It is nearly impossible to open a textbook on Newtonian mechanics without encountering the concept of inertial frames: the frames that are privileged by the theory’s dynamics. In this paper, I argue that extant definitions of inertial frames are unsatisfactory. I criticise two common definitions of inertial frames: law-based definitions, according to which inertial frames are simply those in which the laws are true, and structure-based definitions, according to which inertial frames are those that are ‘adapted’ to spatiotemporal structure. I (...) then offer a new, symmetry-based definition of inertial frames. This definition offers a non-conventional way of specifying the dynamically privileged frames. The result clarifies the foundations of Newtonian mechanics and accounts for the empirical success of coordinate-dependent formulations of it. (shrink)

A salient feature of de Broglie-Bohm quantum theory is that particles have determinate positions at all times and in all physical contexts. Hence, the trajectory of a particle is a well-defined concept. One then may expect that the closely related notion of inertial trajectory is also unproblematically defined. I show that this expectation is not met. I provide a framework that deploys six different ways in which dBB theory can be interpreted, and I state that only in the canonical interpretation (...) the concept of inertial trajectory is the customary one. However, in this interpretation the description of the dynamical interaction between the pilot-wave and the particles, which is crucial to distinguish inertial from non-inertial trajectories, is affected by serious difficulties, so other readings of the theory intend to avoid them. I show that in the alternative interpretations the concept at issue gets either drastically altered, or plainly undefined. I also spell out further conceptual difficulties that are associated to the redefinitions of inertial trajectories, or to the absence of the concept. (shrink)

Au XVIIème siècle, c’est la découverte du principe d’inertie, un concept purement physique, qui permit de débloquer la théorisation du mouvement, en panne depuis Aristote. La plupart des philosophes et historiens des sciences caractérisent le tournant de la « science moderne » par sa mathématisation, arguant, comme Koyré, que le principe d’inertie découlerait de cette dernière, ou bien, comme Duhem, qu’il était déjà contenu dans l’impetus médiéval, ou encore, comme, Husserl et Kojève, en s’abstenant d’en parler. Et pourtant, la mathématisation (...) de la physique était en marche depuis l’époque hellénistique. L’originalité de Galilée est d’avoir mathématisé non pas la nature, mais, via le principe d’inertie, le temps. (shrink)

Le principe d’inertie constitue la loi fondamentale qui a permis à la nouvelle physique du XVIIe siècle de construire son édifice en s’opposant aux explications scolastiques des phénomènes physiques. Tant Descartes que Spinoza ont proposé des démonstrations de cette loi physique en l’intégrant chacun dans son propre système philosophique. Spinoza dans ses Principes de la philosophie de Descartes propose même implicitement une critique de la démonstration cartésienne. Nous analysons cette critique dans la première partie de cet article et dans la (...) suite nous proposons une lecture de la manière dont Spinoza déduit le principe d’inertie dans l’Éthique. Comme ce principe présente quant à son énoncé et quant à sa conceptualisation des affinités avec la théorie du conatus de la troisième partie de l’Éthique, cet article met en valeur la relation de ces deux parties du système et tire de leur confrontation quelques conclusions concernant le statut et la place de la physique dans la philosophie de Spinoza. (shrink)

I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to ``explain'' inertial motion. I argue that there is a sense in which both theories may be understood to explain inertial motion, but that the sense of ``explain'' is rather different from what one might have expected. This sense of explanation is (...) connected with a view of theories---I call it the ``puzzleball view''---on which the foundations of a physical theory are best understood as a network of mutually interdependent principles and assumptions. (shrink)

