It will be argued that Minkowski's implementation of distances is inconsistent. An alternative implementation will be proposed. In the new model the proper time of an object is taken as its fourth coordinate. Distances will be measured according to a four dimensional Euclidean metric. In the present approach mass is a constant of motion. A mass can therefore be ascribed to photons and neutrinos. Mechanics and dynamics will be reformulated in close correspondence with classical physics. Of particular interest (...) is the equation of motion for the proper time momentum. In the classical limit it reduces to the classical law of conservation of (kinetic+potential) energy. In the relativistic limit it is similar to the conservation of energy of the theory of relativity. The conservation of proper time momentum allows for an alternative explanation for Compton scattering and pair annihilation. On the basis of the proper time formulation of electrodynamics also an alternative explanation will be offered for the spectra of hydrogenic atoms. The proper time formulation of gravitational dynamics leads to the correct predictions of gravitational time dilation, the deflection of light and the precession of the perihelia of planets. For this no curvature will be needed. That is, spacetime is flat everywhere, even in the presence of sources of gravitation. Some cosmological consequences will be discussed. The present approach gives a new notion to energy, antiparticles and the structure of spacetime. The contents of the present paper will have important implications for the foundations of physics in general. (shrink)

On the basis of the Woodhouse causal axiomatics, we show that conformal proper times and an extra variable in addition to those of space and time, together give a physical justification for the ‘chronometric hypothesis’ of general relativity. Indeed, we show that, with a lack of these latter two ingredients and of this hypothesis, clock paradoxes exist for which the unparadoxical asymmetry cannot be recovered when using the ‘clock and message functions’ only. These proper times originate from (...) a given conformal structure of the spacetime when ascribing different compatible projective structures to each Woodhouse particle, and then, each defines a specific Weylian ‘sheaf structure’. In addition, the proper time parameterizations are defined via path-dependent conformal scale factors, which act like sockets for any kind of physical interaction and also represent the values of the variable associated with the extra dimension. (shrink)

The canonical proper time formulation of relativistic dynamics provides a framework from which one can describe the dynamics of classical and quantum systems using the clock of those very systems. The framework utilizes a canonical transformation on the time variable that is used to describe the dynamics, and does not transform other dynamical variables such as momenta or positions. This means that the time scales of the dynamics are described in terms of the natural local (...) time coordinates, which is the most meaningful parameterization of phenomena such as the approach to equilibrium, or the back reaction of interacting systems. We summarize the formalism of the canonical proper time framework, and provide example calculations of the eigenvalues of the hydrogen atom and near horizon description of a scalar field near a Schwarzschild black hole. (shrink)

In this paper, we report on a new approach to relativistic quantum theory. The classical theory is derived from a new implementation of the first two postulates of Einstein, which fixes the proper-time of the physical system of interest for all observers. This approach leads to a new group that we call the proper-time group. We then construct a canonical contact transformation on extended phase space to identify the canonical Hamiltonian associated with the proper- (...) class='Hi'>time variable. On quantization we get a new relativistic wave equation for spin 1/2 particles that generalizes the Dirac theory. The Hamiltonian is positive definite so we naturally interpret antiparticles as particles with their proper-time reversed. We show that for the hydrogen atom problem, we get the same fine structure separation. When the proton spin magnetic moment is taken into account, we get the standard hyperfine splitting terms of the Pauli approximation and two additional terms. The first term is small in p-states. It diverges in s-states, and provides more than enough to account for the Lamb-shift when the proton radius is used as a cut off. The last term promises to provide a correction to the hyperfine splitting term. Although incomplete, the general approach offers hope of completely accounting for the hydrogen spectrum as an eigenvalue problem. (shrink)

In the transition to Einstein’s theory of Special Relativity (SR), certain concepts that had previously been thought to be univocal or absolute properties of systems turn out not to be. For instance, mass bifurcates into (i) the relativistically invariant proper mass m0, and (ii) the mass relative to an inertial frame in which it is moving at a speed v = βc, its relative mass m, whose quantity is a factor γ = (1 – β2) -1/2 times the (...) class='Hi'>proper mass, m = γm0. (shrink)

The purpose of this paper is to review relativistic quantum theories with an invariant evolution parameter. Parametrized relativistic quantum theories (PRQT) have appeared under such names as constraint Hamiltonian dynamics, four-space formalism, indefinite mass, micrononcausal quantum theory, parametrized path integral formalism, relativistic dynamics, Schwinger proper time method, stochastic interpretation of quantum mechanics and stochastic quantization. The review focuses on the fundamental concepts underlying the theories. Similarities as well as differences are highlighted, and an extensive bibliography (...) is provided. (shrink)

