THE FUNDAMENTAL EQUATION OF SPECIAL RELATIVITY

The fundamental equation of special relativity, c-v = c, can be applied in general relativity as well:

http://physics.ucsd.edu/students/cou...ecture5-11.pdf
"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 frequency measured at the bottom of the tower is f=c/L, where L is the wavelength. The frequency measured by a stationary observer at the top of the tower is:

f' = f(1-v/c) = f(1-gh/c^2) = (c/L)(1-v/c) = (c-v)/L = c'/L

Accordingly, the speed of light relative to the observer at the top of the tower is:

c' = c-v = c

From the equivalence principle, c' = c-v = c is also the speed of light relative to an observer moving, in gravitation-free space, away from the emitter with speed v. Clearly the fundamental equation c-v = c justifies Steve Carlip's declaration that the speed of light is "constant by definition":

http://math.ucr.edu/home/baez/physic..._of_light.html
Steve Carlip: "Is c, the speed of light in vacuum, constant? At the 1983 Conference Generale des Poids et Mesures, the following SI (Systeme International) definition of the metre was adopted: The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. This defines the speed of light in vacuum to be exactly 299,792,458 m/s. This provides a very short answer to the question "Is c constant": Yes, c is constant by definition!"

Pentcho Valev