We present an approach to understanding the origin of inertia involving the electromagnetic component of the quantum vacuum and propose this as a step toward an alternative to Mach's principle. Preliminary analysis of the momentum flux of the classical electromagnetic zero-point radiation impinging on accelerated objects as viewed by an inertial observer suggests that the resistance to acceleration attributed to inertia may be at least in part a force of opposition originating in the vacuum. This analysis avoids the ad hoc (...) modeling of particle-field interaction dynamics used previously by Haisch, Rueda, and Puthoff (Phys. Rev. A 49, 678, (1994)) to derive a similar result. This present approach is not dependent upon what happens at the particle point, but on how an external observer assesses the kinematical characteristics of the zero-point radiation impinging on the accelerated object. A relativistic form of the equation of motion results from the present analysis. Its manifestly covariant form yields a simple result that may be interpreted as a contribution to inertial mass. We note that our approach is related by the principle of equivalence to Sakharov's conjecture (Sov. Phys. Dokl. 12, 1040, (1968)) of a connection between Einstein action and the vacuum. The argument presented may thus be construed as a descendant of Sakharov's conjecture by which we attempt to attribute a mass-giving property to the electromagnetic component—and possibly other components—of the vacuum. In this view the physical momentum of an object is related to the radiative momentum flux of the vacuum instantaneously contained in the characteristic proper volume of the object. The interaction process between the accelerated object and the vacuum (akin to absorption or scattering of electromagnetic radiation) appears to generate a physical resistance (reaction force) to acceleration suggestive of what has been historically known as inertia. (shrink)

Eleanor Knox has argued that our concept of spacetime applies to whichever structure plays a certain functional role in the laws. I raise two objections to this inertial functionalism. First, it depends on a prior assumption about which coordinate systems defined in a theory are reference frames, and hence on assumptions about which geometric structures are spatiotemporal. This makes Knox’s account circular. Second, her account is vulnerable to several counterexamples, giving the wrong result when applied to topological quantum field theories (...) and parity- and time-asymmetric theories. I advance an alternative account on which our spacetime concept is a cluster concept. On this view, the notion of metaphysical fundamentality may feature in the cluster, in which case spacetime functionalism may be uninformative in the absence of answers to fundamental metaphysical questions like the substantivalist/relationist debate. (shrink)

A “frame of reference” is a standard relative to which motion and rest may be measured; any set of points or objects that are at rest relative to one another enables us, in principle, to describe the relative motions of bodies. A frame of reference is therefore a purely kinematical device, for the geometrical description of motion without regard to the masses or forces involved. A dynamical account of motion leads to the idea of an “inertial frame,” or a reference (...) frame relative to which motions have distinguished dynamical properties. For that reason an inertial frame has to be understood as a spatial reference frame together with some means of measuring time, so that uniform motions can be distinguished from accelerated motions. The laws of Newtonian dynamics provide a simple definition: an inertial frame is a reference-frame with a time-scale, relative to which the motion of a body not subject to forces is always rectilinear and uniform, accelerations are always proportional to and in the direction of applied forces, and applied forces are always met with equal and opposite reactions. It follows that, in an inertial frame, the center of mass of a system of bodies is always at rest or in uniform motion. It also follows that any other frame of reference moving uniformly relative to an inertial frame is also an inertial frame. For example, in Newtonian celestial mechanics, taking the “fixed stars” as a frame of reference, we can determine an inertial frame whose center is the center of mass of the solar system; relative to this frame, every acceleration of every planet can be accounted for as a gravitational interaction with some other planet in accord with Newton 's laws of motion. (shrink)

It is suggested that the mathematically abstract coordinate frames of reference commonly visualized to be centered at the celestial bodies have real counterparts in the shape of well-defined rigid spatial resonant singularities of infinite extension, which accommodate the matter waves from the superimposition of which the body residing at the coordinate origin results. A universally valid inertial reference frame system is proposed. Qualitative explanations are offered for the inertial and gravitational forces, their observed proportionality, and for the occurrence of second-order (...) gravitational effects in the vicinity of massive bodies. The universal redshift is assumed to result from a closure condition of the eigenspaces introduced. (shrink)

