The measurement in classical and quantum theory

TL;DR

This paper explores the relationship between classical and quantum mechanics through the lens of the BGS conjecture, proposing that systems with classical chaotic behavior can be modeled by random matrices, and discusses implications for observation and irreversibility.

Contribution

It introduces a new conjecture linking classical random walks to Gaussian unitary ensemble Hamiltonians and explores its implications for the boundary between micro and macro worlds.

Findings

Proposes a conjecture connecting classical random walks to quantum Hamiltonians.

Derives a relationship between classical and quantum observation processes.

Describes the boundary between micro and macro systems.

Abstract

The Bohigas-Giannoni-Schmit (BGS) conjecture states that the Hamiltonian of a microscopic analogue of a classical chaotic system can be modeled by a random matrix from a Gaussian ensemble. Here, this conjecture is considered in the context of a recently discovered geometric relationship between classical and quantum mechanics. Motivated by BGS, we conjecture that the Hamiltonian of a system whose classical counterpart performs a random walk can be modeled by a family of independent random matrices from the Gaussian unitary ensemble. By accepting this conjecture, we find a relationship between the process of observation in classical and quantum physics, derive irreversibility of observation and describe the boundary between the micro and macro worlds.