A Five Dimensional Space Without Local Lorentz Invariance

TL;DR

This paper explores a five-dimensional space lacking local Lorentz invariance, deriving Einstein and Maxwell equations, and introduces a quantum theory that recovers known spectra like hydrogen and Schwarzschild spaces.

Contribution

It presents a novel five-dimensional framework without local Lorentz invariance, deriving fundamental equations and quantum spectra, expanding theoretical physics models.

Findings

Einstein and Maxwell equations emerge from the 5D theory

Quantum spectra of hydrogen and Schwarzschild spaces are recovered

The theory includes a quantum version of the five-dimensional space

Abstract

A five dimensional space without invariance under local Lorentz transformations is studied, and the transformations under which the theory is invariant are introduced. We show that the Lorentz force is included in the ensuing equations of motion. The four dimensional Einstein and Maxwell equations emerge from the field equations while the homogeneous Maxwell equations naturally appear in the work. A corresponding quantum theory is introduced. The spectrum of a free particle and the hydrogen atom are recovered. Quantum structure of Schwarzschild spaces are also studied.