# Is Light Constant in GR

## Main Question or Discussion Point

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?

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I assume you are asking if the speed of light is constant. Yes it is.

But it also can be viewed as accelerating: that is, it changes direction in a gravitational field, but locally it's speed remains "c".

Also, the frequency/wavelength of light varies: as light climbs out of a gravitational potential, say from a star towards earth, it loses energy and is consequently red shifted....

How can it be constant and viewed as variant?

DaveC426913
Gold Member
How can it be constant and viewed as variant?
Speed (scalar) is constant.
Velocity (vector) is variable.

No, actually it all depends on how the speed of light is measured.

Speed (scalar) is constant.
Velocity (vector) is variable.
What's the difference between speed and velocity?

DaveC426913
Gold Member
What's the difference between speed and velocity?
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/1DKin/U1L1d.html" [Broken] describes it pretty well.

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HallsofIvy
Homework Helper
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.

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.

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/1DKin/U1L1d.html" [Broken] describes it pretty well.

O.K.

Then it is absolutely correct to say that the speed of light is constant in GR?

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djeitnstine
Gold Member
Yes the speed of light for all observers is constant.

DrGreg
Gold Member
O.K.

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.

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.

But I thought that if light is not constant, then relativity must be wrong.

DrGreg
Gold Member
But I thought that if light is not constant, then relativity must be wrong.
Even in Special Relativity, it is only inertial observers who measure a constant speed of light. Accelerating observers do not.

In General Relativity, gravitational tidal effects mean that someone who is an inertial observer of nearby events cannot also be an inertial observer of distant events.

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.
Would you like to try that again? DaveC426913
Gold Member
Would you like to try that again?  HallsofIvy
Homework Helper
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.
Would you like to try that again? 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!

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!
I figured as much but I just couldn't stand to let it go atyy
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.)

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.)
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
Gold Member
... a local region of the earth like Kansas is approximately flat.
Side to side, Kansas has a curvature of 6 degrees. 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!
How are the velocities different?

DaveC426913
Gold Member
How are the velocities different?
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.

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.
Thanks! That clears it up for me.

Now back to the speed of light. Are you saying that the speed of light is same in SP and GR but the velocity can differ?