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Nonconservation of Energy and Loss of Determinism. I. Infinitely many colliding balls

Atkinson, David and Johnson, Porter (2009) Nonconservation of Energy and Loss of Determinism. I. Infinitely many colliding balls. [Published Article or Volume]


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An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This result holds in particular when the total mass of all the balls is finite, and even when the spatial extent and temporal duration of the process are also finite. Further, the process is shown to be indeterministic: there is an arbitrary parameter in the general solution that corresponds to the injection of an arbitrary amount of energy (classically), or energy-momentum (relativistically), into the system at the point of accumulation of the locations of the balls. Specific examples are given that illustrate these counter-intuitive results, including one in which all the balls move with the same velocity after every collision has taken place.

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Item Type: Published Article or Volume
Atkinson, David
Johnson, Porter
Keywords: Mechanics, energy nonconservation, indeterminism.
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Physics > Relativity Theory
Depositing User: David Atkinson
Date Deposited: 25 Dec 2011 15:19
Last Modified: 25 Dec 2011 15:19
Item ID: 8972
Journal or Publication Title: Foundations of Physics

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