An alternative to Minkowski space-time

TL;DR

This paper proposes an alternative 4D space model where particle and photon movements follow geodesics, offering a unified geometric framework that aligns with special relativity, gravitation, and optics, with potential implications for quantum theory.

Contribution

It introduces a novel 4D space framework where geodesics replicate known physics phenomena, providing a new geometric perspective on relativity, gravitation, and electromagnetism.

Findings

Mapping between Minkowski and alternative space geodesics

Reproduction of light propagation in media and gravitation

Electromagnetic equations reduce to geometrical optics

Abstract

The starting point of this work is the principle that all movement of particles and photons must follow geodesics of a 4-dimensional space where time intervals are always a measure on geodesic arc lengths. The last 3 coordinates (alpha = 1,2,3) are immediately associated with the usual physical space coordinates, while the first coordinate (\alpha=0) is later found to be related to proper time. Avoiding the virtually hopeless effort to prove the initial hypothesis, the work goes through several examples of increasing complexity, to show that it is plausible. Starting with special relativity it is shown that there is perfect mapping between the geodesics on Minkowski space-time and on this alternative space. The discussion than follows through light propagation in a refractive medium, and some cases of gravitation, including Schwartzschild's outer metric. The last part of the presentation is dedicated to electromagnetic interaction and Maxwell's equations, showing that there is a particular solution where one of the space dimensions is eliminated and the geodesics become equivalent to light rays in geometrical optics. A very brief discussion is made of the implications for wave-particle duality and quantization.