Wave Theory in Measure Space: From Choquet Capacities to Additive Measure Dynamics

Viktoras Rimsha, Laimontas Rimsha

Published Jul 11, 2026• 0 citations

Abstract

This paper formulates a new framework for general wave theory designed to describe the intensity of interfering waves. Since traditional individual intensities (the squares of amplitude moduli) do not sum up to the total observed intensity during interference, classical measure theory in coordinate space breaks down. To resolve this non-additivity problem, we apply the concept of Choquet capacities, which has not been used in physics until now. It is postulated that the total observed intensity of the system is a global Choquet capacity, which simultaneously acts as a full, additive Lebesgue measure. The true intensities of individual waves are defined as additive Lebesgue measures that sum up to the total Choquet capacity. Utilizing the proportionality between the sought measures and the Choquet capacities of individual waves, analytical expressions for the true intensities are derived for an arbitrary number of alternatives. A temporal evolution via the Fokker-Planck equation is formulated for the obtained additive measures, which opens up avenues for a completely new wave analysis. In the context of quantum mechanics, these intensity-measures naturally acquire a probabilistic meaning, axiomatically resolving fundamental questions of interpretation.

DOI: 10.5281/zenodo.21308519

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