A relativistic Zeno effect
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. The notion that both determinism and the conservation laws might be salvaged via photon creation is shown to be flawed.
Newtonian Supertasks: A Critical Analysis
In two recent papers Perez Laraudogoitia has described a variety of supertasks involving elastic collisions in Newtonian systems containing a denumerably infinite set of particles. He maintains that these various supertasks give examples of systems in which energy is not conserved, particles at rest begin to move spontaneously, particles disappear from a system, and particles are created ex nihilo. An analysis of these supertasks suggests that they involve systems that do not satisfy the mathematical conditions required of Newtonian systems at the time the supertask is due to be completed, or else they rely on the application of the time-reversal transformation to states which are not well-defined. Consequently, it is unjustified to conclude that the paradoxical results are arising from within the framework of Newtonian mechanics. In the last part of this article, we discuss various aspects of the physics of these supertasks.
Infinity Machines and Creation Ex Nihilo
In this paper a simple model in particle dynamics of a well-known supertask is constructed (the supertask was introduced by Max Black some years ago). As a consequence, a new and simple result about creation ex nihilo of particles can be proved compatible with classical dynamics. This result cannot be avoided by imposing boundary conditions at spatial infinity, and therefore is really new in the literature. It follows that there is no reason why even a world of rigid spheres should be eternal, as has been erroneously assumed, especially since the time of Newton.