Many times, what we say proves to be wrong. It might turn out that what we took to be a comforting remark was, in fact, making things worse. Or that a joke was inappropriate. Or that yelling out loud was rude. More importantly for this paper, there are plenty of cases in which what we said turns out to be false: we spoke without paying attention, we were misinformed or tricked, or we made a reasoning mistake. -/- A particular instance (...) of this latter phenomenon is when someone changes their perspective and doesn't find their previous assertions true anymore. For example, imagine that you used to like licorice as a child, and that you went around saying things like "Licorice is tasty." But, growing up, you find licorice too strong and quite boring; your tastes have changed. While the taste of licorice itself has not changed, you are not going around anymore uttering "Licorice is tasty." In fact, in certain cases, you might even think that what you said in your childhood was wrong - at least in light of your present preferences. -/- Sometimes we "take back" the assertions we made when we realize they are no longer true. Such speech acts of taking back can be performed in various ways: more formally, as effected in a court of law or when an official speaks to the press, or more informally in our day-by-day interactions. These acts of taking back are known as retraction. Retraction is usually achieved by employing certain linguistic markers ('I was wrong', 'I was mistaken', 'I retract', "Scratch that' etc.) that signal that the retractor takes their previous speech act to be faulty in a certain way. -/- This phenomenon has formed the basis for a popular argument used by relativists about a variety of natural language expressions (predicates of taste, epistemic modals, moral and aesthetic claims etc.) in support of their view. Recently, several considerations (mostly from contextualists about the same expressions), both from the armchair and based on empirical studies, have been offered to undercut the support retraction was thought to provide for relativism. In this paper, I consider and re-evaluate that support in light of both types of considerations, showing that neither of them decisively undermines it. However, to survive the contextualist counterattack, the relativist needs to pay a price: that is, she will be forced to make some concessions or rethink certain claims. I show what I think those concessions should be and what needs to be rethought (and how). The upshot is that, while the support retraction offers relativism is not as strong as initially believed, appeal to retraction remains a legitimate move in the debate. In section 1, I introduce the views in the debate and clarify the phenomenon of retraction and its dialectical role. Armchair data are investigated in section 2, proper experimental studies in section 3, while section 4 summarizes and concludes. (shrink)

The formulation of manifestly covariant relativistic statistical mechanics as the description of an ensemble of events in spacetime parametrized by an invariant proper-time τ is reviewed. The linear and cubic mass spectra, which result from this formulation (the latter with the inclusion of anti-events) as the actual spectra of an individual hadronic multiplet and hot hadronic matter, respectively, are discussed. These spectra allow one to predict the masses of particles nucleated to quasi-levels in such an ensemble. As (...) an example, the masses of the ground-state mesons and baryons are considered; the results are in excellent agreement with the measured hadron masses. Additivity of inverse Regge slopes is established and shown to be consistent with available experimental data on the D meson and Λc baryon production. (shrink)

A RELATIVISTIC THEORY OF PHENOMENOLOCICAL CONSTITUTION: A SELF-REFERENTIAL, TRANSCENDENTAL APPROACH TO CONCEPTUAL PATHOLOGY. (Vol. I: French; Vol. II: English) -/- Steven James Bartlett -/- Doctoral dissertation director: Paul Ricoeur, Université de Paris Other doctoral committee members: Jean Ladrière and Alphonse de Waehlens, Université Catholique de Louvain Defended publically at the Université Catholique de Louvain, January, 1971. -/- Universite de Paris X (France), 1971. 797pp. -/- The principal objective of the work is to construct an analytically precise methodology which can (...) serve to identify, eliminate, and avoid a certain widespread _conceptual fault_ or _misconstruction_, called a "projective misconstruction" or "projection" by the author. It is argued that this variety of error in our thinking (i) infects a great number of our everyday, scientific, and philosophical concepts, claims, and theories, (ii) has largely been undetected, and (iii), when remedied, leads to a less controversial and more rigorous elucidation of the transcendental preconditions of human knowledge than has traditionally been possible. The dissertation identifies, perhaps for the first time, a _projective_ variety of self-referential inconsistency, and proposes an innovative, self-reflexive approach to transcendental argument in a logical and phenomenological context. The strength of the approach lies, it is claimed, in the fact that a rejection of the approach is possible only on pain of self-referential inconsistency. The argument is developed in the following stages: A general introduction identifies the central theme of the work, defines the scope of applicability of the results reached, and sketches the direction of the studies that follow. The preliminary discussion culminates in a recognition of the need for a _critique of impure reason_. The body of the work is divided into two parts: Section I seeks to develop a methodology, on a purely formal basis, which is, on the one hand, capable of being used to study the transcendental foundations of the special sciences, including its own proper transcendental foundation. On the other hand, the methodology proposed is intended as a diagnostic and therapeutic tool for dealing with _projective_ uses of concepts. The approach initiates an analysis of concepts from a perspective which views _knowledge as coordination_. Section I describes formal structures that possess the status of preconditions in such a coordinative account of knowledge. Special attention is given to the preconditions of _identifying reference_ to logical particulars. The first section attempts, then, to provide a self-referential, transcendental methodology which is essentially revisionary in that it is motivated by a concern for conceptual error-elimination. Phenomenology, considered in its unique capacity as a self-referential, transcendental discipline, is of special relevance to the study. Section II accordingly examines a group of concepts which come into question in connection with the central theme of _phenomenological constitution_. The "_de-projective methodology_" developed in Section I is applied to these concepts that have a foundational importance in transcendental phenomenology. A translation is, in effect, proposed from the language of consciousness to a language in which preconditions of referring are investigated. The result achieved is the elimination of self-defeating, projective concepts from a rigorous, phenomenological study of the constitutive foundations of science. The dissertation was presented in a two volume, double-language format for the convenience of French and English researchers. Each volume contains an analytical index. (shrink)

