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)

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 “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)

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)

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 central aim of this dissertation is to clarify, defend and develop a realist field ontology of the causal-inertial structure of spacetime forcefully advanced by Hermann Weyl. Weyl's field ontology of spacetime structure may roughly be described as follows. The Special and General as well as the non-relativistic spacetime theories are principle theories of spacetime structure. They all postulate various structural constraints, and events within spacetime are held to satisfy these constraints. When interpreted physically, these mathematical structures correspond to (...) physical structural fields on spacetime. ;The thesis begins with a discussion of the significance of Riemann's Dynamical Hypothesis within the context of the debate between geometrical realism and conventionalism. In particular, Grunbaum's unyielding insistence that Riemann's work must be seen as the immediate progenitor of his brand of geometrical conventionalism is challenged and shown to be unsupported by a textual analysis of the relevant works by Riemann. The first two chapters provide a historical/exegetical analysis of Riemann's Habilitationsvortrag. Chapter 3 presents a general account of geometrical conventionalism apart from issues of its alleged historical ancestry as seen by Grunbaum. This is followed by a critical examination of Grunbaum's interpretation of Riemann. ;Grunbaum has repeatedly argued that Weyl's interpretation of Riemann accords with his. It is shown, however, that Weyl's understanding of Riemann is the direct opposite of that of Grunbaum. Chapter 4 provides an examination of Weyl's philosophy of geometry and his interpretation of Riemann. It is shown that Weyl considers Riemann's work to be essentially progenitorial of his version of geometrical realism. . . . UMI. (shrink)

The Hamiltonian structure of General Relativity (GR), for both metric and tetrad gravity in a definite continuous family of space-times, is fully exploited in order to show that: i) the "Hole Argument" can be bypassed by means of a specific "physical individuation" of point-events of the space-time manifold M^4 in terms of the "autonomous degrees of freedom" of the vacuum gravitational field (Dirac observables), while the "Leibniz equivalence" is reduced to differences in the "non-inertial appearances" (connected to gauge variables) (...) of the same phenomena. ii) the chrono-geometric structure of a solution of Einstein equations for given, gauge-fixed, initial data (a "3-geometry" satisfying the relevant constraints on the Cauchy surface), can be interpreted as an "unfolding" in mathematical global time of a sequence of "achronal 3-spaces" characterized by "dynamically determined conventions" about distant simultaneity. This result stands out as an important conceptual difference with respect to the standard chrono-geometrical view of Special Relativity (SR) and allows, in a specific sense, for an "endurantist" interpretations of ordinary physical objects in GR. (shrink)

The dynamics of calcium in the cortical cytoplasm of plant cells has been modeled by Goodwin & Trainor (1985) using a mechanochemical field theory based on the interaction between calcium ions and the cytoskeleton. The resulting mathematical model is a system of two non-linear partial differential equations which rule the evolution of the free calcium concentration and of the cytogel strain field in the cytoplasm. According to the values of parameters such as: calcium diffusion coefficient, strength of the calcium-strain (...) coupling, gel elasticity or total calcium concentration, this system may be stable or unstable around an homogeneous equilibrium state. With the aid of numerical simulations, various kinds of solutions have been observed. When inertial forces ar neglected or for low values of the gel density, most of the solutions are asymptotically stable and are reached after a more or less complex transient. But for higher values of the volumetric density more complex solutions may exist, periodic in time and space or eventually chaotic. (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.

A (Higgs vacuum)–(spacetime geometry) reciprocity principle is proposed and its consequences are explored. While it has been established that configurations of the spacetime metric tensor field, associated with acceleration with respect to local inertial frames, cause the vacuum to become thermalized, it is asserted that the converse is also possible. An appropriate thermal vacuum, through dynamical mass generation, can cause particles to propagate in a spacetime with a Minkowski metric, as if they were in a spacetime with a non-Minkowski (...) metric. The two points of view are equivalent and interchangeable. Invoking the reciprocity principle in the case of the Unruh effect in an accelerated frame, a mechanism is analyzed whereby in the context of the minimal standard model a gradient in the vacuum expectation value of the Higgs field in the direction of acceleration produces an effective inertial force on an accelerated material body. (shrink)

Leibniz coined the word “dynamics,” but his own dynamics has never been completed. However, there are many illuminating ideas scattered in his writings on dynamics and metaphysics. In this paper, I will present my own interpretation of Leibniz’s dynamics and metaphysics. To my own surprise, Leibniz’s dynamics and metaphysics are incredibly flexible and modern. In particular, the metaphysical part, namely Monadology, can be interpreted as a theory of information in terms of monads, which generate both (...) physical phenomena and mental phenomena. The phenomena, i.e., how the world of monads appears to each monad must be distinguished from its internal states, which Leibniz calls perceptions, and the phenomena must be understood as the results of these states and God’s coding. My distinctive claim is that most interpreters ignored this coding. His dynamics and metaphysics can provide a framework good enough for enabling Einstein’s special relativity. And finally, his dynamics and metaphysics can provide a very interesting theory of space and time. In Part 1, we will focus on the relationship between metaphysics and dynamics. Leibniz often says that dynamics is subordinated to metaphysics. We have to take this statement seriously, and we have to investigate how dynamics and metaphysics are related. To this question, I will give my own answer, based on my informational interpretation. On my view, Leibniz’s metaphysics tries, among others, to clarify the following three: How each monad is programmed. How monads are organized into many groups, each of which is governed by a dominant monad ; this can be regarded as a precursor of von Neumann’s idea of cellular automata. And how the same structure is repeated in sub-layers of the organization. This structure is best understood in terms of the hierarchy of programs, a nested structure going down from the single dominant program to subprograms, which again controls respective subprograms, and ad infinitum. If we may use a modern term, this is a sort of recursion, although Leibniz himself did not know this word. And one of my major discoveries is that the same recursive structure is repeated in the phenomenal world, the domain of dynamical investigations. Recursion of what, you may ask. I will argue that it is elastic collision. For Leibniz, aside from inertial motions, dynamical changes of motion are brought about by elastic collisions, at any level of the infinite divisibility of matter. This nicely corresponds to the recursive structure of the program of a monad, or of the program of an organized group of monads. This is the crux of his claim that dynamics is subordinated to metaphysics. Moreover, the program of any monad is teleological, whereas the phenomenal world is governed by efficient cause of dynamics. And it is natural that the pre-established harmony is there, since God is the ultimate programmer, as well as the creator. (shrink)

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least (...) one free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant “Robertson's subfamilies.” It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory. (shrink)

In this paper, we discuss the perspective of intra-organismal ecology by investigating a family of ecological models. We consider two types of models. First order models describe the population dynamics as being directly affected by ecological factors (here understood as nutrients, space, etc). They might be thought of as analogous to Aristotelian physics. Second order models describe the population dynamics as being indirectly affected, the ecological factors now affecting the derivative of the growth rate (that is, the population (...) acceleration), possibly through an impact on non-genetically inherited factors. Second order models might be thought of as analogous to Galilean physics. In the joint paper, we apply these ideas to a situation of gene therapy. (shrink)

Abstract During the Copernican revolution the supporters of the Ptolemaic theory argued that the tower experiment refuted the Copernican hypothesis of the (diurnal) motion of the earth, but was in agreement with the Ptolemaic theory. In his defence of the Copernican theory Galileo argued that the experiment was in agreement both with Copernican and Ptolemaic theory. The reason for these different views of the same experiment was not that the two theories were incommensurable, as Paul Feyerabend argues, but that Galileo (...) introduced a new theory of motion which he used as an auxiliary hypothesis in his discussion of the tower experiment, while those defending the Ptolemaic theory used the old Aristotelian theory of motion. Already before the Copernican revolution the Aristotelian theory of motion was criticized by philosophers in Paris, who suggested the impetus theory of motion. The later versions of this theory had the consequence that the tower experiment no longer refuted the hypothesis of the (diurnal) motion of the earth. Thus the impetus theory removed an old and important objection to the heliocentric theory. Galileo's inertial dynamics had the same function in the discussion of the tower experiment. (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 study deals with a controversy between Leibniz and Clarke concerning the relativity of space. Although substantivalism, i.e. an approach treating space as a substance, is to be indicated as the main target of Leibniz’s attack, it has usually been replaced by Newtonian absolutism instead, as a proper opposition to Leibniz’s relationalism. However, such absolutism has not been defined ontologically, but dynamically, as if the difference between their conceptions consisted of a different approach to the inertiallity of motion. However, this (...) would mean that while Leibniz intended to reduce all motion to an inertial one, Newton reduced it to a noninertial one instead, or that only one of them acknowledged the existence of noninertial motion at all. Nevertheless, none of them actually denied the existence of noninertial motion, and although all motion indeed seemed noninertial to Newton, Leibniz never responded to such a challenge in the course of their correspondence. (shrink)

An inertial frame is one in which a freely falling particle obeys Newton’s first law (i.e., continues in a state of uniform motion). Classically, we have the following: Galilean Principle of Relativity: The laws of dynamics are invariant between all inertial frames. In other words, all inertial observers (at rest in an inertial frame) will get experimentally verify the same dynamical laws.

Using as a starting point recent and apparently incompatible conclusions by Saunders and Knox, I revisit the question of the correct spacetime setting for Newtonian physics. I argue that understood correctly, these two versions of Newtonian physics make the same claims both about the background geometry required to define the theory, and about the inertial structure of the theory. In doing so I illustrate and explore in detail the view—espoused by Knox, and also by Brown —that inertial structure (...) is defined by the dynamics governing subsystems of a larger system. This clarifies some interesting features of Newtonian physics, notably the distinction between using the theory to model subsystems of a larger whole and using it to model complete universes, and the scale-relativity of spacetime structure. _1_ Introduction _2_ Newtonian Mechanics and Galilean Spacetime _3_ Vector Relationism and Maxwellian Spacetime _4_ Recovering the Galilei Group: Dynamics of Subsystems _5_ Knox on Inertial Structure _6_ Connections on Maxwellian Spacetime _7_ Knox on Newtonian Gravity _8_ Vector Relationism and Newton–Cartan Theory _9_ Inertial Structure in Newton–Cartan Gravity _10_ Reconciling Knox and Saunders _11_ Conclusions. (shrink)

In quantum relativistic Hamiltonian dynamics, the time evolution of interacting particles is described by the Hamiltonian with an interaction-dependent term (potential energy). Boost operators are responsible for (Lorentz) transformations of observables between different moving inertial frames of reference. Relativistic invariance requires that interaction-dependent terms (potential boosts) are present also in the boost operators and therefore Lorentz transformations depend on the interaction acting in the system. This fact is ignored in special relativity, which postulates the universality of Lorentz transformations (...) and their independence of interactions. Taking into account potential boosts in Lorentz transformations allows us to resolve the “no-interaction” paradox formulated by Currie, Jordan, and Sudarshan [Rev. Mod. Phys. 35, 350 (1963)] and to predict a number of potentially observable effects contradicting special relativity. In particular, we demonstrate that the longitudinal electric field (Coulomb potential) of a moving charge propagates instantaneously. We show that this effect as well as superluminal spreading of localized particle states is in full agreement with causality in all inertial frames of reference. Formulas relating time and position of events in interacting systems reduce to the usual Lorentz transformations only in the classical limit (ħ→0) and for weak interactions. Therefore, the concept of Minkowski space-time is just an approximation which should be avoided in rigorous theoretical constructions. (shrink)

In General Relativity (GR), it has been claimed that inertia receives a dynamical explanation. This is in contrast to the situation in other theories, such as Special Relativity, because the geodesic principle of GR can be derived from Einstein’s field equations. The claim can be challenged in different ways, all of which question whether the status of inertia in GR is physically different from its status in previous spacetime theories. In this paper I state the original argument for the claim (...) precisely, discuss the different objections to it and then propose a formulation that avoids the problems the original claim encounters. My conclusion is that one can say meaningfully that inertia is dynamically explained in GR. There are two senses in which the derivation of geodetic motion can be said to provide a (more) dynamical explanation of inertia in GR: it holds for any material test body that is a source of the gravitational field; and it is derivable without assuming inertial structures that are fixed independently of matter. (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)

The concept of mass is one of the most fundamental notions in physics, comparable in importance only to those of space and time. But in contrast to the latter, which are the subject of innumerable physical and philosophical studies, the concept of mass has been but rarely investigated. Here Max Jammer, a leading philosopher and historian of physics, provides a concise but comprehensive, coherent, and self-contained study of the concept of mass as it is defined, interpreted, and applied in contemporary (...) physics and as it is critically examined in the modern philosophy of science. With its focus on theories proposed after the mid-1950s, the book is the first of its kind, covering the most recent experimental and theoretical investigations into the nature of mass and its role in modern physics, from the realm of elementary particles to the cosmology of galaxies.The book begins with an analysis of the persistent difficulties of defining inertial mass in a noncircular manner and discusses the related question of whether mass is an observational or a theoretical concept. It then studies the notion of mass in special relativity and the delicate problem of whether the relativistic rest mass is the only legitimate notion of mass and whether it is identical with the classical mass. This is followed by a critical analysis of the different derivations of the famous mass-energy relationship E = mc2 and its conflicting interpretations. Jammer then devotes a chapter to the distinction between inertial and gravitational mass and to the various versions of the so-called equivalence principle with which Newton initiated his Principia but which also became the starting point of Einstein's general relativity, which supersedes Newtonian physics. The book concludes with a presentation of recently proposed global and local dynamical theories of the origin and nature of mass.Destined to become a much-consulted reference for philosophers and physicists, this book is also written for the nonprofessional general reader interested in the foundations of physics. (shrink)

This paper develops and defends three related forms of relationism about spacetime against attacks by contemporary substantivalists. It clarifies Newton's globes argument to show that it does not bear on relations that fail to determine geodesic motions, since the inertial effects on which Newton relies are not simply correlated with affine structure, but must be understood in dynamical terms. It develops remarks by Sklar and van Fraassen into relational versions of Newtonian mechanics, and argues that Earman does not show (...) them to trivialize the debate. (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 main focus of the book is the presentation of the 'inertial' view of population growth. This view provides a rather simple model for complex population dynamics, and is achieved at the level of the single species without invoking species interactions. An important part of this account is the maternal effect. Investment of mothers in the quality of their daughters makes the rate of reproduction of the current generation depend not only on the current environment, but also on (...) the environment experienced by the previous generation. (shrink)

Discusses the Meditationes, its reception, and Descartes's response. In this work, Descartes avoided theological questions. Describes the structure of the Principia, the culmination of his metaphysics dealing with the cogito, freedom of the will, divine predestination, inertial principles, the conservation of motion, dynamic relativism, and his theory of vortices, which he used to account for planetary orbits, weight or gravity, tides, and magnetism. Chronicles Descartes's religious controversy with Voetius and his dispute with Regius, whom he accused of plagiarizing his (...) work. (shrink)

The action-reaction principle (AR) is examined in three contexts: (1) the inertial-gravitational interaction between a particle and space-time geometry, (2) protective observation of an extended wave function of a single particle, and (3) the causal-stochastic or Bohm interpretation of quantum mechanics. A new criterion of reality is formulated using the AR principle. This criterion implies that the wave function of a single particle is real and justifies in the Bohm interpretation the dual ontology of the particle and its associated (...) wave function. But it is concluded that the Bohm theory is not dynamically complete because the particle and its associated wave function do not satisfy the AR principle. (shrink)

A class of theories which satisfy the Relativity Principle has been overlooked. The kinematics for these theories is derived by relaxing the 'boost isotropy' symmetry normally invoked, and the role the dynamical fields play in determining the inertial coordinate systems is emphasised, leading to a criticism of Friedman's (1983) practice of identifying them via the absolute objects of a spacetime theory alone. Some theories complete with 'boost anisotropic' dynamics are given.

The concept of the vacuum in quantum field theory is a subtle one. Vacuum states have a rich and complex set of properties that produce distinctive, though usually exceedingly small, physical effects. Quantum vacuum noise is familiar in optical and electronic devices, but in this paper I wish to consider extending the discussion to systems in which gravitation, or large accelerations, are important. This leads to the prediction of vacuum friction: The quantum vacuum can act in a manner reminiscent of (...) a viscous fluid. One result is that rapidly changing gravitational fields can create particles from the vacuum, and in turn the backreaction on the gravitational dynamics operates like a damping force. I consider such effects in early universe cosmology and the theory of quantum black holes, including the possibility that the large-scale structure of the universe might be produced by quantum vacuum noise in an early inflationary phase. I also discuss the curious phenomenon that an observer who accelerates through a quantum vacuum perceives a bath of thermal radiation closely analogous to Hawking radiation from black holes, even though an inertial observer registers no particles. The effects predicted raise very deep and unresolved issues about the nature of quantum particles, the role of the observer, and the relationship between the quantum vacuum and the concepts of information and entropy. © 2001 American Institute of Physics. (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)

It has been shown by Gupta and Padmanabhan that the radiation reaction force of the Abraham–Lorentz–Dirac equation can be obtained by a coordinate transformation from the inertial frame of an accelerating charged particle to that of the laboratory. We show that the problem may be formulated in a flat space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg–Feynman–Schwinger covariant mechanics (the zero mode fields (...) of the 0, 1, 2, 3 components correspond to the Maxwell fields). Without additional constraints, the particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five dimensional field equations provides the classical Abraham–Lorentz–Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution as well as an autonomous non-linear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that mass-shell deviation is bounded when the external field is removed. (shrink)

Contrary to our immediate and vivid sensation of past, present, and future as continually shifting non-relational modalities, time remains as tenseless and relational as space in all of the established theories of fundamental physics. Here an empirically adequate generalized theory of the inertial structure is discussed in which proper time is causally compelled to be tensed within both spacetime and dynamics. This is accomplished by introducing the inverse of the Planck time at the conjunction of special relativity and (...) Hamiltonian mechanics, which necessitates energies and momenta to be invariantly bounded from above, and lengths and durations similarly bounded from below, by their respective Planck scale values. The resulting theory abhors any form of preferred structure, and yet captures the transience of now along timelike worldlines by causally necessitating a genuinely becoming universe. This is quite unlike the scenario in Minkowski spacetime, which is prone to a block universe interpretation. The minute deviations from the special relativistic effects such as dispersion relations and Doppler shifts predicted by the generalized theory remain quadratically suppressed by the Planck energy, but may nevertheless be testable in the near future, for example via observations of oscillating flavor ratios of ultrahigh energy cosmic neutrinos, or of altering pulse rates of extreme energy binary pulsars. (shrink)

In his monumental 1687 work, _Philosophiae Naturalis Principia Mathematica_, known familiarly as the _Principia_, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles. (...) This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the _Principia_ also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system. The illuminating Guide to Newton's _Principia_ by I. Bernard Cohen makes this preeminent work truly accessible for today's scientists, scholars, and students. (shrink)

In his monumental 1687 work, _Philosophiae Naturalis Principia Mathematica_, known familiarly as the _Principia_, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles. (...) This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the _Principia_ also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system. The translation-only edition of this preeminent work is truly accessible for today's scientists, scholars, and students. (shrink)

In his monumental 1687 work, _Philosophiae Naturalis Principia Mathematica_, known familiarly as the _Principia_, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles. (...) This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the _Principia_ also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system. The translation-only edition of this preeminent work is truly accessible for today's scientists, scholars, and students. (shrink)

This paper argues against a standard view that all deterministic and conservative classical mechanical systems are time-reversible, by asking how the temporal evolution of a system modulates parametric imprecision (either ontological or epistemic). It notes that well-behaved systems (e.g. inertial motion) can possess a dynamics which is unstable enough to fail at reversing uncertainties—even though exact values are reliably reversed. A limited (but significant) source of irreversibility is thus displayed in classical mechanics, closely analogous the lack of predictability (...) revealed by unstable chaotic systems. (shrink)

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

The article analyzes the reports of the Club of Rome issued subsequent to its semicentennial celebration. The analysis uncovers the evolutionary trajectory of the Club’s conceptual frameworks, transitioning from the stark alarmism prevalent in the early 1970s to a grounded optimism characteristic of the early 21st century. The majority of its publications, in explicit or implicit form, essentially respond to a question of Hamletian scale that arose within the discussions of the “limits to growth” model: Is it possible, and if (...) so, how, to overcome the antagonism between the continuous growth of the needs of an increasing humanity and the relatively limited natural-resource potential of the biosphere? The analysis introduces an analysis of world development scenarios by 2050, ranging from inertial extrapolation of current trends to radical transformations of global political, socio-economic, and cultural processes. The discourse reflects on the report authors’ contemplations regarding societal adaptability to undergo a “true human revolution,” entailing a fundamental reassessment of established economic models and advancement toward innovative global governance strategies. The paper scrutinizes the assertion that society’s “unlearnability” is one of the key obstacles to the sustainable development of civilization. Significant emphasis is placed on the imperative for a comprehensive transformation encompassing the global educational landscape and the cultivation of a novel (sustainable) mindset, one that appreciates the intricate interplay among economic, environmental, and sociocultural perspectives on the global dynamics of the “humanity – biosphere – civilization” system. Humanity, overcoming the turbulences of contemporary world development, possesses all the prerequisites for a constructive analysis and design of strategic perspectives of the foreseeable future. (shrink)

In Part 2, drawing on the results of Part 1, I will present my own interpretation of Leibniz’s philosophy of space and time. As regards Leibniz’s theory of geometry and space, De Risi’s excellent work appeared in 2007, so I will depend on this work. However, he does not deal with Leibniz’s view on time, and moreover, he seems to misunderstand the essential part of Leibniz’s view on time. Therefore I will begin with Richard Arthur’s paper, and J. A. Cover’s (...) improvement. Despite some valuable insights contained in their papers, I have to conclude their attempts fail in one way or another, because they disregard the order of state-transition of a monad, which is, on my view, one of the essential features of the monads. By reexamining Leibniz’s important text Initia Rerum, I arrived at the following interpretation. Since the realm of monads is timeless, the order of state-transition of a monad provides only the basis of time in phenomena. What Leibniz calls “simultaneity” should be understood as a unique 1- to-1 correspondence of the states of different monads. With this understanding, whatever is correct in Arthur’s and Cover’s interpretation can be reproduced in my interpretation. On this basis, we can introduce a metric of time based on congruence of duration. Leibniz connected time with space in Initia Rerum by means of motion, and introduced the notion of path of a moving point; thus the congruence of duration can be reduced to congruence of distance. Then, I can show both classical metric and relativistic metric can be reconstructed on the same basis, depending on the coding for phenomena. The relativistic metric can be combined with Leibniz’s idea of internal living force, suggesting a relation of mass with energy. However, since Leibniz has never shown the ground of constant speed of an inertial motion, there may be a vicious circle. In order to avoid this, we can extend the notion of path to whole situation, thus yielding a trajectory of the whole phenomenal world. Then, by applying optimality to possible paths, we may arrive at the law of motion, without vicious circle. A comparison of Leibniz’s dynamics with Barbour’s concludes Part 2. (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)

In a recent article in this journal, Barbara Lariviere offers a very useful distinction between two ways of understanding the claims that Leibniz, or relational theorists in general, might wish to make about the nature of motion and the structure of space and time; viz., There is no real inertial structure to space-time.and There is a real inertial structure to space-time, but it is dynamical rather than absolute.Citing the authority of Weyl, the author argues that L1 is untenable; (...) indeed, the argument purports to show that if L1 were true, then there would be no coherent basis for a theory of motion, not even a relational theory. My main goal in this note is to point out why this argument is mistaken while at the same time sketching the real reason why the relational conception of motion is untenable. In addition I will offer a few remarks about the relevance of L2 to the absolute-relational controvery. (shrink)

The λ model suggests that detailed kinematics arise from changes in control variables and need not be explicitly planned. However, we have shown that when moving a grasped object, grip force is precisely modulated in phase with acceleration-dependent inertial load. This suggests that the motor system can predict detailed kinematics. This prediction may be based on a forward model of the dynamics of the loaded limb.

In Part 2, drawing on the results of Part 1, I will present my own interpretation of Leibniz’s philosophy of space and time. As regards Leibniz’s theory of geometry and space, De Risi’s excellent work appeared in 2007, so I will depend on this work. However, he does not deal with Leibniz’s view on time, and moreover, he seems to misunderstand the essential part of Leibniz’s view on time. Therefore I will begin with Richard Arthur’s paper, and J. A. Cover’s (...) improvement. Despite some valuable insights contained in their papers, I have to conclude their attempts fail in one way or another, because they disregard the order of state-transition of a monad, which is, on my view, one of the essential features of the monads. By reexamining Leibniz’s important text Initia Rerum, I arrived at the following interpretation. Since the realm of monads is timeless, the order of state-transition of a monad provides only the basis of time in phenomena. What Leibniz calls “simultaneity” should be understood as a unique 1-to-1 correspondence of the states of different monads. With this understanding, whatever is correct in Arthur’s and Cover’s interpretation can be reproduced in my interpretation. On this basis, we can introduce a metric of time based on congruence of duration. Leibniz connected time with space in Initia Rerum by means of motion, and introduced the notion of path of a moving point; thus the congruence of duration can be reduced to congruence of distance. Then, I can show both classical metric and relativistic metric can be reconstructed on the same basis, depending on the coding for phenomena. The relativistic metric can be combined with Leibniz’s idea of internal living force, suggesting a relation of mass with energy. However, since Leibniz has never shown the ground of constant speed of an inertial motion, there may be a vicious circle. In order to avoid this, we can extend the notion of path to whole situation, thus yielding a trajectory of the whole phenomenal world. Then, by applying optimality to possible paths, we may arrive at the law of motion, without vicious circle. A comparison of Leibniz’s dynamics with Barbour’s concludes Part 2. (shrink)

In Part 3, I will discuss the problems of inertia and gravity in Leibniz, and present three conjectures: If Leibniz were really ready to insist on relativity, he would have to assert the relativity of inertial motion. In Leibniz’s theories of dynamics and geometry, there was a struggle between his predilection for straight line and his adherence to an optimality principle. Gravity, as well as inertia, can be considered as a universal feature of the world, so that the (...) foundation of both may have a common root. Further, drawing on the results in Part 1 and Part 2, I will argue for the need of a unified interpretation of Leibniz’s metaphysics and dynamics. My three conjectures as regards Leibniz’s possible treatment of inertia and gravity are proposed along a unified interpretation, in terms of my informational reconstruction of Leibniz’s philosophy. Finally, the most important features of the informational interpretation are summarized. The synopsis of the whole paper is added. (shrink)

In Part 3, I will discuss the problems of inertia and gravity in Leibniz, and present three conjectures: If Leibniz were really ready to insist on relativity, he would have to assert the relativity of inertial motion. In Leibniz’s theories of dynamics and geometry, there was a struggle between his predilection for straight line and his adherence to an optimality principle. Gravity, as well as inertia, can be considered as a universal feature of the world, so that the (...) foundation of both may have a common root. Further, drawing on the results in Part 1 and Part 2, I will argue for the need of a unified interpretation of Leibniz’s metaphysics and dynamics. My three conjectures as regards Leibniz’s possible treatment of inertia and gravity are proposed along a unified interpretation, in terms of my informational reconstruction of Leibniz’s philosophy. Finally, the most important features of the informational interpretation are summarized. The synopsis of the whole paper is added. (shrink)

In physics, mass is a property of matter that describes how material elements are arranged in space and opposed to forces, and also how they generate forces such as gravitation forces. Electric charge remains enigmatic. This charge is a universal constant, and it is discrete rather than continuous. Spin can be interpreted as a reversal movement that allows the outer side of matter to fold back on itself. Finally, Maxwell's theory on the propagation of light also belongs to the physics (...) of information. Relativistic cosmology does not easily lend itself to an interpretation that reveals the dynamics of communication. It is conceived in its principle as a physics of arrangements. Einstein completes modern physics, where "completes" must be considered in a broad sense. One of the key questions concerns the link between mathematics and physical things or, in other words, what is represented and "what is" or "happens" in the world. (shrink)

It is argued that, under the assumption that the strong principle of equivalence holds, the theoretical realization of the Mach principle (in the version of the Mach-Einstein doctrine) and of the principle of general relativity are alternative programs. That means only the former or the latter can be realized—at least as long as only field equations of second order are considered. To demonstrate this we discuss two sufficiently wide classes of theories (Einstein-Grossmann and Einstein-Mayer theories, respectively) both embracing Einstein's theory (...) of general relativity (GRT). GRT is shown to be just that “degenerate case” of the two classes which satisfies the principle of general relativity but not the Mach-Einstein doctrine; in all the other cases one finds an opposite situation.These considerations lead to an interesting “complementarity” between general relativity and Mach-Einstein doctine. In GRT, via Einstein's equations, the covariant and Lorentz-invariant Riemann-Einstein structure of the space-time defines the dynamics of matter: The symmetric matter tensor Ttk is given by variation of the Lorentz-invariant scalar densityL mat, and the dynamical equations satisfied by Tik result as a consequence of the Bianchi identities valid for the left-hand side of Einstein's equations. Otherwise, in all other cases, i.e., for the “Mach-Einstein theories” here under consideration, the matter determines the coordinate or reference systems via gravity. In Einstein-Grossmann theories using a holonomic representation of the space-time structure, the coordinates are determined up to affine (i.e. linear) transformations, and in Einstein-Mayer theories based on an anholonomic representation the reference systems (the tetrads) are specified up to global Lorentz transformations. The corresponding conditions on the coordinate and reference systems result from the postulate that the gravitational field is compatible with the strong equivalence of inertial and gravitational masses. (shrink)

I consider the contrast between Leibniz's relational concept of spacetime and Einstein's special and general theories of relativity. I suggest that there are two interpretations of Leibniz's view, which I call L1 and L2. L1 amounts to saying that there is no real inertial structure to spacetime, whereas in general relativity the inertial structure is dynamical or real in Lande's sense ; i.e., it can be ‘kicked’ and ‘kicks back,’ causing gravitational effects. If there is no real (...) class='Hi'>inertial structure to space-time then, as Weyl points out, the concept of the relative motive of several bodies has no more foundation than the concept of absolute motion for a single body. Thus, L1 seems to be untenable. L2 is a more sophisticated view which rejects the geometrical aspect of Newtonian space-time as a container for events, but accepts the existence of a real structure which determines the inertial properties of matter. (shrink)