Classical mechanics as the many-particle limit of quantum mechanics

TL;DR

This paper derives the classical mechanics limit from quantum mechanics by analyzing the center of mass of many particles, showing how quantum commutators become Poisson brackets in the large particle limit.

Contribution

It provides a rigorous derivation of classical mechanics as the many-particle limit of quantum mechanics, focusing on the behavior of the center of mass.

Findings

Commutator between position and velocity becomes infinitesimal in the large particle limit.

Position and velocity can be simultaneously known with high precision in this limit.

Quantum commutators reduce to Poisson brackets, linking quantum and classical descriptions.

Abstract

We derive the classical limit of quantum mechanics by describing the center of mass of a system constituted by a large number of particles. We will show that in that limit the commutator between the position and velocity of the center of mass is infinitesimal, which allows both to be known with great precision. We then show how the infinitesimal commutator allows for the definition of functions of position and velocity, and how the commutator reduces to a Poisson bracket.