We study the acceleration and collisions of rigid bodies in special relativity. After a brief historical review, we give a physical definition of the term ‘rigid body’ in relativistic straight line motion. We show that the definition of ‘rigid body’ in relativity differs from the usual classical definition, so there is no difficulty in dealing with rigid bodies in relativistic motion. We then describe The motion of a rigid body (...) undergoing constant acceleration to a given velocity.The acceleration of a rigid body due to an applied impulse.Collisions between rigid bodies. (shrink)

The meaning of Lorentz contraction in special relativity and its connection with Bell’s spaceships parable is discussed. The motion of Bell’s spaceships is then compared with the accelerated motion of a rigid body. We have tried to write this in a simple form that could be used to correct students’ misconceptions due to conflicting earlier treatments.

When two bodies collide with each other, they change their motion. Many physics textbooks explain that the change in motion is caused by the force or impulse exerted on the body during the collision. This is not the whole story, I argue, in case the bodies are rigid. In this case, the change in motion cannot be causally explained solely by how the bodies are configured before and during the collision but instead should be explained (...) partly by what happens after the collision. That is, the collision between rigid bodies should better be interpreted as a case of retrocausation where the future causally affects the past or present. This retrocausal interpretation of the collision does not suffer a general problem raised against retrocausation, known as the bilking argument. And how the influence of the cause propagates backward in time to the effect in the collision is no more mysterious than how a body moves continuously in classical mechanics or how the future affects the past in proposed retrocausal models for the EPR thought experiment in quantum mechanics. (shrink)

Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the 'principle theory' approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein's treatment of the relativistic behaviour of rigid bodies and clocks in (...) class='Hi'>motion in the kinematical part of his great paper, and suggested that the dynamical understanding of length contraction and time dilation intimated by the immediate precursors of Einstein is more fundamental. Harvey Brown both examines and extends these arguments, after giving a careful analysis of key features of the pre-history of relativity theory. He argues furthermore that the geometrization of the theory by Minkowski in 1908 brought illumination, but not a causal explanation of relativistic effects. Finally, Brown tries to show that the dynamical interpretation of special relativity defended in the book is consistent with the role this theory must play as a limiting case of Einstein's 1915 theory of gravity: the general theory of relativity.Appearing in the centennial year of Einstein's celebrated paper on special relativity, Physical Relativity is an unusual, critical examination of the way Einstein formulated his theory. It also examines in detail certain specific historical and conceptual issues that have long given rise to debate in both special and general relativity theory, such as the conventionality of simultaneity, the principle of general covariance, and the consistency or otherwise of the special theory with quantum mechanics. Harvey Brown' s new interpretation of relativity theory will interest anyone working on these central topics in modern physics. (shrink)

ArgumentAccording to Hermann von Helmholtz, free mobility of bodies seemed to be an essential condition of geometry. This free mobility can be interpreted either as matter of fact, as a convention, or as a precondition making measurements in geometry possible. Since Henri Poincaré defined conventions as principles guided by experience, the question arises in which sense experiential data can serve as the basis for the constitution of geometry. Helmholtz considered muscular activity to be the basis on which the form of (...) space could be construed. Yet, due to the problem of illusion inherent in the subject’s self-assessment of muscular activity, this solution yielded new difficulties, in that if the manifold is abstracted from rigid bodies which serve as empirical justification of the geometrical notion of space, then illusionary bodies will produce fictive manifolds. The present article is meant to disentangle these difficulties. (shrink)

One of the widespread confusions concerning the history of the 1887 Michelson-Morley experiment has to do with the initial explanation of this celebrated null result due independently to FitzGerald and Lorentz. In neither case was a strict, longitudinal length contraction hypothesis invoked, as is commonly supposed. Lorentz postulated, particularly in 1895, any one of a certain family of possible deformation effects for rigid bodies in motion, including purely transverse alteration, and expansion as well as contraction; FitzGerald may well (...) have had the same family in mind. A careful analysis of the Michelson-Morley experiment (which reveals a number of serious inadequacies in many text-book treatments) indeed shows that strict contraction is not required. (shrink)

We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them (...) are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation. (shrink)

