DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Journal Article · · Symmetry

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.

Sponsoring Organization:
USDOE Office of Science (SC), Nuclear Physics (NP)
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
2301764
Journal Information:
Symmetry, Journal Name: Symmetry Journal Issue: 2 Vol. 16; ISSN SYMMAM; ISSN 2073-8994
Publisher:
MDPI AGCopyright Statement
Country of Publication:
Switzerland
Language:
English

References (33)

On Unitary Ray Representations of Continuous Groups journal January 1954
Combining 3-Momentum and Kinetic Energy on Galilei/Newton Spacetime journal October 2020
Non-relativistic gravity and its coupling to matter journal June 2020
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter journal October 2015
Bargmann structures and Newton-Cartan theory journal April 1985
Galilean Mechanics and Thermodynamics of Continua January 2016
Galilean Tensor Calculus journal November 1968
The pedagogical role and epistemological significance of group theory in quantum mechanics journal January 1974
Newtonian gravity and the Bargmann algebra journal April 2011
General theory of Galilean gravity journal October 2018
Lorentz-like covariant equations of non-relativistic fluids journal February 2003
Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie) journal January 1923
Special Relativity in General Frames book August 2013
Sur les variétés à connexion affine, et la théorie de la relativité généralisée (première partie) (Suite) journal January 1924
Nonrelativistic Wave Equations with Gauge Fields journal April 2003
Covariant Newtonian limit of Lorentz space-times journal May 1976
Quantum fact and classical fiction: Clarifying Landé’s pseudo-paradox journal November 1976
Post-Newtonian extension of the Newton - Cartan theory journal January 1997
Minkowski and Galilei/Newton Fluid Dynamics: A Geometric 3 + 1 Spacetime Perspective journal December 2018
3+1 Formalism in General Relativity book February 2012
Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations journal December 2005
Celestial mechanics, conformal structures, and gravitational waves journal June 1991
On the uniqueness of the Newtonian theory as a geometric theory of gravitation journal June 1975
Lectures on General Relativity journal October 1965
World invariant kinematics journal January 1957
Towards Full ‘Galilei General Relativity’: Bargmann-Minkowski and Bargmann-Galilei Spacetimes book August 2023
Torsional Newton–Cartan gravity from the large c expansion of general relativity journal August 2017
Action Principle for Newtonian Gravity journal February 2019
Four-Dimensional Formulations of Newtonian Mechanics and Their Relation to the Special and the General Theory of Relativity journal October 1964
Galilean Covariance and the Schrödinger Equation journal January 1989
Bargmann group, momentum tensor and Galilean invariance of Clausius–Duhem inequality journal January 2012
Relativistic and non-relativistic classical field theory on five-dimensional spacetime journal September 1986
5-Dimensional Thermodynamics of Dissipative Continua book January 2017

Related Subjects