# Why is speed of light a constant while distance in space is not?

Disclaimer: I asked this at Astronomy.SE, but got no answer whatsoever, so I am trying my luck here.

As you probably know current state-of-the art physics (i.e. gravitational waves, cosmic expansion) basically states that space itself is subject to expansion or contraction. Since there is no moving matter or energy involved, this might even happen at a "speed" faster than light.

So far, so good and obscure. What strikes me is the principle that the speed of light as a fundamental constant can only be expressed as a function of space-time. Where do we know that the one is constant but the other can suddenly be variable?

Is there any reason why the point of view of an expanding or contracting space is preferred over, say, a reduction in the speed of light or an increase in the "speed" of time? Is there any objective difference, a mathmatical model being a better fit or is it just the good old rubber metaphor being stretched (pun intended) too far?

In case the answer is: Both are equal w.r.t. current observations: How do we know that not both are actually variable?

• Re: "Is there any reason why the point of view of an expanding or contracting space is preferred over, say, a reduction in the speed of light or an increase in the "speed" of time?"...'any reason' covers a lot of territory. Mar 12 '16 at 22:31
• It has been mostly answered in this link: physics.stackexchange.com/q/2230 Mar 12 '16 at 22:31
• @choeger Actually the idea of a variable speed of light is/has been considered, even by Einstein himself, and nowadays in the context of the inflationary scenario, you may like to take a look at en.wikipedia.org/wiki/Variable_speed_of_light
– udrv
Mar 13 '16 at 4:56
• " this might even happen at a 'speed' faster than light": no. Mar 13 '16 at 9:43
• So you have to bring in the machinery of general relativity. And since general relativity can already explain everything with a constant speed of light, you don't get anything out of making it vary. Mar 14 '16 at 20:52

Is there any reason why the point of view of an expanding or contracting space is preferred over, say, a reduction in the speed of light or an increase in the "speed" of time

The postulate that the speed of light is the same in different reference frame led to a whole theory that can explain observations well and solved problems you would see otherwise. There is no theoretical preference for it otherwise.

• So a space time geometry where instead of (just) changing space and time (also) c is variable has just not been defined in a satisfactory way (yet)? Mar 14 '16 at 8:41
• Well not satisfactory in the sense that such a theory would be in conflict with experiments to great precision. Mar 14 '16 at 14:12
• This seems to be a rather bold statement. How can you assert that there is no equivalent formulation of the currently accepted theories that holds space constant and varies c? From a purely mathematical point of view this seems to be possible, since both quantities are related. Mar 14 '16 at 15:40
• It is not that clear to me what "equivalent formulation" means if $c$ is allowed to vary. The constancy of $c$ is the crux of special relativity. I'm sure there are theories out there in which $c$ is allowed to vary but I can not see how they could be called equivalent nor how they could be accepted since experiments for now tell us otherwise. Mar 15 '16 at 0:09
• I am basing my assumption on the observation that c is a relation between time and distance. In a simple scenario between two points in the same frame of reference if the distance grows/shrinks you should be able to explain your observations as well with a (local) reduction/increase of c. Mar 15 '16 at 8:12

When we observe very distant objects, the spectral lines of atoms seems to keep the same, and the physics (and the objects it permits) as well, despite c appears in many balances of the microphysics. So c does not seems to change in all the observable Universe. Beside, some pulsing phenomena seems to be slowered as predicted by time contraction in relativity. Therefore the red-shift really means expansion of space, and not change in the light.

• Can you elaborate this? How would a (minimal) change of c change e.g. the spectral lines of hydrogen? Mar 14 '16 at 8:39
• en.wikipedia.org/wiki/Fine-structure_constant Mar 14 '16 at 20:48