Although there is good experimental evidence for the Aharonov–Bohm phase shift occurring when a solenoid is placed between the beams forming a double-slit electron interference pattern, there has been very little analysis of the relevant classical electromagnetic forces. These forces between a point charge and a solenoid involve subtle relativistic effects of order v 2 /c 2 analogous to those discussed by Coleman and Van Vleck in their treatment of the Shockley–James paradox. In this article we show that a (...) treatment exactly analogous to that given by Coleman and Van Vleck predicts classical electromagnetic forces which provide the basis for the Aharonov–Bohm phase shift. The magnetic force on the solenoid due to the passing charge leads to a displacement of the solenoid center of energy which must be balanced by the displacement of the passing charge. This classical displacement of the passing charge is exactly what is required to account for the Aharonov–Bohm phase shift. Also, we discuss a magnetic moment model which appears frequently in the literature and note that although the model provides conservation of linear momentum, it does not satisfy the general requirements for relativistic theories. We give an example suggesting that the new equation of motion for a magnetic moment proposed by Aharonov, Pearle, and Vaidman based upon the hidden momentum of the magnetic moment is completely inappropriate. Finally, we emphasize that the Aharonov–Casher phase shift is also explained by classical electromagnetic forces exactly parallel to those explaining the Aharonov–Bohm phase shift. (shrink)

Richard Feynman has claimed that anti-particles are nothing but particles `propagating backwards in time'; that time reversing a particle state always turns it into the corresponding anti-particle state. According to standard quantum field theory textbooks this is not so: time reversal does not turn particles into anti-particles. Feynman's view is interesting because, in particular, it suggests a nonstandard, and possibly illuminating, interpretation of the CPT theorem. In this paper, we explore a classical analog of Feynman's view, in the context (...) of the recent debate between David Albert and David Malament over time reversal in classical electromagnetism. (shrink)

I want to compliment the author on the obvious care and expertise with which he assembled this text. If I were to teach a yearlong graduate-level electromagnetism course, I would use this book.

It is deeply entrenched dogma that relativity theory prohibits superluminal propagation. It is also experimentally well-established that under some circumstances, classical electromagnetic fields propagate through a dielectric medium with superluminal group velocities and superluminal phase velocities. But it is usually claimed that these superluminal velocities do not violate the relativistic prohibition. Here I analyze electromagnetic fields in a dielectric medium within a framework for understanding superluminal propagation recently developed by Geroch and elaborated by Earman. I will argue that for (...) some parameter values, electromagnetic fields do propagate superluminally in the Geroch-Earman sense. (shrink)

The classical relativistic theory is developed of electric and magnetic fields in terms of boost and rotation generators, respectively, of the Lorentz group of space-time. This development shows that Minkowski geometry requires that there be threestates of polarization of radiation in free space. The magnetic components in a circular basis are right and left circular and longitudinal. The longitudinal component is real and physical, and proportional to one of the three, nonzero, rotation generators of the Lorentz group. The longitudinal (...) electric component is pure imaginary, and proportional to one of the three boost generators. These theoretical arguments conform with experimental data from the Planck radiation law and from magnetic effects of light such as the inverse Faraday effect. (shrink)

One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell’s equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon’s quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave (...) function for the photon :1914–1919, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell’s equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon. (shrink)

Electromagnetism is usually understood as a theory describing how charged particles and eletromagnetic fields interact. In this paper I argue that a double ontology comprising both particles and fields is problematic. Either we should think of electromagnetism as a theory about charged particles directly interacting with each other, or as theory of fields whose local interactions are manifested as field quanta, called "particles." From a purely theoretical point of view the choice between a particle and a field interpretation (...) does not matter much when it concerns classical electromagnetism; both interpretations are possible and, as shown by Quine, there is a general method for translating a theory about one kind of objects into a theory assuming another kind of objects, provided these theories are empirically equivalent. From an empiricist point of view, however, the particle interpretation is the choice, since some particles are directly observable. Testable predictions of electromagnetism are predictions of the motion of charged bodies, in theory represented as particles, so this must be the empiricists' choice of ontology. In quantum electrodynamics one is however forced to chose a field ontology, since a particle ontology for this theory is impossible. So called "quantum particles" are field quanta, which cannot be treated as individuals making up a domain of quantification. There is thus a tension regarding ontology between classical and quantum electrodynamics. But this tension is nothing else than the much debated measurement problem of quantum mechanics. (shrink)

