(May 8, 2011 at 5:16 pm)little_monkey Wrote:(May 5, 2011 at 4:31 am)Wormhole199 Wrote:
Sorry for being late on this thread. However, that is totally wrong. The speed of light near a black hole, or anywhere else, is the same. Deny that, and you're denying the foundation of Special and General Relativity.
Inside the black hole, the light doesn't escape because it is bent by gravity into a circle, and so doesn't escape, but its speed remains the same. Outside the BH, your clock will slow down and your ruler will shrink, nevertheless, you will end up measuring the speed of light to be c.
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.
To measure the speed of light at a different location than yours first you have to define a local inertial frame. (If your frame is non-inertial, rotating for example, then the following is not for you). With the same clock and ruler the velocity of light becomes a variable depending on the reference frame of the observer. You can find the full derivation by Einstein himself (1955) from the full theory of general relativity in the weak field approximation:
'The Meaning of Relativity', A. Einstein, Princeton University Press (1955).
See pages 92-93, eqn (107); the variable velocity of light expressed in coordinates is:
![[Image: speed_of_light_23.gif]](https://images.weserv.nl/?url=www.speed-light.info%2Fspeed_of_light%2Fspeed_of_light_23.gif)
If your frame of reference is near a black hole and you are measuring the speed of light outside gravitational fields then the result is a zillion km/sec.
If your frame of reference is outside gravitational fields and you are measuring the speed of light near a black hole then the result is a few meters/sec. This scenario by convention is called the coordinate speed of light.
If your frame of reference is at the same location where light is propagating (both near a black hole or both outside gravitational fields) then the result is always 299792.458 km/sec. But remember that you defined a local inertial frame to begin with.
So it is absolutely meaningless to talk about the speed of light without defining your frame of reference.
My favorite site: Speed of Light.
