Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-19T04:26:49.657Z Has data issue: false hasContentIssue false
  • English
  • Français

THREE DIFFERENT FORMALISATIONS OF EINSTEIN’S RELATIVITY PRINCIPLE

Published online by Cambridge University Press:  28 March 2017

JUDIT X. MADARÁSZ ,
GERGELY SZÉKELY  and
MIKE STANNETT
JUDIT X. MADARÁSZ*
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences
GERGELY SZÉKELY*
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences
MIKE STANNETT*
Affiliation:
Department of Computer Science, The University of Sheffield
*
*ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS HUNGARIAN ACADEMY OF SCIENCES P.O. BOX 127 BUDAPEST 1364, HUNGARY E-mail: madarasz.judit@renyi.mta.huURL: http://www.renyi.hu/∼madarasz
†ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS HUNGARIAN ACADEMY OF SCIENCES P.O. BOX 127 BUDAPEST 1364, HUNGARY E-mail: szekely.gergely@renyi.mta.huURL: http://www.renyi.hu/∼turms
‡DEPARTMENT OF COMPUTER SCIENCE THE UNIVERSITY OF SHEFFIELD 211 PORTOBELLO, SHEFFIELD S1 4DP, UK E-mail: m.stannett@sheffield.ac.ukURL: http://www.dcs.shef.ac.uk/∼mps
Get access Rights & Permissions [Opens in a new window]

Abstract

We present three natural but distinct formalisations of Einstein’s special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made equivalent by introducing a small number of additional, intuitively acceptable axioms.

Keywords

03B3083A05special principle of relativityspecial relativityrelativity theoryaxiomatic methodfirst order logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 3 , September 2017 , pp. 530 - 548
Copyright
Copyright © Association for Symbolic Logic 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Andréka, H., Madarász, J. X., & Németi, I. (2007). Logic of space-time and relativity theory. In Aiello, M., Pratt-Hartmann, I., & Benthem, J., editors. Handbook of Spatial Logics. Dordrecht: Springer Netherlands, pp. 607–711.CrossRefGoogle Scholar
Andréka, H., Madarász, J. X., Németi, I., Stannett, M., & Székely, G. (2014). Faster than light motion does not imply time travel. Classical and Quantum Gravity, 31(9), 095005.CrossRefGoogle Scholar
Andréka, H., Madarász, J. X., Németi, I., & Székely, G. (2008). Axiomatizing relativistic dynamics without conservation postulates. Studia Logica, 89(2), 163–186.Google Scholar
Andréka, H., Madarász, J. X., Németi, I., & Székely, G. (2011). A logic road from special relativity to general relativity. Synthese, 186(3), 633–649.CrossRefGoogle Scholar
Borisov, Y. F. (1978). Axiomatic definition of the Galilean and Lorentz groups. Siberian Mathematical Journal, 19(6), 870–882.CrossRefGoogle Scholar
Einstein, A. (1916). Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik (ser. 4), 49, 769–822. Available in English translation as Einstein (1996).CrossRefGoogle Scholar
Einstein, A. (1996). The foundation of the general theory of relativity. In Klein, M. J., Kox, A. J., and Schulman, R., editors. The Collected Papers of Albert Einstein, Volume 6, The Berlin Years: Writings, 1914–1917. Princeton, New Jersey: Princeton University Press, pp. 146–200.Google Scholar
Friedman, M. (1983). Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science. Princeton, New Jersey: Princeton University Press.Google Scholar
Galileo (1953). Dialogue Concerning the Two Chief World Systems. Berkeley and Los Angeles: University of California Press. Originally published in Italian, 1632. Translated by Stillman Drake.Google Scholar
Gömöri, M. (2015). The Principle of Relativity—An Empiricist Analysis. Ph.D. Thesis, Eötvös University, Budapest.Google Scholar
Gömöri, M. & Szabó, L. E. (2013a). Formal statement of the special principle of relativity. Synthese, 192(7), 2053–2076.CrossRefGoogle Scholar
Gömöri, M. & Szabó, L. E. (2013b). Operational understanding of the covariance of classical electrodynamics. Physics Essays, 26, 361–370.Google Scholar
Ignatowski, W. V. (1910). Das Relativitätsprinzip. Archiv der Mathematik und Physik, 17, 1–24. (Part 1).Google Scholar
Ignatowski, W. V. (1911). Das Relativitätsprinzip. Archiv der Mathematik und Physik, 18, 17–41. (Part 2).Google Scholar
Lévy-Leblond, J.-M. (1976). One more derivation of the Lorentz transformation. American Journal of Physics, 44(3), 271–277.CrossRefGoogle Scholar
Madarász, J. X. (2002). Logic and Relativity (in the Light of Definability Theory). Ph.D. Thesis, MTA Alfréd Rényi Institute of Mathematics.Google Scholar
Madarász, J. X., Stannett, M., & Székely, G. (2014). Why do the relativistic masses and momenta of faster-than-light particles decrease as their speeds increase? Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 10(005), 20.Google Scholar
Madarász, J. X. & Székely, G. (2014). The existence of superluminal particles is consistent with relativistic dynamics. Journal of Applied Logic, 12, 477–500.CrossRefGoogle Scholar
Marker, D. (2002). Model Theory: An Introduction. New York: Springer.Google Scholar
Mendelson, E. (2015). An Introduction to Mathematical Logic (sixth edition). Boca Raton, London, New York: CRC Press.Google Scholar
Misner, C., Thorne, K., & Wheeler, J. (1973). Gravitation. San Francisco: W. Freeman.Google Scholar
Molnár, A. & Székely, G. (2015). Axiomatizing relativistic dynamics using formal thought experiments. Synthese, 192(7), 2183–2222.CrossRefGoogle Scholar
Muller, F. A. (1992). On the principle of relativity. Foundations of Physics Letters, 5(6), 591–595.Google Scholar
Pal, P. B. (2003). Nothing but relativity. European Journal of Physics, 24(3), 315.CrossRefGoogle Scholar
Pelissetto, A. & Testa, M. (2015). Getting the Lorentz transformations without requiring an invariant speed. American Journal of Physics, 83(4), 338–340.Google Scholar
Stewart, I. (2009). Galois Theory (third edition). Boca Raton, London, New York, Washington, D.C.: Chapman & Hall.Google Scholar
Szabó, L. E. (2004). On the meaning of Lorentz covariance. Foundations of Physics Letters, 17(5), 479–496.CrossRefGoogle Scholar
Székely, G. (2013). The existence of superluminal particles is consistent with the kinematics of Einstein’s special theory of relativity. Reports on Mathematical Physics, 72(2), 133–152.CrossRefGoogle Scholar