Nonconservation of Energy and Loss of Determinism I. Infinitely Many Colliding Balls

Foundations of Physics 39 (8):937-957 (2009)
Abstract
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
Keywords Mechanics  Energy nonconservation  Indeterminism
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DOI 10.1007/s10701-009-9306-9
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References found in this work BETA
A Beautiful Supertask.Jon Perez Laraudogoitia - 1996 - Mind 105 (417):81-83.
Tasks and Supertasks.James Thomson - 1954 - Analysis 15 (1):1--13.
A Relativistic Zeno Effect.David Atkinson - 2008 - Synthese 160 (1):5-12.
Note on Achilles and the Tortoise.C. D. Broad - 1913 - Mind 22 (4):318-b-319.

View all 6 references / Add more references

Citations of this work BETA
Nonconservation of Momentum in Classical Mechanics.Chunghyoung Lee - 2011 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42 (1):68-73.

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