Advertisement

Where to Put It? The Direction of Time Between Axioms and Supplementary Conditions

  • Michael StöltznerEmail author

Abstract

This paper discusses the problem of implementing the unidirectionality of time into physical theory. I understand a physical theory as an axiom system instantiating some basic laws or equations that contains various models or solutions, among which the physical models form a subset. The theory expressed on these three levels must be supplemented with a set of application rules. There are, I argue, four possible ways to implement time into a theory thus conceived. They are distinguished by the systematic status of the specifically temporal concepts, that is, whether they are part of the laws, the models, or the application rules. (1) One may consider the direction of time so fundamental as to require its being expressed in the basic axioms or basic laws of nature. Given the fact that our present basic theories are time-reversal invariant, we have to search for new or modified basic laws. (2) According to reductionist explanations, the manifest arrow of time arises from a more fundamental theory, in which time does not play a role at all. (3) The direction of time is expressed in lower level laws or supplementary conditions that single out those models that correspond to the macroscopically observable direction of time. (4) The unidirectionality of time expresses some peculiar non-lawlike fact about initial conditions, perhaps of our whole Universe or the space-time region we inhabit. I will illustrate these four classes at two historical confrontations that concern Boltzmann’s legacy statistical mechanics and causality-violating solutions of the general theory of relativity.

Keywords

Direction of time Axiomatic method Basic laws and lower level laws Physical models of an axiom system Physical meaning criteria Syntactic and semantic incompleteness Time in general relativity Time in statistical mechanics Indeterminism Reversibility Second law of thermodynamics Time travel Gödel’s rotating universe Causality in general relativity Boltzmann’s legacy Empiricist causality Reductionism and emergence Ludwig Boltzmann Franz Serafin Exner David Hilbert Kurt Gödel Max Planck John Earman 

