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The Dome



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The Dome An Unexpectedly Simple Failure of Determinism John D Norton1 Department of History and Philosophy of Science University of Pittsburgh Newton s equations of motion tell us that a mass at rest at the apex of a dome with the shape specified here can spontaneously move It has been suggested that this indeterminism should be discounted since it draws on an incomplete rendering of Newtonian physics or it is unphysical or it employs illicit idealizations I analyze and reject each of these reasons 1 Introduction It has been widely recognized for over two decades that contrary to the long standing lore Newtonian mechanics is not a deterministic theory The clarion call came in John Earman s 1986 Ch III which recounted the failure of determinism including the then recent discovery by Mather and McGehee of space invader systems of interacting particles that spontaneously rush into an empty space from spatial infinity Further simpler violations of determinism emerged P rez Laraudogoitia 1996 described an especially simple example of supertask indeterminism in which a countable infinity of masses confined to a unit interval are spontaneously energized and Norton 1999 described a correspondingly simple example of a countable infinity of masses connected by springs that are spontaneously energized In this developing tradition the simplest example so far of indeterminism in Newtonian physics is what has come to be known as the dome described in Norton 2003 3 The indeterminism involves none of the complications of infinitely many systems interacting or masses appearing with unbounded speed from spatial infinity A mass sits on a dome in a 1 My thanks to my co symposiasts John Earman and David Malament to Michael Dickson Bernie Goldstein Stephan Hartmann Alexandre Korolev and Dmitri Tymoczko and to Visiting Fellows of the Center for Philosophy of Science Boris Grozdanoff Antigone Nounou Hernan Pringe and St phanie Ruphy 1 gravitational field After remaining motionless for an



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