Standard quantum theory is inadequate to explain the mechanisms by which potential becomes actual. It is inadequate and therefore unable to describe generation of events. Niels Bohr emphasized long ago that the classical part of the world is necessary. John Bell stressed the same point: that “measurement≓ cannot even be defined within the standard quantum theory, and he sought a solution within hidden variable theories and his concept of “beables.≓Today it is customary to try to explain emergence of the classical (...) world through a decoherence mechanism due to “environment.≓ But, we believe, as it was with the concept of measurement, “environment≓ itself cannot be defined within the standard quantum theory.We have proposed a semiphenomenological solution to this problem by introducing explicitly, from the very beginning, classical degrees of freedom, and by coupling these degrees of freedom, through a Lindblad type coupling, to the quantum world. The resulting theory, we call “event-enhanced quantum theory.≓ EEQT allows us to describe an event-generating mechanism for individual quantum systems under continuous observation. The objections of John Bell are met and precise definitions of an “experiment≓ and of a “measurement≓ have been given within EEQT. However EEQT is, essentially, a nonrelativistic theory.In the present paper we extend the ideas of L. P. Horwitz and C. Piron and we propose a relativistic version of EEQT, with an event-generating algorithm for spin one-half particle detectors. The algorithm is based on proper time formulation of the relalivistic quantum theory. Although we use indefinite metric, all the probabilities controlling the random process of the detector clicks are nonnegative. (shrink)

It was shown in Dirac A117, 610; A118, 351, 1928) that the ultra-violet divergence in quantum electrodynamics is caused by a violation of the time-energy uncertainly relationship, due to the implicit assumption of infinitesimal time information. In Wheeler et al. it was shown that Einstein’s special theory of relativity and Maxwell’s field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact transformation on (...) configuration space, which leaves phase space invariant. The special theory has a dual version in the sense that, for any set of n particles, every observer has two unique sets of global variables \\) and \\) to describe the dynamics, where \ is the canonical center of mass. In the \\) variables, time is relative and the speed of light is unique, while in the \\) variables, time is unique and the speed of light is relative with no upper bound. In the Maxwell case, the two sets of particle wave equations are not equivalent. The dual version contains an additional longitudinal radiation term that appears instantaneously with acceleration, leading to the prediction that radiation from a cyclotron will not produce photoelectrons. A major outcome is the dual unification of Newtonian mechanics and classical electrodynamics with Einstein’s special theory of relativity, without the need for point particles, without a self-energy divergency and, without need for the problematic Lorentz–Dirac equation. The purpose of this paper is to introduce the dual theory of relativistic quantum mechanics. In our approach, we obtain three distinct dual relativistic wave equations that reduce to the Schrödinger equation when minimal coupling is turned off. We show that the dual Dirac equation provides a new formula for the anomalous magnetic moment of a charged particle. We can obtain the exact value for the electron g-factor and phenomenological values for the muon and proton g-factors. (shrink)

In this work we study the relativistic mechanics of continuous media on a fundamental level using a manifestly covariant proper time procedure. We formulate equations of motion and continuity (and constitutive equations) that are the starting point for any calculations regarding continuous media. In the force free limit, the standard relativistic equations are regained, so that these equations can be regarded as a generalization of the standard procedure. In the case of an inviscid fluid we derive (...) an analogue of the Bernoulli equation. For irrotational flow we prove that the velocity field can be derived from a potential. If in addition, the fluid is incompressible, the potential must obey the d'Alembert equation, and thus the problem is reduced to solving the d'Alembert equation with specific boundary conditions (in both space and time). The solutions indicate the existence of light velocity sound waves in an incompressible fluid (a result known in previous literature (19) ). Relaxing the constraints and allowing the fluid to become linearly compressible one can derive a wave equation, from which the sound velocity can again be computed. For a stationary background flow, it has been demonstrated that the sound velocity attains its correct values for the incompressible and nonrelativistic limits. Finally viscosity is introduced, bulk and shear viscosity constants are defined, and we formulate equations for the motion of a viscous fluid. (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)

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an (...) interaction with an external electromagnetic field. The physical meaning of σ is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter σ is shown to tend to the particle’s proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by σ as the dynamical temporal parameter. (shrink)