References

  1. 1.
    Bettini, S.: Anthropic reasoning in cosmology. A historical perspective. In: Stöltzner, M., Weingartner, P. (eds.) Formale Teleologie und Kausalität, pp. 35–76. Mentis, Paderborn (2005) Google Scholar
  2. 2.
    Boltzmann, L.: On certain questions on the theory of gases. Nature 51, 413–415 (1895) CrossRefGoogle Scholar
  3. 3.
    Corry, L.: From Mie’s electromagnetic theory of matter to Hilbert’s unified foundations of physics. Stud. Hist. Philos. Mod. Phys. 30B, 159–183 (1999) Google Scholar
  4. 4.
    Earman, J.: Bangs, Crunches, Whimpers, and Shrieks. Oxford University Press, New York (1995) Google Scholar
  5. 5.
    Ehrlich, P.A., Emch, G.G.: Gravitational waves and causality. Rev. Math. Phys. 4, 163–221 (1992) CrossRefGoogle Scholar
  6. 6.
    Einstein, A.: Remarks to the essays appearing in the collective volume. In: Schilpp, P.A. (ed.) Albert Einstein: Philosopher-Scientist, pp. 687–688. Open Court, Evanston (1949) Google Scholar
  7. 7.
    Ellis, G.F.R.: Contributions of K. Gödel to relativity and cosmology. In: Hájek, P. (ed.): Gödel’96. Logical Foundations of Mathematics, Computer Science and Physics – Kurt Gödel’s Legacy, pp. 34–49. Springer, Berlin (1996) Google Scholar
  8. 8.
    Exner, F.S.: Über Gesetze in Naturwissenschaft und Humanistik. Alfred Hölder, Wien & Leipzig (1909) Google Scholar
  9. 9.
    Exner, F.S.: Vorlesungen über die physikalischen Grundlagen der Naturwissenschaften, 2nd edn. Franz Deuticke, Leipzig-Wien (1922) Google Scholar
  10. 10.
    Fasol-Boltzmann, I.M. (ed.): Ludwig Boltzmann. Principien der Naturfilosofi. Lectures on Natural Philosophy. Springer, Berlin (1990) Google Scholar
  11. 11.
    Gödel, K.: (1949) A remark about the relationship between relativity theory and idealistic philosophy. In: Fefermann, S., et al. (eds.) Collected Works, vol. 2, pp. 202–207. Oxford University Press, Oxford (1990) Google Scholar
  12. 12.
    Gödel, K.: Some observations about the theory of relativity and Kantian philosophy (manuscript B2). In: Fefermann, S., et al. (eds.) Collected Works, vol. 3, pp. 230–246. Oxford University Press, Oxford (1995) Google Scholar
  13. 13.
    Hilbert, D.: Mathematische Probleme. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse, pp. 253–297 (1900). English translation reprinted in Bull. Math. Soc. 37, 407–436 (2000) Google Scholar
  14. 14.
    Hilbert, D.: Die Grundlagen der Physik (1924). Second version, reprinted in Hilbertiana – Fünf Aufsätze von David Hilbert, WBG, Darmstadt, pp. 47–78 (1964) Google Scholar
  15. 15.
    Hilbert, D.: Naturerkennen und Logik. Naturwissenschaften 18, 959–963 (1930) CrossRefGoogle Scholar
  16. 16.
    Hilbert, D.: Natur und Mathematisches Erkennen. Vorlesungen gehalten in Göttingen 1919–1920, ed. by David E. Rowe, Birkhäuser, Basel (1992) Google Scholar
  17. 17.
    Höflechner, W. (ed.): Ludwig Boltzmann. Leben und Briefe. Akademische Druck- und Verlagsanstalt, Graz (1994) Google Scholar
  18. 18.
    Klein, M.J.: The development of Boltzmann’s statistical ideas. In: Cohen, E.G.D., Thirring, W. (eds.) The Boltzmann Equation. Theory and Applications. Acta Physica Austriaca, Suppl. X, pp. 53–106 (1973) CrossRefGoogle Scholar
  19. 19.
    Malament, D.B.: Minimal acceleration requirements for ‘Time travel’ in Gödel spacetime. J. Math. Phys. 26, 774–777 (1985) CrossRefGoogle Scholar
  20. 20.
    McTaggart, J.E.: The unreality of time. Mind 18, 457–474 (1908) CrossRefGoogle Scholar
  21. 21.
    Planck, M.: Die Einheit des physikalischen Weltbildes. In: Wege zur Physikalischen Erkenntnis. Reden und Vorträge, pp. 1–24. S. Hirzel, Leipzig (1944) Google Scholar
  22. 22.
    Planck, M.: Dynamische und statistische Gesetzmäßigkeit. In: Wege zur Physikalischen Erkenntnis. Reden und Vorträge, pp. 54–67. S. Hirzel, Leipzig (1944) Google Scholar
  23. 23.
    Price, H.: Time’s arrow, time’s fly-bottle. In: Stadler, F., Stöltzner, M. (eds.): Time and History. Proceedings of the 28th International Ludwig Wittgenstein Symposium, pp. 253–273. Ontos, Frankfurt am Main (2006) Google Scholar
  24. 24.
    Reichenbach, H.: The Direction of Time. University of California Press, Berkeley (1956) Google Scholar
  25. 25.
    Sauer, T.: The relativity of discovery: Hilbert’s first note on the foundations of physics. Arch. Hist. Exact Sci. 53, 529–575 (1999) Google Scholar
  26. 26.
    Stadler, F., Stöltzner, M. (eds.): Time and History. Proceedings of the 28th International Ludwig Wittgenstein Symposium. Ontos, Frankfurt am Main (2006) Google Scholar
  27. 27.
    Stöltzner, M.: Gödel and the theory of everything. In: Hájek, P. (ed.): Gödel’96. Logical Foundations of Mathematics, Computer Science and Physics – Kurt Gödel’s Legacy, pp. 291–306. Springer, Berlin (1996) Google Scholar
  28. 28.
    Stöltzner, M.: Vienna Indeterminism: Mach, Boltzmann, Exner. Synthese 119, 85–111 (1999) CrossRefGoogle Scholar
  29. 29.
    Yourgrau, P.: The Disappearance of Time. Kurt Gödel and the Idealistic Tradition in Philosophy. Cambridge University Press, Cambridge (1991) Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of South CarolinaColumbiaUSA

Personalised recommendations