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

Cardall, Christian Y.

doi:10.3390/sym16020214

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

Journal Article · Sat Feb 10 04:00:00 EST 2024 · Symmetry

DOI:https://doi.org/10.3390/sym16020214· OSTI ID:2301764

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.

View Journal Article

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 2301764

Alternate ID(s):: OSTI ID: 2573670

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)

Galilean Mechanics and Thermodynamics of Continua de Saxcé, Géry; Vallée, Claude https://doi.org/10.1002/9781119057956		January 2016
Galilean Covariance and the Schrödinger Equation Omote, M.; Kamefuchi, S.; Takahashi, Y. Fortschritte der Physik/Progress of Physics, Vol. 37, Issue 12 https://doi.org/10.1002/prop.2190371203	journal	January 1989
Towards Full ‘Galilei General Relativity’: Bargmann-Minkowski and Bargmann-Galilei Spacetimes Cardall, Christian Y. Lecture Notes in Computer Science https://doi.org/10.1007/978-3-031-38299-4_8	book	August 2023
5-Dimensional Thermodynamics of Dissipative Continua de Saxcé, Géry Springer Series in Solid and Structural Mechanics https://doi.org/10.1007/978-3-319-48884-4_1	book	January 2017
3+1 Formalism in General Relativity Gourgoulhon, Eric Lecture Notes in Physics https://doi.org/10.1007/978-3-642-24525-1	book	February 2012
Special Relativity in General Frames Gourgoulhon, Éric Graduate Texts in Physics https://doi.org/10.1007/978-3-642-37276-6	book	August 2013
World invariant kinematics Toupin, R. A. Archive for Rational Mechanics and Analysis, Vol. 1, Issue 1 https://doi.org/10.1007/BF00298004	journal	January 1957
Covariant Newtonian limit of Lorentz space-times Künzle, H. P. General Relativity and Gravitation, Vol. 7, Issue 5 https://doi.org/10.1007/BF00766139	journal	May 1976
On the uniqueness of the Newtonian theory as a geometric theory of gravitation Dixon, W. G. Communications in Mathematical Physics, Vol. 45, Issue 2 https://doi.org/10.1007/BF01629247	journal	June 1975
The pedagogical role and epistemological significance of group theory in quantum mechanics Lévy-Leblond, J. M. La Rivista Del Nuovo Cimento Series 2, Vol. 4, Issue 1 https://doi.org/10.1007/BF02747079	journal	January 1974
Non-relativistic gravity and its coupling to matter Hansen, Dennis; Hartong, Jelle; Obers, Niels A. Journal of High Energy Physics, Vol. 2020, Issue 6 https://doi.org/10.1007/JHEP06(2020)145	journal	June 2020
Bargmann group, momentum tensor and Galilean invariance of Clausius–Duhem inequality de Saxcé, Géry; Vallée, Claude International Journal of Engineering Science, Vol. 50, Issue 1 https://doi.org/10.1016/j.ijengsci.2011.08.001	journal	January 2012
Nonrelativistic Wave Equations with Gauge Fields de Montigny, M.; Khanna, F. C.; Santana, A. E. International Journal of Theoretical Physics, Vol. 42, Issue 4, p. 649-671 https://doi.org/10.1023/A:1024485810807	journal	April 2003
Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations Marek, A.; Dimmelmeier, H.; Janka, H. -Th. Astronomy & Astrophysics, Vol. 445, Issue 1 https://doi.org/10.1051/0004-6361:20052840	journal	December 2005
Galilean Tensor Calculus Pinski, G. Journal of Mathematical Physics, Vol. 9, Issue 11 https://doi.org/10.1063/1.1664527	journal	November 1968
Lectures on General Relativity Trautman, A.; Romain, Jacques E. Physics Today, Vol. 18, Issue 10 https://doi.org/10.1063/1.3046958	journal	October 1965
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M. Journal of Mathematical Physics, Vol. 56, Issue 10 https://doi.org/10.1063/1.4932967	journal	October 2015
