[ReaLNero]

AFAIK under the current quantum model (QFT) specifying a precision finer than the Planck length will not make your predictions more accurate. So you only need a finite number of bits to describe a field over a finite volume using a 3-d matrix for each lattice point's amplitude.

[barakm]

You’re right to go to Planck length to get a number of bits to represent an atom, but here’s another angle:

To best guess, there are about 10^24 stars in the sky. That’s about 2^80.

That means you could simply, on Earth-prime, give an id to all the stars in 2^944 universes. Way way less than the multi-multiverse in question, let alone anything atomic.

[charcircuit]

Usually the volume isn't assumed to be finite. Sure there is the observable universe, but I don't think many models prohobit atoms from living outside of it.