Bohmian mechanics is not deterministic

Abstract

I argue that Bohmian mechanics (or any similar pilot-wave theory) cannot reasonably be claimed to be a deterministic theory. If one assumes the "quantum equilibrium distribution" provided by the wave function of the universe, Bohmian mechanics requires an external random oracle in order to describe the (Kolmogorov-Levin-Chaitin) algorithmic randomness properties of typical outcome sequences of long runs of repeated identical experiments (which provably follow from the Born rule). This oracle lies beyond the scope of Bohmian mechanics (or any deterministic extension thereof), including the impossibility of explaining the randomness property in question from "random" initial conditions. Thus the advantages of Bohmian mechanics over other interpretations of quantum mechanics, if any, must lie at an ontological level, and in its potential to derive the quantum equilibrium distribution and hence the Born rule.

arXiv comment14 pages. Accepted by the forthcoming special issue of Foundations of Physics: The pilot-wave and beyond: Celebrating Louis de Broglie's and David Bohm's quest for a quantum ontology. Version 2 doubles size of v1

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