Even if you had a perfect 3D coordinate system and atoms worked on float64 boundaries, you’d still have 64 bits to represent one atom. So you could fit, at best, 128 atoms. These are the competing scales.
Unless you knew ahead of time the exact state of an entire universe, then the kilobyte would be your key into that value, as it were.
(Ninja edit again: you’d need 3 float64s! So 128/3 atoms in a kilobyte. Not much. Point stands)
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.
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.
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.
Even if you had a perfect 3D coordinate system and atoms worked on float64 boundaries, you’d still have 64 bits to represent one atom. So you could fit, at best, 128 atoms. These are the competing scales.
Unless you knew ahead of time the exact state of an entire universe, then the kilobyte would be your key into that value, as it were.
(Ninja edit again: you’d need 3 float64s! So 128/3 atoms in a kilobyte. Not much. Point stands)