Abstract.As an undergraduate at Cambridge, Newton entered into his ‘Waste Book’ an assumption that we have named the Equivalence Assumption (The Younger): ‘‘ If a body move progressively in some crooked line [about a center of motion]..., [then this] crooked line may bee conceived to consist of an infinite number of streight lines. Or else in any point of the croked line the motion may bee conceived to be on in the tangent.’’ In this assumption, Newton somewhat (...) imprecisely describes two mathematical models, a ‘‘polygonal limit model’’ and a ‘‘tangent deflected model,’’ for ‘‘one-body motion,’’ that is, for the motion of a ‘‘body in orbit about a fixed center,’’ and then claims that these two models are equivalent. In the first part of this paper, we study the Principia to determine how the elder Newton would more carefully describe the polygonal limit and tangent deflected models. From these more careful descriptions, we then create Equivalence Assumption (The Elder), a precise interpretation of Equivalence Assumption (The Younger) as it might have been restated by Newton, after say 1687. We then review certain portions of the Waste Book and the Principia to make the case that, although Newton never restates nor even alludes to the Equivalence Assumption after his youthful Waste Book entry, still the polygonal limit and tangent deflected models, as well as an unspoken belief in their equivalence, infuse Newton’s work on orbital motion. In particular, we show that the persuasiveness of the argument for the Area Property in Proposition 1 of the Principia depends crucially on the validity of Equivalence Assumption (The Elder). After this case is made, we present the mathematical analysis required to establish the validity of the Equivalence Assumption (The Elder). Finally, to illustrate the fundamental nature of the resulting theorem, the Equivalence Theorem as we call it, we present three significant applications: we use the Equivalence Theorem first to clarify and resolve questions related to Leibniz’s ‘‘polygonal model’’ of one-body motion; then to repair Newton’s argument for the Area Property in Proposition 1; and finally to clarify and resolve questions related to the transition from impulsive to continuous forces in ‘‘De motu’’ and the Principia. (shrink)

There is broad consensus as to what a rigid body is in classical mechanics. The idea is that a rigid body is an undeformable body. In this paper I show that, if this identification is accepted, there are therefore rigid bodies which are unstable. Instability here means that the evolution of certain rigid bodies, even when isolated from all external influence, may be such that their identity is not preserved over time. The result (...) is followed by analyzing supertasks that are possible in infinite systems of rigid bodies. I propose that, if we wish to preserve our original intuitions regarding the necessary stability of rigid bodies, then the concept of rigid body must be clearly distinguished from that of undeformable body. I therefore put forward a new definition of rigid body. Only the concept of undeformable body is holistic and every connected part of a rigid body in this new sense is always a rigid body in this new sense. Finally, I briefly discuss the connection between this conceptual distinction and the dimensionality of space, thereby enabling it to be supported from a new and interesting perspective. (shrink)

Understanding employee stress has become a key issue for top management for corporate growth and risk reduction. So far, annual employee satisfaction surveys have been conducted to assess the soundness of an organization. However, since it is difficult to collect questionnaires quantitatively and continuously, there is a need for a practical method that can be used to frequently measure group stress levels with a small burden on employees. We propose such a method and evaluated four combinations of approaches, using activity/rest (...) duration distributions from body motion data and generating estimation models on an individual/group basis. The optimal result was obtained when modeling was made on a group basis by using the activity duration distribution, making it possible to assess the degree of the stress of employees quantitatively and easily, and this showed the possibility of this method being useful as a management guide for companies. (shrink)

In order to reduce the influence of athlete’s body shape on the difficulty coefficient of diving, a more reasonable calculation method of body shape correction coefficient is proposed based on the original calculation rules of diving difficulty coefficient. First, the composition of the original diving difficulty coefficient and influencing factors is analyzed and the relationship between the various structural parts is fully clarified. Second, a coupled nonrigid body dynamics model is established and a 2-body model is (...) used to simulate complex diving actions, and it is concluded that diving time is positively correlated with body shape. Finally, the air movement part and the water entry part of diving are discussed separately, the calculation model of the difficulty coefficient of body shape correction is established, and the original difficulty coefficient is corrected. The results show that the difficulty coefficient of each movement is obviously increased. This effectively avoids the influence of body shape on the diving difficulty coefficient. (shrink)

