Your question touches upon the characteristic features and controversies of quantum mechanics. You want to know whether any theory can predict or explain which slit a photon passed through in a double-slit experiment.
With a few caveats, the answer is that there is no such theory. Relativity, quantum field theory, string theory etc say nothing about the puzzles in quantum mechanics. In quantum mechanics, it makes no sense to speak of the behaviour of a system in between your observations. In that time, it won't have definite values for observable quantities and photons etc, won't follow definite paths, but superpositions of all possible paths.
Now, of course, many over the years objected to this situation, and attempted to construct so-called "hidden-variable" theories, in which a system had predictable behaviour, including "which path" in a double-slit experiment. As it turned out, though, there are strong constraints on such a theory (e.g. Bell's inequalities) - the fact is that experiments demonstrate quantum mechanical rather than classical behaviour.
It seems quite unlikely that any theory in the future could be constructed that agrees with our observations and predicts/explains which path a photon travelled through in a double-slit experiment. The interefence fringes on the screen result from the fact that the particles don't travel through a definite slit.