Does time speed up as space expands

T.O.E Dream

If the speed of light takes sometime to travel a certain distance and that distance expands (like for example the universe expanding) then wouldn't time have to speed up to keep the speed of light constant?

Fredrik

Why would it, and what would it mean for time to "speed up"?

If you mean e.g. that the time it takes light to travel from galaxy A to galaxy B should stay the same as the universe expands, the answer is that it doesn't.

Naty1

Alas, the poor old photon appears to be restricted to travel at speed c for it's existence. Time and distance may change during the life of a photon, and the energy of the photon may change, but the poor old photon just keeps chugging along at c. It's one constant that seems really constant.

T.O.E Dream

So now I have a different question. If i were to measure a meter in space and then the space expands by 2 times would it still be a meter or does it change to 2 meters?

Fredrik

A meter stick doesn't expand with the cosmological expansion, at least not enough to have any noticeable effect on measurements, so it will be 2 meters.

T.O.E Dream

So take two points, maybe of a distance of one light second. Now if the space expanded the two points are further away and not a light second apart. But don't we already know that the speed if light is the only constant?

sylas

You can't just "take two points". A point is an abstraction; you need some way of identifying a point; and probably what you want is not a "point" in space and time but a "worldline", or a trajectory. You can identify a point with a particle; but if you pick two particles, the expansion of space does not work like a force to drive them apart. Two particles that are at rest with respect to each other might actually start to move closer together as a result of the expansion of space; this depends on the nature of the expansion.

Regardless of any of this... the speed of light remains constant. The speed of light is measured locally; as the speed at which a photon moves past any other particle.

To makes things even worse, the idea of being "at rest" or having a certain speed is actually ambiguous when particles are separated from each other.

If a photon is at some distance away from a particle, then the speed in relation to that particle is not well defined; it can depends on how you put co-ordinates on spacetime; and there's no one way to do that. The speed of light (or anything else) only becomes unambiguous when it is "local" to the observer.

Cheers -- sylas

Naty1

Empty space itself is rather weakly held together; masses like meter sticks are held by relatively strong forces like electromagnetic attraction and nuclear forces. Even gravity, usually considered the weakest of the forces at everyday distances is often stronger than the cosmological expansion: our galaxy is pretty much held together by gravity but at intergalactic distances where there is a lot more empty space, space is apparently able to expand.

stone1

I have a similar question (if not the same question really). If there is no space and there is no time, but only spacetime, why do people talk about space expanding? Is spacetime expanding?

Fredrik

Each solution of Einstein's equation describes a possible geometry of spacetime. One important class of solutions was discovered in the 1920's. They are called FLRW solutions (at least by Wikipedia). To find them, you start with the assumption that spacetime can be sliced into a one-parameter family (with time being the parameter) of 3-dimensional spaces S_t ("spacelike hypersurfaces") that you can think of as "space, at time t". You also assume that each of these hypersurfaces is homogeneous (translationally invariant) and isotropic (rotationally invariant). (You would have to use a very technical definition of the concepts "homogeneous" and "isotropic").

Our universe is neither. For example, there's a chair under me, but not above me. But if we look at very large regions of space, the distribution of matter is starting to look more and more homogeneous and isotropic. This suggests that some of the FLRW solutions might be good approximate descriptions of the large-scale behavior of the universe.

The geometric properties of the S_t are determined by the geometric properties of spacetime. So each FLRW solution specifies a geometry of space, at each time. That's why it's meaningful to talk about how the geometry changes with time.

Now all of these solutions have the property that the time parameter t can only be defined for values of t larger than some value which we can choose to be 0, and all of them have the property that as t grows, so does S_t (in one of the three main classes of solutions S_t reaches a maximum size after a while and then starts shrinking). The geometry of any S_t can be described by a formula that's the same for all t, except for a number R(t) called a scale factor. In all of these solutions we have R(t)→0 as t→0.

That last bit is why the claim that the large-scale behavior of the universe can be approximated by a FLRW solution is known as "the big bang theory". The distance in space between any two objects depends on R(t) in a way that means that the distance goes to 0 as t goes to 0.

So it's not spacetime that's expanding. (What would that even mean? Wouldn't we need a second time parameter?) Space is expanding. It makes sense to talk about space because we live in a universe which has a large-scale behavior that can be approximated by a solution of Einstein's equation that includes a natural way to slice spacetime into subspaces that we can think of as "space, at time t".

Fredrik

I have never really been able to make sense of that explanation. Gravity isn't even a force in GR, so how does it make sense to say that the reason is that gravity is weaker? How do you even compare them?

I think it's better to just point out that expansion is a result derived from assumptions of homogeneity and isotropy, and that the universe is neither homogeneous and isotropic on the scale of a meter stick, so we can't expect that result to apply to the meter stick.

T.O.E Dream

Another question, I hope this is a big one. If space is expanding than it is obvously moving. Wouldn't that mean we need to apply relativity for space?

Fredrik

Not really. It just has a time dependent scale factor.

I don't understand this question.

T.O.E Dream

Okay maybe i should rephrase it. Would relativity change if space was expanding?

Fredrik

Space is expanding.

sylas

Great explanation... with one quibble. The first solution found by Friedman (I think) was the simplest case of empty space with a cosmological constant... this is the "pure inflation" case in which R(t) is proportional to e^kt; and hence extends indefinitely into the past. (k is 1/H; the inverse of the Hubble constant. This solution is actually a kind of "steady state" of expansion; it is the only solution in which the Hubble constant really is a constant.)

Of course; as the scale factor reduces any contribution from matter or radiation becomes more significant, and that drives the solution to a singularity, but the pure inflation with a constant energy density is still a theoretical solution with no singularity and an infinite past.

Cheers -- sylas