# Does the speed of light change? [duplicate]

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?

## marked as duplicate by John Rennie, Bill N, Qmechanic♦Feb 13 '16 at 5:33

• 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
• 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
• @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
• Thanks again @igael ! Really good material to get more information on that topic. Very nice! – Derb Feb 12 '16 at 13:09

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.

• "So the answer to your question is that whether the universe is expanding, contracting or turning cartwheels the speed of light is always constant": you're saying this because GR says so, and GR has worked so far, is that so? – Saravanabalagi Ramachandran Jun 21 '18 at 7:56
• @SaravanabalagiRamachandran yes. For more on this see this answer. – John Rennie Jun 21 '18 at 8:24

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.