THIS PAPER IS THE CO-WINNER OF THE FRED BERGER PRIZE IN PHILOSOPHY OF LAW FOR THE 1999 AMERICAN PHILOSOPHICAL ASSOCIATION FOR THE BEST PUBLISHED PAPER IN THE PREVIOUS TWO YEARS. -/- The conflict between liberal legal theory and critical legal studies (CLS) is often framed as a matter of whether there is a theory of justice that the law should embody which all rational people could or must accept. In a divided society, the CLS critique of this view is overwhelming: (...) there is no such justice that can command universal assent. But the liberal critique of CLS, that it degenerates into an unpalatable moral relativism on which there is no non-arbitrary basis between a justice that underwrites forms of domination such as slavery and a justice that condemns such forms of domination is equally powerful and compelling. I show that there is a way to harmonize both views that is subject to empirical test. -/- First I show that the most widely accepted and influential formulation of liberal justice, John Rawls' Justice as Fairness, in. e.g, A Theory of Justice, cannot avoid the relativistic challenge because it would not be accepted, as a matter of sociological fact, by real people in a divided society once the "veil of Ignorance" is removed and real people step out from the Original Position. To put it differently, different reflective equilibria are inevitable in a divided society. Given the weight that Rawls properly puts on the realizability of a conception of justice and its stability in practice, this is a fatal objection. There can be no divided society that is "well ordered" in Rawls' sense, governed by a shared conception of justice and known to be so governed. -/- I then turn to the most powerful statement of the CLS view, Milton's Fisk's relativistic account in The State and Justice. For Fisk, justice is a compromise between what the dominant groups can compel and what the the subordinate groups will acquiesce to., There is no one such compromise in any given situation, so the account is in that sense relativistic, but more deeply, it is relativistic in that it offers no non-arbitrary, non-question begging way to choose between the official justice of, e.g., a slaveholding society and and the radical justice of the slaves, which has no place for slaveholders as a group or slavery as an institution.All that Fisk can offer is an arbitrary existential choice: I'm with the slaves. (Or the slaveowners.) Most of us would find this disconcerting or even unacceptable. -/- I show that Fisk's general sort of account can be modified to allow for an non-arbitrary choice. Given general facts about human nature, societies based on domination will produce resistance that over the long run will diminish or eliminate various forms of domination. Through a sort of ratchet effect, rights won will be hard if not impossible to reverse. Societies embodying forms of domination can therefore be compared on dimensions of stability: the more domination, the more resistance, and the less stability. Such societies are inferior on the dimension of justice to more emancipatory society on the terms of both kinds of justice, official and radical. -/- This is not question begging because regimes of domination incorporate stability no less than more emancipatory social orders. The choice between official justice embodying domination and radical justice that does not is not arbitrary because it is based on a shared commitment to long term stability. This offers an empirical test of which social orders are more justice, and a prediction that over time, domination will tend to decrease. (shrink)

This thesis introduces a new theoretical tool to explore the notion of time and temporal order in quantum mechanics: the relativistic quantum "clock" framework. It proposes novel thought experiments showing that proper time can display quantum features, e.g. when a "clock" runs different proper times in superposition. The resulting new physical effects can be tested in near-future laboratory experiments (with atoms, molecules and photons as "clocks"). The notion of time holds the key to the (...) regime where quantum theory and general relativity overlap, which has not been directly tested yet and remains largely unexplored by the theory. The framework also applies to scenarios in which causal relations between events become non-classical and which were previously considered impossible to address without refuting quantum theory. The relativistic quantum "clock" framework offers new insights into the foundations of quantum theory and general relativity. (shrink)

A Schrödinger-like formalism of relativistic quantum theory is presented based on an alternative Lagrangian formalism of relativistic mechanics with the proper time as the evolution parameter. The Schrödinger-like formalism resolves the great difficulties of negative probability density, Klein paradox, and Zitterbewegung. Ehrenfest's theorem is preserved in the Schrödinger-like formalism.

In this work, a neo-classical relativistic mechanics theory is presented where the spin of an electron is an inherent part of its world space-time path as a point particle. The fourth-order equation of motion corresponds to the same covariant Lagrangian function in proper time as in special relativity except for an additional spin energy term. The theory provides a hidden-variable model of the electron where the dynamic variables give a complete description of its motion, giving a (...) classical mechanics explanation of the electron’s spin, its dipole moments, and Schrödinger’s zitterbewegung, These features are also described mathematically by quantum mechanics theory, of course, but without any physical picture of an underlying reality. The total motion of the electron can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called here the spin center. The global motion is sub-luminal and described by Newton’s Second Law in proper time, the time for a clock fixed at the spin center, while the total motion occurs at the speed of light c, consistent with the eigenvalues of Dirac’s velocity operators having magnitude c. The local spin motion is an inherent perpetual motion, which for a free electron is periodic at the ultra-high zitterbewegung frequency and its path is circular in a spin-center reference frame. In an electro-magnetic field, this spin motion generates magnetic and electric dipole energies through the Lorentz force on the electron’s point charge. The electric dipole energy corresponds to the spin-orbit coupling term involving the electric field that appears in the corrected Pauli non-relativistic Hamiltonian, which has long been used to explain the doublet structure of the spectral lines of the excited hydrogen atom. Pauli’s spin-orbit term is usually derived, however, from his magnetic dipole energy term, including also the effect of Thomas precession, which halves this energy. The magnetic dipole energy from Pauli’s and Dirac’s theory is twice that in the neo-classical theory, a discrepancy that has not been resolved. By defining a spin tensor as the angular momentum of the electron’s total motion about its spin center, the fundamental equations of motion can be re-written in an identical form to those of the Barut–Zanghi electron theory. This allows the equations of motion to be expressed in an equivalent form involving operators applied to a state function of proper time satisfying a neo-classical Dirac–Schrödinger spinor equation. This state function produces the dynamic variables from the same operators as in Dirac’s theory for the electron but without any probability implications. It leads to a neo-classical wave function that satisfies Dirac’s relativistic wave equation for the free electron by applying the Lorentz transformation to express proper time in the state function in terms of an observer’s space-time coordinates, showing that there is a close connection between the neo-classical theory and quantum mechanics theory for the electron’s dynamics. (shrink)

