Over at her blog, BackReAction, physicist Sabine Hossenfelder has written a cogently argued article titled, No, we probably don’t live in a computer simulation (March 15, 2017). I’ll quote the most relevant excerpts:
According to Nick Bostrom of the Future of Humanity Institute, it is likely that we live in a computer simulation…
Among physicists, the simulation hypothesis is not popular and that’s for a good reason – we know that it is difficult to find consistent explanations for our observations…
If you try to build the universe from classical bits, you won’t get quantum effects, so forget about this – it doesn’t work. This might be somebody’s universe, maybe, but not ours. You either have to overthrow quantum mechanics (good luck), or you have to use qubits. [Note added for clarity: You might be able to get quantum mechanics from a classical, nonlocal approach, but nobody knows how to get quantum field theory from that.]
Even from qubits, however, nobody’s been able to recover the presently accepted fundamental theories – general relativity and the standard model of particle physics…
Indeed, there are good reasons to believe it’s not possible. The idea that our universe is discretized clashes with observations because it runs into conflict with special relativity. The effects of violating the symmetries of special relativity aren’t necessarily small and have been looked for – and nothing’s been found.