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An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite number of elements. With this restriction indeterminism, energy nonconservation and creatio ex nihilo no longer occur. A numerical analysis of finite systems of colliding balls is given, and the asymptotic behaviour that corresponds to the potentially infinite system is inferred.

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Nonconservation of Energy and Loss of Determinism II. Colliding with an Open Set

Atkinson

Johnson

2009

Found Phys

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A relativistic Zeno effect

Atkinson¹

2006

Synthese

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A Zenonian supertask involving an infinite number of identical colliding balls is generalized to include balls with different masses. Under the restriction that the total mass of all the balls is finite, classical mechanics leads to velocities that have no upper limit. Relativistic mechanics results in velocities bounded by that of light, but energy and momentum are not conserved, implying indeterminism. By entertaining the possibility that the missing energy and momentum are carried away by a photon, however, one can restore the conservation laws and determinism.

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The Infinity from Nothing paradox and the Immovable Object meets the Irresistible Force

Shackel

2018

Euro Jnl Phil Sci

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In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. I then show how this leads to the Infinity from Nothing paradox, in which we have the spontaneous eruption of infinite mass and energy out of nothing. I conclude by showing how our supertask models at least something of an old conundrum, the question of what happens when the immovable object meets the irresistible force.

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Cited by 9 publications

References 9 publications

Nonconservation of Energy and Loss of Determinism II. Colliding with an Open Set

Nonconservation of Energy and Loss of Determinism II. Colliding with an Open Set

A relativistic Zeno effect

The Infinity from Nothing paradox and the Immovable Object meets the Irresistible Force

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