Skip to main content
×
×
Home

THREE DIFFERENT FORMALISATIONS OF EINSTEIN’S RELATIVITY PRINCIPLE

  • JUDIT X. MADARÁSZ (a1), GERGELY SZÉKELY (a1) and MIKE STANNETT (a2)
Abstract
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.

Copyright
Corresponding author
*ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS HUNGARIAN ACADEMY OF SCIENCES P.O. BOX 127 BUDAPEST 1364, HUNGARY E-mail: madarasz.judit@renyi.mta.hu URL: 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.hu URL: 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.uk URL: http://www.dcs.shef.ac.uk/∼mps
References
Hide All
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. 607711.
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.
Andréka H., Madarász J. X., Németi I., & Székely G. (2008). Axiomatizing relativistic dynamics without conservation postulates. Studia Logica, 89(2), 163186.
Andréka H., Madarász J. X., Németi I., & Székely G. (2011). A logic road from special relativity to general relativity. Synthese, 186(3), 633649.
Borisov Y. F. (1978). Axiomatic definition of the Galilean and Lorentz groups. Siberian Mathematical Journal, 19(6), 870882.
Einstein A. (1916). Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik (ser. 4), 49, 769822. Available in English translation as Einstein (1996).
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. 146200.
Friedman M. (1983). Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science. Princeton, New Jersey: Princeton University Press.
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.
Gömöri M. (2015). The Principle of Relativity—An Empiricist Analysis. Ph.D. Thesis, Eötvös University, Budapest.
Gömöri M. & Szabó L. E. (2013a). Formal statement of the special principle of relativity. Synthese, 192(7), 20532076.
Gömöri M. & Szabó L. E. (2013b). Operational understanding of the covariance of classical electrodynamics. Physics Essays, 26, 361370.
Ignatowski W. V. (1910). Das Relativitätsprinzip. Archiv der Mathematik und Physik, 17, 124. (Part 1).
Ignatowski W. V. (1911). Das Relativitätsprinzip. Archiv der Mathematik und Physik, 18, 1741. (Part 2).
Lévy-Leblond J.-M. (1976). One more derivation of the Lorentz transformation. American Journal of Physics, 44(3), 271277.
Madarász J. X. (2002). Logic and Relativity (in the Light of Definability Theory). Ph.D. Thesis, MTA Alfréd Rényi Institute of Mathematics.
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.
Madarász J. X. & Székely G. (2014). The existence of superluminal particles is consistent with relativistic dynamics. Journal of Applied Logic, 12, 477500.
Marker D. (2002). Model Theory: An Introduction. New York: Springer.
Mendelson E. (2015). An Introduction to Mathematical Logic (sixth edition). Boca Raton, London, New York: CRC Press.
Misner C., Thorne K., & Wheeler J. (1973). Gravitation. San Francisco: W. Freeman.
Molnár A. & Székely G. (2015). Axiomatizing relativistic dynamics using formal thought experiments. Synthese, 192(7), 21832222.
Muller F. A. (1992). On the principle of relativity. Foundations of Physics Letters, 5(6), 591595.
Pal P. B. (2003). Nothing but relativity. European Journal of Physics, 24(3), 315.
Pelissetto A. & Testa M. (2015). Getting the Lorentz transformations without requiring an invariant speed. American Journal of Physics, 83(4), 338340.
Stewart I. (2009). Galois Theory (third edition). Boca Raton, London, New York, Washington, D.C.: Chapman & Hall.
Szabó L. E. (2004). On the meaning of Lorentz covariance. Foundations of Physics Letters, 17(5), 479496.
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), 133152.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 44 *
Loading metrics...

Abstract views

Total abstract views: 190 *
Loading metrics...

* Views captured on Cambridge Core between 28th March 2017 - 18th January 2018. This data will be updated every 24 hours.