This paper addresses two objections raised against anomalous monism. Firstly, on the basis of Davidson's assertion that all causal relations fall under strict laws, many critics conclude mental properties are causally inert since they are non-nomic. I argue that this conclusion follows only on the further assumption that all causally efficacious properties are nomic properties. It is perfectly consistent, however, to hold that there is a law covering each causal relation without each causal statement being the instantiation of a law. (...) Secondly, I countervail Kim's claim that the only option open to the physicalists is reductionism by showing how weak supervenience preserves both the dependence of the mental on the physical and the irreducibility of mental explanations to physical ones. (shrink)

The history of mechanics has been extensively investigated in a number of historical works. The full story from the Greeks and medievals through the Scientific Revolution to the modern era is long and complex. But it is also incomplete. Studies to date have been admirably thorough in putting empirical discoveries into proper perspective and in making clear the great importance of mathematical innovations. But there has been surprisingly little regard for the role of thought experiments in the development of mechanics. (...) We attempt to rectify this, at least in part. After a brief account of Greek ideas of space and motion, we focus on late medieval and early modern physics, especially the development of inertial motion. In particular, we examine the thought experiments of Buridan, Oresme, and Galileo, which did so much to undermine Aristotle’s account of motion and lead the way to the modern concept of inertia. (shrink)

It is no inconsiderable endeavor to undertake a philosophical analysis of the notions of inertia and absolute space from Newton to Einstein. This is all the more so insofar as Ghins' approach is far from the orthodoxy of the logical empiricists: his claim is that the scientists themselves were seeking to attribute the effects of inertia to real causes, or, in other words, "to specify adequately the system or systems of reference relative to which motions, whether accelerated or not, would (...) give rise or not to such effects". In terms of this causal point of view, he then defines the fundamental question as that of the determination of the inertial or noninertial character of a motion or of a reference system. (shrink)

The usual macroscopic theory of relativistic mechanics and electromagnetism is formulated so that all assumptions but one are consistent with both special relativity and Newtonian mechanics, the distinguishing assumption being that to any energyE, whatever its form, there corresponds an inertial massE/c 2 . The speed of light enters this formulation only as a consequence of the inertial equivalent of energy1/c 2 . While, for1/c 2 >0 the resulting theory has symmetry under the Poincaré group, including Lorentz transformations, all its (...) physical consequences can be derived and tested in any one inertial frame. In particular, an account is given in one inertial frame for the dynamic causes of relativistic effects for simple accelerated clocks and roads. (shrink)

The concept of inertial frame of reference in classical physics and special theory of relativity is analysed. It has been shown that this fundamental concept of physics is not clear enough. A definition of inertial frame of reference is proposed which expresses its key inherent property. The definition is operational and powerful. Many other properties of inertial frames follow from the definition, or it makes them plausible. In particular, the definition shows why physical laws obey space and time symmetries and (...) the principle of relativity, it resolves the problem of clock synchronization and the role of light in it, as well as the problem of the geometry of inertial frames. (shrink)

We present a fully relational definition of inertial systems based in the No Arbitrariness Principle, that eliminates the need for absolute inertial frames of reference or distinguished reference systems as the ``fixed stars'' in order to formulate Newtonian mechanics. The historical roots of this approach to mechanics are discussed as well. The work is based in part in the constructivist perspective of space advanced by Piaget. We argue that inertial systems admit approximations and that what is of practical use are (...) precisely such approximations. We finally discuss a slightly larger class of systems that we call ``relatively inertial'' which are the fundamental systems in a relational view of mechanics. (shrink)

In the context of a particular framework of emergent quantum mechanics, it is argued the emergent origin of the inertial mass of a physical system. Two main consequences of the theory are discussed: an emergent interpretation of the law of inertia and a derivation of the energy-time uncertainty relation.

