Random matrices: Application to quantum paradoxes

TL;DR

This paper explores the geometric embedding of classical and quantum states, applying random matrix theory to analyze quantum paradoxes, measurement, and the transition from quantum to classical behavior.

Contribution

It introduces a novel geometric framework linking classical and quantum dynamics and applies random matrix theory to reinterpret quantum paradoxes and measurement processes.

Findings

Embedding reproduces classical Newtonian dynamics from Schrödinger evolution.

Random Hamiltonians provide new insights into quantum measurement and collapse.

Geometric approach offers fresh perspectives on quantum paradoxes.

Abstract

Recently, a geometric embedding of the classical space and classical phase space of an n-particle system into the space of states of the system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the particles was recovered from the Schroedinger dynamics by constraining the state of the system to the classical phase space submanifold of the space of states. A series of theorems related to the embedding and the Schroedinger evolution with a random Hamiltonian was proven and shown to be applicable to the process of measurement in classical and quantum mechanics. Here, these results are applied to have a fresh look at the main quantum-mechanical thought experiments and paradoxes and to provide a new insight into the process of collapse and the motion of macroscopic bodies in quantum mechanics.