Born's Rule as Signature of a Superclassical Current Algebra

TL;DR

This paper introduces a superclassical current algebra framework that reproduces quantum interference phenomena and derives Born's rule from an emergent sub-quantum theory based on classical physics principles.

Contribution

It presents a new superclassical theory that explains quantum interference and Born's rule without standard quantum mechanics, using a current algebra and relational causality.

Findings

Reproduces Talbot patterns and distances exactly without quantum tools.

Proves the absence of third-order interferences in three-path systems.

Derives Born's rule as a natural consequence of the superclassical framework.

Abstract

We present a new tool for calculating the interference patterns and particle trajectories of a double-, three- and N-slit system on the basis of an emergent sub-quantum theory developed by our group throughout the last years. The quantum itself is considered as an emergent system representing an off-equilibrium steady state oscillation maintained by a constant throughput of energy provided by a classical zero-point energy field. We introduce the concept of a "relational causality" which allows for evaluating structural interdependences of different systems levels, i.e. in our case of the relations between partial and total probability density currents, respectively. Combined with the application of 21st century classical physics like, e.g., modern nonequilibrium thermodynamics, we thus arrive at a "superclassical" theory. Within this framework, the proposed current algebra directly leads to a new formulation of the guiding equation which is equivalent to the original one of the de Broglie-Bohm theory. By proving the absence of third order interferences in three-path systems it is shown that Born's rule is a natural consequence of our theory. Considering the series of one-, double-, or, generally, of N-slit systems, with the first appearance of an interference term in the double slit case, we can explain the violation of Sorkin's first order sum rule, just as the validity of all higher order sum rules. Moreover, the Talbot patterns and Talbot distance for an arbitrary N-slit device can be reproduced exactly by our model without any quantum physics tool.