Emergence of Classicality in Stern-Gerlach Experiment via Self-Gravity

TL;DR

This paper investigates how self-gravity influences the transition from quantum to classical behavior in a Stern-Gerlach experiment, showing that increasing mass leads to classical trajectories, unlike decoherence which results in mixed states.

Contribution

It demonstrates that self-gravitational interactions can induce classical trajectories in massive particles, providing a novel perspective on the quantum-classical transition.

Findings

For small mass, wavepacket splits as in standard Stern-Gerlach.

For high mass, wavepacket follows a classical path without splitting.

Self-gravity causes emergence of classicality in massive particles.

Abstract

Emergence 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 Schr\"odinger-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 \emph{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.