’t Hooft’s latest paper is the first in which he maps a full QFT to a CA, and the QFT in question is a free field theory. So I think that in this case he evades Bell’s theorem, quantum complexity theorems, etc, by working in a theory where physical detectors, quantum computers, etc don’t exist, because interactions don’t exist. It’s like how you can evade the incompleteness theorems if your arithmetic only has addition but not multiplication. Elsewhere he does appeal to superselection / cosmological initial conditions as a way to avoid cat states (macroscopic superpositions), but I don’t see that playing a role here.
The mapping itself has something to do with focusing on the fractional part of particle momentum as finite, and avoiding divergences by focusing on a particular subspace. It’s not a trivial result. But extending it to interacting field theory will require new ideas, e.g. making the state space of each individual cell in the CA into a Fock space, or permitting CTCs in the CA grid. Surely you need radical ingredients like that in order to recover the full quantum state space…
’t Hooft’s latest paper is the first in which he maps a full QFT to a CA, and the QFT in question is a free field theory. So I think that in this case he evades Bell’s theorem, quantum complexity theorems, etc, by working in a theory where physical detectors, quantum computers, etc don’t exist, because interactions don’t exist. It’s like how you can evade the incompleteness theorems if your arithmetic only has addition but not multiplication. Elsewhere he does appeal to superselection / cosmological initial conditions as a way to avoid cat states (macroscopic superpositions), but I don’t see that playing a role here.
The mapping itself has something to do with focusing on the fractional part of particle momentum as finite, and avoiding divergences by focusing on a particular subspace. It’s not a trivial result. But extending it to interacting field theory will require new ideas, e.g. making the state space of each individual cell in the CA into a Fock space, or permitting CTCs in the CA grid. Surely you need radical ingredients like that in order to recover the full quantum state space…