Using a framework of Dirac algebra, the Clifford algebra appropriate for Minkowski space-time, the formulation of classical electromagnetism including both electric and magnetic charge is explored. Employing the two-potential approach of Cabibbo and Ferrari, a Lagrangian is obtained that is dyality invariant and from which it is possible to derive by Hamilton's principle both the symmetrized Maxwell's equations and the equations of motion for both electrically and magnetically charged particles. This latter result is achieved by defining the variation (...) of the action associated with the cross terms of the interaction Lagrangian in terms of a surface integral. The surface integral has an equivalent path-integral form, showing that the contribution of the cross terms is local in nature. The form of these cross terms derives in a natural way from a Dirac algebraic formulation, and, in fact, the use of the geometric product of Dirac algebra is an essential aspect of this derivation. No kinematic restrictions are associated with the derivation, and no relationship between magnetic and electric charge evolves from the (classical) formulation. However, it is indicated that in bound states quantum mechanical considerations will lead to a version of Dirac's quantization condition. A discussion of parity violation of the generalized electromagnetic theory is given, and a new approach to the incorporation of this violation into the formalism is suggested. Possibilities for extensions are mentioned. (shrink)

The theory of scale-covariant gravity is extended to include charged matter and electromagnetism at the classical level. The possibility of charge creation exists and the creation rate of charge differs from the creation rate of matter. A variational principle for scale-covariant gravity and electromagnetism coupled to a charged perfect fluid is given.

Internal global symmetries exist for the free non-relativistic Schrodinger particle, whose associated Noether charges---the space integrals of the wavefunction and the wavefunction multiplied by the spatial coordinate---are exhibited. Analogous symmetries in classical electromagnetism are also demonstrated.

This paper provides a survey of several philosophical issues arising in classical electrodynamics arguing that there is a philosophically rich set of problems in theories of classical physics that have not yet received the attention by philosophers that they deserve. One issue, which is connected to the philosophy of causation, concerns the temporal asymmetry exhibited by radiation fields in the presence of wave sources. Physicists and philosophers disagree on whether this asymmetry reflects a fundamental causal asymmetry or is (...) due to statistical or thermodynamic considerations. I suggest that an explanation appealing to the asymmetry of causation is more promising. Another issue concerns the conceptual structure of the theory. Despite its empirical success, classical electrodynamics faces serious foundational problems. Models of charged particles involve what by the theory's own lights are idealizations, I maintain, and this is a feature that is not readily captured by traditional philosophical accounts of scientific theories. Other issues I discuss concern (i) the relation between Lorentz's theory of the electron and Einstein's Theory of Special Relativity; (ii) the notion of the domain of a theory, the question of theory reduction, and the relation between classical and more fundamental quantum theories; and (iii) the role of locality constraints, their relation to the concept of causation; and the status of locality conditions in the semi-classical theory of the Aharanov-Bohm effect. (shrink)

This article examines the implications of the holonomy interpretation of classical electromagnetism. As has been argued by Richard Healey and Gordon Belot, classical electromagnetism on this interpretation evinces a form of nonseparability, something that otherwise might have been thought of as confined to nonclassical physics. Consideration of the differences between this classical nonseparability and quantum nonseparability shows that the nonseparability exhibited by the classical electromagnetism on the holonomy interpretation is closer to separability than (...) might at first appear. (shrink)

This paper discusses the discrete symmetries of off-shell electromagnetism, the Stueckelberg–Schrodinger relativistic quantum theory and its associated 5D local gauge theory. Seeking a dynamical description of particle/antiparticle interactions, Stueckelberg developed a covariant mechanics with a monotonically increasing Poincaré-invariant parameter. In Stueckelberg’s framework, worldlines are traced out through the parameterized evolution of spacetime events, which may advance or retreat with respect to the laboratory clock, depending on the sign of the energy, so that negative energy trajectories appear as antiparticles when (...) the observer describes the evolution using the laboratory clock. The associated gauge theory describes local interactions between events (correlated by the invariant parameter) mediated by five off-shell gauge fields. These gauge fields are shown to transform tensorially under under space and time reflections—unlike the standard Maxwell fields—and the interacting quantum theory therefore remains manifestly Lorentz covariant. Charge conjugation symmetry in the quantum theory is achieved by simultaneous reflection of the sense of evolution and the fifth scalar field. Applying this procedure to the classical gauge theory leads to a purely classical manifestation of charge conjugation, placing the CPT symmetries on the same footing in the classical and quantum domains. In the resulting picture, interactions do not distinguish between particle and antiparticle trajectories—charge conjugation merely describes the interpretation of observed negative energy trajectories according to the laboratory clock. (shrink)

