https://scottaaronson.blog/?p=7705
I wanted to make a deeper point. Even if the fermion doubling problem had been a fundamental obstruction to simulating Nature on a Turing machine, rather than (as it now seems) a technical problem with technical solutions, it still might not have refuted the version of the simulation hypothesis that people care about. We should really distinguish at least three questions:
- Can currently-known physics be simulated on computers using currently-known approaches?
- Is the Physical Church-Turing Thesis true? That is: can any physical process be simulated on a Turing machine to any desired accuracy (at least probabilistically), given enough information about its initial state?
- Is our whole observed universe a “simulation” being run in a different, larger universe?
Crucially, each of these three questions has only a tenuous connection to the other two! As far as I can see, there aren’t even nontrivial implications among them. For example, even if it turned out that lattice methods couldn’t properly simulate the Standard Model, that would say little about whether any computational methods could do so—or even more important, whether any computational methods could simulate the ultimate quantum theory of gravity. A priori, simulating quantum gravity might be harder than “merely” simulating the Standard Model (if, e.g., Roger Penrose’s microtubule theory turned out to be right), but it might also be easier: for example, because of the finiteness of the Bekenstein-Hawking entropy, and perhaps the Hilbert space dimension, of any bounded region of space.
