The generalized imaging theorem: quantum to classical transition without decoherence

TL;DR

This paper proves that quantum systems can exhibit classical behavior over large distances and times without environmental decoherence, by showing their wave functions become proportional to initial momentum wave functions, aligning with classical mechanics.

Contribution

It demonstrates a generalized imaging theorem that explains quantum to classical transition without decoherence, based on deterministic evolution of wave functions over large scales.

Findings

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

Classical trajectories emerge from quantum evolution without environmental decoherence.

Detection results align with classical mechanics predictions without wave function collapse.

Abstract

The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic interaction with a quantum environment. Here we prove that, in the absence of de-phasing environmental interaction, the asymptotic spatial wave function of any quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to arbitrary deterministic fields, becomes proportional to the initial momentum wave function, \emph{where the particle positions and momenta are related by classical mechanics.} This implies that detection of particle positions and momenta at different times will yield results in accordance with classical mechanics, without the need to postulate decoherence of the wave function.