Studia Logica

, Volume 95, Issue 1–2, pp 161–182 | Cite as

A Geometrical Characterization of the Twin Paradox and its Variants

Article

Abstract

The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent to the assumption of the slowing down of moving clocks, and the lack of TwP is not logically equivalent to the Newtonian assumption of absolute time. The logical connection between TwP and a symmetry axiom of special relativity is also studied.

Keywords

twin paradox geometrical characterization logical foundations axiomatization special relativity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andréka, H., J. X.Madarász, and I. Németi, On the logical structure of relativity theories, With contributions from: A. Andai, G. Sági, I. Sain and Cs. Tőke. Research report, Alfréd Rényi Institute of Mathematics, Hungar. Acad. Sci., Budapest, 2002. http://www.math-inst.hu/pub/algebraic-logic/Contents.html.
  2. Andréka H., Madarász J.X., Németi I.: ‘Logical axiomatizations of spacetime Samples from the literature’. In: Prékopa, A., Molnár, E. (eds) Non-Euclidean geometries, pp. 155–185. Springer-Verlag, New York (2006)CrossRefGoogle Scholar
  3. Andréka H., Madarász J.X., Németi I.: ‘Logic of space-time and relativity theory’. In: Aiello, M., Pratt-Hartmann, I., Benthem, J. (eds) Handbook of spatial logics, pp. 607–711. Springer-Verlag, Dordrecht (2007)CrossRefGoogle Scholar
  4. Ax J.: ‘The elementary foundations of spacetime’. Found. Phys. 8(7-8), 507–546 (1978)CrossRefGoogle Scholar
  5. Benda T.: ‘A formal construction of the spacetime manifold’. J. Phil. Logic 37(5), 441–478 (2008)CrossRefGoogle Scholar
  6. Chang C.C., Keisler H.J.: Model theory. North-Holland Publishing Co, Amsterdam (1990)Google Scholar
  7. Corry, L., ‘On the origins of Hilbert’s sixth problem: physics and the empiricist approach to axiomatization’, in Marta Sanz-Solé et al. (eds.), Proceedings of the International Congress of Mathematicians, Madrid 2006, Vol.3, Zurich, European, pp. 1679–1718.Google Scholar
  8. Einstein A.: ‘Zur Elektrodynamik bewegter Körper’. Annalen der Physik, 17, 891–921 (1905)CrossRefGoogle Scholar
  9. Fock V.: The theory of space, time and gravitation. Pergamon press, New York (1959)Google Scholar
  10. Goldblatt R.: Orthogonality and spacetime geometry. Springer-Verlag, New York (1987)Google Scholar
  11. Gömöri M., and L. E. Szabó., Is the relativity principle consistent with electrodynamics? Towards a logico-empiricist reconstruction of a physical theory, 2009. arXiv:0912.4388v1.Google Scholar
  12. Guts A.K.: ‘The axiomatic theory of relativity’. Russ. Math. Surv. 37(2), 41–89 (1982)CrossRefGoogle Scholar
  13. Madarász, J. X., Logic and Relativity (in the light of definability theory), PhDthesis, Eötvös Loránd Univ., Budapest, 2002. http://www.math-inst.hu/pub/algebraiclogic/Contents.html.
  14. Madarász, J. X., I. Németi, and G. Székely, ‘Twin paradox and the logical foundation of relativity theory’, Found. Phys. 36(5):681–714, 2006.CrossRefGoogle Scholar
  15. Madarász, J. X., I. Németi, and G. Székely, A logical analysis of the time-warp effect of general relativity, 2007. arXiv:0709.2521.Google Scholar
  16. Mundy, B., ‘Optical axiomatization of Minkowski space-time geometry’, Philos. Sci. 53(1):1–30, 1986.CrossRefGoogle Scholar
  17. Mundy, B., ‘The physical content of Minkowski geometry’, The British Journal for the Philosophy of Science 37(1):25–54, 1986.CrossRefGoogle Scholar
  18. Pambuccian, V., ‘Alexandrov-Zeeman type theorems expressed in terms of definability’, Aequationes Math. 74(3):249–261, 2007.CrossRefGoogle Scholar
  19. Robb, A.A., A Theory of Time and Space, Cambridge University Press, Cambridge, 1914.Google Scholar
  20. Schutz, J. W., Foundations of special relativity: kinematic axioms for Minkowski space-time, Springer-Verlag, Berlin, 1973.Google Scholar
  21. Schutz, J. W., ‘An axiomatic system for Minkowski space-time’, J. Math. Phys. 22(2):293–302, 1981.CrossRefGoogle Scholar
  22. Schutz, J. W., Independent axioms for Minkowski space-time, Longoman, London, 1997.Google Scholar
  23. Sfarti, A., ‘Single Postulate Special Theory of Relativity’, in Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory, Budapest, 2007. http://www.phil-inst.hu/~szekely/PIRTBudapest/ft/Sfartifull.pdf
  24. Suppes, P., ‘The desirability of formalization in science’, J. Philos. 27:651–664, 1968.CrossRefGoogle Scholar
  25. Suppes, P., ‘Some open problems in the philosophy of space and time’, Synthese 24:298–316, 1972.CrossRefGoogle Scholar
  26. Szabó, L.E., ‘Empirical Foundation of Space and Time’, in M. Suárez, M. Dorato and M. Rédei (eds.), EPSA07: Launch of the European Philosophy of Science Association, Springer, 2009.Google Scholar
  27. Székely, G., ‘Twin paradox in first-order logical approach’, TDK paper, Eötvös Loránd Univ., Budapest, 2003. In Hungarian. http://www.renyi.hu/~turms/tdk.pdf
  28. Székely, G., A first order logic investigation of the twin paradox and related subjects, Master’s thesis, Eötvös Loránd Univ., Budapest, 2004. http://www.renyi.hu/~turms/master-thesis.pdf
  29. Székely, G., First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers, PhD thesis, Eötvös Loránd Univ., Budapest, 2009. http://www.renyi.hu/~turms/phd.pdf
  30. Székely, G., ‘Why-questions in physics’, in F. Stadler, (ed.), Wiener Kreis und Ungarn, Veröffentlishungen des Instituts Wiener Kreis, Vienna, 2009. To appear, preprinted at: http://philsci-archive.pitt.edu/archive/00004600/.
  31. Väänänen J.: ‘Second-order logic and foundations of mathematics’. Bull. Symbolic Logic 7(4), 504–520 (2001)CrossRefGoogle Scholar
  32. Vroegindewey P.G.: ‘An algebraic generalization of a theorem of E. C. Zeeman. Indag. Math. 36(1), 77–81 (1974)Google Scholar
  33. Vroegindewey, P. G., V. Kreinovic, and O. M. Kosheleva, ‘An extension of a theorem of A. D. Aleksandrov to a class of partially ordered fields’, Indag. Math. 41(3):363–376, 1979.Google Scholar
  34. Woleński, J., ‘First-order logic: (philosophical) pro and contra’, in V. F. Hendricks et al., (eds.), First-Order Logic Revisited, Logos Verlag, Berlin, 2004, pp. 369–398.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, BudapestBudapestHungary
  2. 2.Zrínyi Miklós University of National Defence, BudapestBudapestHungary

Personalised recommendations