An Argument for 4D Blockworld from a Geometric Interpretation of Non-relativistic Quantum Mechanics

Abstract

We use a new distinctly "geometrical" interpretation of non-relativistic quantum mechanics (NRQM) to argue for the fundamentality of the 4D blockworld ontology. Our interpretation rests on two formal results: Kaiser, Bohr & Ulfbeck and Anandan showed independently that the Heisenberg commutation relations of NRQM follow from the relativity of simultaneity (RoS) per the Poincare Lie algebra, and Bohr, Ulfbeck & Mottelson showed that the density matrix for a particular NRQM experimental outcome may be obtained from the spacetime symmetry group of the experimental configuration. Together these formal results imply that contrary to accepted wisdom, NRQM, the measurement problem and so-called quantum non-locality do not provide reasons to abandon the 4D blockworld implication of RoS. After discussing the full philosophical implications of these formal results, we motivate and derive the Born rule in the context of our ontology of spacetime relations via Anandan. Finally, we apply our explanatory and descriptive methodology to a particular experimental set-up (the so-called "quantum liar experiment") and thereby show how the blockworld view is not only consistent with NRQM, not only an implication of our geometrical interpretation of NRQM, but it is necessary in a non-trivial way for explaining quantum interference and "non-locality" from the spacetime perspective.