On the role of mass in the mathematical structure of Newtonian and special relativistic mechanics

TL;DR

This paper geometrically unifies mass, space-time, and physical quantities within five-dimensional spaces, providing a natural framework for Newtonian and special relativistic mechanics.

Contribution

It introduces a geometric approach that incorporates mass into the structure of space-time geometries for Newtonian and relativistic mechanics.

Findings

Mass is geometrized alongside space-time in a natural way.

The geometries are suitable for Newtonian and relativistic mechanics.

Provides a unified geometric framework for physical quantities.

Abstract

We consider five-dimensional real linear spaces with a (otherwise well-known) linear action of the Galilei and the Poincare group on them, describe the geometry of these two spaces, and show, that these geometries comprise the notions of space-time, mass, momentum, force and physical dimensions in a natural way. In this way we geometrize the quantity of mass and integrate it together with space-time into two geometries in a natural way, so that these geometries are perfectly suitable for underlying the Newtonian and special relativistic mechanics of pointlike bodies.