Decoherence and Probability
Richard Dawid, Karim P. Y. Thébault
TL;DR
This work addresses how classical probability can emerge from quantum mechanics without positing new postulates. It proposes a constructive framework combining a partially interpreted quantum phase-space quasi-probability with $O(\hbar)$-neglecting semi-classical averaging to produce an emergent coarse-grained classical probability model. The authors formalize classical and quantum phase-space models, distinguish quasi-probability from true probability, and show that Wigner positivity can arise through decoherence yet is not by itself sufficient for classicality. A double emergence mechanism—quasi-probabilistic emergence via decoherence followed by coarse-grained, factual semi-classical limiting processes—produces a robust bridge from quantum possibilities to classical probabilities within a coherent interpretive stance.
Abstract
One cannot justifiably presuppose the physical salience of structures derived via decoherence theory based upon an entirely uninterpreted use of the quantum formalism. Non-probabilistic accounts of the emergence of probability via decoherence are unconvincing. An alternative account of the emergence of probability involves the combination of a partially interpreted decoherence model and an averaging of observables with respect to a positive-definite quasi-probability function and neglect of terms $O(\hbar)$. Our analysis delimits the context in which the combination of decoherence and a semi-classical averaging allows us to recover a classical probability model within an emergent coarse-grained description.