This paper shows that the general homogeneous solution to equations of evolution for some infinite systems of particles subject to mutual binary collisions does not depend on a single arbitrary constant but on a potentially infinite number of such constants. This is because, as I demonstrate, a single self-excitation of a system of particles can depend on a potentially infinite number of parameters. The recent homogeneous solution obtained by Atkinson and Johnson, which depends on a single arbitrary constant, is only (...) a particular case. (shrink)

Pérez Laraudogoitia (1996) presented an isolated system of infinitely many particles with infinite total mass whose total classical energy and momentum are not necessarily conserved in some particular inertial frame of reference. With a more generalized model Atkinson (2007) proved that a system of infinitely many balls with finite total mass may evolve so that its total classical energy and total relativistic energy and momentum are not conserved in any inertial frame of reference, and yet concluded that its total classical (...) momentum is necessarily conserved. Contrary to this conclusion of Atkinson, I show that Atkinson's model has a solution in which the total momentum fails to be conserved in every inertial frame of reference. This result, combined with Atkinson's, demonstrates that both classical and relativistic mechanics allow the energy and momentum of a system of infinitely many components to fail to be conserved in every inertial frame of reference. (shrink)

The present article provides an analysis of the instants of a system that performs a Newtonian supertask. For each instant it studied the possibility of the system having, from the instant in question, more than one possible course of evolution. This analysis shows that some supertasks presented as deterministic by Pérez Laraudogoitia are in fact indeterministic and specifies the difficulties ahead in showing the radical indeterminism suggested by Atkinson and Johnson.

It is shown that the following three common understandings of Newton’s laws of motion do not hold for systems of infinitely many components. First, Newton’s third law, or the law of action and reaction, is universally believed to imply that the total sum of internal forces in a system is always zero. Several examples are presented to show that this belief fails to hold for infinite systems. Second, two of these examples are of an infinitely divisible continuous body with finite (...) mass and volume such that the sum of all the internal forces in the body is not zero and the body accelerates due to this non-null net internal force. So the two examples also demonstrate the breakdown of the common understanding that according to Newton’s laws a body under no external force does not accelerate. Finally, these examples also make it clear that the expression ‘impressed force’ in Newton’s formulations of his first and second laws should be understood not as ‘external force’ but as ‘exerted force’ which is the sum of all the internal and external forces acting on a given body, if the body is infinitely divisible. (shrink)

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. (shrink)

A supertask is a task that consists in infinitely many component steps, but which in some sense is completed in a finite amount of time. Supertasks were studied by the pre-Socratics and continue to be objects of interest to modern philosophers, logicians and physicists. The term “super-task” itself was coined by J.F. Thomson (1954). Here we begin with an overview of the analysis of supertasks and their mechanics. We then discuss the possibility of supertasks from the perspective of general relativity.