To relax the apparent tension between nonlocal hidden variables and relativity, we propose that the observable proper time is not the same quantity as the usual proper-time parameter appearing in local relativistic equations. Instead, the two proper times are related by a nonlocal rescaling parameter proportional to |ψ|2, so that they coincide in the classical limit. In this way particle trajectories may obey local relativistic equations of motion in a manner consistent with the (...) appearance of nonlocal quantum correlations. To illustrate the main idea, we first present two simple toy models of local particle trajectories with nonlocal time, which reproduce some nonlocal quantum phenomena. After that, we present a realistic theory with a capacity to reproduce all predictions of quantum theory. (shrink)

We present a general relativistic model of a spherical shell of matter with a perfect fluid on its surface coupled to an internal oscillator, which generalizes a model recently introduced by the authors to construct a self-gravitating interferometer. The internal oscillator evolution is defined with respect to the local proper time of the shell, allowing the oscillator to serve as a local clock that ticks differently depending on the shell’s position and momentum. A Hamiltonian reduction is performed (...) on the system, and an approximate quantum description is given to the reduced phase space. If we focus only on the external dynamics, we must trace out the clock degree of freedom, and this results in a form of intrinsic decoherence that shares some features with a proposed “universal” decoherence mechanism attributed to gravitational time dilation. We note that the proposed decoherence remains present in the limit of flat spacetime, emphasizing that the effect can be attributed entirely to proper time differences, and thus is not necessarily related to gravity. Whereas the effect described in vanishes in the absence of an external gravitational field, our approach bootstraps the gravitational contribution to the time dilation decoherence by including self-interaction, yielding a fundamentally gravitational intrinsic decoherence effect. (shrink)

Ted Sider aptly and concisely states the self-visitation paradox thus: 'Suppose I travel back in time and stand in a room with my sitting 10-year-old self. I seem to be both sitting and standing, but how can that be?' (2001, 101). I will explore a relativist resolution of this paradox offered by, or on behalf of, endurantists.1 It maintains that the sitting and the standing are relative to the personal time or proper time of the (...) class='Hi'>time traveler and is intended to yield the result that Ted is sitting at a certain initial personal/proper time but is not standing relative to that time. Similarly, it is also supposed to yield that Ted is standing relative to a later personal/proper time, but not sitting relative to that .. (shrink)

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell’s equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point (...) radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics. (shrink)

Some of the problems associated with the construction of a manifestly covariant relativistic quantum theory are discussed. A resolution of this problem is given in terms of the off mass shell classical and quantum mechanics of Stueckelberg, Horwitz and Piron. This theory contains many questions of interpretation, reaching deeply into the notions of time, localizability and causality. A proper generalization of the Maxwell theory of electromagnetic interaction, required for the well-posed formulation of dynamical problems of systems with (...) electromagnetic interaction is discussed, and some of the significance of recently found (classical) relativistic chaotic behavior is pointed out. Many results of a technical nature have been achieved in this framework; in this paper, some of these are reviewed, but I shall concentrate on a discussion of the basic ideas and foundations of the theory. (shrink)

When addressing the notion of proper time in the theory of relativity, it is usually taken for granted that the time read by an accelerated clock is given by the Minkowski proper time. However, there are authors like Harvey Brown that consider necessary an extra assumption to arrive at this result, the so-called clock hypothesis. In opposition to Brown, Richard TW Arthur takes the clock hypothesis to be already implicit in the theory. In this paper (...) I will present a view different from these authors by taking into account Einstein’s notion of natural clock and showing its relevance to the debate. (shrink)

A new approach to developing formulisms of physics based solely on laws of mathematics is presented. From simple, classical statistical definitions for the observed space-time position and proper velocity of a particle having a discrete spectrum of internal states we derive u generalized Schrödinger equation on the space-time manifold. This governs the evolution of an N component wave function with each component square integrable over this manifold and is structured like that for a charged particle in an (...) electromagnetic field but also includes SU(N) gauge field couplings. This construction reveals a new hasis for gauge invariance and new insight into the appearance of spin and other such properties in relativistic quantum mechanics and suggests a new charged particle model. (shrink)

