A one-world interpretation of quantum mechanics

TL;DR

This paper proposes a one-world, classical-quantum interpretation of quantum mechanics in which a definite classical degree of freedom interacts with a quantum system through a shared noise process. Using four natural axioms, the authors derive the standard quantum structure—unitary evolution and Born-rule probabilities—from classical probabilistic reasoning via a change of measure, while keeping the quantum state pure conditioned on the classical trajectory and avoiding decoherence. A central result shows that unitary-invariant dynamics uniquely recover quantum mechanics, or reduce to a trivial theory, implying the Born rule and wavefunction collapse arise from the classical–quantum coupling. The framework also yields a linear-picture representation and reveals a landscape of quantum-like theories from alternative choices of a state-dependent function g, offering connections to existing interpretations while outlining open questions about classical–quantum composition and heating constraints.

Abstract

The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules of probability theory apply to it when it interacts with a quantum system. Under mild assumptions, we recover the unitary dynamics, collapse and Born rule postulates from quantum theory. Nonetheless, there is no decoherence, because the quantum state remains pure conditioned on the classical trajectory. This results in one world, rather than many-worlds. Our main technical tool is to exploit a change of measure on the space of classical paths, the functional form of which is shown to characterise the quantum dynamics and Born rules of a class of quantum-like theories.