Quantum Mechanical Probability of Electrodynamic Particle(s)

TL;DR

This paper derives quantum probability functions for an electromagnetic particle model based on statistical mechanics principles, linking wave functions to particle interactions and state exploration.

Contribution

It introduces a novel IED particle model and derives probability functions from first principles, connecting classical electromagnetic theory with quantum statistical mechanics.

Findings

Probability functions in position space are of the form ||^2.

The model links electromagnetic field distributions to quantum probabilities.

States are discrete at scale h, consistent with quantum theory.

Abstract

A distribution of electromagnetic fields presents a statistical assembly of a particular type, which is at scale h a quantum statistical assembly itself and has also been instrumental to concretisation of the basic probability assumption of quantum mechanics. Of specific concern in this discussion is an extensive train of radiation fields, of a total wave function \psi, which are continuously (re)emitted and (re)absorbed by an oscillatory (point) charge of a zero rest mass and yet a finite dynamical mass, with the waves and charge together making up an extensive undulatory IED particle. The IED particle will as any real particle be subject to interactions with the environmental fields and particles, hence to excitations, and therefore will explore all possible states over time; at scale $h$ the states are discrete. On the basis of the principles of statistics and statistical mechanics combined with first principles solutions for the IED particle, we derive for the IED particle the probability functions in position space, of a form |\psi|^2, and in dynamical-variable space.