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Space looks like time depending on the motion of the observer so I was going to ask if space expansion was the same as the unfolding of time, but this was asked on physics.stackexchange before and the answer was that in GR time does not flow - there is no more a flow of time than there is a flow of space.

So instead I'll ask: is space expansion the same as time dilation ?

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Not at all, because the time-dilation is a local thing, it happens in small regions that don't care about the global expansion of the universe, and it has to do with the speed with which you traverse a closed loop in space, just like the length of a spiral along one turn is different if the spiral is stretched or smooshed. If you have a muon going in a circle fast in a magnetic field, the time-dilation is only a function of the speed, as can be seen by how fast the muon decays. It has no relation to the expansion of the universe, which is only visible on galactic distance scales.

The effect of time-dilation is very simple, it's geometry, except with a different sign in the pythagorian theorem between time and space. You can learn about it here: What are the mechanics by which Time Dilation and Length Contraction occur?

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What about trying to attribute the cosmological red-shift, commonly attributed to the expansion of space, to gravitational red-shift? That is, the universe isn't expanding, the apparent shifted light is a consequence of the shape of space, just like the red-shift of light leaving the Sun. – kηives Sep 17 '12 at 20:27
@kηives: That's part of the redshift in a certain point of view. Where the redshift is large, that's low gravitational potential, so gravity pulls you to where time ticks slower, so you would be pulled out in such a picture, the galaxies wouldn't stand still. You can't have galaxies standing still in redshift. The self-consistent solution motion plus redshift which makes that motion, is what we see, in the picture within a single causal volume. – Ron Maimon Sep 17 '12 at 21:56

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