A Unified Perspective on Poincaré and Galilei Relativity: I. Special Relativity †

Christian Y. Cardall

doi:10.3390/sym16020214

A Unified Perspective on Poincaré and Galilei Relativity: I. Special Relativity †

Christian Y. Cardall

Theoretical and Computational Physics

Research output: Contribution to journal › Article › peer-review

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 Poincaré 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 Poincaré group—analogous to the Bargmann group that is a central extension of the Galilei group—is presented that deepens a unified perspective on Poincaré 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 Poincaré 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.

Original language	English
Article number	214
Journal	Symmetry
Volume	16
Issue number	2
DOIs	https://doi.org/10.3390/sym16020214
State	Published - Feb 2024

Funding

This work was supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under contract number DE-AC05-00OR22725. This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ).

Funders	Funder number
U.S. Department of Energy
Office of Science
Nuclear Physics	DE-AC05-00OR22725

Keywords

Bargmann group
Galilei group
Poincaré group
relativity

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10.3390/sym16020214

Cite this

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title = "A Unified Perspective on Poincar{\'e} and Galilei Relativity: I. Special Relativity †",

abstract = "A semantic adjustment to what physicists mean by the terms {\textquoteleft}special relativity{\textquoteright} and {\textquoteleft}general relativity{\textquoteright} 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 ({\textquoteleft}special relativity{\textquoteright} 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 {\textquoteleft}Galilei general relativity{\textquoteright} more extensive than generally known, to be pursued in the sequel.",

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A Unified Perspective on Poincaré and Galilei Relativity: I. Special Relativity †

Abstract

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Keywords

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