A clock-transport method of synchronization employing proper time is described that yields in any given inertial system the same result as slow transport, but that imposes no limit on transport proper speed. It is argued that because the method involves only the empirically validated kinematic invariant proper time, on which all observers must agree, there exists an option to synchronize clocks in such a way that thesimultaneity of spatially separated events is agreed upon by all (...) observers, hence is “absolute.” Such agreement refers only to phase equality of members (present at the events judged simultaneous) of comoving clock sets, not to clock rates or clock phase numerical values in different inertial systems. The demonstration employs only the on-worldline assertions of Einstein's kinematics. It thus depends on a limited subset of his ideas and allows a different identification of the spacelike invariant. (shrink)

The direct proof of transcendental idealism, in the Transcendental Aesthetic of Kant's First Critique, has borne the brunt of enormous criticism. Much of this criticism has arisen from a confusion regarding the epistemological nature of the arguments Kant proposes with the alleged ontological conclusions he draws. In this paper I attempt to deflect this species of criticism. I concentrate my analysis on the Metaphysical Expositions of Space and Time. I argue that the argument form of the Metaphysical Expositions is (...) that of disjunctive syllogism and that Kant's primary target of attack is that of Leibnizian relativism. I provide a detailed analysis and reconstruction of the arguments of the Metaphysical Expositions, defending Kant against various claims of argumentative invalidity and incoherence. I conclude by identifying what can properly be inferred regarding the ontological nature of space and time, given my reconstructions of the arguments, and by suggesting the manner in which Kant can deflect objections from the other major proponent of transcendental realism, namely, Newtonian absolutism. (shrink)

In this paper we shall discuss the relativistic space-time metric. Even if all inertial frames of reference are treated as equivalent in the formalism of the theory of relativity, there is an important difference between them if we take possible observers into account. The class of possible frames of reference for human or man-made observers is a proper part of the class of conceivable frames of reference. This subclass is privileged with respect to human knowledge: Descriptions of (...) physical phenomena with respect to members of it have a different epistemological status from descriptions with respect to other frames of reference. This fact is often neglected in presentations of the theory of relativity. We shall attempt to show that an emphasis on the observer's position sheds light on some features of the theory of relativity. (shrink)

This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory. Here, we first show that there are two versions of Maxwell’s equations. The new version fixes the clock of the field source for all inertial observers. However now, the (natural definition of the effective) speed of light is no longer an invariant for (...) all observers, but depends on the motion of the source. This approach allows us to account for radiation reaction without the Lorentz-Dirac equation, self-energy (divergence), advanced potentials or any assumptions about the structure of the source. The theory provides a new invariance group which, in general, is a nonlinear and nonlocal representation of the Lorentz group. This approach also provides a natural (and unique) definition of simultaneity for all observers.The corresponding particle theory is independent of particle number, noninvariant under time reversal (arrow of time), compatible with quantum mechanics and has a corresponding positive definite canonical Hamiltonian associated with the clock of the source.We also provide a brief review of our work on the foundational aspects of the corresponding relativistic quantum theory. Here, we show that the standard square-root and Dirac equations are actually two distinct spin- $\frac{1}{2}$ particle equations. (shrink)

The genesis of Feynman's original approach to QED is reviewed. The main ideas of his original presentation at the Pocono Conference are discussed and compared with the ones involved in his action-at-distance formulation of classical electrodynamics. The role of the de Sitter group in Feynman's visualization of space-time processes is emphasized.

Several years ago, in quantum mechanics, Davies proposed a method to calculate particle’s traveling time with the phase difference of wave function. The method is convenient for calculating the sojourn time inside a potential step and the tunneling time through a potential hill. We extend Davies’ non-relativistic calculation to relativistic quantum mechanics, with and without particle-antiparticle creation, using Klein–Gordon equation and Dirac Equation, for different forms of energy-momentum relation. The extension is successful only when the (...) particle and antiparticle creation/annihilation effect is negligible. (shrink)

This article analyzes Toole’s novel from a causal perspective, focusing on the cause-effect dynamics that make the plot advance, from the initial event at D.H. Holmes until the outcome in the Night of Joy. A combination of qualitative and quantitative methodologies has been applied to identify a series of 47 causal events that summarize all actions with an impact on plot development. Our research shows that the causal study of the novel is a useful approach that can reinforce or modify (...) qualitative assessments of previous studies. The relevance of “Night of Joy” plot within the whole narrative and its key role in the rest of the subplots are verified in numerical terms. Besides, we have expanded and quantified the causal chains operating in the novel; and we have made sure, as well, that every subplot is essential in order to reach the final outcome (with the only exception of Dr. Talc’s story). Finally, we have formulated an alternative outline of secondary plots than the ones supported by preceding research by using numeric metrics, demonstrating that “Paradise Vendors” and “Dorian Greene”, previously considered secondary storylines, exert a high impact on Confederacy’s finale, and are, perhaps, not so secondary plots after all. (shrink)

