How can the size of the universe change over time when time is part of the universe?

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...

• 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). Jul 19, 2016 at 19:13
• Related: physics.stackexchange.com/q/119708/2451 , physics.stackexchange.com/q/166632/2451 and links therein. Jul 19, 2016 at 19:13
• 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?
– John
Jul 19, 2016 at 19:29
• 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 Jul 19, 2016 at 21:17
• @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. Jul 19, 2016 at 21:28