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Indeterminism, Asymptotic Reasoning, and Time Irreversibility in Classical Physics.

Korolev, Alexandre (2006) Indeterminism, Asymptotic Reasoning, and Time Irreversibility in Classical Physics. In: [2006] Philosophy of Science Assoc. 20th Biennial Mtg (Vancouver) > PSA 2006 Contributed Papers.

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    Abstract

    A recent proposal of 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 physical significance of an often overlooked and yet important Lipschitz condition the violation of which leads to the existence of anomalous non-trivial 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. To further support this view we also discuss how certain solutions in hydrodynamics associated with first order differential equations (ODEs) with spatially non-Lipschitz right-hand side lead to lack of important properties such as stability with respect to perturbations and Markovianity in time.


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    Item Type: Conference or Workshop Item (UNSPECIFIED)
    Keywords: determinism, indeterminism, acausality, time irreversibility, Lipschitz condition, non-Lipschitz indeterminism, Markov's condition
    Subjects: Specific Sciences > Physics > Classical Physics
    General Issues > Models and Idealization
    General Issues > Causation
    Conferences and Volumes: [2006] Philosophy of Science Assoc. 20th Biennial Mtg (Vancouver) > PSA 2006 Contributed Papers
    Depositing User: Alexandre Korolev
    Date Deposited: 21 Oct 2006
    Last Modified: 07 Oct 2010 11:14
    Item ID: 3003
    URI: http://philsci-archive.pitt.edu/id/eprint/3003

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