Pilot-waves and copilot-particles: A nonstochastic approach to objective wavefunction collapse

Abstract

We seek an extension to Schrodinger's equation that incorporates the macroscopic measurement-induced wavefunction collapse phenomenon. We find that a suitable hybrid between two leading approaches, the Bohm-de Broglie pilot-wave and objective collapse theories, accomplishes this goal in a way that is consistent with Born's rule. Our theory posits that the Bohmian particle is guided by the wavefunction and, conversely, the wavefunction gradually localizes towards the particle's position. As long as the particle can visit any state, as in a typical microscopic system, the localization effect does not favor any particular quantum state and, on average, the usual Schrodinger-like time evolution results. However, when the wavefunction develops spatially well-separated lobes, as would happen during a macroscopic measurement, the Bohmian particle can remain trapped in one lobe, which causes the wavefunction to eventually localizes. This proposed loss of ergodicity mechanism recasts one of the foundational postulate of quantum mechanics as a emergent feature and has important implications regarding the feasibility of large-scale quantum computing.