Edward Fredkin, a (former?) professor at MIT has been working on digital mechanics for years.
Note that even if this replaced ordinary physics, the predictions of ordinary physics would still be true to a high degree of accuracy. I don't think that was the question. Rathere it was, are we being suckered into a false trail that yields (for the moment) good predictions, but leads away from the right trail.
I think we can get some hints.
1. Mathematical physicists have never been able to create a rigorous 4-dimensional quantum field theory, although one of these theories, QED, makes superaccurate predictions.
2. Physicists believe there is physics beyond the standard model, but every initiative to find it (supersymmetry, strings, superstrings, branes, M-theory) seems to run into the sand, and the papers on the preprint archive for the last couple of years seem to be churning without getting anywhere. Maybe there isn't any real physics in that direction?
3. The promoters of the loop quantum gravity enterprise, to replace classical GR with a quantized theory, have also been unable to define a fully valid 4-dimensional version of their baby.
What is the common factor of all these efforts? I would say it is the use of operator algebras acting on Hilbert (resp. Fock) spaces. The deeper that method goes, the shakier it becomes. We need something new. Page the mathematicians.
(Example, not plug. See Christopher Isham's category quantization scheme).
