Conventional wisdom says that quantum mechanics is a theory of discreteness, describing a world of irreducible building blocks. It stands to reason that computers—which process information in discrete chunks—should be able to simulate nature fully, at least in principle. But it turns out that certain asymmetries in particle physics cannot be discretized; they are irreducibly continuous. In that case, says David Tong, author of "Is Quantum Reality Analog after All?" in the December 2012 issue of Scientific American, the world can never be fully simulated on a computer.Tong's essay is quite sensible, but I do not believe his claim that "certain asymmetries in particle physics cannot be discretized". I had thought that lattice gauge theories had advanced to where they could approximate experiments. I would be amazed if someone has actually proved that convergence is impossible.
Here is the audio download.
Update: Tong's references are A Method for Simulating Chiral Fermions on the Lattice, Chiral Symmetry and Lattice Fermions, and Chiral gauge theories revisited. I don't see where any of these papers say that chiral fermion lattice gauge theories are impossible.