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

TL;DR

The paper proposes a unified dynamical framework in which measurement, state reduction, and the quantum–classical transition arise from stochastic yet unitary evolution in the projective state space $\mathbb{CP}^{L_2}$ driven by random Hamiltonians from the Gaussian Unitary Ensemble (GUE). Classical observables and trajectories emerge from equivalence classes of detector-indistinguishable states on the classical submanifolds $M^{\sigma}_{3,3}$, with the Born rule derived from state-space geometry via the isometry $\Omega$; macroscopic realism and nonlocal correlations are explained without nonunitary collapse or superluminal signaling. The approach resolves classic paradoxes (e.g., Schrödinger's cat, Wigner's friend, decoherence, and the double-slit experiment) by showing that what is measured corresponds to dynamical proximity to classical submanifolds, while superpositions reflect off-manifold state-space motion. Irreversibility and the arrow of time emerge from the combination of stochastic dynamics, time-reversal breaking by GUE, and coarse-graining through equivalence classes and recording. Overall, the framework offers a coherent, geometrical, and testable account of quantum measurements and the emergence of classicality within unitary evolution.

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 Schrödinger 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.