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David Tong and Lubos Motl have argued that our universe can't possibly be a digital computer simulation because chiral gauge theories can't be discretized, and the Standard Model is a chiral gauge theory. Certainly, you can't regulate them on a lattice. However, that doesn't mean they're not limit computable. There are only two alternatives. Either chiral gauge theories are uncomputable (extremely unlikely), or they can be simulated on a digital computer. How do you simulate a chiral gauge theory on a digital computer? Attempts by Erich Poppitz have fallen a bit short of the goal.

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Define "digital computer"... as it stands, this question is subjective. The argument for "our universe can't be a digital computer" on face-value is simply the statement "a definite integral can only be approximated by a discrete finite sum". – Chris Gerig Jul 27 '12 at 10:58
If you're asking what's better than domain wall fermions, then you're asking an open question. – user1504 Jul 27 '12 at 11:26
Is there something involved, which has a decission on what to simulate? Are there different possible things to be simulated? – NikolajK Jul 27 '12 at 11:32
Just for clarification, is the problem with discretization that you're referring to the one described in sections 1 and 2 here? – twistor59 Jul 27 '12 at 11:53
@ChrisGerig I think we can safely suggest that in the term digital computer, Turing Machine is implied. However, I am not suggesting this is the only problem with this question... – Killercam Jul 27 '12 at 16:32

Overlap fermion approach may be the answer (I think for U(1) gauge symmetry only). Ounce a theory is defined on a lattice, it can be simulated by a computer that we already have. Here is a review on overlap fermion approach:

Tata lectures on overlap fermions arXiv:1103.4588

R. Narayanan

Overlap formalism deals with the construction of chiral gauge theories on the lattice. These set of lectures provide a pedagogical introduction to the subject with emphasis on chiral anomalies and gauge field topology. Subtleties associated with the generating functional for gauge theories coupled to chiral fermions are discussed.

==== A new result ===

One can simulate any anomaly-free chiral gauge theories on a computer by simply putting it on lattice and turning on a proper direct fermion-fermion interaction. See my new papers and

The paper was rejected by PRL (see the referee's comments and my reply ). It is now published in CPL.

The papers claim to solve a long standing problem in lattice gauge theory: the chiral fermion problem. So far they fails to attract any attention from lattice gauge community ( ).

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See also this paper: arxiv-1307.7480: Lattice Non-Perturbative Definition of 1+1D Anomaly-Free Chiral Fermions and Bosons. This paper follows Prof. Wen's general thinking and provide a proof between the following two conditions:

"Topological Boundary (Gapping) Conditions"

is equivalent to

"t' Hooft anomaly matching conditions"

The proof is given for the case of the a theory with a U(1) symmetry and in 1+1D.

Using this equivalent relation, one can design the very constrained specific boundary gapping terms to open the mass gap of the mirror sectors.

The untouched sector in principle can provide a lattice chiral fermion model. (or, for the next step, chiral gauge theory in 1+1D.)

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