An Argument for 4D Block World from a Geometric Interpretation of Nonrelativistic Quantum Mechanics

We use a new, distinctly “geometrical” interpretation of nonrelativistic quantum mechanics (NRQM) to argue for the fundamentality of the 4D block world ontology. We argue for a geometrical interpretation whose fundamental ontology is one of space-time relations as opposed to constructive entities whose time-dependent behavior is governed by dynamical laws. Our view rests on two formal results: Kaiser (1981, 1990), Bohr and Ulfbeck (1995), and Anandan (2003) showed independently that the Heisenberg commutation relations of NRQM follow from the relativity of simultaneity (RoS) per the Poincaré Lie algebra. And, Bohr, Ulfbeck, and Mottelson (2004a, 2004b) showed that the density matrix for a particular NRQM experimental outcome may be obtained from the space-time symmetry group of the experimental configuration. This shows how the block world view is not only consistent with NRQM, not only an implication of our geometrical interpretation of NRQM, but it is necessary in a nontrivial way for explaining quantum interference and “non-locality” from the space-time perspective. Together the formal results imply that contrary to accepted wisdom, NRQM, the measurement problem and socalled quantum nonlocality do not provide reasons to abandon the 4D block world implication of RoS. Rather, the deep noncommutative structure of the quantum and the deep structure of space-time as given by the Minkowski interpretation of special relativity (STR) are deeply unified in a 4D space-time regime that lies between Galilean space-time (G4) and Minkowski space-time (M4).