We discuss the question of whether or not a general Weyl structure is a suitable mathematical model of space–time. This is an issue that has been in debate since Weyl formulated his unified field theory for the first time. We do not present the discussion from the point of view of a particular unification theory, but instead from a more general standpoint, in which the viability of such a structure as a model of space–time is investigated. Our (...) starting point is the well known axiomatic approach to space–time given by Elhers, Pirani and Schild. In this framework, we carry out an exhaustive analysis of what is required for a consistent definition for proper time and show that such a definition leads to the prediction of the so-called “second clock effect”. We take the view that if, based on experience, we were to reject space–time models predicting this effect, this could be incorporated as the last axiom in the EPS approach. Finally, we provide a proof that, in this case, we are led to a Weyl integrable space–time as the most general structure that would be suitable to model space–time. (shrink)

Relativity allegedly contradicts presentism, the dynamic view of time and reality, according to which temporal passage is conceived of as an existentially distinguished ‘moving’ now. Against this common belief, the paper motivates a presentist interpretation of spacetime: It is argued that the fundamental concept of time—proper time—cannot be characterized by the earlier-later relation, i.e., not in the B-theoretical sense. Only the presentist can provide a temporal understanding of the twins’ paradox and of universes with closed timelike (...) curves. (shrink)

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

I argue that David Lewis’s philosophically dominant conception of time travel cannot straightforwardly handle what we might call cases of relativistic time travel—that is, the sort of time travel which could only plausibly occur in a relativistic setting. I evaluate whether or not the Lewisian account can be successfully adapted such that it would able to analyse potential cases of relativistic time travel satisfactorily while still being employable in the analysis of those cases (...) that make no mention of physics or the structure of spacetime. This is primarily an analytical and explanatory exercise, rather than a polemical one. (shrink)

Albert Einstein's bold assertion of the form-invariance of the equation of a spherical light wave with respect to inertial frames of reference became, in the space of six years, the preferred foundation of his theory of relativity. Early on, however, Einstein's universal light-sphere invariance was challenged on epistemological grounds by Henri Poincaré, who promoted an alternative demonstration of the foundations of relativity theory based on the notion of a light-ellipsoid. Drawing in part on archival sources, this paper shows how an (...) informal, international group of physicists, mathematicians, and engineers, including Einstein, Paul Langevin, Poincaré, Hermann Minkowski, Ebenezer Cunningham, Harry Bateman, Otto Berg, Max Planck, Max Laue, A. A. Robb, and Ludwig Silberstein, employed figures of light during the formative years of relativity theory in their discovery of the salient features of the relativistic worldview. (shrink)

Already in 1835 Lobachevski entertained the possibility of multiple geometries of the same type playing a role. This idea of rival geometries has reappeared from time to time but had yet to become a key idea in space-time philosophy prior to Brown's _Physical Relativity_. Such ideas are emphasized towards the end of Brown's book, which I suggest as the interpretive key. A crucial difference between Brown's constructivist approach to space-time theory and orthodox "space-time realism" pertains (...) to modal scope. Constructivism takes a broad modal scope in applying to all local classical field theories---modal cosmopolitanism, one might say, including theories with multiple geometries. By contrast the orthodox view is modally provincial in assuming that there exists a _unique_ geometry, as the familiar theories have. These theories serve as the "canon" for the orthodox view. Their historical roles also suggest a Whiggish story of inevitable progress. Physics literature after c. 1920 is relevant to orthodoxy primarily as commentary on the canon, which closed in the 1910s. The orthodox view explains the spatio-temporal behavior of matter in terms of the manifestation of the real geometry of space-time, an explanation works fairly well within the canon. The orthodox view, Whiggish history, and the canon have a symbiotic relationship. If one happens to philosophize about a theory outside the canon, space-time realism sheds little light on the spatio-temporal behavior of matter. Worse, it gives the _wrong_ answer when applied to an example arguably _within_ the canon, a sector of Special Relativity, namely, _massive_ scalar gravity with universal coupling. Which is the true geometry---the flat metric from the Poincare' symmetry group, the conformally flat metric exhibited by material rods and clocks, or both---or is the question faulty? How does space-time realism explain the fact that all matter fields see the same curved geometry, when so many ways to mix and match exist? Constructivist attention to dynamical details is vindicated; geometrical shortcuts can disappoint. The more exhaustive exploration of relativistic field theories in particle physics, especially massive theories, is a largely untapped resource for space-time philosophy. (shrink)

A new description of gravitational motion will be proposed. It is part of the proper time formulation of physics as presented on the IARD 2000 conference. According to this formulation the proper time of an object is taken as its fourth coordinate. As a consequence, one obtains a circular space–time diagram where distances are measured with the Euclidean metric. The relativistic factor turns out to be of simple goniometric origin. It further follows that the (...) Lagrangian for gravitational dynamics does not require an interpretation in terms of curvature of space–time. The flat space model for gravitational dynamics leads to the correct predictions for the bending of light, the perihelion shift of Mercury and gravitational red-shift. The new theory is free of singularities. More important, the new formulation of gravitational dynamics restores the validity of the principle of addition of potentials. One therefore can find solutions for static gravitational configurations for which it is difficult to find the solution of the corresponding Einstein equations. The method will be illustrated by means of the orbital precession for non-spherical stellar mass distributions. In case of the bipole mass distribution the agreement with the predictions of the general theory of relativity is very striking. Nevertheless, the new model is far more simple. (shrink)

