Einstein's Worries and Actual Physics: Beyond Pilot Waves

TL;DR

The paper argues that standard quantum mechanics lacks a satisfactory ontology and dynamics and that Bohmian mechanics, while helpful, remains incomplete due to quantum equilibrium and explicit nonlocality. It then advocates a deeper completion via stochastic mechanics, where diffusion underpins the wavefunction and Born rule, and a contextual, category-theoretic semantics reframes measurement outcomes as context-dependent rather than dynamically mysterious. A sigma-lambda dynamical scheme provides a continuous quantum–classical interpolation, removing the need for a sharp Heisenberg cut. By combining diffusion-based ontic randomness with contextual truth via presheaves, the approach dissolves the measurement problem and recasts nonlocal correlations as logical obstructions to global truth, with potential connections to categorical quantum mechanics for a fuller understanding of classical–quantum structure.

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 Schrödinger equation'' provides a continuous passage between quantum and classical regimes, eliminating any sharp Heisenberg cut.