# 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).

21. Jan 14, 2014

### Agerhell

I am sure you are correct but if you want to calculate how long time it will take for a signal to travel from Earth to a distant spacecraft with and without Jupiter interfering you will get the correct result (I think) if you assume that Fermats principle holds and that the light slows down close to Jupiter.

How do you perform the same calculation by assuming "changing spatial geometry along the path"?

22. Jan 14, 2014

### PAllen

You do neither. No source I find since 1921 uses Fermat's principle for this problem. Especially, the first standard textbook on GR, Bergmann's 1942 book (highly praised by Einstein) makes no mention of it at all (for any purpose) for calculating light bending. Nor does it mention varying lightspeed (in any way, shape or form). Instead, it just computes null geodesics in in the Schwarzschild metric. All my later books do likewise.

[Edit: Just for kicks I checked Pauli's 1921 classic on SR and GR. NO MENTION at all of Fermat's principle or varying light speed. Already used the exact same modern approach used in Bergmann (1942). Thus, this highly coordinate dependent interpretation appears to have been emphasized only by Einstein, and only in his very earliest writings on GR.]

[Ditto Eddington's 1923 book. Uses only the modern method used in Pauli and Bergmann and later books. No mention of Fermat or varying light speed. ].

[One final note: I read over Einstein's use of this method in his lectures at Princeton that became "The Meaning of Relativity", his most technical early presentation on relativity. Here he does use Fermat and varying light speed - but basically apologizes that to do so he had to construct very special coordinates. Then he states that despite the argument depending on special coordinates, the observable conclusion (light bending) cannot be coordinate dependent.]

Last edited: Jan 15, 2014
23. Jan 15, 2014

### subquantumboy

I still have some questions.

1. No absolute things? That means short or tall people actually don't exist. So only relationship between things or persons exists,right?

2. If we chose to use a ruler as our reference measuring stick, it will never change? I mean atoms of the ruler will never change? the length of the ruler will never change? But that is possible? Everything always changes, don't you think? Some force always push or pull persons or things, doesn't it?

24. Jan 16, 2014

### haael

OK, has anyone mentioned the fine structure constant in this thread yet?

"Speed of light" may mean two things.
1. The invariant speed from relativity, the "c".
2. The actual speed of electromagnetic field disturbances, the speed of photons.

Varying fine structure constant will give you different "speed of light" in the 2nd sense, leaving the relativity theory intact.

There were measurements of the historical fine structure constant based on distant star observations and they concluded that the FS constant was indeed a constant within the experimental error and thus the speed of light in the second sense.

Kaluza-Klein theory has a curled fifth dimension. The size of this fifth dimension gives a value of the fine structure constant (the smaller the dimension, the greater the constant). If the FS constant were ever found to be a variable, it could be immediately explained in the context of GR by the fifth dimension changing size.

25. Jan 18, 2014

### stevmg

This is the argument that quasi-sophisticated "Young Earth Creationists" have been trying to use for some time in the twentieth Century to back up their claim that the Earth and Universe which were formed simultaneously are only six thousand years old. But, in their rationale, the speed of light was initially very fast and has been slowing down to the current 300,000,000 m/sec. This would explain the large distances starlight could travel in these six thousand years so as to appear that they are further away than they actually are.

1) No observed or experimental evidence that has suggested a decay of light-speed over the several hundred years we have been guessing at it. In fact, earlier estimates of c were less than the 300,000 km/sec but in the same magnitude.
2) As stated above, earlier in the "Big Bang" mass and energy (with concomitant mass equivalent of m=E/c^2) was more concentrated and close which, by General Relativity, would retard the speed of light in the earlier stages of the Universe.

It is most important to steer these people to the Bishop St. Augustine of Hippo who, in 408 AD, debunked literal Creationism in his treatise on "The Literal Interpretation of Genesis." Yes, that's right, 408 AD! Time hasn't spread up or slowed down since then.

Sorry for the diversion into Philosophy and Religion, but it seemed appropriate on this interesting blog.