Jon Perez Laraudogoitia

The paper takes a detailed look at a surprising new aspect of the dynamics of rigid bodies. Far from the usual consideration of rigid body theory as a merely technical chapter of classical physics, I demonstrate here that there are solutions to the conservation equations of mechanics that imply the spontaneous, unpredictable splitting of a rigid body in free rotation, something that has direct implications for the problem of causality. The paper also shows that the instability revealed in indeterminist splitting processes does not depend solely on the bodies’ inertial properties but also on the number of dimensions of the physical space they inhabit. The paper concludes with a conjecture on the behavior of rigid bodies in four-dimensional space.

The first aim of this paper is to introduce a new way of looking at supertasks in the light of special relativity which makes use of the elementary dynamics of relativistic point particles subjected to elastic binary collisions and constrained to move unidimensionally. In addition, this will enable us to draw new physical consequences from the possibility of supertasks whose ordinal type is higher than the usual ω or ω * considered so far in the literature. Thus, the paper shows how an entire collection of infinitely many particles may place itself spontaneously in motion (mechanical self-acceleration) or even reach the speed of light in a way compatible with special relativity. Interesting implications for classical mechanics are also derived, particularly the possibility of a system of particles disappearing spontaneously in spatial infinity even under the condition of the non-existence of non-collision singularities

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.

In this paper, an example is presented for a dynamic system analysable in the framework of the mechanics of rigid bodies. Interest in the model lies in three fundamental features. First, it leads to a paradox in classical mechanics which does not seem to be explainable with the conceptual resources currently available. Second, it is possible to find a solution to it by extending in a natural way the idea of global interaction in the context of what is called interaction by impenetrability. Third, the solution presented throws light on a problem posed and discussed in the recent literature in connection with the mass conservation principle.

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

In a recent volume of this journal, L. Angel ([2002]) proposed a collision mechanics leading to such strange results as the possibility that a particle may be in several places at the same time, or the existence of unprepared spatially-separated correlations. I will here show that neither of these results follows from his theory or, if it does, the theory, contrary to what Angel claims, is not a plausible extension of Newtonian collision dynamics. No bilocation No quantum leap No unprepared spatially-separated correlations.

Until the present, the Newtonian theory of gravitation has only been studied in any detail through the usual, presupposed ontology of point particles. This paper shows that changing our ontology into one which makes use of continuous bodies (non-point particles) allows us to obtain in a simple way two important results relevant to the theory: (a) The Newtonian theory of gravitation is indeterministic in a way apparently unparalleled when non-point particle models of it are used. (b) In the Newtonian theory of gravitation it is possible to find non-collision singularities qualitatively different from the ones presented in point particle models.

Norton’s very simple case of indeterminism in classical mechanics has given rise to a literature critical of his result. I am interested here in posing a new objection different from the ones made to date. The first section of the paper expounds the essence of Norton’s model and my criticism of it. I then propose a specific modification in the absence of gravitational interaction. The final section takes into consideration a surprising consequence for classical mechanics from the new model introduced here

This paper presents three interesting consequences that follow from admitting an ontology of rigid bodies in classical mechanics. First, it shows that some of the most characteristic properties of supertasks based on binary collisions between particles, such as the possibility of indeterminism or the non-conservation of energy, persist in the presence of gravitational interaction. This makes them gravitational supertasks radically different from those that have appeared in the literature to date. Second, Sect. 6 proves that the role of gravitation in supertasks of this kind may be highly non-trivial. Third,, the gravitational supertasks found in the first part enable us to show that indeterminism of classical mechanics with gravitation is much more general than has been supposed until now. This result is especially interesting from the philosophical viewpoint, as it links the scope of indeterminism in a theory like classical mechanics directly with the nature of its ontological hypotheses

In “Nonconservation of Energy and loss of Determinism II. Colliding with an Open Set” (2010) Atkinson and Johnson argue in favour of the idea that an actual infinity should be excluded from physics, at least in the sense that physical systems involving an actual infinity of component elements should not be admitted. In this paper I show that the argument Atkinson and Johnson use is erroneous and that an analysis of the situation considered by them is possible without requiring any type of rejection of the idea of infinity