The generalised imaging theorem: autonomous quantum to classical transitions

TL;DR

This paper proves a generalized imaging theorem demonstrating that multi-particle quantum systems evolve into states that resemble classical trajectories over large distances and times, without requiring environmental decoherence.

Contribution

The paper introduces a generalized imaging theorem showing quantum systems naturally evolve into classical-like states through unitary propagation, independent of environmental decoherence.

Findings

Quantum wave functions become proportional to initial momentum functions over large scales.

Simultaneous position and momentum measurements define unique classical trajectories.

Less complete measurements can still reveal quantum interference effects.

Abstract

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. Here we prove the generalized iimaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Currently, the quantum to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schroedinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.