In 1912, Henri Poincaré published an argument which apparently shows that the hypothesis of quanta is both necessary and sufficient for the truth of Planck''s experimentally corroborated law describing the spectral distribution of radiant energy in a black body. In a recent paper, John Norton has reaffirmed the authority of Poincarés argument, setting it up as a paradigm case in which empirical data can be used to definitively rule out theoretical competitors to a given theoretical hypothesis. My goal is to (...) dispute Norton ''s claim that there is no theoretical underdetermination problem arising between classical physics and early quantum theory. The strategy I use in defending my view is to adopt a suggestion made by Jarrett Leplin and Larry Laudan on how to assess the relative merits of competing theoretical alternatives, where each alternative has an equal capacity to save the phenomena. In the course of the paper, I distinguish between two branches of classical physics: classical mechanics and classical electromagnetism. The former is claimed by Norton and Poincaré to be determinately ruled out by the black body evidence; and it is the former that I argue is compatible with this evidence. (shrink)

The relation is developed between rotation generators of the Lorentz group and the magnetic fields of free-space electromagnetism. Using these classical relations, it is shown that in the quantum field theory there exists a longitudinal photomagneton, a quantized magnetic flux density operator which is directly proportional to the photon spin angular momentum. Commutation relations are given in the quantum field between the longitudinal photomagneton and the usual transverse magnetic components of quantized electromagnetism. The longitudinal component is phase (...) free, but the transverse components are phase dependent. All three components can magnetize material in general, but only the transverse components contribute to Planck's law. The photon therefore has three, not two, relativistically invariant degrees of polarization, an axial, longitudinal, polarization, and the usual right and left circular transverse polarizations. Since the longitudinal polarization is axial, it is a phase- free magnetic field. (shrink)

The laser, first operated in 1960, produced light with coherence properties that demanded explanation. While some attempted a treatment within the framework of classical coherence theory, others insisted that only quantum electrodynamics could give adequate insight and generality. The result was a sharp and rather bitter controversy, conducted over the physics and mathematics that were being deployed, but also over the criteria for doing good science. Three physicists were at the center of this dispute, Emil Wolf, Max Born’s collaborator (...) on a canonical text on optics as a branch of classical electromagnetism, Roy J. Glauber, a student of Julian Schwinger and a high-energy particle theorist, and Leonard Mandel, both experimentalist and theorist and versed in the physics of photodetection. The story told here is thus one of three distinct research trajectories and of the explosion that occurred when, pushed into the well-financed field of laser studies, these trajectories collided. (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)

It is suggested that an understanding of blackbody radiation within classical physics requires the presence of classical electromagnetic zero-point radiation, the restriction to relativistic (Coulomb) scattering systems, and the use of discrete charge. The contrasting scaling properties of nonrelativistic classical mechanics and classical electrodynamics are noted, and it is emphasized that the solutions of classical electrodynamics found in nature involve constants which connect together the scales of length, time, and energy. Indeed, there are analogies between (...) the electrostatic forces for groups of particles of discrete charge and the van der Waals forces in equilibrium thermal radiation. The differing Lorentz- or Galilean-transformation properties of the zero-point radiation spectrum and the Rayleigh-Jeans spectrum are noted in connection with their scaling properties. Also, the thermal effects of acceleration within classical electromagnetism are related to the existence of thermal equilibrium within a gravitational field. The unique scaling and phase-space properties of a discrete charge in the Coulomb potential suggest the possibility of an equilibrium between the zero-point radiation spectrum and matter which is universal (independent of the particle mass), and an equilibrium between a universal thermal radiation spectrum and matter where the matter phase space depends only upon the ratio mc 2/k B T. The observations and qualitative suggestions made here run counter to the ideas of currently accepted quantum physics. (shrink)

