Actual Infinity in Reality?

[polymath257]

Which ultimately means that the concept of 'spacetime' as literally *all* of space and *all* of time as a single entity is part of your difficulty. Absent a multiverse (which only pushes the problem up one level since in almost every multiverse model, the multiverse is expanding), everything is part of spacetime.

There is no 'outside'. And expansion is just to the next cross section, not into anything 'outside'.

If it's an infinite universe expanding, there's no "outside" problem. If the totality of existence is finite, however, then yes, there is an "outside" that is "nonexistence", even if the expansion itself is just to the next cross section.

Just trying to counter this with words like "there's no outside, everything that exists is all contained in the spacetime" doesn't negate the logical mandate that there is an "outside". If we go with the premise, we have to follow through with it to the conclusion implied. We can't just stop at the premise and be satisfied.

OK, so to be clear. There is no 'outside' of spacetime. There is an outside of any particular spatial cross section (any other spatial cross section). But the collection of *all* such cross sections is 'spacetime'.

And again, the best answer to what the universe is expanding into, even for finite space, is 'the future'.

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Hmmm...a finite space does NOT imply an outside. That may be one of the issues here.

So, suppose that space is curved. In practice, what that means is that whatever direction you set off, if you keep going you will eventually come back around to your starting point (no actual travel--stay on one spatial cross section). So, you decide to take off in the 'up' direction and travel for a few billion light years, you will come back around to the start from the 'south' direction. Same with East vs West, and any direction and its opposite.

The reason I say not to actually travel is the time aspect of such: motion requires time and the time it would take to go 'around' is enough that the size changes during the trip.

So, just take a specific spatial cross section and go off in one direction, staying on that cross section. Eventually, with a finite space, you will come back around.

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Also, don't confuse the 'totality of all existence' with the 'totality of space at this time'.