(2+3) dimensional geometrical dual of the complex Klein-Gordon equation

TL;DR

This paper demonstrates a (2+3) dimensional geometric dual to the complex Klein-Gordon equation derived from Einstein's equations, providing a new geometric perspective on quantum wave functions.

Contribution

It introduces a novel geometric dual framework linking Einstein's equations in higher dimensions to the complex Klein-Gordon equation.

Findings

Derived the (2+3) dimensional Einstein equations equivalent to the Klein-Gordon equation.

Provided explicit matching conditions for phase, amplitude, and mass of the wave function.

Established a geometric interpretation of quantum wave properties.

Abstract

In this paper it is shown that an equivalent to the complex Klein-Gordon equation can be obtained from the (2+3) dimensional Einstein equations coupled to a conserved energy momentum tensor. In an explicit toy model we give matching conditions for what corresponds to the phase, the amplitude, and the mass of the complex wave function.