofar as the measured speed of light, c', is concerned:
(A) c' = c-v = c(1-gh/c^2) ; L' = L (Goodbye Einstein: the speed of light as measured by the receiver varies with the speed of the receiver).
(B) c' = c ; L' = L/(1-v/c) = L/(1-gh/c^2) (Goodbye Einstein: c'=c is incompatible with general relativity where the speed of light is VARIABLE and obeys the equation c'=c(1-2gh/c^2)).
Pentcho Valev
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