# Is Light Constant in GR

• MetricBrian
I figured as much but I just couldn't stand to let it go :biggrin: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.f

#### MetricBrian

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?

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?

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?

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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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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Yes the speed of light for all observers is constant.

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.

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?

Would you like to try that again?

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

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?

... 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?

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?

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.

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Side to side, Kansas has a curvature of 6 degrees.

That must have been a harder measurement than Michelson and Morley's!

That must have been a harder measurement than Michelson and Morley's!
Sure it was.

At 417 miles across, Kansas spans approximately 1/60th of the Earth's 25,000 mile girth...

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.

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These issues are fairly complex and explaining them accurately and unambiguously to someone who is asking a "simple" question is not so simple. Dr Greg's posts above are, I believe, precisely accurate. Rereading my own initial post, I would now change a few words, but likely the poster would not have gained any additional insights anyway...

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.

This statement is not precisely accurate because special relativity implies constant velocity and no curvature of space (no gravity); general relativity involves curvature of space and acceleration and only simplifies to special relativity under certain circumstances...no gravity, no acceleration...