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Bit of an awkward way to phrase it, but basically:

Time in relativity is just one of four dimensions of space-time. Nothing really special about it. Yet the universe was once smaller than it is now and has evolved, changed, from a singularity till its size today.

But this implies that the whole of space-time (since you can't separate time from space) is evolving over time. Which time, then, is it evolving over? There's not supposed to be a global time for the universe, only time as perceived for an observer at a particular location.

So it seems very strange to me that the volume of the entire universe's space-time could change over time when time is part of the thing that's changing. It sounds like we're talking about two different kinds of time...

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  • $\begingroup$ Time is that which the clock shows. It's not a forth dimension, even though we treat it like that in special relativity due to a mathematical trick introduced by Minkowski. In practice time, just like space, is tied to the existence of systems that can measure it, i.e. matter. Whereas space can be measured by matter in thermodynamic equilibrium (rulers), time measurement requires an energy source and a heat sink, i.e. it qualifies the behavior of systems far from thermodynamic equilibrium (clocks). $\endgroup$ – CuriousOne Jul 19 '16 at 19:13
  • $\begingroup$ Related: physics.stackexchange.com/q/119708/2451 , physics.stackexchange.com/q/166632/2451 and links therein. $\endgroup$ – Qmechanic Jul 19 '16 at 19:13
  • $\begingroup$ According to those questions, only co-moving observers will agree on the age of the universe. Does that mean that only c0-moving observers will agree on the size of the universe, too? So, if you spent the last few billion years cruising around at nearly light speed, you'll think the universe is smaller? $\endgroup$ – John Jul 19 '16 at 19:29
  • $\begingroup$ If you are cruising at a significant fraction of light speed, the universe actually IS smaller, due to length contraction. en.wikipedia.org/wiki/Length_contraction $\endgroup$ – Keith Knauber Jul 19 '16 at 21:17
  • $\begingroup$ @John: Re your question "If you spent the last few billion years cruising around at nearly light speed, you'll think the universe is smaller?". This depends on what you mean by "The Universe". Given the foliation defined by the comoving observers, do you mean the volume of the leaf that you currently occupy? If so, everyone will agree on the volume of that leaf. Or do you mean some other three-dimensional slice that is locally orthogonal to your worldline? If so, you first need to worry about how you're going to (globally) define that slice. $\endgroup$ – WillO Jul 19 '16 at 21:28
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One talks about the size of the universe in the context of a model where spacetime is foliated by three-dimensional spacelike leaves. The "size of the universe" means the size of one of those leaves, not of all spacetime.

For example: If you imagine spacetime to be filled with galaxies, the worldlines of those galaxies give a preferred global time coordinate, and you can take your three-dimensional leaves to be the three-manifolds whose tangent spaces are everywhere orthogonal to the tangents to those worldlines. You can then talk about the volume of a leaf as a function of the global time coordinate to get the rate at which the universe is expanding.

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