A discrete approach to the vacuum Maxwell equations and the fine structure constant

TL;DR

This paper explores discretizing the vacuum Maxwell equations to uncover unexpected phenomena, revealing that specific coupling factors related to the fine structure constant influence wave maxima behavior in electromagnetic fields.

Contribution

It demonstrates a novel discrete approach to Maxwell's equations and links the fine structure constant to wave maxima patterns in a new computational framework.

Findings

Wave maxima heights vary and show specific patterns

Coupling factors related to the fine structure constant affect wave development

Unexpected exponential growth in wave maxima after initial decrease

Abstract

We recommended consequent discrete combinatorial research in mathematical physics. Here we show an example how discretization of partial differential equations can be done and that quickly unexpected new findings can result from research in this up to now unexplored area. We transformed the vacuum Maxwell equations into finite-difference equations, provided simple initial conditions and studied the development of the electromagnetic fields using special software (see http://www.orthuber.com). The development is wave-like as expected. But it is not trivial, the wave maxima have different heights. If all (by definition minimal) finite differences of the location coordinates are multiplied by numbers (coupling factors) whose squares are equal to the fine structure constant, we noticed: 1. The first two wave maxima have nearly the same height. Of course this can be also coincidental. 2. The following maxima are at first slightly decreasing and then, beginning with the 6th maximum, exponentially increasing.