Preliminary words One important feature of Poincaré's conventionalism of geometry is linked to the relation between the abstract notion of space geometry and the representations of the free mobility of our bodies. In this sense «the group of rigid motions» identified by Helmholtz and Lie as the foundation of geometries of constant curvature is, according to Poincaré, an idealization of the primitive experience that acquaints us with the properties of space in the first place. 2 Furthermore, since Poincaré thinks (...) that the only adequate candidates for physical geometry – the geometries of constant curvature – are equivalent from a mathematical point of view (they are homeomorphic), we can choose any one of these. Actually, according to Poincaré, the idealization involved in passing from our own local motions to the group of motions makes use of temporal intuition: our notion of the large-space structure of space assumes that our displacements are infinitely iterables and this assumes temporal intuition. 3 Thus, it looks as Poincaré's notion of convention assumes some kind of idealization process. Indeed, the notion of convention involved in this cases seems to assume that in relation to a target system the choice between two idealizations is determined by some kind of equivalence relation, which in our case is displayed 1. (shrink)

A theorem due to Bob Geroch and Pong Soo Jang [“Motion of a Body in General Relativity.” Journal of Mathematical Physics 16, ] provides the sense in which the geodesic principle has the status of a theorem in General Relativity. Here we show that a similar theorem holds in the context of geometrized Newtonian gravitation. It follows that in Newtonian gravitation, as in GR, inertial motion can be derived from other central principles of the theory.

In this paper I want to examine in some detail one eighteenth-century attempt to restructure the foundations of mechanics, that of Leonhard Euler. It is now generally recognized that the idea, due to Mach, that all that happened in the eighteenth century was the elaboration of a deductive and mathematical mechanics on the basis of Newton's Laws is misleading at best. Newton's Principia needed much more than a reformulation in analytic terms if it was to provide the basis for the (...) comprehensive mechanics that was developed in the eighteenth century. Book II of the Principia, in particular, where the problem of the resistance offered to the motion of a finite body by a fluid medium was raised, was generally thought to be in large part mistaken and confused. There were also a number of areas crucial to the unification of mechanics which Newton did not deal with at all in the Principia: particularly the dynamics of rigid, flexible and elastic bodies, and the dynamics of several bodies with mutual interactions. Although a start had been made on some of these topics in the seventeenth century , it was only in the eighteenth century that they were subjected to detailed examination, and Euler's contribution to the development of these topics, and hence to the unification of mechanics, was immense. (shrink)

There seems to exist a dilemma in the literature as to the correct relativistic formula for the Sagnac phase-shift. The paper addresses this issue in the light of a novel, kinematically equivalent linear Sagnac-type thought experiment, which provides a vantage point from which the effect of rotation in the usual Sagnac effect can be analyzed. The question is shown to be related to the so-called rotating disc problem known as the Ehrenfest paradox. The relativistic formula for the Sagnac phase-shift seems (...) to depend on the way the paradox is resolved. Kinematic resolution of the Ehrenfest paradox proposed by some authors predicts the usually quoted formula for the Sagnac delay but the resolution itself is shown to be based upon some implicit assumptions regarding the behaviour of solid bodies under acceleration. In order to have a greater insight into the problem, a second version of the thought experiment involving linear motion of a “special type” of a non-rigid frame of reference is discussed. It is shown by analogy that the usually quoted special relativistic formula for the Sagnac delay follows, provided the material of the disc matches the “special type.”. (shrink)

We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics. This result clarifies the relationship between approaches that model such bodies as distributions supported on a curve, and those that employ smooth fields supported in small neighborhoods of a curve. This result also applies to "bodies" constructed from wave packets of Maxwell or Klein-Gordon fields. There follows a simple and precise formulation of the optical limit for (...) Maxwell fields. (shrink)

Resumen En este trabajo evaluamos el impacto que la adopción de la relatividad del movimiento tiene en la metafísica de Leibniz. En particular argumentamos que el abandono de la comprensión absolutista del mismo anula su noción juvenil de sustancia corpórea. En primer lugar analizamos cómo entiende Leibniz las nociones de cuerpo y movimiento en el periodo juvenil y defendemos que la comprensión absolutista de este último constituye una piedra angular en su primera concepción de la sustancia corpórea. En segundo lugar (...) exponemos los argumentos leibnizianos a favor de la relatividad del movimiento durante el período parisino y mostramos su repercusión en el concepto juvenil de sustancia corpórea.In this paper we evaluate the impact of Leibniz's defense of relativity of motion on his metaphysics. We argue that the abandonment of the absolutist position makes void his first notion of corporeal substance. First, we analyze Leibniz's conception of body and movement in his youth and explain how the assumption of absolute motion during these years plays a role in his notion of corporeal substance. Second, we examine his arguments in favor of relativity of motion during the Parisian period and show the repercussion on his first conception of the corporeal substance. (shrink)

