Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction

Abstract

Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive nonrelativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.

12 pages; comments welcome

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Cited by in corpus (8)

• Objective quantum fields, retrocausality and ontology
• Quantum mechanics is a calculus for estimation under epistemic restriction
• Epistemically restricted phase space representation, weak momentum value, and reconstruction of quantum wave function
• Quantum uncertainty as classical uncertainty of real-deterministic variables constructed from complex weak values and a global random variable
• Nonlinear Schrödinger equations and generalized Heisenberg uncertainty principle violating the principle of estimation independence
• Efficient classical computation of expectation values in a class of quantum circuits with an epistemically restricted phase space representation
• Estimation independence as an axiom for quantum uncertainty
• Epistemic uncertainty from an averaged Hamilton-Jacobi formalism