In Pérez Laraudogoitia (1996), I introduced a simple example of a supertask that involved the possibility of spontaneous self-excitation and, therefore, of a particularly interesting form of indeterminism in classical dynamics. Alper and Bridger (1998) criticised (among other things) this result. In the present article, I answer their criticisms. In what follows I assume familiarity both with Pérez Laraudogoitia (1996) and Alper and Bridger’s subsequent article.
Bridger and Alper (1999) maintain that the nonphysical featuresof the supertasks described by Pérez Laraudogoitia (1996) involving a system containing an infinite number of particles may be avoided by introducing, in a specific way, Hilbert space in classical dynamics. I argue that it is possible to interpret their proposal in two ways, neither of which is acceptable for the purpose for which it was introduced.
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. (shrink)
The paper shows a new example of nonuniqueness of the solutionto Newtonian equations of motion for infinite gravitational systems. Unlike otherexamples, the gravitational field presents no singularity, nor are the non-gravitational forcesintroduced in the model singular (in particular, there are no collisions). The result is also ofinterest because it points to an interesting limitation of the elementary (Newtonian) formulationof classical mechanics.
This paper proves that certain supertasks constitute counterexamples to countable additivity even in the frame of an objective (not subjective, à la de Finetti) conception of probability. The argument requires taking conditional probability as a primitive notion.
In “Action without interaction” (2005) I showed that one might act on a physical system (there, a particle), without interacting with it, by the procedure of making it disappear. This paper presents further extensions and a critique of that result. These extensions show why physical actions without interaction are possible, while underscoring the philosophical fertility of a characteristic approach to the actual infinite inaugurated by Benardete.
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. (shrink)
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. (shrink)
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. (shrink)
In this article I propose what I call the inverse spaceship paradox. The article's interest lies in the fact that, contrary to what appears to be an implicit agreement in the literature on indeterminism, it shows that coming from infinity can be a perfectly predictable and therefore deterministic process in a classical universe.
Although the current literature on supertasks concentrates largely on their supposed physical implications (extending the tradition of Zeno’s classical paradoxes of movement), in this study I propose a new model of supertask that explores for the first time some of their information-related consequences and I defend these consequences from a possible criticism.
The examples of dynamic supertasks analyzed to date in the philosophical literature, in which both determinism and the classical laws of conservation of energy and momentum are violated, all share the important limitation of requiring material systems of infinite mass. This paper demonstrates that this limitation is not necessary. This has important consequences for the scope and meaning of such violations.
This paper considers a recent criticism of the physical possibility of supertasks which involves Achilles’s staccato run. It is held that the criticism fails and that the underlying fallacy can be linked with interesting developments in the modern literature on physical supertasks.
In this paper a model in particle dynamics of a well-known supertask is constructed. As a consequence, a new and simple result about the failure of determinism of classical particle dynamics can be proved which is related to the non-existence of boundary conditions at spatial infinity. This result is much more accessible to the non-technical reader than similar ones in the scientific literature.
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. (shrink)
In a recent volume of this journal, L. Angel () 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. (shrink)
The paper presents a new paradox in the sphere of the classical mechanics of infinite systems. The paradox, which implies the existence of an interaction at a distance as well as gravitation, would seem to require an extension of the concept of mechanical explanation. However, it is not clear how such an extension might be carried out.
In this paper I will put forward a simple case of a dynamical system which can exhibit both the indeterminism linked to escape to infinity and that linked to self-excitation. The case depends neither on the gravitational interaction between particles nor on their mutual collisions, and thus reveals the existence of a new kind of constraint that Newton's laws lay on the predictive power of classical dynamics.
A detailed consideration of the Trojan fly supertask reveals certain unsuspected characteristics relating to determinism and causation. I propose here a solution to the new difficulty in terms of bare dispositions.
In “The Train Paradox”(Philosophia (2006) 34: 437–438) Gwiazda proposes the use of the relativity of simultaneity to formulate a new paradox. My purpose here is to show that there is no Train Paradox in Gwiazda’s sense.
In a recent article, L. Angel () argues that if we do not implement Newtonian physics adding to it a certain usual type of boundary condition, then this leads to the rejection of what he calls the P principle: ‘the composition of contact interactions does not create a noncontact interaction.’ Here I shall demonstrate that this conclusion does not follow. However, as will be made clear, this in no way diminishes the interest or importance of the model introduced by Angel (...) in his paper. 1 Introduction 2 The ‘impact without contact’ argument 3 Taking self-excitations seriously 4 Some interesting implications. (shrink)
Recently, Alper, Bridger, Earman and Norton have all proposed examples of dynamic systems that, in their view, are incompatible with classical (Newtonian) mechanics. In the first section of the present paper I shall show that their arguments are all undermined by the same fallacy. The second section proves that their conclusions of incompatibility are indeed false, and that what we are really looking at are new forms of indeterminist evolution of the same kind as that found recently in the literature (...) on supertasks. In the third section of the paper, I argue that one of these new forms of evolution is particularly interesting, and that analysis of it leads to a new vision of the relation between interaction by contact and impenetrability. (shrink)
Continuing the conversation between Achilles and the tortoise begun by Carroll, this paper proves that, in a supertask context, there are free actions (in general, contingent states of affairs) that can be predicted by means of purely logical reasons.
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. (shrink)
In this paper, we present a (propositionaI) modal-Iogic approximation to Quantum Mechanics from a reduced and characteristic number of “crucial experiments” and so independently of the lattice of subspaces of Hilbert space. Kripke’s semantics, which determinates this system, allows to define, from a new point of view, the notions of “measurement process” and “virtual world” and admits a natural interpretation which in turn can help us to understand the measurement problem. In this way, we can attempt a “many-worlds” interpretation of (...) Quantum Mechanics, in the way of Everett. (shrink)
We discuss two supertasks invented recently by Laraudogoitia [1996, 1997]. Both involve an infinite number of particle collisions within a finite amount of time and both compromise determinism. We point out that the sources of the indeterminism are rather different in the two cases—one involves unbounded particle velocities, the other involves particles with no lower bound to their sizes—and consequently that the implications for determinism are rather different—one form of indeterminism affects Newtonian but not relativistic physics, while the other (...) form is insensitive to the classical vs relativistic distinction. We also note some interesting linkages among supertasks, indeterminism and foundations problems in the general theory of relativity. (shrink)
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. (shrink)