A Connection between Minkowski and Galilean Spacetimes in Quantum Mechanics

Relativistic quantum theories are equipped with a background Minkowski spacetime and non-relativistic quantum theories with a Galilean spacetime. Traditional investigations have distinguished their distinct spacetime structures and have examined ways in which relativistic theories become sufficiently like Galilean theories in a low velocity approximation or limit. A different way to look at their relationship is to see that both kinds of theories are special cases of a certain five-dimensional generalization involving no limiting procedures or approximations. When one compares them, striking features emerge that bear on philosophical questions, including the ontological status of the wave function and time reversal invariance.