Year: 2025
Type: article
Abstract: We continue Riemann’s program of geometrizing physics, extending it to encompass gravitational and electromagnetic fields as well as media, all of which influence the geometry of spacetime. The motion of point-like objects—both massive and massless—follows geodesics in this modified geometry. To describe this geometry, we generalize the notion of a metric to local scaling functions which permit not only quadratic but also linear dependence on temporal and spatial separations. Our local scaling functions are defined on flat spacetime coordinates. We demonstrate how to construct various geometries directly from field sources, using symmetry and superposition, without relying on field equations. For each geometry, two key visualizations elucidate the connection between the geometry and the dynamics as follows: (1) the cross-sections of the ball of admissible velocities, and (2) the cross-sections of the local scaling function.
Source: Geometry
Authors: Yaakov Friedman, Tzvi Scarr
Institution: Jerusalem College of Technology
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,207
OpenAlex ID: W4410360557