WannabeNewton said:
I'm saying your point doesn't make sense because you can't unambiguously define the velocity of a photon if you are making global measurements.
Hmmm. Well, velocity is defined wrt your own coordinate system as stationary. It seems to me that spacetime is flat, with wells here and there due to mass. All the wells are in the same direction wrt flat spacetime. All wells must create a longer pathlength (non-euclidean) than what is apparent (since we perceive them as euclidean). This concept should apply globally.
Here's a couple supporting links ...
http://www.speed-light.info/speed_of_light_variable.htm" ...
In 1915 (10 years after Special Relativity) Einstein developed another theory called General Relativity that deals with gravitational fields and according to this latest theory the velocity of light appears to vary with the intensity of the gravitational field. For example, an observer outside gravitational fields measures the speed of light locally (in his location) at 299792.458 km/s but when he looks towards a black hole he sees the speed of light there to be as slow as a few meters/sec.
http://www.physlink.com/Education/AskExperts/ae13.cfm" ...
A non-mathematical discussion of this can be found in:
'The Riddle of Gravitation,' Peter G. Bergmann, Charles Scribner's Sons, NY (1987).
See, in particular, pages 65-66 and, especially, the first full paragraph on page 66. Here, Bergmann takes the deflection of light by the gravitational field of a star as evidence of the decreased speed of light in a gravitational field.
The speed of light is _not_ constant in a gravitational field, but depends upon the reference frame of the observer. An observer anywhere in free fall will measure (locally) the traditional value of c. An observer sufficiently far away from the source of the field will conclude likewise that the speed of light is c (locally). But, the observer far away from the source will likewise conclude that the speed of light closer into the source decreases as the source is approached.
Also ...
http://www.speed-light.info/speed_of_light_variable.htm" ... Suppose that you have a clock and a ruler (which is not rotating with respect to stars) and that you are not accelerating (inertial). Locally (where you are) you will always measure the speed of light at 299792.458 km/sec. However in the presence of gravity if I am at a different location than yours then I could measure the speed of light at your location to be any value smaller than or greater than 299792.458 km/sec. It depends on where I am and where you are (it depends on locations). So in the presence of gravity the speed of light becomes relative (variable depending on the reference frame of the observer). This does not mean that photons accelerate or decelerate. This is just gravity causing clocks to run slower and rulers to shrink.
GrayGhost