# Does the speed of light change with the age of the universe?

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1. Jan 10, 2014

### vinven7

Is there any reason to think that that the speed of light could vary with time (taking t=0 at Big Bang), ie, could light have been slower or faster billions of years ago? Also, is there any experimental evidence so far that either confirms or denies this? Do we know of any experiment that proves that light had the same value at some other point of time?

2. Jan 10, 2014

### phinds

No. I don't know of any experiments (we don't have a time machine) but there is no reason to believe that it did.

3. Jan 10, 2014

### Staff: Mentor

4. Jan 10, 2014

### Integral

Staff Emeritus
Here is a book about that very question.

5. Jan 12, 2014

### bcrowell

Staff Emeritus
6. Jan 12, 2014

### Agerhell

The speed of light is known to (depending upon how you look at it) vary with gravitational potential. In the Big bang theory the universe used to be a lot denser in the past, thus the average speed of light in the universe back in the days should have been lower than now...

7. Jan 12, 2014

### phinds

That is not true. Locally, light always travels at c, doing so in a curved space-time geodesic that can make is appear to observers in a different reference frame to be slowed down.

8. Jan 12, 2014

### vinven7

I don't think gravity alters the speed of light - only it's direction

9. Jan 12, 2014

### my_wan

The key word word here is 'local'. In SR the speed of light was a global constant. In GR it became a local constant. This has lead some to quote Einstein stating that the speed of light can no longer be considered an absolute constant to make all sorts of wild claims.

One of the ways you can map a gravitational field is to treat each point in space as a clock. The change in clock rates as you move from point to point defines the curvature of that space. The local clock will always represent the proper time. Alternative, more abstractly as it applies to points, you can treat each point in space as a unit ruler, and the change in the length of the ruler defines the curvature. Again the local ruler will represent the proper unit length. A third, more general, way is to define a variable speed of light for each point in space. Again the local point will represent the proper speed of light, and the variability will define the curvature, i.e., gravitational field.

So yes,the 'local' speed of light is always constant. Just as the proper length and time is always constant.

10. Jan 12, 2014

### my_wan

I found one quote that describes the situation:
http://www.bartleby.com/173/27.html

Last edited by a moderator: May 6, 2017
11. Jan 12, 2014

### bcrowell

Staff Emeritus
The coordinate velocity of light can be anything you like, and this is true in both SR and GR. (This is presumably what the quoted material in #10 is about.) But coordinate velocities are not that interesting. The actual speed of light is locally always the same. That's why we normally do relativity (both SR and GR) in units where c=1. 1 doesn't have a varying value.

12. Jan 12, 2014

### my_wan

Yes, I was merely expanding on that fact. No disagreement from me. The only difference is, as you say, coordinate dependence. SR you could extrapolate a coordinate choice out globally. In GR this is no longer possible. New people trying to get a handle on it tend to start from a coordinate dependent perspective, and it gets confusing when that is denied. Even though it gets much easier once you get past it, it makes figuring it out easier for some people.

13. Jan 12, 2014

### subquantumboy

How do you know light ALWAYS travels at c? Light is not a bunch of particles? No force can pull or push it?

14. Jan 13, 2014

### georgir

If light suddenly became twice as fast but also other processes became twice as fast, would we even have any way of knowing? That's the thing about measurements, they are never absolute. We measure things only in relation to other things, and if we chose to use light as our reference measuring stick, it will never change.

15. Jan 13, 2014

### WannabeNewton

This is not possible in SR either, not in general anyways. Just because global inertial frames have coordinate system which cover all of space-time doesn't mean all frames in flat space-time have the same property. The coordinates of a uniformly rotating frame certainly cannot cover all of flat space-time because the tangential velocity is bounded above by $c$.

16. Jan 13, 2014

### Agerhell

I think Fermats principle holds even in general relativity. If you for instance is sending an electromagnetic signal from Earth to some spacecraft beyond Jupiter, the signal will bend in the gravitational field of Jupiter, but in such a way that the time for the signal to travel from the Earth to the spacecraft is minimized.

17. Jan 14, 2014

### my_wan

When you extend your inertial frame over all space-time, assuming it is flat, not all frames have the same properties even without rotation. If it is a rotating frame then it is by definition not an inertial frame as defined by SR. There is nothing unusual about an 'apparent' speed of light exceeding $c$, or even multiples of that. We see it all the time. Why would the tangential velocity of a coordinate choice out to some distance be any different?

18. Jan 14, 2014

### WannabeNewton

Well obviously but this completely defeats your original point that in SR you can always extend a coordinate system to cover all of space-time. Clearly the natural coordinates introduced in a rotating frame cannot cover all of space-time.

You're going off on a tangent now that is unrelated to the original statement. If the frame has angular velocity $\omega$ relative to a global inertial frame then the radial coordinate has to satisfy $\omega r < c$ so the $r$ coordinate clearly cannot cover all of space-time when we transform to the rotating frame.

19. Jan 14, 2014

### Pippo

I would say that C is not a characteristic of the light but a consequence of space/time in our universe, so it can not be a costant value.

20. Jan 14, 2014

### PAllen

It is entirely coordinate dependent whether the minimized time is achieved by varying light speed or by changing spatial geometry (reducing distance) along the path. There is absolutely no coordinate independent way to talk about varying light speed in GR. On the other hand, locally being c is built into the mathematical structure of the theory (simply by the requirement that the manifold is pseudo-riemannian).

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