In this article I propose to understand inertia in art as a “disposition to meaning”. I compare inertia in art with that of a face of a person recently deceased. To acquaintances, i.e. to family and friends, it holds a promise of memories (of the deceased); to all the others the corpse offers the possibility of a projection of meanings. Art is made of plain, or extra-ordinary stuff, which is turned into artistic material. The artist is to bring the inert (...) potency of stuff to artistic life, and to turn it into something that is expressive. If she is successful, then the work will offer its audience a concentrated, absorbing experience. Art is autonomous in that the aimed for experience is morally neutral. In the view of many contemporary artists, such experiences fail art’s deeper significance: absorbing experiences are, simply, too easy. If artists want to really move the audience (to emotion), or so they feel, they should also move the audience into action. Wanting to achieve this is not just difficult; it is a paradox. (shrink)

This paper enquires into a paradigmatic change concerning the concept of motion: from a phenomenological conception of motion understood as a continuous and finite process of translation, to a physical conception of motion as rectilinear, uniform and continuous, that is, as an inertial state that if unhindered, can extend infinitely – the former held by Aristotle, the latter by Koyré, a shift that is evidenced by their contrasting treatment of Zeno’s paradoxes. I argue that both ontologies of motion can be (...) understood in phenomenological terms: Motion is accomplished by the real itself. However, while Aristotle’s continuous motion as actualization of the form of a given body involves its formal determination and constitution of sense, Koyré’s conceives of motion and rest as kinds of being and motion itself as exemplifcation of the mathematization of nature that Husserl described in the Crisis. Taken together, these changes presuppose a transformation of metaphysical and epistemic frameworks. (shrink)

From late 1684 through mid-1685, Isaac Newton turned to developing and refining the conceptual foundations presupposed by his emerging physics. Analysis of his manuscripts from this period reveals that Newton’s understanding of the relativity of acceleration led him to seek a spatiotemporally invariant quantity of matter. He found two such quantities and then designed an experiment to discover their relationship. Interpreting the experiment, however, required distinguishing a new notion of force. Others have recognized the conceptual distinction between inertial and gravitational (...) mass. I show here that Newton clearly saw this distinction and that he provisionally established their equivalence. (shrink)

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each (...) non-inertial coordinate frame has its own vacuum state. In particular, there is a distinction between the “Minkowski vacuum” for a box at rest in an inertial frame and a “Rindler vacuum” for an accelerating box which has fixed spatial coordinates in an (accelerating) Rindler frame. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. The behavior of classical zero-point radiation in a noninertial frame is found by tensor transformations and still depends only upon the geodesic separations, now expressed in the non-inertial coordinates. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. The classical analysis gives no grounds for the “heating effects of acceleration through the vacuum” which appear in the literature of quantum field theory. Thus this distinction provides (in principle) an experimental test to distinguish the two theories. (shrink)

Previous studies have shown that the motion intention recognition for lower limb prosthesis mainly focused on the identification of performed gait. However, the bionic prosthesis needs to know the next movement at the beginning of a new gait, especially in complex operation environments. In this paper, an upcoming locomotion prediction scheme via multilevel classifier fusion was proposed for the complex operation. At first, two motion states, including steady state and transient state, were defined. Steady-state recognition was backtracking of a completed (...) gait, which would be used as prior knowledge of motion prediction. In steady-state recognition, surface electromyographic and inertial sensors were fused to improve recognition accuracy; five typical locomotion modes were recognized by random forest classifier with over 97.8% accuracy. The transient state was defined as an observation period at the initial stage of upcoming movement, in which only the sEMG signal was recorded due to the limitation of sliding window length. LightGBM classifier was validated to outperform other methods in the accuracy and prediction time of transient-state recognition. Finally, a simplified HMM model based on prior knowledge and observation result was constructed to predict upcoming locomotion. The results indicated that the locomotion prediction was over 91% accuracy. The proposed scheme implements the locomotion prediction at the initial stage of each gait and provides critical information for the gait control of lower limb prosthesis. (shrink)

