How is motion in space different than motion in spacetime?

[Pjpic]

If two particles are moving apart, how is it determined if they are moving through space or if the motion is due to the expansion of space-time? Especially if there was no other frame of reference.

 

[Chalnoth]

If two particles are moving apart, how is it determined if they are moving space or if the motion is due to the expansion of space-time? Especially if there was no other frame of reference.

With two particles only, the expansion of space doesn't make sense.

The expansion of space is a description of a particular space-time. That space-time includes, in its simplest form, a uniform density of matter/energy everywhere in the universe. With two particles, there just isn't a uniform density, so the description doesn't apply. With our own universe, on large scales (greater than a couple hundred million light years), the density is approximately uniform, so we can talk about average expansion between far-away galaxies.

 

[PeterDonis]

If two particles are moving apart, how is it determined if they are moving through space or if the motion is due to the expansion of space-time?

Spacetime doesn't expand. "Space" can expand, if you choose coordinates appropriately (and if the spacetime geometry permits such a coordinate choice); in such a case, that choice of coordinates might also show the particles "moving apart" or it might not. However, none of that is really to do with the actual physics; it's to do with your coordinate choice. The only real physical invariant is that the particles are moving apart--you can tell that by having them exchange light signals and measuring increasing round-trip travel times of those signals, according to clocks moving with each particle. There's no need to talk about "space expanding" or "moving through space" at all.