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I know that there is a similar questions, but I think mine is a bit different. I wonder if with the expansion of the universe the speed of light changes. It seems that the speed of light is very connected to the space-time continuum, e.g. it follows all it's deformations etc. So if the space-time continuum expands, does the speed of light change?

Qmechanic
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Derb
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    Hi Derb. You need to have a look at all the many other questions asking why the speed of light is constant, and then refine your question to explain exactly why you think the speed of light might be changing. – John Rennie Feb 12 '16 at 12:39
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    I'm voting to close this question as off-topic because it shows insufficient prior research. – John Rennie Feb 12 '16 at 12:39
  • I'm pretty sure "the universe is expanding" refers to all the matter and energy in spacetime spreading out, not spacetime itself "expanding" (whatever that would mean). – Ixrec Feb 12 '16 at 12:45
  • Hi @John I have a basic notion why the speed of light is a constant. (I am not a professional physicist, and try to understand a little bit more about it). What I understand is that the light speed is a constant without really a reason. It is a kind of axiom (measured and determined) which consequently leads to all the results of the theory of relativity. The kind of: If the speed of light never changes....we will have many things to consider to be relative (the flow of time needs to change if for all observers the speed of light is the same). – Derb Feb 12 '16 at 12:46
  • I think my questions is similar to the question if the gravitational constant changes by an expanding universe. (Again I am just an amateur, but did some research before on this topic, but not in a way that I could publish a scientific paper on it :-) ). Just curious! – Derb Feb 12 '16 at 12:48
  • in theories like G4V , yes. But, yesterday, G4V was refuted and GR again checked with success. –  Feb 12 '16 at 12:49
  • @DerbR. this is a site for, and I quote from the tour, a question and answer site for active researchers, academics and students of physics and astronomy. Everyone is welcome, but we expect you to be willing to put some effort into your questions and a basic search of this site is part of the required effort. In relativity the speed of light is constant because it's a geometrical property. Have a browse through the search I suggested in my first comment to learn more. – John Rennie Feb 12 '16 at 12:53
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    @igael This info help me to conduct further research. If you have some quick info why G4V would allow it, please let me know (I need to read into G4V now). Thanks again!!! – Derb Feb 12 '16 at 12:53
  • Gravitational Waves in G4v by Carver Mead from Caltech. The deflection computation seems nice but the theory predicted G.W. with another signature. Search for the author on Youtube –  Feb 12 '16 at 12:57
  • @JohnRennie Thank you for your comment. I have to apologize I was not aware that it is only for active researchers, academics and students of physics and astronomy. Since you mentioned that the speed of light is a geometric property, could you please give me a reference on this? Until now I thought that there is "no reason" for the speed of light (as constant) having exactly the numeric value it has. (see the other questions). But if it is a geometric property, this numeric value for the speed of light can be derived from the space-time geometry. Any reference would help me! – Derb Feb 12 '16 at 13:08
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    Thanks again @igael ! Really good material to get more information on that topic. Very nice! – Derb Feb 12 '16 at 13:09

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In general relativity we describe the geometry of spacetime using a function called the metric. This metric is derived from the distribution of matter - indeed solving Einstein's equations normally involves starting with some distribution of matter and solving the equations to calculate the metric.

If we assume that matter is approximately spread out evenly in the universe then we end up with a surprisingly simple form for the metric. This is called the The Friedmann–Lemaître–Robertson–Walker metric and it is this metric that describes the expanding universe. When a relativist talks about the expanding universe they almost invariably mean the FLRW metric (or something closely related).

The FLRW metric is:

$$ c^2d\tau^2 = c^2dt^2 - a^2(t)(dx^2 + dy^2 + dz^2) $$

Exactly what the equation means is somewhat opaque to non-GR nerds, but the relevant fact here is that the parameter $c$ is a constant. With some jiggery-pokery we can work out what the constant $c$ means, and it turns out to be the speed of light.

So in general relativity the speed of light (technically only the local speed of light) is a constant because GR assumes it's constant. This is an important point to appreciate - GR doesn't prove $c$ is a constant it assumes $c$ is a constant. So the answer to your question is that whether the universe is expanding, contracting or turning cartwheels the speed of light is always constant.

GR could be wrong, and one day an experiment could demonstrate that the speed of light isn't constant. The trouble is that GR is pretty well supported by experiments, and of course the recent detection of gravitational waves adds more support. There are competing theories in which the speed of light can be variable but (so far) none them have proven a better description of the universe than general relativity.

John Rennie
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Well, an axiom that is "measured and determined" is not really an axiom :-)

If the speed of light was different in another time or place in the visible universe, we could see it at least indirectly, since c occurs in a lot of physical balances, e.g., the structure or fine structure of bands in the spectrum of light emission or absorption by stars and gazs.

And for a start, the condition and result of creation of matter, molecules, galaxies, stars, would also be different.

We don't observe that, so it's reasonnable to say that in all the visible universe, and in the past since the formation of the first galaxies, c has not changed.

Fabrice NEYRET
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