Through an analysis of particular sections in Proust's A la recherche du temps perdu and several pieces by Stein, I examine how their search for bodily presence fosters the development of new styles of writing as the perceptual responses of both authors override the function of the narrator. The dissertation analyzes Husserl's phenomenological ideas on motion and the body and how they are further developed in France by Merleau-Ponty. I then use their phenomenological research in order to expand (...) upon notions of physicality in both literary authors. The action of the author writing, of the body "making marks" on paper, are qualities of the physicality of writing. In Proust the visceral is a key to the mnemonic: the body 'recalls' memory to us, where we then find bodily experiences---not just images of memories, but the physical feeling of what has been and what remains physical, I demonstrate how the episodes in which Proust encounters involuntary recollection are places of physical activity; some physical presence has to occur, or some physical activity must be taking place in order for memory to become present. Stein's experiments with language are renditions of how the author makes sense of her body and the world through perception. Her language actually 'stands in' for the spoken voice of a narrator who records a world in flux rather then narrating a story. (shrink)

Introduction: sport and the event -- Ron Artest: the black body at rest (Alain Badiou) -- Eric Cantona: the body in motion (Gilles Deleuze) -- Zinedine Zidane: coup de boule (Jacques Derrida) -- Epilogue: being, event, and the philosophy of sport.

Radiationless motion of a charge distribution is reviewed, and the necessary condition conjectured by Goedecke is proved. Then it is shown that a nonrotating, uniformly charged, spherical shell (as seen from its own rest frame) which moves in a relativistically invariant fashion does not have any bounded radiationless motions, unlike its nonrelativistic counterpart.

This article explores how Plato, in his “metaphysical” dialogues, sees the specific properties of motion (and especially of motion in music), which lend themselves to adaptation for the purposes of maintaining or restoring the health of the soul. Plato explores the property of regular or rhythmic motion in particular. The attention has been drawn to the analogy between the calming effect of music, at the human level, and the Demiurge’s achievement in willing the world into existence. The (...) focus of the article lays on the Laws, in which the principle of musical motion plays a central role in resolution of the contradictions between material and spiritual, natural and physiological, medical and educative. (shrink)

Margaret Cavendish (1623-1673) argues that when someone throws a ball, their hand does not cause the ball to move. Instead, the ball moves itself. In this chapter, I reconstruct Cavendish’s argument that material things—like the ball—are self-moving. Cavendish argues that body-body interaction is unintelligible. We cannot make sense of interaction in terms of the transfer of motion nor the more basic idea that one body acts in another body. Assuming something moves bodies around, Cavendish concludes (...) that bodies move themselves. Still, Cavendish needs to explain why bodies appear to causally interact even if they do not really. Balls do not usually throw themselves without a helping hand. I offer a new reading of the way bodies respond to their external circumstances in terms of prerequisites or enabling conditions. (shrink)

Thomas Lynch, called "a cross between Garrison Keillor and William Butler Yeats" (New York Times), reminds us not only of how we die but also of how we live. "The facts of life and death remain the same. We live and die, we love and grieve, we breed and disappear. And between these existential gravities, we search for meaning, save our memories, leave a record for those who will remember us." So writes Thomas Lynch, poet and funeral director, and author (...) of the highly praised The Undertaking, winner of an American Book Award and finalist for the National Book Award, as he continues to examine the relations between the "literary and mortuary arts." The essays assembled here explore the human condition at the intersection of millennia, beleaguered by choices and changes, encumbered by merger and acquisition, numbed by maths and technologies, in search of the meaning of life and time, our lives and times. Lynch tenders life and times--sextons, muckrakers, clergy, caskets, condoms, loved poems, a hated cat, the mall, Main Street. In an age that seeks to define human experience in retail, high-tech, or pop-psyche terms, these essays speak to the existentials: between being human and ceasing to be, between birth and death, we are bodies in motion and at rest. (shrink)

The concept of rigid reference frame and of constricted spatial metric, given in the previous work [Class. Quantum Grav. 21, 3067 (2004)] are here applied to some specific space-times: in particular, the rigid rotating disc with constant angular velocity in Minkowski space-time is analyzed, a new approach to the Ehrenfest paradox is given as well as a new explanation of the Sagnac effect. Finally the anisotropy of the speed of light and its measurable consequences in a reference frame (...) co-moving with the Earth are discussed. (shrink)

