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

Abstract: We propose an extension of Schr\"odinger's equation that incorporates the macroscopic measurement-induced wavefunction collapse phenomenon. Our approach relies on a hybrid between Bohm-de Broglie pilot-wave and objective collapse theories. 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 Schr\"odinger-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, and the wavefunction eventually localizes there. The end result, in macroscopic systems, is a wavefunction collapse that is consistent with Born's rule. We illustrate the theory with a simple double-slit experiment simulation.