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

Agung Budiyono,Daniel Rohrlich

doi:10.1038/s41467-017-01375-w

Agung Budiyono, Daniel Rohrlich

Open Access

https://doi.org/10.1038/s41467-017-01375-w

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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 non-relativistic 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.

Highlights

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
This program prompts the following question: Can we reconstruct quantum mechanics as a clear, physical modification of classical statistical mechanics? (An answer could be of practical interest toward understanding the physical resource responsible for the advantages of quantum over classical information protocols.) To answer this question, we note two essential features of quantum mechanics that distinguish it from classical mechanics: entanglement and the uncertainty principle
Bohmian mechanics[17] is an “ontic extension” of classical mechanics: it posits a physically real or ontic and in general nonseparable wave function defined in a multi-dimensional configuration space, satisfying the Schrödinger equation, that guides the dynamics of the particles

Summary

Introduction

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. 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. 7,13,14, we shall call the underlying physical state the “ontic state” and the probability distribution over the ontic states associated with a given quantum state the “epistemic state” This program prompts the following question: Can we reconstruct quantum mechanics as a clear, physical modification of classical statistical mechanics? There have been attempts to explain (parts of) quantum mechanics starting from classical statistical models by assuming a fundamental restrictions on the class of possible epistemic states that can be prepared[6,7,9,10,11,12,15] Such an “epistemic restriction” captures, to an extent, the uncertainty principle. We conjecture and argue that, unlike Bohmian mechanics, the wave function in our ontological model is not physically real; what is real is a nonseparable, global random variable

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