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

TL;DR

This work proposes a nonstochastic, nonrelativistic framework that blends Bohmian pilot-wave dynamics with objective-collapse concepts to produce wavefunction localization correlated with a Bohmian particle. A central feature is a mutual feedback: the wavefunction collapses toward the particle’s position, while the particle dynamics are guided by a logarithmic potential derived from the wavefunction with a controlled delay, yielding unitary evolution for microscopic systems and localization into a single macroscopic outcome when lobes become distinct. The theory recovers Schrödinger evolution under rapid thermalization but predicts collapse via loss of ergodicity in macroscopic regimes, providing a mechanism for Born-rule statistics and an objective selection rule without resorting to many-world interpretations. It also establishes a density-matrix formulation, discusses EPR correlations, subsystem measurements, and potential objections, and outlines experimental tests with mesoscopic interferometry to probe the collapse dynamics and the feasibility of large-scale quantum computation.

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.

Figures (3)

• Figure 1: (Color online) Microscopic vs. macroscopic behaviors. Upper left: For a spatially localized wavefunction, the Bohmian particle (represented by a grey spheres trail) can access all regions where the wavefunction is nonnegligible (here represented by fictitious potential surface proportional to $- \ln| \psi(r,t)|^2$). Middle: As a superposition of states starts to involve spatially well-separated states, the particle remains trapped in one of the "lobes" of the wavefunction. Lower right: Loss of ergodicity causes wavefunction localization around one of the macroscopically distinct outcomes
• Figure 2: (Color online) Snapshots of double-slit experiment simulation with modified Schrödinger dynamics. Wavefunction magnitude indicated by intensity and phase by color. Position of the Bohmian particle marked by white lozenge. (Simulation parameters: electron particle, 7.5 nm $\times$ 6.0 nm area, 0.08 fs duration, $\kappa=2\times10^{15}$ s$^{-1}$, $\sigma=0.02$ nm, $\tau/\mu=5\times10^{13}$ m$^{2}$/s$^{2}.$) Magnitude of the decay rate parameter $\kappa$ exaggerated to show wavefunction collapse over a short simulation time.
• Figure 3: (Color online) Schematic representation of the measurement of the position $x_1$ of one particle, while other degrees of freedom (represented by $x_2$) are left unaffected. Connectivity is lost only along the $x_1$ dimension. (Particles are considered distinguishable for simplicity.)