In Minkowski spacetime, because of the relativity of simultaneity to the inertial frame chosen, there is no unique world-at-an-instant. Thus the classical view that there is a unique set of events existing now in a three dimensional space cannot be sustained. The two solutions most often advanced are that the four-dimensional structure of events and processes is alone real, and that becoming present is not an objective part of reality; and that present existence is not an absolute notion, but is (...) relative to inertial frame; the world-at-an-instant is a three dimensional, but relative, reality. According to a third view, advanced by Robb, Capek and Stein, what is present at a given spacetime point is, strictly speaking, constituted by that point alone. I argue here against the first of these views that the four-dimensional universe cannot be said to exist now, already, or indeed at any time at all; so that talk of its existence or reality as if that precludes the existence or reality of the present is a non sequitur. The second view assumes that in relativistic physics time lapse is measured by the time co-ordinate function; against this I maintain that it is in fact measured by the proper time, as I argue by reference to the Twin Paradox. The third view, although formally correct, is tarnished by its unrealistic assumption of point-events. This makes it susceptible to paradox, and also sets it at variance with our normal intuitions of the present. I argue that a defensible concept of the present is nonetheless obtainable when account is taken of the non-instantaneity of events, including that of conscious awareness, as that region of spacetime comprised between the forward lightcone of the beginning of a small interval of proper time t and the backward lightcone of the end of that interval. This gives a serviceable notion of what is present to a given event of short duration, as well as saving our intuition of the “reality” or robustness of present events. (shrink)

This is a short, nontechnical introduction to features of time in classical and relativistic physics and their representation in the four-dimensional geometry of spacetime. Topics discussed include: the relativity of simultaneity in special and general relativity; the ‘twin paradox’ and differential aging effects in special and general relativity; and time travel in general relativity.

I argue that there is natural relationist interpretation of Newtonian and relativistic non-quantum physics. Although relationist, this interpretation does not fall prey to the traditional objections based on the existence of inertial effects.

This essay examines the case for relativism about future contingents in light of a distinction between two ways of interpreting the ‘branching time’ framework. Focussing on MacFarlane (2014), we break the argument for relativism down into two steps. The first step is an argument for something MacFarlane calls the "Non-Determination Thesis", which is essentially the view that there is no unique actual future. The second step is an argument from the Non-Determination Thesis to relativism. I first argue that first (...) step of this argument fails. But despite that result, the second step is still of interest, since many philosophers have maintained something like the Non-Determination Thesis on alternative grounds. I then argue that whether the second step of the argument suc- ceeds depends on how the Non-Determination Thesis is motivated, and how the ‘branching time’ framework is interpreted in light of that moti- vation. If the branches in an intended branching time model are ersatz possible worlds, then the argument for relativism might go through; but if, instead, the branches are concrete parts of a ‘branching multiverse’, then the argument for relativism turns out to make implausible assumptions about the nature of personal identity over time. That argument can thus be rejected by rejecting those assumptions. One upshot of this is that the case for relativism about future contingents is much weaker than has been appreciated; a broader lesson is that philosophers who invoke the branching time framework need to pay close attention to different ways of interpreting it. (shrink)

It is shown that the time operatorQ 0 appearing in the realization of the RCCR's [Qμ,Pv]=−jhgμv, on Minkowski quantum spacetime is a self adjoint operator on Hilbert space of square integrable functions over Σ m =σ×v m , where σ is a timelike hyperplane. This result leads to time-energy uncertainty relations that match their space-momentum counterparts. The operators Qμ appearing in Born's metric operator in quantum spacetime emerge as internal spacetime operators for exciton states, and the condition that (...) the metric operator should possess a ground exciton state assumes the significance of achieving minimal spacetime4-momentum uncertainty in fundamental standards for spacetime measurements. (shrink)

The debate about the passage of time is usually confined to Minkowski‟s geometric interpretation of space-time. It infers the block universe from the notion of relative simultaneity. But there are alternative interpretations of space-time – so-called axiomatic approaches –, based on the existence of „optical facts‟, which have thermodynamic properties. It may therefore be interesting to approach the afore-mentioned debate from the point of view of relativistic thermodynamics, in which invariant parameters exist, which may serve to (...) indicate the passage of time. Of particular interest is the use of entropic clocks, gas clocks and statistical thermometers, which suggest that two observers in Minkowski space-time could agree on an objective passing of time. (shrink)

The concept of an objective spatial direction in special relativity is investigated and theories assuming light-speed isotropy while accepting the existence of a privileged spatial direction are classified, including so-called very special relativity. A natural generalization of the proper time principle is introduced which makes it possible to devise non-optical experimental tests of spatial isotropy. Several common misunderstandings in the relativistic literature concerning the role of spatial isotropy are clarified.