The Dispersion Relation for Matter Waves in a Two-Phase Vacuum

TL;DR

This paper derives a bimodal dispersion relation for matter waves in a two-phase vacuum model, linking cosmological constant variations to wave properties and suggesting a resolution to the cosmological-constant problem.

Contribution

It introduces a toy two-phase vacuum model that yields a bimodal dispersion relation for matter waves, connecting cosmological constant dynamics with wave behavior.

Findings

Dispersion relation is bimodal with a high-frequency transmission window.

The model links vacuum phase variations to matter wave properties.

Provides a potential resolution to the cosmological-constant problem.

Abstract

The cosmological constant (lambda) of general relativity is a natural consequence of embedding Einstein's theory in a five-dimensional theory of the type needed for unification. The exact 5D solution for lambda less than 0 shows waves in ordinary 3D space with properties similar to those of de Broglie or matter waves. Here the dispersion relation is derived for matter waves in a toy two-phase model, where regions with lambda less than 0 and lambda greater than 0 average on the large scale to lambda = 0, thus providing in principle a resolution of the cosmological-constant problem. A striking result of the analysis is that the dispersion relation is bimodal, with a well-defined window of high-frequency transmission which effectively defines the speed of light.