This book is a stimulating and engaging discussion of philosophical issues in the foundations of classical electromagnetism. In the rst half, Frisch argues against the standard conception of the theory as consistent and local. The second half is devoted to the puzzle of the arrow of radiation: the fact that waves behave asymmetrically in time, though the laws governing their evolution are temporally symmetric. The book is worthwhile for anyone interested in understanding the physical theory of electromagnetism, (...) as well for the views it presents on philosophical issues such as causation, counterfactuals, laws, scienti c theories, models, and explanation. While philosophers of physics tend to focus on quantum mechanics and relativity, Frisch’s book shows that there are deep foundational issues in classical physics, equally worthy of attention. That said, let me lodge disagreement on some key points. Frisch argues from an alleged inconsistency in classical electromagnetism— that Maxwell’s equations, the Lorentz force law, and the conservation of energy cannot be jointly true—to the conclusion that the standard view of scienti c theories as a formalism plus an interpretation is incorrect. Consistency is a necessary condition of any view on which scienti c theories give us an account of “ways the world could be” (Frisch, , ). Since classical electromagnetism is successfully used by practicing physicists, consistency must be just one criterion of theory choice weighed equally among others. This is an intriguing idea, but I am not sure that consistency can be given up so easily. That road leads dangerously close to accepting orthodox ‘Copenhagen’ quantum mechanics. Surely the inconsistency of.. (shrink)

Faraday's field concept presupposes that field stresses should share the axial symmetry of the lines of force. In the present article, the field dynamics is similarly required to depend only on field properties that can be tested through the motion of test-particles. Precise expressions of this 'Faradayan' principle in field-theoretical language are shown to severely restrict the form of classical field theories. In particular, static forces must obey the inverse square law in a linear approximation. Within a Minkowskian and (...) Lagrangian framework, the Faradayan principle automatically leads to Maxwell's theory of electromagnetism and to Einstein's theory of gravitation, without appeal to the equivalence principle. A comparison is drawn between this, Feynman's, and Einstein's way to arrive at general relativity. (shrink)

A cornerstone of physics, Maxwell‘s theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the electromagnetic field energy and the self-mass of an electron of finite extension do not obey Einstein‘s famous equation, \, but instead fulfill this relation with a factor 4/3 on the left-hand side. Furthermore, the energy and momentum of the electromagnetic field associated with the charge fail to transform as a four-vector. Many famous physicists have contributed to the debate of this so-called (...) 4/3-problem without arriving at a complete solution. It has generally been assumed that, as originally suggested by Poincaré, the problems are connected to the question of stability of the charge distribution, and that relativistic equivalence between energy and self-mass can only be restored by inclusion of stabilizing forces. Alternative solutions to the problems have also been proposed. Nearly a century ago Fermi suggested a covariant definition of the electromagnetic energy and momentum, and sixty years later Kalckar et al. argued that the 4/3 problem is caused by omission of a relativistic correction in the standard evaluation of the self-force from Coulomb self-interaction. However, the relation between these suggestions has not been clear. We show that the relativistic correction implies that the mechanical momentum of an accelerated rigid body must be defined as the sum of the momenta of its parts for fixed time in the momentary rest frame of the body. For the total momentum of particles and field to be conserved, the total energy–momentum tensor must be divergence free, and this then requires that the momentum of the associated electromagnetic field be defined in the same way, consistent with the suggestion by Fermi. This comprehensive solution of the 4/3-problem demonstrates that there is no conflict of Maxwell‘s theory with special relativity and the questions of equivalence of electromagnetic energy and self-mass and of stability of a classical charge distribution are independent. In appendices we discuss the relations of our treatment with Fermi‘s seminal paper and with a classic paper by Dirac where he evaluated the damping self-force on a point electron from transport of energy and momentum in the electromagnetic field. (shrink)

Standard lore holds that magnetic forces are incapable of doing mechanical work. More precisely, the claim is that whenever it appears that a magnetic force is doing work, the work is actually being done by another force, with the magnetic force serving only as an indirect mediator. However, the most familiar instances of magnetic forces acting in everyday life, such as when bar magnets lift other bar magnets, appear to present manifest evidence of magnetic forces doing work. These sorts of (...) counterexamples are often dismissed as arising from quantum effects that lie outside the classical regime. In this paper, we show that quantum theory is not needed to account for these phenomena, and that classical electromagnetism admits a model of elementary magnetic dipoles on which magnetic forces can indeed do work. In order to develop this model, we revisit the foundational principles of the classical theory of electromagnetism, showcase the importance of constraints from relativity, examine the structure of the multipole expansion, and study the connection between the Lorentz force law and conservation of energy and momentum. (shrink)