There is considerable debate among scholars over whether Descartes allowed for genuine body–body interaction. I begin by considering Michael Della Rocca’s recent claim that Descartes accepted such interaction, and that his doctrine of the creation of the eternal truths indicates how this interaction could be acceptable to him. Though I agree that Descartes was inclined to accept real bodily causes of motion, I differ from Della Rocca in emphasizing that his ontology ultimately does not allow for them. (...) This is not the end of the story, however, since two of Descartes’s successors offered incompatible ways of developing his conflicted account of motion. I contrast the occasionalist view of Nicolas Malebranche that changes in motion derive directly from divine volitions with the non-occasionalist claim of Pierre-Sylvain Regis that such changes derive from a nature distinct from God. In light of Della Rocca’s interpretation, it is noteworthy that the issue of eternal truths is relevant to both alternative accounts. Indeed, Regis took the doctrine that such truths are created to provide crucial support for his alternative to an occasionalist account of body–body interaction. What does not help Della Rocca, however, is that Regis’s view of motion requires a fundamental revision of Descartes’s ontology. Author Keywords: Descartes; Malebranche; Regis; Causation; Motion; Eternal Truths. (shrink)

This study focuses on the physical expressions and intensity of embodiment that occur in the Ironman Triathlon. More specifically, the study investigates the transformational bodily experiences taking place during Ironman competitions. Using an ethnographic approach, a total of 29 Ironman triathletes participated in the study (15 men and 14 women). Theoretically, the article focuses on how triathletes’ bodies ‘move’ between different forms of embodiment. The results show that, in the process of disciplining the body, the athletes reconceptualized feelings of (...) pain, nausea and even disgust, making these emotionally expressive aspects of the corpus into a part of the experience and bending them towards the pleasure of reaching potential divinity. Situated in a long tradition of philosophical and sociological explorations of the transgressing and transcending body, the study interprets and understands the performing body as a site for change and utopian possibilities. Thus the study adds to existing debates on contemporary individuals’ exploration of the existential and corporeal dimensions of modernity. (shrink)

In this essay, the author sets out the question: where bodies move according to Spinoza's physical thought? The question is linked to another one Oldenberg asked him then, about how objects acquire their unique individuality and the way nature behaves as a unit, despite the complexity of its constitution. The response refers not only to Spinoza's criticism to Cartesian mechanics, as usual, but will appeal to Spinoza's own interpretation, consistent with his system, about the constitution and dynamics of the physical (...) world, in terms of a mechanic interaction between bodies, firm enough to accomplish the task for which it was designed. (shrink)

This article, which seeks to connect philosophy, polite culture, and the Enlightenment, shows how Malebranche’s Cartesian science presented a full-frontal attack on the worldly notion of a good taste aligned with reason. It did this by arguing that the aesthetic tastes that people experience were the result of mechanically-transmitted sensations that, like all physical sensations, were inaccurate, erroneous and relativistic. The mechanics of this process is explored in detail to show how Malebranche was challenging honnête thinking. The article suggests that (...) Malebranche’s demystifying approach was at once a hallmark of the Enlightenment, and that his views would ironically come to inform much Enlightenment thought about taste in ways he would have despised. (shrink)

The traditional (Leibnizian) reading of Descartes on mind-body interaction is given a more rigorous reformulation, explaining how Descartes could assert that the mind while not affecting the quantity of motion in the world could change its direction. It is shown, contrary to the trend in recent literature, that this reading has a reliable textual base, and it is argued that it attributes to Descartes a philosophical position of more substance and interest. The kind of interpretation favored depends on (...) the status that the reader attributes to the assertion of the causal closer of the material world. (shrink)

This essay argues that moral self-cultivation as described in the Confucian tradition involves the cultivation of the body. Preparing the body in certain ways, perhaps by making it healthy, is a necessary part of moral self-cultivation. This claim includes: (a) nourishing the body in a proper way is a first step in moral self-cultivation, and the bodily care is instrumentally valuable to one’s flourishing life; (b) making and keeping a healthy body is partly constitutive of a (...) moral well-being and hence bodily care is also intrinsically valuable to a flourishing life. This perspective on embodied virtue is established through a discussion of qi. The body as the storehouse of qi is not only a passive reservoir of knowledge that serves as moral guidance, but also actively plays an indispensable and integral role in activities related to one’s moral transformation. A well-cared for body provides a moral agent with the temporal and spatial possibility for moral refinement and an enhanced good life. (shrink)