An alternative to Minkowski space-time

TLDR

The paper posits that particle and photon motion follows geodesics in a 4‑dimensional space where time intervals are measured along arc lengths, with spatial coordinates α=1–3 and proper time α=0, and briefly considers implications for wave‑particle duality and quantization. The authors illustrate the hypothesis by progressively more complex examples, including light propagation in refractive media and Schwarzschild gravitation, to demonstrate its plausibility. They find a perfect mapping between Minkowski geodesics and those of the alternative space, and show that a particular Maxwell solution eliminates one spatial dimension, making the geodesics equivalent to light rays in 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 (α=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.