In a way similar to classical mechanics where we have the concept of inertial time as expressed in the motions of bodies, in the theory of relativity we can regard the inertial time as the only notion of time at play. The inertial time is expressed also in the propagation of light. This gives rise to a notion of clock—the light clock, which we can regard as a notion derived from the inertial time. The light clock can be seen as (...) a solution of the theory, which complies with the requirement that a clock to be so must have a rate that is independent from its past history. Contrary to Einstein’s view, we do not need the concept of “clock” as an independent concept. This implies, in particular, that we do not need to rely on the notions of atomic clock or atomic time in the theory of relativity. (shrink)

Le présent essai se propose d'appréhender la doctrine cartésienne selon laquelle ce qui existe ne saurait subsister sans que Dieu le soutienne dans l'être par une activité créatrice continuée. Comment Dieu soutient-il l'existence et pourquoi lui est-il nécessaire de le faire ? L'auteur analyse l'apparente contradiction, qui fait problème, entre la doctrine de la création continuée et l'affirmation par Descartes que le mouvement se poursuit à moins que n'intervienne quelque force extérieure. Il examine ensuite, pour la récuser, la thèse (défendue (...) par Gilson et par Gueroult) selon laquelle la doctrine de la création continuée impliquerait la discontinuité du temps. This essay seeks to understand Descartes's doctrine that what exists cannot continue to exist unless God sustains it by continuous creative activity. How does God sustain existence and why is it necessary for Him to do this ? The essay explores a puzzling apparent contrast between the doctrine of continuous creation and Descartes's claim that motion continues unless an external force interferes. Further, it considers and rejects the thesis (maintained by Gilson and Gueroult) that the doctrine of continuous creation entails that time is discontinuous. (shrink)

”The last remnant of physical objectivity of space-time” is disclosed in the case of a continuous family of spatially non-compact models of general relativity. The physical individuation of point-events is furnished by the autonomous degrees of freedom of the gravitational field, which represent -as it were -the ontic part of the metric field. The physical role of the epistemic part is likewise clarified as embodying the unavoidable non-inertial aspects of GR. At the end the philosophical import of the Hole Argument (...) is substantially weakened and in fact the Argument itself dis-solved, while a specific four-dimensional holistic and structuralist view of space-time emerges, including elements common to the tradition of both substantivalism and relationism. The observables of our models undergo real temporal change: this gives new evidence to the fact that statements like the frozen-time character of evolution, as other ontological claims about GR, are model dependent. (shrink)

I explain and assess here Huygens’ concept of relative motion. I show that it allows him to ground most of the Law of Inertia, and also to explain rotation. Thereby his concept obviates the need for Newton’s absolute space. Thus his account is a powerful foundation for mechanics, though not without some tension.

We present a novel method, called graph sparse nonnegative matrix factorization, for dimensionality reduction. The affinity graph and sparse constraint are further taken into consideration in nonnegative matrix factorization and it is shown that the proposed matrix factorization method can respect the intrinsic graph structure and provide the sparse representation. Different from some existing traditional methods, the inertial neural network was developed, which can be used to optimize our proposed matrix factorization problem. By adopting one parameter in the neural network, (...) the global optimal solution can be searched. Finally, simulations on numerical examples and clustering in real-world data illustrate the effectiveness and performance of the proposed method. (shrink)

Cette étude examine la philosophie naturelle de Nicolas Malebranche et son devenir au cours du XVIIIe siècle. Des savants énoncent ou discutent des principes, des lois et des méthodes explicatives dont l'origine est à chercher dans De la recherche de la vérité. La présence de Malebranche se manifeste alors par un occasionnalisme physique et par une critique de la force des corps au repos de Descartes, ce qui conduit à une conception nomologique de la causalité et à un rejet de (...) la force d'inertie, et par une interprétation des phénomènes physico-chimiques à l'aide de la théorie des petits tourbillons. Malebranche est ainsi à l'origine d'une des formes prises par la philosophie mécanique dont ce livre établit les caractéristiques essentielles."--Page 4 of cover. (shrink)