In the framework of classical electromagnetism, a charge however accelerated with respect to an inertial frame radiates energy, in any circumstance. Regarding the energy as made of photons, the hypothesis is here introduced that the emission of a photon is only possible as a result of a change of the energy of the charge, which requires an energy-work exchange with the accelerating field. On such an hypothesis an elementary impulsive-dissipative model for the photon emission is constructed, in the (...) framework of special relativity, in which no energy radiation is emitted from a charge in a central Coulomb field uniformly describing a circular orbit. (shrink)

This book offers an ideal first reader in ancient Greek. It presents a selection of extracts from a comprehensive range of Greek authors, from Homer to Plutarch, together with generous help with vocabulary and grammar. The passages have been chosen for their intrinsic interest and variety, and brief introductions set them in context. All but the commonest Greek words are glossed as they occur and a general vocabulary is included at the back. Although the book is designed to be used (...) by students who have only completed a beginner's course in Greek, students of all ages will find that it helps them to improve their ability and confidence in reading a wide range of prose and verse texts, while at the same time providing a fascinating and copiously illustrated introduction to the riches and variety of ancient Greek literature over a period of almost a thousand years. (shrink)

Examines interrelated topics in Medieval and Renaissance Latin literature: the status of women as writers, the status of women as rhetorical figures, and the status of women in society from the fifth to the early seventeenth century.

This is the BJPS Short Read version of the article When Fields Are Not Degrees of Freedom. In our article, Vera Hartenstein and I show that the world of classical electromagnetism might differ radically from the one we see in physics textbooks and experience day-to-day. First, light may not exist; second, the laws of electromagnetism are either incomplete or completely different; and, third, the mathematics needed to make exact calculations with these novel laws is in early development (...) and not part of the general mathematics curriculum at colleges and universities. (shrink)

The electric field of an orbiting charge or electron observed in the rotating frame takes on a circular trajectory with a maximum radius of \. The resultant extended electromagnetic structure is used to derive the spin–orbit energy of the orbiting electron. A surprising result of the derived expression is that the orbital velocity has a specific value ) in close agreement ) with the experimentally determined value for the fine structure constant ). Furthermore, the derived spin–orbit expression does not include (...) a g-factor ) which means that the Larmor and Thomas precessions are equal and opposite, resulting in zero net precession in the lab frame. These results suggest that the quantised fine structure constant and by extension Planck’s constant, are a natural extension of classical electromagnetism and conservation of energy in a rotating frame. (shrink)

In this article I argue for an empiricist view on laws. Some laws are fundamental in the sense that they are the result of inductive generalisations of observed regularities and at the same time in their formulation contain a new theoretical predicate. The inductive generalisations simul- taneously function as implicit definitions of these new predicates. Other laws are either explicit definitions or consequences of other previously established laws. I discuss the laws of classical mechanics, relativity theory and electromagnetism (...) in detail. Laws are necessary, whereas acciden- tal generalisations are not. But necessity here is not a modal concept, but rather interpreted as short for the semantic predicate “... is necessarily true”. Thus no modal logic is needed. The neces- sity attributed to law sentences is in turn interpreted as “necessary condition for the rest of the the- ory”, which is true since fundamental laws are implicit definitions of theoretical predicates use in the theory. (shrink)

