Bohmian mechanics is not deterministic

TL;DR

This paper argues that Bohmian mechanics cannot be truly deterministic because it requires an external source of randomness to account for the algorithmic randomness observed in quantum outcomes, challenging its claimed determinism.

Contribution

It demonstrates that Bohmian mechanics depends on an external random oracle to explain outcome randomness, questioning its deterministic nature.

Findings

Bohmian mechanics needs an external oracle for randomness.

Outcome sequences follow from the Born rule and are algorithmically random.

Determinism in Bohmian mechanics is insufficient to explain quantum randomness.

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.