A unified perspective on Poincar\'e and Galilei relativity: I. Special relativity

TL;DR

This paper proposes a unified conceptual framework for special relativity and Galilei physics by adjusting their definitions and exploring group extensions in 4D and 5D spacetimes, potentially leading to a broader 'Galilei general relativity.'

Contribution

It introduces a central extension of the Poincaré group in 5D spacetime, deepening the unification of relativistic and non-relativistic physics.

Findings

Unified perspective on Poincaré and Galilei physics via group extensions.

Extension of Poincaré group analogous to Bargmann group in 5D.

Potential for a broader 'Galilei general relativity' framework.

Abstract

A semantic adjustment to what physicists mean by the terms `special relativity' and `general relativity' is suggested, which prompts a conceptual shift to a more unified perspective on physics governed by the Poincar\'e group and physics governed by the Galilei group. After exploring the limits of a unified perspective available in the setting of 4-dimensional spacetime, a particular central extension of the Poincar\'e group -- analogous to the Bargmann group that is a central extension of the Galilei group -- is presented that deepens a unified perspective on Poincar\'e and Galilei physics in a 5-dimensional spacetime setting. The immediate focus of this paper is classical physics on affine 4-dimensional and 5-dimensional spacetimes (`special relativity' as redefined here), including the electrodynamics that gave rise to Poincar\'e physics in the first place; but the results here may suggest the existence of a `Galilei general relativity' more extensive than generally known, to be pursued in the sequel.