It is widely recognized that ‘global’ symmetries, such as the boost invariance of classical mechanics and special relativity, can give rise to direct empirical counterparts such as the Galileo-ship phenomenon. However, conventional wisdom holds that ‘local’ symmetries, such as the diffeomorphism invariance of general relativity and the gauge invariance of classical electromagnetism, have no such direct empirical counterparts. We argue against this conventional wisdom. We develop a framework for analysing the relationship between Galileo-ship empirical phenomena on the (...) one hand, and physical theories that model such phenomena on the other, that renders the relationship between theoretical and empirical symmetries transparent, and from which it follows that both global and local symmetries can give rise to Galileo-ship phenomena. In particular, we use this framework to exhibit an analogue of Galileo’s ship for the local gauge invariance of electromagnetism. 1 Introduction2 Analogues of Galileo’s Ship? Faraday’s Cage and t’Hooft’s Beam-Splitter2.1 Faraday’s cage2.2 t’Hooft’s beam-splitter3 A Framework for Symmetries I: Systems and Subsystems4 An Example: Coulombic Electrostatics5 A Framework for Symmetries II: The Relationship between Theoretical and Empirical Symmetries6 Newtonian Gravity7 Local Symmetries that Are Not Boundary-Preserving: Classical Electromagnetism and Faraday’s Cage8 Local Boundary-Preserving Symmetries: Klein-Gordon-Maxwell Gauge Theory and t’Hooft’s Beam-Splitter9 Summary10 Conclusions. (shrink)

I consider two usages of the expression "gauge theory". On one, a gauge theory is a theory with excess structure; on the other, a gauge theory is any theory appropriately related to classical electromagnetism. I make precise one sense in which one formulation of electromagnetism, the paradigmatic gauge theory on both usages, may be understood to have excess structure, and then argue that gauge theories on the second usage, including Yang-Mills theory and general relativity, do not generally (...) have excess structure in this sense. (shrink)

The special and general relativity theories are used to demonstrate that the velocity of an unradiative particle in a Schwarzschild metric background, and in an electrostatic field, is the group velocity of a wave that we call a “particle wave,” which is a monochromatic solution of a standard equation of wave motion and possesses the following properties. It generalizes the de Broglie wave. The rays of a particle wave are the possible particle trajectories, and the motion equation of a particle (...) can be obtained from the ray equation. The standing particle wave equation generalizes the Schrödinger equation of wave amplitudes. The particle wave motion equation generalizes the Klein–Gordon equation; this result enables us to analyze the essence of the particle wave frequency. The equation of the eikonal of a particle wave generalizes the Hamilton–Jacobi equation; this result enables us to deduce the general expression for the linear momentum. The Heisenberg uncertainty relation expresses the diffraction of the particle wave, and the uncertainty relation connecting the particle instant of presence and energy results from the fact that the group velocity of the particle wave is the particle velocity. A single classical particle may be considered as constituted of geometrical particle wave; reciprocally, a geometrical particle wave may be considered as constituted of classical particles. The expression for a particle wave and the motion equation of the particle wave remain valid when the particle mass is zero. In that case, the particle is a photon, the particle wave is a component a classical electromagnetic wave that is embedded in a Schwarzschild metric background, and the motion equation of the wave particle is the motion equation of an electromagnetic wave in a Schwarzschild metric background. It follows that a particle wave possesses the same physical reality as a classical electromagnetic wave. This last result and the fact that the particle velocity is the group velocity of its wave are in accordance with the opinions of de Broglie and of Schrödinger. We extend these results to the particle subjected to any static field of forces in any gravitational metric background. Therefore we have achieved a synthesis of undulatory mechanics, classical electromagnetism, and gravitation for the case where the field of forces and the gravitational metric background are static, and this synthesis is based only on special and general relativity. (shrink)

We give a overview of the main areas in theoretical physics, with emphasis on their relation to Lagrangian formalism in classical mechanics. This review covers classical mechanics; the road from classical mechanics to Schrodinger's quantum mechanics; electromagnetism, special and general relativity, and (very briefly) gauge field theory and the Higgs mechanism. We shun mathematical rigor in favor of a straightforward presentation.

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study (...) of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry of spacetime. (shrink)

