Space time may be a lot of things but in modern physics it is not "nothing".
Nor is space infinitely divisible and empty.
It is clear there is something wrong with the logic of "space and matter cannot exist" just as there is something wrong with Zeno's paradox.
Personally I subscribe to the view that space and time are both quantum just like matter and energy.

Suppose you have some nonphysical things, and these nonphysical things bear an ordered relation to each other: each one has a unique "previous" and "next" thing, and something that is the next thing after the next thing after the next thing is further down the order in that direction, while something that is previous to the previous thing before the previous thing is further up the order in the other direction. Like numbers: you can just put them in order and make a line out of them.

Suppose this set of things has two kinds of ordering to it: some things may be "previous" or "next" in one way, while others are not related by that ordering, but are related by a different ordering, being "previous" or "next" in some different way. Complex numbers are like this: 1 is next after 0 in one way, but i is next after 0 in a different way, and 1+i is next after i in the first way again. Because of this, the complex numbers form a plane.

You can also do this in three dimensions, or more, and forum a volume, or some other higher kind of space.

Boom, there you go with a space made out of non-physical stuff. If you use the right kinds of non-physical stuff, you can make a space that behaves like the physical space we're used to, basically one that's locally flat-ish, and smooth-ish enough to do calculus on: a differentiable manifold.

And if that space is made of, say, unitary matrices instead of ordinary numbers, you can make something like a special unitary group, in which you can build structures identical to the physical stuff that makes up our universe.

If you build a structure identical to a human in there, they'd find themselves experiencing the rest of that math as physical stuff in physical space and time.

So to say that our physical space and time is real is just to say that whatever the thing is of which we're a part, whatever all this stuff we're interacting with that we call "the universe" is, it has a kind of ordered structure similar as described here. That's all space is: an orderly feature of the structure of the universe, whatever "the universe" is.

I honestly can’t tell if this is a joke or not. “since nothing cannot occupy any space since its size is zero” what? Physical things have sizes. Nothing doesn’t have a size. This is an example of using concepts simply where they don’t apply

And if that space is made of, say, unitary matrices instead of ordinary numbers, you can make something like a special unitary group, in which you can build structures identical to the physical stuff that makes up our universe — Pfhorrest

Maybe a reference would help.

As I understand it, the Standard Model uses U, SU(2) and SU(3) to model all the fundamental fields besides gravity, so you could build a gravity-free model of any physical thing with those, in principle. Wikipedia can probable tell you more details than I could.

Thanks. Wish I knew more about modern physics.

I took a year of physics in college 65 years ago and of course used some of the elementary ideas in calculus courses I taught. The group SU(2) is as close as I get to contemporary physics as it concerns 2X2 matrices of real or complex numbers. The multiplication of 2X2 matrices corresponds to composing two linear fractional transformations, and I have long explored infinite compositions of LFTs. Apart from that it's Greek to me! :cool: