In the metaphor of behavioral momentum, the rate of a free operant in the presence of a discriminative stimulus is analogous to the velocity of a moving body, and resistance to change measures an aspect of behavior that is analogous to its inertial mass. An extension of the metaphor suggests that preference measures an analog to the gravitational mass of that body. The independent functions relating resistance to change and preference to the conditions of reinforcement may be construed (...) as convergent measures of a single construct, analogous to physical mass, that represents the effects of a history of exposure to the signaled conditions of reinforcement and that unifies the traditionally separate notions of the strength of learning and the value of incentives. Research guided by the momentum metaphor encompasses the effects of reinforcement on response rate, resistance to change, and preference and has implications for clinical interventions, drug addiction, and self-control. In addition, its principles can be seen as a modern, quantitative version of Thorndike's (1911) Law of Effect, providing a new perspective on some of the challenges to his postulation of strengthening by reinforcement. Key Words: behavioral momentum; clinical interventions; drug addiction; preference; reinforcement; resistance to change; response strength; self-control. (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)

Pérez Laraudogoitia (1996) presented an isolated system of infinitely many particles with infinite total mass whose total classical energy and momentum are not necessarily conserved in some particular inertial frame of reference. With a more generalized model Atkinson (2007) proved that a system of infinitely many balls with finite total mass may evolve so that its total classical energy and total relativistic energy and momentum are not conserved in any inertial frame of reference, and yet concluded (...) that its total classical momentum is necessarily conserved. Contrary to this conclusion of Atkinson, I show that Atkinson's model has a solution in which the total momentum fails to be conserved in every inertial frame of reference. This result, combined with Atkinson's, demonstrates that both classical and relativistic mechanics allow the energy and momentum of a system of infinitely many components to fail to be conserved in every inertial frame of reference. (shrink)

This paper considers questions of continuity and change in education from the perspective of complexity theory, introducing the field to educationists who might not be familiar with it. Given a significant degree of complexity in a particular environment , new properties and behaviours, which are not necessarily contained in the essence of the constituent elements or able to be predicted from a knowledge of initial conditions, will emerge. These concepts of emergent phenomena from a critical mass, associated with notions of (...) lock‐in, path dependence, and inertial momentum, suggest that it is in the dynamic interactions and adaptive orientation of a system that new phenomena, new properties and behaviours, emerge. The focus thus shifts from a concern with decontextualised and universalised essence to contextualised and contingent complex wholes. This is where complexity theory seeks the levers of history. The paper posits the notion of inertial momentum as the conceptual link between the principle of emergent phenomena as developed principally in the natural sciences and the notion of socio‐historical change in human society. It is argued that educational and institutional change is less a consequence of effecting change in one particular factor or variable, and more a case of generating momentum in a new direction by attention to as many factors as possible. Complexity theory suggests, in other words, that what it might take to change a school's inertial momentum from an ethos of failure is massive and sustained intervention at every possible level until the phenomenon of learning excellence emerges from this new set of interactions among these new factors, and sustains itself autocatalytically. The paper concludes with a summary consideration of the conditions that contribute to the emergence of new properties and behaviours in a system. (shrink)

This paper considers questions of continuity and change in education from the perspective of complexity theory, introducing the field to educationists who might not be familiar with it. Given a significant degree of complexity in a particular environment (or ‘dynamical system’), new properties and behaviours, which are not necessarily contained in the essence of the constituent elements or able to be predicted from a knowledge of initial conditions, will emerge. These concepts of emergent phenomena from a critical mass, associated with (...) notions of lock‐in, path dependence, and inertial momentum, suggest that it is in the dynamic interactions and adaptive orientation of a system that new phenomena, new properties and behaviours, emerge. The focus thus shifts from a concern with decontextualised and universalised essence to contextualised and contingent complex wholes. This is where complexity theory seeks the levers of history. The paper posits the notion of inertial momentum as the conceptual link between the principle of emergent phenomena as developed principally in the natural sciences and the notion of socio‐historical change in human society. It is argued that educational and institutional change is less a consequence of effecting change in one particular factor or variable, and more a case of generating momentum in a new direction by attention to as many factors as possible. Complexity theory suggests, in other words, that what it might take to change a school's inertial momentum from an ethos of failure is massive and sustained intervention at every possible level until the phenomenon of learning excellence emerges from this new set of interactions among these new factors, and sustains itself autocatalytically. The paper concludes with a summary consideration of the conditions that contribute to the emergence of new properties and behaviours in a system. (shrink)

Max Jammer’s recent book, Concepts of Simultaneity: From Antiquity to Einstein and Beyond, traces the history of our ideas on simultaneity as they evolved alongside sweeping changes in our understanding of physics. One of the interesting lessons of the book is that, even as our physical theories have become increasingly successful, the question of the proper understanding or interpretation of those theories remains extremely puzzling. The central issue is this: Is the simultaneity of events a real feature of the world? (...) Or does it depend on the particular choice of reference frame, with any such frame as good as any other? In ancient times, Jammer suggests, most people took the notion of simultaneity for granted: Two events were simultaneous if they happened at the same time. Simultaneity was considered an objective feature of the world. This simple idea appeared con rmed by classical Newtonian mechanics. In Newtonian physics different inertial reference frames (ones that move at a constant velocity relative to one another) are equally good (the laws of motion hold in all of them), even though some attributes of an object, say velocity or momentum, differ from one reference frame to another. However, some features, such as simultaneity, hold in all allowable reference frames and are thus frame independent and in some sense more objective. But what if two events whose simultaneity is in question took place far from each other? How would you know whether they were simultaneous? One solution (available for the last few centuries anyway) is for the observers of each event to look at their (previously synchronized) clocks. The question then becomes, How can clocks that are distant from one.. (shrink)

The energy-momentum relationship is obtained in para-Lorentzian dynamics. It is shown that the well-known correspondence rule for the operators energy and momentum holds in any inertial system if it is assumed to hold in the preferred reference frame. The new Dirac equation is obtained. Some qualitative features of the new theory are given; one of then is the spontaneous appearance of conserved-vector and nonconserved-axial weak currents. Finally one evaluates the convenience of further developments of the present theory (...) in view of the excellent agreement of QED with experiment. (shrink)

As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the energy-momentum tensor associated with non-interacting matter is covariantly divergence-free, in connection with such theorems. I argue that the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories. (...) I conclude by discussing what it means to posit a certain spacetime geometry and the relationship between that geometry and the dynamical properties of matter. (shrink)

The introduction of an “elementary length”a representing the ultimate limit for the smallest measurable distance leads to a generalization of Einstein's energy-momentum relation and of the usual Lorentz transformation. The value ofa is left unspecified, but is found to be equal tohc/2E u, whereE u is the total energy content of our universe. Particles of zero rest mass can only move at the velocityc of light in vacuum, while material bodies can move slower or faster than light, whena≠0, without (...) violating the principle of causality. The laws of relativistic mechanics are actually generalized so that they include Mach's principle, since it is found that the universe as a whole can only be in a state of rest for any particular inertial observer. (shrink)

We considered peculiarities of the evolution of a region with sharp boundaries that is filled with a partially ionized plasma and is a part of the volume of a condensed target. The creation of such a region in the near-surface layer of the target can be related to the action of an external impulse symmetric ionizator or to the action of an intense small-extension shock wave on the target surface. We defined the conditions such that their fulfilment during the establishment (...) of the equilibrium between the Coulomb attraction of electrons and ions with atom ionization multiplicity Z* 1 and the kinetic pressure of electrons causes both the compression of this region and its ionization to the state with Z* 2 > Z* 1. The last leads to a further additional compression and ionization. Under these conditions, the spontaneous avalanche-like ionization of atoms of the target to the state of ‘‘bare’’ nuclei occurs synchronously with the avalanche-like metallization and the self-compression of the target. We showed that the avalanche-like ionization and the self-compression of the target happen in the case where the gas of degenerate electrons has drift momentum. If the region with initial ionization has the form of thin spherical layer, the process of avalanche-like ionization and self-compression of the target in this region is accompanied by the accelerated movement of the plasma layer to the target center. One of the reasons for the accelerated movement is the surface tension in a bounded domain of the nonequilibrium plasma layer neutralized by ions of the target. With increase in the velocity of movement of this layer to the target center, the additional self-compression of the system of electrons and nuclei to the state of degenerate electron gas occurs. At the leading edge of the running layer with extremely high electron density which is neutralized by nuclei of the target, the formation of a collapse of the electron--nucleus system proceeds, and the binding energy maximum for the electron--nucleus system shifts from A≈60 to A ≫ 60. This result makes possible the fast synthesis of superheavy nuclei. The decay of the collapse state, a partial restoration of the target structure, its rapid cooling, and the condensation of a part of the products of nuclear reactions happen in the target volume at the trailing edge of the moving plasma layer. Upon such a scanning propagation of the wave with high electron density, all the target substance is involved, step-by-step, to the process of nuclear transformations. At the target center, the moving plasma layer is squeezed with the formation of the state of quasistationary collapse under inertial confinement. Then the collapse state decays irreversibly. (shrink)

This dissertation elucidates the notion of physical system which opens new conceptual pathways that connect the three realms of physical theory; spacetime, material bodies and their properties, and the laws of nature which govern their evolution. The notion of physical system includes two presuppositions regarding their structure. The first presupposition is a description of isolated systems and their evolution in time, which amounts to a Paradigm of Uniform Motion. The second presupposition describes how parts of a physical system are combined (...) into wholes. This presupposition amounts to a Rule of Composition. Once we make these presuppositions explicit we can derive the spacetime structures and the fundamental equations of motion. "Newtonian" and "relativistic" systems are shown to differ with respect to the paradigm of uniform motion, a difference that leads to the respective structures of Newtonian mechanics and the Special Theory of Relativity. ;The philosophical framework offered in this dissertation provides a new interpretation of the concept of mass, and a new elucidation of the relation between the conservations of mass and momentum. Previous analyses of the concept have claimed that "mass" cannot be defined and broken down to more primitive predicates. The framework offered here, on the other hand, enables the systematic reduction of the concept of mass to motions and the presuppositions we have regarding the nature of physical systems. The new interpretation of mass reveals a surprising connection between mass and inertial reference frames, as they are both shown to be derived, in a similar way, from our definition of physical systems. Mass is by necessity attributed to bodies in virtue of the frame we use to describe their motions. This account also enables us to understand the different conceptual roles of mass and their interconnections. In the context of Newtonian mechanics, the roles of mass as a Quantity of Matter, as the Inertial property of bodies, and as Gravitational mass are shown to be various aspects of a single role the concept has in the new framework offered here. In the context of the Special Theory of Relativity, rest mass and relativistic mass are similarly analyzed as consequences of our presuppositions regarding physical systems. (shrink)

This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called "Hole Argument" in general relativity. Such achievements include: 1) the analysis of the "Hole" phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the "weak" ADM energy; 2) a re-interpretation of "active" diffeomorphisms as "passive and metric-dependent" (...) dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (up to now unknown) connection to gauge transformations on-shell; understanding such connection also enlightens the real content of the Hole Argument or, better, dis-solves it together with its alleged "indeterminism"; 3) the utilization of the Bergmann-Komar "intrinsic pseudo-coordinates", defined as suitable functionals of the Weyl curvature scalars, as tools for a peculiar gauge-fixing to the super-hamiltonian and super-momentum constraints; 4) the consequent construction of a "physical atlas" of 4-coordinate systems for the 4-dimensional "mathematical" manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent "Dirac observables"). Such construction embodies the "physical individuation" of the points of space-time as "point-events", independently of the presence of matter, and associates a "non-commutative structure" to each gauge fixing or four-dimensional coordinate system; 5) a clarification of the multiple definition given by Peter Bergmann of the concept of "(Bergmann) observable" in general relativity. This clarification leads to the proposal of a "main conjecture" asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). A by-product of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) "change" in the observable quantities of general relativity. 6) a clarification of the physical role of Dirac and gauge variables as their being related to "tidal-like" and "inertial-like" effects, respectively. This clarification is mainly due to the fact that, unlike the standard formulations of the equivalence principle, the Hamiltonian formalism allows to define notion of "force" in general relativity in a natural way; 7) a proposal showing how the physical individuation of point-events could in principle be implemented as an experimental setup and protocol leading to a "standard of space-time" more or less like atomic clocks define standards of time. We conclude that, besides being operationally essential for building measuring apparatuses for the gravitational field, the role of matter in the non-vacuum gravitational case is also that of "participating directly" in the individuation process, being involved in the determination of the Dirac observables. This circumstance leads naturally to a peculiar new kind of "structuralist" view of the general-relativistic concept of space-time, a view that embodies some elements of both the traditional "absolutist" and "relational" conceptions. In the end, space-time point-events maintain a "peculiar sort of objectivity". Some hints following from our approach for the quantum gravity programme are also given. (shrink)

In the history of Newtonian Mechanics physicists and astronomers did not rely on so-called inertial frames, indeed they were not able to identify such frames. So the usual neo-Newtonian formalism of Newtonian Mechanics contains some superfluous components. In the present paper I will formulate a formal system for classical particle mechanics in Leibnizian space-time, where a relation, a counterpart of the second law of motion, between force on bodies and derivative of their momentum will be defined relative to (...) every, inertial or not, reference frame. And I will present a view that in the research process under Newtonian mechanics the accumulation of those models of the relation that satisfied some realistic conditions determined an additional structure of non-rotating frames to Leibnizian space-time. (shrink)

Localised configurations of the free electromagnetic field are constructed, possessing properties of massive, spinning, relativistic particles. In an inertial frame, each configuration travels in a straight line at constant speed, less than the speed of lightc, while slowly spreading. It eventually decays into pulses of radiation travelling at speedc. Each configuration has a definite rest mass and internal angular momentum, or spin. Each can be of “electric” or “magnetic” type, according as the radial component of the magnetic or (...) electric field vanishes in the rest frame, and each has an “antiparticle.” Any such configuration, of electric or magnetic type, is characterized in part by a set of labels (κ, ω0, σ,l, m), where ω0 is the mean of the angular frequencies of the plane waves making up the configuration, σ is the variance of those frequencies, κ is a positive constant with dimensions of action, andl, m are angular momentum “quantum numbers” withl a positive integer andm an integer such that ‖m‖≤l. The rest energy of the “particle” is κω0, its spin is κ ‖m‖, and its lifetime is of the order of 1/σ. Its antiparticle has ω0 replaced by −ω0. (shrink)

The question of the cause of inertial reaction forces and the validity of “Mach's principle” are investigated. A recent claim that the cause of inertial reaction forces can be attributed to an interaction of the electrical charge of elementary particles with the hypothetical quantum mechanical “zero-point” fluctuation electromagnetic field is shown to be untenable. It fails to correspond to reality because the coupling of electric charge to the electromagnetic field cannot be made to mimic plausibly the universal coupling (...) of gravity and inertia to the stress-energy-momentum (i.e., matter) tensor. The gravitational explanation of the origin of inertial forces is then briefly laid out, and various important features of it explored in the last half-century are addressed. (shrink)

In this paper an attempt is made to interpret inertial mass as a consequence of the invariant periodicity associated with physical de Broglie waves. In the case of a free particle, such waves, observed from an arbitrary reference frame, would exhibit the velocity-dependent wavelength given by de Broglie's relation; and it is conjectured that the inertial and additive properties of mass (or, more precisely, the conservation of momentum and energy) can be related to nonlinear interference effects occurring (...) between the de Broglie waves for different particles. This picture could throw light on the physical meaning of quantization and suggests the possibility of reformulating classical and quantum mechanics in terms of a “quasi-classical” nonlinear field theory in which both inertial and quantization effects result essentially from the periodicity of de Broglie waves. (shrink)

The proposal to add the behavioral momentum metaphor to Skinnerian psychology and the use of other borrowed physical explanatory concepts such as velocity and inertial mass has only superficial value. The basic problem is that, in contrast to Newtonian physics, the “laws” do not apply to a significant proportion of the phenomena to be explained, and these evidential discrepancies are ignored, rather than being used to modify the scientific explanations and improve technological applications that are based on those (...) explanations. (shrink)

The frame associated with a classical point particle is generally noninertial. The point particle may have a nonzero velocity and force with respect to an absolute inertial rest frame. In time–position–energy–momentum-space {t, q, p, e}, the group of transformations between these frames leaves invariant the symplectic metric and the classical line element ds2 = d t2. Special relativity transforms between inertial frames for which the rate of change of momentum is negligible and eliminates the absolute rest (...) frame by making velocities relative but still requires the absolute inertial frame. The Lorentz group leaves invariant the symplectic metric and the line elements $ds^{2} = -dt^{2} + \frac{1}{c^{2}} dq^{2}$ and $d \mu^{2} = dp^{2}-\frac{1}{c^{2}}de^{2}$ . General relativity for particles under only the influence of gravity avoids the issue of noninertial frames as all particles follow geodesics and hence have locally inertial frames. For other forces, the question of the absolute inertial frame remains.) Born conjectured that the line element should be generalized to the pseudo-orthogonal metric $ds^{2} = -d t^{2}+\frac{1}{c^{2}} dq^{2} + \frac{1}{b^{2}}(dp^{2}-\frac{1}{c^{2}}de^{2})$ . The group leaving this metrics and the symplectic metric invariant is the pseudo-unitary group of transformations between noninertial frames. We show that these transformations also eliminate the need for an absolute inertial frame by making forces relative and bounded by b and so embodies a relativity that is shape reciprocal in the sense of Born. The inhomogeneous version of this group is naturally the semidirect product of the pseudo-unitary group with the nonabelian Heisenberg group. This is the quaplectic group. (shrink)

The structure of the Lorentz transformation depends intimately on the conventional operations for measurement of lengths (L) and time intervals (T). The prescription for length measurement leads to justifiable utilization of Euclidean geometry over finite values of the coordinates. Then T-values can be regarded as ratios of length measurements within a suitably defined clock. In certain cases the synchronization process should be supplemented by measurements providing position certification. The Lorentz transformation emerges from three specific symmetry statements, assured by the nature (...) of the L and T operations: (1) one-one correspondence of finite values of the coordinates of two inertial frames, (2) frame reciprocity, and (3) spatial isotropy. (Light signaling is not needed in this derivation. Afterward, it is assumed that light is indeed an agent moving with the common speed revealed by the transformation.) When rest masses have been determined in the conventional fashion, the conservation of momentum and of energy follow from the kinematics—a result due to Einstein. (shrink)

In 1907, Einstein set out to fully relativize all motion, no matter whether uniform or accelerated. After five failed attempts between 1907 and 1918, he finally threw in the towel around 1920, setting himself a new goal. For the rest of his life he searched for a classical field theory unifying gravity and electromagnetism. As he struggled to relativize motion, Einstein had to readjust both his approach and his objectives at almost every step along the way; he got himself hopelessly (...) confused at times; he fooled himself with fallacious arguments and sloppy calculations; and he committed what he later allegedly called the biggest blunder of his career: he introduced the cosmological constant. There is a very uplifting moral to this somber tale. Although Einstein never reached his original destination, the harvest of his thirteen-year odyssey is quite impressive. First of all, what is left of absolute motion in general relativity is far more palatable than absolute motion in special relativity or Newtonian theory. And general relativity does seem to eliminate absolute space. More importantly, from a modern physics point of view, Einstein produced a spectacular new theory of gravity based on what he called the equivalence principle. This principle says that inertial and gravitational effects are due to one and the same structure, the inertio-gravitational field, which in Einstein’s theory is represented by a metric tensor field. In addition to laying the foundations of this theory, Einstein, among other things, launched relativistic cosmology, suggested the possibility of gravitational waves, gave the first sensible definition of a space-time singularity, and caught on to the intimate connection between general covariance and energy-momentum conservation, an example of the general connection between symmetries and conservation laws of Noether’s theorems. These results more than make up for the—at least by the standards of modern philosophy of science—rather opportunistic way in which they were obtained.. (shrink)

A well-known relativistic action at a distance interaction of two unequal masses is altered so as to yield purely Newtonian radial forces with fixed particle rest masses in the system center-of-momentum inertial frame. Although particle masses experience no kinematic mass increase in this frame, speeds are naturally restricted to less than the speed of light. We derive a relation between the center-of-momentum frame total Newtonian energy and the composite rest mass. In a new proper time quantum formalism, (...) we obtain an L2(R4 ⊗ R4, C) Hilbert space by varying individual particle rest masses. We propose the use of density operators, recognizing that the auxiliary proper time parameter is not an observable. The quantum formalism is applied to our altered version of the relativistic harmonic oscillator. Our generalized coherent states yield four-dimensional wave packets which follow the correct classical world lines. Appendices contain reviews of classical Hamiltonian reparametrization (incorporating our notion of manifest covariance), and a comparison of this work with the literature. (shrink)

With the interaction interpretation, the Lorentz transformation of a system arises with selection from a superposition of its states in an observation-interaction. Integration of momentum states of a mass over all possible velocities gives the rest-mass energy. Static electrical and magnetic fields are not found to form such a superposition and are to be taken as irreducible elements. The external superposition consists of those states that are reached only by change of state of motion, whereas the internal superposition contains (...) all the states available to an observer in a single inertial coordinate system. The conjecture is advanced that states of superposition may only be those related by space-time transformations (Lorentz transformations plus space inversion and charge conjugation). The continuum of external and internal superpositions is examined for various masses, and an argument for the unity of the super-positions is presented. (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)

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)

Psychological momentum (PM) is thought to be a force that influences judgment, emotion, and performance. Based on a review of the extant literature, we elucidate two distinct approaches that researchers have adopted in their study of PM: the input-centered approach and the output-centered approach. Consistent with the input-centered approach, we conceptualize PM as a process whereby temporal and contextual PM-like stimuli (i.e., perceptual velocity, perceptual mass, perceptual historicity, and perceptually interconnected timescales)—initially perceived as an impetus—are extrapolated to imagined future (...) outcomes through mental simulation. In turn, and consistent with the output-centered approach, we posit that mental simulation elicits experiential (e.g., perceptual, cognitive, emotional) and behavioral states that govern goal pursuit, and that the pursuit of goals further influences perceptions of self, environment, and action quality. In all, we suggest that PM is interdependently linked to perceptions and behaviors in the sense that PM both influences and is influenced by changes in self-perceptions, environmental perceptions, and behavior, and we conclude by linking the PM construct to recent work on prospection. (shrink)

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)

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)

For Knox, ‘spacetime’ is to be defined functionally, as that which picks out a structure of local inertial frames. Assuming that Knox is motivated to construct this functional definition of spacetime on the grounds that it appears to identify that structure which plays theoperationalrole of spacetime—i.e., that structure which is actually surveyed by physical rods and clocks built from matter fields—we identify in this paper important limitations of her approach: these limitations are based upon the fact that there is (...) a gap between inertial frame structure and that which is operationally significant in the above sense. We present five concrete cases in which these two notions come apart, before considering various ways in which Knox’s spacetime functionalism might be amended in light of these issues. (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)

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)

Nevin & Grace's behavioral-momentum model accommodates a large body of data. This commentary highlights some experimental findings that the model does not always predict. The model does not consistently predict resistance to change when response-independent food is delivered simultaneously with response-contingent food, when drugs are used as response disrupters, and when responding is reinforced under single rather than multiple schedules of reinforcement.

The present research examines psychological momentum (PM), a perceived force that lay intuition suggests influences performance. PM theory is proposed to account for how momentum perceptions arise, and four studies demonstrate the influence of lay intuitions about PM on expectations regarding performance outcomes. Study 1 establishes that individuals share intuitions about the types of events that precipitate PM, and Study 2 finds that defeating a rival increases momentum perception. Study 3 provides evidence for the lay belief that (...) as more PM accumulates during a prior task, there should be more residual momentum left to carry over to a subsequent task, and Study 4 finds that an individual whose PM is interrupted is expected to have greater difficulty completing a task than is an individual whose steady progress is interrupted. Discussion focuses on linkages between PM and related constructs. (shrink)

The notions of ``motion'' and ``conserved quantities'', if applied to extended objects, are already quite non-trivial in Special Relativity. This contribution is meant to remind us on all the relevant mathematical structures and constructions that underlie these concepts, which we will review in some detail. Next to the prerequisites from Special Relativity, like Minkowski space and its automorphism group, this will include the notion of a body in Minkowski space, the momentum map, a characterisation of the habitat of globally (...) conserved quantities associated with Poincare symmetry -- so called Poincare charges --, the frame-dependent decomposition of global angular momentum into Spin and an orbital part, and, last not least, the likewise frame-dependent notion of centre of mass together with a geometric description of the Moeller Radius, of which we also list some typical values. (shrink)

In reply to the comments on our target article, we address a variety of issues concerning the generality of our major findings, their relation to other theoretical formulations, and the metaphor of behavioral momentum that inspired much of our work. Most of these issues can be resolved by empirical studies, and we hope that the ideas advanced here will promote the analysis of resistance to change and preference in new areas of research and application.

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)

We have analyzed many discrimination learning difficulties as reflecting multiple stimulus control topographies (SCTs). Nevin & Grace's analysis offers new variables to consider in the design of stimulus-control shaping procedures and cross-setting generalization of newly established behavior. A multiple-SCT perspective also suggests that fixed-trial discrimination procedures may offer advantages for reconciling momentum theory and partial reinforcement extinction effects.

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)

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)

The Desarguesian nature of angular-momentum theory is illustrated by drawing correspondences between relations satisfied by then-j symbols and various collinearity properties of the appropriate diagrams. No examples of Pappus' theorem have been found. A relation is suggested between the operations of angular-momentum theory and Hilbert's constructions for the addition and multiplication of points on a line.

The method of projection is applied to a relativistic field theory of fermions interacting with a nonlinear scalar field, specifically the Friedberg-Lee soliton model. Projection is effected by operating on a localized “bag” state with the translation operator exp (iP·Z), and integrating overZ. The resulting state is an eigenstate of zero momentum. The energy and the expectation value of other physical operators can be expressed as Gaussian moments of the Hamiltonian or the physical operator times powers of the (...) class='Hi'>momentum operator taken with respect to the bag state. Renormalization in the one-loop approximation is discussed in detail for the boson sector, and briefly for the fermion sector. The method can be tested for convergence against nonexpansion techniques. The latter, however, cannot so easily handle distortion of the Bose modes or the distortion of the Dirac sea. (shrink)