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MetricBrian
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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?
MetricBrian said:How can it be constant and viewed as variant?
DaveC426913 said:Speed (scalar) is constant.
Velocity (vector) is variable.
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/1DKin/U1L1d.html" describes it pretty well.MetricBrian said:What's the difference between speed and velocity?
DaveC426913 said:http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/1DKin/U1L1d.html" describes it pretty well.
MetricBrian said:O.K.
Then it is absolutely correct to say that the speed of light is constant in GR?
DrGreg said: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.MetricBrian said:But I thought that if light is not constant, then relativity must be wrong.
HallsofIvy said: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.
jefswat said:Would you like to try that again?
HallsofIvy said: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!jefswat said:Would you like to try that again?
HallsofIvy said: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!
atyy said: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.)
Side to side, Kansas has a curvature of 6 degrees.atyy said:... a local region of the Earth like Kansas is approximately flat.
HallsofIvy said: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!
Velocity is a vector. It has a magnitude (60) and a direction (East).MetricBrian said:How are the velocities different?
DaveC426913 said: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.
MetricBrian said: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?
DaveC426913 said:Side to side, Kansas has a curvature of 6 degrees.
Sure it was.atyy said:That must have been a harder measurement than Michelson and Morley's!
atyy said: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/ ). 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.
MetricBrian said:Asking for the speed of light in a curved space sounds meaningless when you put it that way.
The speed of light being constant to all observers is one of the fundamental aspects of special relativity, so it can't be different in general relativity, as it arose from special relativity.
There is ongoing debate among scientists about whether the speed of light is constant in general relativity. Some theories suggest that the speed of light may vary in certain situations, while others argue that it is always constant.
One of the main pieces of evidence for the constancy of the speed of light in general relativity is the fact that the equations of general relativity are consistent with the principle of special relativity, which states that the speed of light is always constant in a vacuum.
The alternative theory to constant light speed in general relativity is known as variable speed of light (VSL) theory. This theory proposes that the speed of light may have been much faster in the early universe and has since slowed down.
Several experiments have been conducted to test the constancy of light speed in general relativity, including the Michelson-Morley experiment, which showed that the speed of light is the same in all directions, and the Pound-Rebka experiment, which demonstrated that light does not lose energy as it travels through a gravitational field.
If the speed of light is not constant in general relativity, it could have significant implications for our understanding of the universe. It could potentially change our understanding of the laws of physics and the behavior of light, and could also impact our theories about the origins and evolution of the universe.