Einstein's Worries and Actual Physics: Beyond Pilot Waves

TL;DR

This paper critiques pilot-wave theory, proposing stochastic mechanics and category-theoretic semantics as deeper, more coherent foundations for quantum physics that address measurement and nonlocality issues.

Contribution

It introduces stochastic mechanics and a category-theoretic approach as novel frameworks surpassing pilot-wave theory in explaining quantum phenomena.

Findings

Wavefunction and Born rule emerge from diffusion processes

Measurement and Bell correlations are reinterpreted as contextual truths

Classical Schrödinger equation provides a continuous quantum-classical transition

Abstract

Tim Maudlin has argued that the standard formulation of quantum mechanics fails to provide a clear ontology and dynamics and that the de Broglie--Bohm pilot-wave theory offers a better completion of the formalism, more in line with Einstein's concerns. I suggest that while Bohmian mechanics improves on textbook quantum theory, it does not go far enough. In particular, it relies on the ``quantum equilibrium hypothesis'' and accepts explicit nonlocality as fundamental. A deeper completion is available in stochastic mechanics, where the wavefunction and the Born rule emerge from an underlying diffusion process, and in a contextual, category-theoretic semantics in which measurement and EPR--Bell correlations are reinterpreted as features of contextual truth rather than of mysterious dynamics. In this framework, the measurement problem and ``spooky action-at-a-distance'' are dissolved rather than solved. Finally, a dynamics based on Rosen's ``classical Schr\"odinger equation'' provides a continuous passage between quantum and classical regimes, eliminating any sharp Heisenberg cut.