Post-Newtonian extension of the Newton - Cartan theory Dautcourt, G. Classical and Quantum Gravity, Vol. 14, Issue 1A https://doi.org/10.1088/0264-9381/14/1A/009	journal	January 1997
Newtonian gravity and the Bargmann algebra Andringa, Roel; Bergshoeff, Eric; Panda, Sudhakar Classical and Quantum Gravity, Vol. 28, Issue 10 https://doi.org/10.1088/0264-9381/28/10/105011	journal	April 2011
Relativistic and non-relativistic classical field theory on five-dimensional spacetime Kunzle, H. P.; Duval, C. Classical and Quantum Gravity, Vol. 3, Issue 5 https://doi.org/10.1088/0264-9381/3/5/024	journal	September 1986
Lorentz-like covariant equations of non-relativistic fluids Montigny, M. de; Khanna, F. C.; Santana, A. E. Journal of Physics A: Mathematical and General, Vol. 36, Issue 8 https://doi.org/10.1088/0305-4470/36/8/301	journal	February 2003
Torsional Newton–Cartan gravity from the large c expansion of general relativity Van den Bleeken, Dieter Classical and Quantum Gravity, Vol. 34, Issue 18 https://doi.org/10.1088/1361-6382/aa83d4	journal	August 2017
Bargmann structures and Newton-Cartan theory Duval, C.; Burdet, G.; Künzle, H. P. Physical Review D, Vol. 31, Issue 8 https://doi.org/10.1103/PhysRevD.31.1841	journal	April 1985
Celestial mechanics, conformal structures, and gravitational waves Duval, Christian; Gibbons, Gary; Horváthy, Péter Physical Review D, Vol. 43, Issue 12 https://doi.org/10.1103/PhysRevD.43.3907	journal	June 1991
General theory of Galilean gravity Cariglia, Marco Physical Review D, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevD.98.084057	journal	October 2018
Action Principle for Newtonian Gravity Hansen, Dennis; Hartong, Jelle; Obers, Niels A. Physical Review Letters, Vol. 122, Issue 6 https://doi.org/10.1103/PhysRevLett.122.061106	journal	February 2019
Four-Dimensional Formulations of Newtonian Mechanics and Their Relation to the Special and the General Theory of Relativity Havas, Peter Reviews of Modern Physics, Vol. 36, Issue 4 https://doi.org/10.1103/RevModPhys.36.938	journal	October 1964
Quantum fact and classical fiction: Clarifying Landé’s pseudo-paradox Lévy-Leblond, J. -M. American Journal of Physics, Vol. 44, Issue 11 https://doi.org/10.1119/1.10206	journal	November 1976
On Unitary Ray Representations of Continuous Groups Bargmann, V. The Annals of Mathematics, Vol. 59, Issue 1 https://doi.org/10.2307/1969831	journal	January 1954
Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie) Cartan, Elie Annales scientifiques de l'École normale supérieure, Vol. 40 https://doi.org/10.24033/asens.751	journal	January 1923
Sur les variétés à connexion affine, et la théorie de la relativité généralisée (première partie) (Suite) Cartan, Elie Annales scientifiques de l'École normale supérieure, Vol. 41 https://doi.org/10.24033/asens.753	journal	January 1924
Minkowski and Galilei/Newton Fluid Dynamics: A Geometric 3 + 1 Spacetime Perspective Cardall, Christian Fluids, Vol. 4, Issue 1 https://doi.org/10.3390/fluids4010001	journal	December 2018
Combining 3-Momentum and Kinetic Energy on Galilei/Newton Spacetime Cardall, Christian Y. Symmetry, Vol. 12, Issue 11 https://doi.org/10.3390/sym12111775	journal	October 2020

Similar Records

A Unified Perspective on Poincaré and Galilei Relativity: II. General Relativity: A. Kinematics

Journal Article · Tue Aug 05 00:00:00 EDT 2025 · Symmetry · OSTI ID:2586894

Towards Full ‘Galilei General Relativity’: Bargmann-Minkowski and Bargmann-Galilei Spacetimes

Conference · Tue Aug 01 00:00:00 EDT 2023 · OSTI ID:1999050

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

Citation Formats

References (33)

Similar Records

Related Subjects