John D. Norton
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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
|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
See also "The Dome: A Simple Violation of Determinism in Newtonian Mechanics" in Goodies.
|Ready for a little light entertainment? What happens if one asks whether an infinite tower of turtles could overcome gravity and support the world? What happens if we ask if there is some mechanism in ordinary Newtonian mechanics that would let a castle float in the air.||"Turtles
all the way down."
Castles in the air.