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Some Relativistic and Higher Order Supertasks

Published online by Cambridge University Press:  01 April 2022

Jon Pérez Laraudogoitia
Jon Pérez Laraudogoitia*
Affiliation:
Department of Logic and Philosophy of Science, University of the Basque Country
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Abstract

The first aim of this paper is to introduce a new way of looking at supertasks in the light of special relativity which makes use of the elementary dynamics of relativistic point particles subjected to elastic binary collisions and constrained to move unidimensionally. In addition, this will enable us to draw new physical consequences from the possibility of supertasks whose ordinal type is higher than the usual ω or ω* considered so far in the literature. Thus, the paper shows how an entire collection of infinitely many particles may place itself spontaneously in motion (mechanical self-acceleration) or even reach the speed of light in a way compatible with special relativity. Interesting implications for classical mechanics are also derived, particularly the possibility of a system of particles disappearing spontaneously in spatial infinity even under the condition of the non-existence of non-collision singularities.

Type
Research Article
Information
Philosophy of Science , Volume 65 , Issue 3 , September 1998 , pp. 502 - 517
Copyright
Copyright © Philosophy of Science Association 1998

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Footnotes

†

Send requests for reprints to the author, Departamento de Lògica y Filosofia de la Ciencia, Facultad de Filología y Geografia e Historia, Universidad del País Vasco, Paseo de la Universidad, 5, Apartado Postai 2111, 01006 Vitoria-Gasteiz, ESPAÑA.

References

Benacerraf, Paul (1962), “Tasks, Super-Tasks, and Modern Eleatics”, Journal of Philosophy LIX: 765–784.CrossRefGoogle Scholar
Berry, M. V. (1981), “Regularity and Chaos in Classical Mechanics, Illustrated by Three Deformations of a Circular ‘Billiard‘”, European Journal of Physics 2: 91–102.CrossRefGoogle Scholar
Clark, Peter and Read, Stephen (1984), “Hypertasks”, Synthese 61: 387–390.CrossRefGoogle Scholar
Earman, John (1986), A Primer on Determinism. Dordrecht: Reidel.CrossRefGoogle Scholar
Earman, John (1995), Bangs, Crunches, Whimpers, and Shrieks. Singularities and Acausalities in Relativistic Spacetimes. New York: Oxford University Press.Google Scholar
Earman, John and Norton, John D. (1996), “Infinite Pains: The Trouble with Supertasks”, in Morton, Adam and Stich, Stephen P. (eds.), Benacerraf and his Critics. Oxford: Blackwell Publishers, 231–261.Google Scholar
Echeverría, Fernando, Klinkhammer, Gunnar, and Thorne, Kip S. (1991), “Billiard Balls in Wormhole Spacetimes with Closed Timelike Curves. I. Classical Theory”, Physical Review D 44: 1077–1099.CrossRefGoogle ScholarPubMed
Eisberg, Robert M. (1961), Fundamentals of Modern Physics. New York: John Wiley and Sons, Inc.Google Scholar
Gerver, Joseph L. (1984), “A Possible Model for a Singularity without Collisions in the Five Body Problem”, Journal of Differential Equations 52: 76–90.CrossRefGoogle Scholar
Grünbaum, Adolf (1970), “Modern Science and Zeno's Paradoxes of Motion”, in Salmon, Wesley C. (ed.), Zeno's Paradoxes. Indianapolis: Bobbs-Merrill Company, Inc., 200–250.Google Scholar
Landau, Lev D. and Lifshitz, Evgeny M. (1962), The Classical Theory of Fields. Reading, MA: Addison-Wesley.Google Scholar
Lanford, Oscar E. (1975), “Time Evolution of Large Classical Systems”, in Jürgen Moser (ed.), Dynamical Systems: Theory and Applications. New York: Springer, 1–111.CrossRefGoogle Scholar
Littlewood, John E. (1953), A Mathematician's Miscellany. London: Methuen and Co. Ltd.Google Scholar
Mather, John and McGehee, Richard (1975), “Solutions of the Collinear Four-body Problem which Become Unbounded in a Finite Time”, in Jürgen Moser (ed.), Dynamical Systems: Theory and Applications. New York: Springer, 573–597.CrossRefGoogle Scholar
McGehee, Richard (1975), “Triple Collisions in Newtonian Gravitational Systems”, in Jürgen Moser (ed.), Dynamical Systems: Theory and Applications. New York: Springer, 550–572.CrossRefGoogle Scholar
Maudlin, Tim (1994), Quantum Non-Locality and Relativity. Metaphysical Intimations of Modern Physics. Oxford: Blackwell.Google Scholar
Pérez Laraudogoitia, Jon (1996), “A Beautiful Supertask”, Mind 105: 81–83.CrossRefGoogle Scholar
Pérez Laraudogoitia, Jon (1997), “Classical Particle Dynamics, Indeterminism and a Supertask”, British Journal for the Philosophy of Science 48: 49–54.CrossRefGoogle Scholar
Pitowsky, I. (1990), “The Physical Church Thesis and Physical Computational Complexity”, Iyyun 39: 81–99.Google Scholar
Rohrlich, Fritz (1965), Classical Charged Particles. Reading, MA: Addison-Wesley.Google Scholar
Ross, S. (1988), A First Course on Probability. New York: Macmillan.Google Scholar
Schutz, Bernard F. (1986), A First Course in General Relativity. Cambridge: Cambridge University Press.Google Scholar
Sinai, Y. (1976), Introduction to Ergodic Theory. Princeton: Princeton University Press.Google Scholar
Sperling, H. J. (1970), “On the Real Singularities of the N-body Problem”, Journal für die Reine und Angewandte Mathematik 245: 15–40.Google Scholar
Van Bendegem, Jean P. (1994), “Ross' Paradox is an Impossible Super-Task”, British Journal for the Philosophy of Science 45: 743–748.CrossRefGoogle Scholar