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In "Beables for quantum field theory", John Bell has presented a realistic interpretation of any fermionic quantum field theory, along the pilot-wave ideas. This model is formulated on a spatial lattice (discrete space), but he had suspected that the theory could become deterministic in the continuum limit (where the lattice spacing goes to zero).

My question is why he hasn't considered the possibility for the theory to be deterministic on a discrete space lattice, that is, why he has thought that the QFT might be deterministic only in the continuum limit. What prevents the theory from being deterministic in a discrete space?

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  • $\begingroup$ I don't think this rises to the level of an answer, but I just read the paper and it looks like he did consider continuum and/or deterministic alternatives but failed to make them work, so he presented what he had and a hope that in the future someone would fix it by taking the right limit. Mainstream realistic QFTs are plagued with mathematical problems, and I suspect he hit some of the same problems. $\endgroup$
    – benrg
    Commented Jan 18, 2019 at 19:49
  • $\begingroup$ @benrg Yes, he couldn't make it deterministic even in the continuum, but he didn't say anything about determinism on the discrete lattice. He said that it might get deterministic, but only in the continuum. Anyone working on deterministic QFTs after Bell has only worked on the continuum limit. Maybe as mentioned here: arxiv.org/pdf/1606.02883.pdf , discretization of space necessitates randomness, but I wanted a comprehensive answer about its reason here. $\endgroup$
    – Alex L
    Commented Jan 18, 2019 at 20:07

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