Is the Speed of Light Truly Constant in General Relativity?

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Discussion Overview

The discussion centers around the constancy of the speed of light in the context of General Relativity (GR) and its relationship to Special Relativity (SR). Participants explore the implications of gravitational effects on light, the definitions of speed and velocity, and the conditions under which light's speed may appear to vary.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants assert that the speed of light is constant in GR, while others suggest that this constancy depends on how speed is measured.
  • It is proposed that while the speed (scalar) remains constant, the velocity (vector) can vary due to gravitational influences.
  • Some participants highlight that measurements of light speed can differ based on whether an observer is in free fall or undergoing proper acceleration.
  • There is a discussion about the difference between speed and velocity, with examples provided to clarify these concepts.
  • One participant notes that experimental evidence for light speed is primarily based on local measurements, raising questions about measuring light speed in curved spacetime.
  • Another participant mentions that measuring light speed in globally curved spacetime lacks a standard definition due to the absence of global "right-angled" axes.

Areas of Agreement / Disagreement

Participants express differing views on whether the speed of light is truly constant in all contexts within GR. While some agree on its constancy under specific conditions, others emphasize the complexities and variations that arise in different scenarios.

Contextual Notes

Limitations in the discussion include the dependence on definitions of speed and velocity, the conditions of measurement, and the challenges in measuring light speed in curved spacetime.

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?
 
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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?
 
MetricBrian said:
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.
 
DaveC426913 said:
Speed (scalar) is constant.
Velocity (vector) is variable.

What's the difference between speed and velocity?
 
MetricBrian said:
What's the difference between speed and velocity?
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/1DKin/U1L1d.html" 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.
 
  • #10
DaveC426913 said:
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/1DKin/U1L1d.html" 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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  • #11
Yes the speed of light for all observers is constant.
 
  • #12
MetricBrian said:
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.
 
  • #13
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.


But I thought that if light is not constant, then relativity must be wrong.
 
  • #14
MetricBrian said:
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.
 
  • #15
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.

Would you like to try that again? :confused:
 
  • #16
jefswat said:
Would you like to try that again? :confused:
:biggrin:
 
  • #18
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? :confused:
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!
 
  • #19
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!

I figured as much but I just couldn't stand to let it go :biggrin:
 
  • #20
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.)
 
  • #21
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.)

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?
 
  • #22
atyy said:
... a local region of the Earth like Kansas is approximately flat.
Side to side, Kansas has a curvature of 6 degrees. :biggrin:
 
  • #23
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!

How are the velocities different?
 
  • #24
MetricBrian said:
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.
 
  • #25
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.

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?
 
  • #26
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?

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.
 
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  • #27
DaveC426913 said:
Side to side, Kansas has a curvature of 6 degrees. :biggrin:

That must have been a harder measurement than Michelson and Morley's! :smile:
 
  • #28
atyy said:
That must have been a harder measurement than Michelson and Morley's! :smile:
Sure it was. :rolleyes:

At 417 miles across, Kansas spans approximately 1/60th of the Earth's 25,000 mile girth...
 
  • #29
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.

Asking for the speed of light in a curved space sounds meaningless when you put it that way.
 
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