I've had a debate with someone recently about whether or not light is constant in GR. I think that it is. Is there any debate on this point?
Then it is absolutely correct to say that the speed of light is constant in GR?
Actually the whole truth is not quite so simple as that. It depends how you measure speed.
If you are falling freely and you use your own clock and ruler to measure the speed of some light that is near you, then yes you will always get the same answer, no matter where you are or how quickly you are falling. But if you are not falling freely (i.e. you are undergoing proper acceleration) or if you try to measure the speed of some light that is some distance away from you, you might get a different answer.
Even in Special Relativity, it is only inertial observers who measure a constant speed of light. Accelerating observers do not.But I thought that if light is not constant, then relativity must be wrong.
Just what DaveC426913 said:
"Velocity" is a vector. "Speed" is the norm of the velocity vector.
A car driving east at 50 mph and a car driving north at 60 mph have different velocities but the same speed.
Oh, blast! Always a typo to mess things up! I meant to say that a car moving east at 50 mph and a car moving north at 50 mph have the same speed but different velocities!Would you like to try that again?
In special relativity, spacetime is flat and the speed of light is constant.
In general relativity, spacetime is globally curved, but local regions of spacetime are approximately flat - just like the earth is round, but a local region of the earth like Kansas is approximately flat. Within every local, approximately flat region of globally curved spacetime, the speed of light is constant. If one measures the speed of light over globally curved spacetime, then its speed will not be constant (actually there isn't even a standard way to measure the speed of light globally over curved spacetime, so one has to define that first, whereas to measure the speed of light in local approximately flat bits of spacetime, one just takes over the definitions from special relativity.)
Velocity is a vector. It has a magnitude (60) and a direction (East).
Here's a more basic example:
One car is going forward at 60mph. It's velocity is 60mph.
Another car is reversing. It's velocity is -60mph.
That's very interesting. The only experimental evidence available is the local measurement of light speed. We can't meausure light speed in curved space. is that right?
It is possible to measure the "speed of light" in globally curved space, eg. Shapiro time delay (Section 3.4.2 o Will's http://relativity.livingreviews.org/Articles/lrr-2006-3/ [Broken]). However, there is no canonical meaning for such a "speed of light", because there are no global "right-angled" axes in curved space. In flat space, or locally flat space, there are "right-angled" axes, and the "speed of light" is canonically defined as that measured using those axes. So in globally curved space, if one wishes to talk about the "speed of light", then one must specify which set of weird axes one is using.
Asking for the speed of light in a curved space sounds meaningless when you put it that way.