If there is a big crunch will space collapse with the matter?
It's difficult to talk about 'space itself'. Other than being 'bent' by mass, energy, and stress, space doesn't seem to have any properties that could collapse. It would certainly be heavily altered by the presence of extreme amounts of mass in a small volume, but I don't know I'd go so far to say that 'space collapses'.
If space can expand, how couldn't it collapse...?
Think of it as running time backwards in time until the Big Bang, so space itself would collapse, yes.
If I understand the standard big bang theory correctly, space is like a balloon and is taking the clumps of matter along for the ride as it is expanding, so to initiate a big crunch would space have to start collapsing, or would matter start collapsing, in effect the air would be let out of the balloon? But, what is more interesting to me is how, by what physical means does space latch onto clumps of matter, how does space become a balloon?
That's a good point and one I hadn't thought about. Unfortunately I don't have a good answer for you.
This is a complicated issue and I'm sorry to say that I, again, don't have a good answer for it. I'm sure General Relativity says something on the matter. As far as I understand it, everything ultimately boils down to describing the behavior of objects within spacetime, not to 'spacetime itself' unless you're talking about what the metric is doing. But that's all a little over my head to be honest.
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