Hostname: page-component-7f64f4797f-9t7q9 Total loading time: 0 Render date: 2025-11-04T02:27:50.873Z Has data issue: false hasContentIssue false
  • English
  • Français

Indeterminism, Asymptotic Reasoning, and Time Irreversibility in Classical Physics

Published online by Cambridge University Press:  01 January 2022

Alexandre Korolev
Get access Rights & Permissions [Opens in a new window]

Abstract

A recent proposal by Norton (2003) to show that a simple Newtonian system can exhibit stochastic acausal behavior by giving rise to spontaneous movements of a mass on the dome of a certain shape is examined. We discuss the physical significance of an often overlooked and yet important Lipschitz condition the violation of which leads to the existence of anomalous nontrivial solutions in this and similar cases. We show that the Lipschitz condition is closely linked with the time reversibility of certain solutions in Newtonian mechanics and the failure to incorporate this condition within Newtonian mechanics may unsurprisingly lead to physically impossible solutions that have no serious metaphysical implications.

Information

Type
Physics: New Solutions to Historical Problems
Information
Philosophy of Science , Volume 74 , Issue 5: Proceedings of the 2006 Biennial Meeting of the Philosophy of Science Association. Part I: Contributed Papers. Edited by Cristina Bicchieri and Jason Alexander , December 2007 , pp. 943 - 956
Copyright
Copyright © The Philosophy of Science Association

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.)

Article purchase

Temporarily unavailable

Footnotes

‡

I thank Steven Savitt of the Philosophy Department at the University of British Columbia for drawing my attention to the Lipschitz condition, and Alexei Cheviakov of the Mathematics Department at the University of British Columbia for useful discussions.

References

Arnold, Vladimir (1992), Ordinary Differential Equations. Translated by Cooke, Roger. Berlin: Springer-Verlag.Google Scholar
Batterman, Robert W. (2002), The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence. Oxford: Oxford University Press.Google Scholar
Earman, John (1986), A Primer on Determinism. Dordrecht: Reidel.CrossRefGoogle Scholar
Earman, John, and Norton, John (1996), “Infinite Pains: The Trouble with Supertasks”, in A. Morton and S. Stich (eds.), Benacerraf and His Critics. Cambridge, MA: Blackwell, 231–261Google Scholar
Landau, Lev D., and Lifshitz, Evgenii D. (1959), Theory of Elasticity. Vol. 7 of Course of Theoretical Physics. Translated by Sykes, J. B. and Reid, W. H.. London: Pergamon.Google Scholar
Norton, John (2003), “Causation as Folk Science”, Philosopher’s Imprint 3. http://www.philosophersimprint.org/003004.Google Scholar