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Systems with infinite degrees of freedom can have properties
entirely different from those we expect from examining their finite
counterparts. In the Newtonian case, they display both indeterminism
and violations of energy and momentum conservation. These supertasks
systems continue a tradition of puzzlement that was initiated by
Zeno in antiquity. I have examined many aspects of these supertasks
systems in classical and relativistic physics in papers with John
Earman. I also set up a supertask system in quantum theory and found
that, while there were some pathologies, they turned out to be
better behaved than classical supertasks. |
With J. Earman, "Forever is a Day: Supertasks in
Pitowsky and Malament-Hogarth Spacetimes," Philosophy of Science,
60 (1993), 22-42. Download
With John Earman, "Infinite Pains: The Trouble with Supertasks," in
A. Morton and S. Stich (eds.) Benacerraf and his Critics
(Cambridge, MA: Blackwells, 1996) pp.231-261. Download
With John Earman "Comments on Laraudogoitia's 'Classical Dynamics,
Indeterminism and a Supertask," British Journal for the
Philosophy of Science, 49 (1998), pp.123-33. Download
"A Quantum Mechanical Supertask" Foundations of Physics, 29,
pp. 1265-1302. Download
With Joseph S. Alper, Mark Bridger and John Earman, "What is a
Newtonian System? The Failure of Energy Conservation and Determinism
in Supertasks," Synthese, 124(2000), pp. 281-293. Download
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Because of the specific shape of the dome at its apex, Newton's
equations of motion tell us that a mass at rest at the apex can
spontaneously be set into motion. 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. |
"The Dome: An Unexpectedly Simple Failure of
Determinism," download.
See also "The Dome: A Simple Violation
of Determinism in Newtonian Mechanics" in Goodies.
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