Emergence of Classicality in Stern–Gerlach Experiment via Self‐Gravity

Abstract

AbstractEmergence of classicality from quantum mechanics, a hotly debated topic, has had no satisfactory resolution so far. Various approaches including decoherence and gravitational interactions have been suggested. In the present work, the Schrödinger–Newton model is used to study the role of semi‐classical self‐gravity in the evolution of massive spin‐1/2 particles in a Stern‐Gerlach experiment. For small mass, evolution of the initial wavepacket in a spin superposition shows a splitting in the magnetic field gradient into two trajectories as in the standard Stern–Gerlach experiment. For larger mass, the deviations from the central path are less than in the standard Stern–Gerlach case, while for high enough mass, the wavepacket does not split, and instead follows the classical trajectory for a magnetic moment in inhomogeneous magnetic field. This indicates the emergence of classicality due to self‐gravitational interaction when the mass is increased. In contrast, decoherence which is a strong contender for emergence of classicality, leads to a mixed state of two trajectories corresponding to the spin‐up and spin‐down states, and not the classically expected path. The classically expected path of the particle probably cannot be explained even in the many‐worlds interpretation of quantum mechanics. Stern–Gerlach experiments in the macroscopic domain are needed to settle this question.