Is spacetime an actual tangible "fabric of the universe", or a mathematical construct? There's a compelling theory put forth (or at least reiterated) I believe by Feynman(?) (Edit: Sorry it was Penrose) , that, assuming all subatomic particles eventually decay, the resulting empty universe becomes a singularity and a big bang happens again, birthing a new universe.
Surely spacetime isn't changing size in such a case - lest the planck length change with it.
It seems, then, that in the absence of anything to measure it, spacetime just doesn't really exist and is just a mathematical construct simplifying the description of how forces and matter interact based on whatever laws govern physics. This might seem like semantics, but when it comes to discussing space being shaped to connect two different "regions" as with wormholes the distinction seems to matter.
So is spacetime a real tangible fabric of the universe or is it more of a description of a range of interactions and behaviors?
Edit: I'm not dissenting spacetime's success at describing reality. But rather, it seems to me that in reality, the way particles interact is based on individual and entangled wave functions and the way those particles interact with all of the fundamental forces. So then isn't spacetime just a simplified construct? Einstein's equations predict wormholes but I'm curious if they just show up as a mathematical quirk because of the equations treat spacetime as a 3+1D fabric, when it seems like perhaps it's more complicated than that.
Or maybe it's not. Maybe spacetime really is a fabric filled with dark energy that exists even in a true vacuum. Seems like a valid question to me, despite the comments it's getting.
 A: I'll address the question in the title.
All of physics consists of mathematical descriptions, written down by humans, of natural phenomena that we observe and study in the interests of understanding those phenomena well enough to enable predictions to be made. So our description of spacetime is a mathematical construct created by humans to formalize and codify the behavior of the real world, and enable accurate predictions to be made about the real world via calculation.
But at the deepest levels, the real world behaves exactly as if spacetime were an integral part of that reality; furthermore, we also know that if it wasn't, there would be easily-observed consequences which have been assiduously sought after for over a hundred years (for which the finder's reward would be a Nobel Prize)- and never seen.
This suggests quite strongly that the functioning of the real world with respect to for example things like 4-dimensional spacetime really is governed by things which admit precise mathematical description i.e., the story of the universe is actually written in the language of mathematics- whether or not there happen to be any sufficiently smart & clever humans hanging around to figure out and write down the equations.
A: Einstein told us that an empty globally developing spacetime can't exist. For a globally developing spacetime to exist there has to be matter inside it. That is not to say that an empty spacetime that only locally develops (while the global structure stays the same) can't exist. You can read this here. It could be the Feynman universe you talk about, before a new big bang. But you can't touch it... You can't measure the time there neither can you make distance measurements, because of the simple fact that there are no clocks and distance measurement devices. Notice that for time to exist in such a structure there is no need for the irreversible processes we encounter in thermodynamics. That is, there isn't a global direction of time, only a local one. To deny that spacetime exists, independently of human beings, would be to deny that we exist, though there are people who see the material universe as a mere chimera.
To say what spacetime (or the matter inside it) is an Sich, who knows? We can't know. It's something very mysterious though. Luckily! It makes us feel, love, fight and think.
