Quantum Paradoxes and the Quantum-Classical Transition under Unitary Measurement Dynamics with Random Hamiltonians

TL;DR

This paper presents a unified dynamical framework where quantum measurement, state reduction, and the quantum-classical transition emerge from stochastic unitary evolution driven by random Hamiltonians, without nonunitary collapse.

Contribution

It introduces a novel approach using stochastic unitary dynamics with random Hamiltonians to explain measurement and classicality within quantum mechanics.

Findings

Measurement and classicality emerge from unitary dynamics alone.

Transition probabilities follow the Born rule.

Entanglement and EPR correlations are explained geometrically.

Abstract

We develop a dynamical framework for quantum measurement based on stochastic but unitary evolution in projective state space. Random Hamiltonians drawn from the Gaussian Unitary Ensemble generate stochastic unitary dynamics of the quantum state, while equivalence classes reflecting finite detector resolution define classical observables as well as classical configuration-space and phase-space submanifolds. When the evolution is constrained to the phase-space submanifold, free Schr\"odinger dynamics reduces to Newtonian motion, while stochastic motion constrained to the classical configuration-space submanifold yields ordinary Brownian motion in classical space. Transition probabilities under the stochastic dynamics satisfy the Born rule, whereas the constrained classical evolution produces the normal probability distributions characteristic of classical measurements. We show that, in this setting, measurement, state reduction, and the quantum-classical transition emerge from unitary dynamics alone, without invoking nonunitary collapse or additional postulates. Entanglement and EPR correlations arise geometrically from the evolution of joint states in composite state space, preserving locality in spacetime. The framework provides a unified dynamical account of measurement and classicality compatible with the structure of quantum mechanics.