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

We propose an extension to Schrödinger's equation that incorporates macroscopic measurement-induced wavefunction collapse. We find that a hybrid between two leading approaches, the Bohm-de Broglie pilot-wave and objective collapse theories, accomplishes this goal in accordance with Born's rule. We posits that the wavefunction guides Bohmian particle 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 Schrödinger-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 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.