Born's rule yields classical states and classical mechanics

TL;DR

This paper demonstrates that Schrödinger's equation combined with Born's rule explains how macroscopic systems exhibit classical behavior, including localized states following classical trajectories with quantum noise, under realistic conditions.

Contribution

It shows that Born's rule and Schrödinger's equation alone can account for the emergence of classical states and dynamics in macroscopic systems without additional assumptions.

Findings

Macroscopic states are localized in phase space and follow classical trajectories.

Quantum noise in these states is indistinguishable from classical Brownian motion.

Localization rate exceeds the Lyapunov exponent in realistic systems.

Abstract

It is shown that Schrodinger's equation and Born's rule are sufficient to ensure that the states of macroscopic collective coordinate subsystems are microscopically localized in phase space and that the localized state follows the classical trajectory with random quantum noise that is indistinguishable from the pseudo-random noise of classical Brownian motion. This happens because in realistic systems the localization rate determined by the coupling to the environment is greater than the Lyapunov exponent that governs chaotic spreading in phase space. For realistic systems, the trajectories of the collective coordinate subsystem are at the same time an "unravelling" and a set of "consistent/decoherent histories". Different subsystems have their own stochastic dynamics that generally knit together to form a global dynamics, although in certain contrived thought experiments, most notably Wigner's friend, in the contrary, there is observer complementarity.