[thechao]

As far as we can tell, GR implies, and we have measured, space-time is completely continuous. Draw a square on a piece of paper; or, better yet, outline a cube with some sticks: within that square (or cube) is an infinite set of points of either the integral or real cardinality — whichever you’d like.

The “no physical infinity” thing sounds like a very Greek sort of axiom — like their “nature abhors a vacuum” thing, etc.

[bubblyworld]

To my mind GR (or at least the standard textbook version of it, anyway) _assumes_ that space-time is continuous, it does not _imply_ it as such. Continuity is baked into the foundations of any physical theory that is expressed in the language of differential equations.

You probably know this, but it's easy to confuse the map (a physical theory) with the territory (reality, which is far more complicated).

[dist-epoch]

We have stuff like the Plank length.

And most physicists assume space and time are quantized, we just don't know how.

[smallnamespace]

No, physicists do not think that space is like a tinily subdivided grid. Lots of physics would break if that were the case, including QM.

We have a lot of hints that the amount of information in any given space might be bounded, but yet that space appears continuous. How exactly you reconcile this is (one of) the mystery of quantum gravity.

[enugu]

Is there a good write-up somewhere of the problems with discretization of space for physics?

Interestingly, some great mathematicians (including Grothendieck) thought that modelling space as continuum was an approximation and not the reality.