Mechanics: non-classical, non-quantum

TL;DR

This paper introduces a class of non-classical, non-quantum theories (NCQ) that differ from classical and quantum mechanics, aiming to improve approximation methods and explore viable alternative theories with classical limits.

Contribution

It proposes a formal framework for NCQ mechanics based on a probability density functional generalization of classical mechanics, expanding the landscape of theoretical physics.

Findings

NCQ theories can reproduce quantum results in tested regimes

NCQ models have well-defined classical limits

The proposed class of NCQ mechanics extends classical probability frameworks

Abstract

A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of interest for two primary reasons. Firstly, NCQs arise prominently in semi-classical approximation schemes. Their formal study may yield improved approximation techniques in the near-classical regime. More importantly for the purposes of this note, it may be possible for NCQs to reproduce quantum results over experimentally tested regimes while having a well defined classical limit, and hence are viable alternative theories. We illustrate an NCQ by considering an explicit class of NCQ mechanics. Here this class will be arrived at via a natural generalization of classical mechanics formulated in terms of a probability density functional.