This dissertation explores several issues related to the CPT theorem. Chapter 2 explores the meaning of spacetime symmetries in general and time reversal in particular. It is proposed that a third conception of time reversal, 'geometric time reversal', is more appropriate for certain theoretical purposes than the existing 'active' and 'passive' conceptions. It is argued that, in the case of classical electromagnetism, a particular nonstandard time reversal operation is at least as defensible as the standard view. This unorthodox (...) time reversal operation is of interest because it is the classical counterpart of a view according to which the so-called 'CPT theorem' of quantum field theory is better called 'PT theorem'; on this view, a puzzle about how an operation as apparently non-spatio-temporal as charge conjugation can be linked to spacetime symmetries in as intimate a way as a CPT theorem would seem to suggest dissolves. In chapter 3, we turn to the question of whether the CPT theorem is an essentially quantum-theoretic result. We state and prove a classical analogue of the CPT theorem for systems of tensor fields. This classical analogue, however, appears not to extend to systems of spinor fields. The intriguing answer to our question thus appears to be that the CPT theorem for spinors is essentially quantum-theoretic, but that the CPT theorem for tensor fields applies equally to the classical and quantum cases. Chapter4 explores a puzzle that arises when one puts the CPT theorem alongside a standard way of understanding spacetime symmetries, according to which spacetime symmetries are to be understood in terms of background spacetime structure. The puzzle is that a 'PT theorem' amounts to a statement that the theory may not make essential use of a preferred direction of time, and this seems odd. We propose a solution to that puzzle for the case of tensor field theories. (shrink)

Classically, a gauge potential was merely a convenient device for generating a corresponding gauge field. Quantum-mechanically, a gauge potential lays claim to independent status as a further feature of the physical situation. But whether this is a local or a global feature is not made any clearer by the variety of mathematical structures used to represent it. I argue that in the theory of electromagnetism (or a non-Abelian generalization) that describes quantum particles subject to a classical interaction, the (...) gauge potential is best understood as a feature of the physical situation whose global character is most naturally represented by the holonomies of closed curves in space-time. (shrink)

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation laws’ violations (...) are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Special relativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work. (shrink)

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe ϑ α and a (metric compatible) Lorentz connection Γ α β . These two potentials yield the field strengths torsion T α and curvature R α β . Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe ϑ α to be proportional to four (...) extended electromagnetic potentials $\mathcal{A}^{\alpha }$ ; these are assumed to encompass the conventional Maxwellian potential A in a suitable limit. The viable Einstein-Cartan (-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans’ ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete. (shrink)

This book gives an excellent introduction to the theory of special relativity. Professor Resnick presents a fundamental and unified development of the subject with unusually clear discussions of the aspects that usually trouble beginners. He includes, for example, a section on the common sense of relativity. His presentation is lively and interspersed with historical, philosophical and special topics (such as the twin paradox) that will arouse and hold the reader's interest. You'll find many unique features that help you grasp the (...) material, such as worked-out examples,summary tables,thought questions and a wealth of excellent problems. The emphasis throughout the book is physical. The experimental background, experimental confirmation of predictions, and the physical interpretation of principles are stressed. The book treats relativistic kinematics, relativistic dynamics, and relativity and electromagnetism and contains special appendices on the geometric representation of space-time and on general relativity. Its organization permits an instructor to vary the length and depth of his treatment and to use the book either with or following classical physics. These features make it an ideal companion for introductory courses. (shrink)

Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space of possible dynamical models in such a way that forces and charges are appropriately coupled. We review the most well-known application of this kind, known as the 'gauge argument' or 'gauge principle', discuss its difficulties, and then reconstruct the gauge argument (...) as a valid theorem in quantum theory. We then present what we take to be a better and more general gauge argument, based on Noether's second theorem in classical Lagrangian field theory, and argue that this provides a more appropriate framework for understanding how gauge symmetry helps to constrain the dynamics of physical theories. (shrink)

Mathematically, gauge theories are extraordinarily rich --- so rich, in fact, that it can become all too easy to lose track of the connections between results, and become lost in a mass of beautiful theorems and properties: indeterminism, constraints, Noether identities, local and global symmetries, and so on. -/- One purpose of this short article is to provide some sort of a guide through the mathematics, to the conceptual core of what is actually going on. Its focus is on the (...) Lagrangian, variational-problem description of classical mechanics, from which the link between gauge symmetry and the apparent violation of determinism is easy to understand; only towards the end will the Hamiltonian description be considered. -/- The other purpose is to warn against adopting too unified a perspective on gauge theories. It will be argued that the meaning of the gauge freedom in a theory like general relativity is (at least from the Lagrangian viewpoint) significantly different from its meaning in theories like electromagnetism. The Hamiltonian framework blurs this distinction, and orthodox methods of quantization obliterate it; this may, in fact, be genuine progress, but it is dangerous to be guided by mathematics into conflating two conceptually distinct notions without appreciating the physical consequences. (shrink)