Canadian Journal of Philosophy, 37: 263–282. [preprint] This paper is a critical discussion of Mathias Frisch’s book Inconsistency, Asymmetry, and Nonlocality.

In a recent issue of this journal, M. Frisch claims to have proven that classical electrodynamics is an inconsistent physical theory. We argue that he has applied classical electrodynamics inconsistently. Frisch also claims that all other classical theories of electromagnetic phenomena, when consistent and in some sense an approximation of classical electrodynamics, are haunted by “serious conceptual problems” that defy resolution. We argue that this claim is based on a partisan if not misleading (...) presentation of theoretical research in classical electrodynamics. (shrink)

In the past, a few researchers have presented arguments indicating that a statistical equilibrium state of classical charged particles necessarily demands the existence of a temperature-independent, incident classical electromagnetic random radiation. Indeed, when classical electromagnetic zero-point radiation is included in the analysis of problems with macroscopic boundaries, or in the analysis of charged particles in linear force fields, then good agreement with nature is obtained. In general, however, this agreement has not been found to hold for charged (...) particles bound in nonlinear force fields. The point is raised here that this disagreement arising for nonlinear force fields may be a premature conclusion on this classical theory for describing atomic systems, because past calculations have not directed strict attention to electromagnetic interactions between charges. This point is illustrated here by examining the classical hydrogen atom and showing that this problem has still not been adequately solved. (shrink)

I show that the standard approach to modeling phenomena involving microscopic classical electrodynamics is mathematically inconsistent. I argue that there is no conceptually unproblematic and consistent theory covering the same phenomena to which this inconsistent theory can be thought of as an approximation; and I propose a set of conditions for the acceptability of inconsistent theories.

It is assumed that the coupling of the field quantities Dμv (x) and F αβ (x) is nonlocal. This hypothesis leads to a theory of an electromagnetic field that has the following properties.(1) The source of the field F αβ (x) exhibits a center of charge and a center of mass that do not coincide, in general.(2) The field componentF 0i=−c2Ei is regular at the origin.(3) In the first-order approximation the new field equations are equivalent to the conventional Maxwell field (...) equations.(4) The conventional cutoff procedure in momentum space as practiced in the Maxwell-Lorentz theory is equivalent to the first-order approximation in terms of an invariant length ξ2.(5) The gyromagnetic ratio of the source of F αβ (x) is equal toc/mc for a quantum of chargee and massm. (shrink)

In Frisch 2004 and 2005 I showed that the standard ways of modeling particle-field interactions in classical electrodynamics, which exclude the interactions of a particle with its own field, results in a formal inconsistency, and I argued that attempts to include the self-field lead to numerous conceptual problems. In this paper I respond to criticism of my account in Belot 2007 and Muller 2007. I concede that this inconsistency in itself is less telling than I suggested earlier but (...) argue that existing solutions to the theory's foundational problems do not support the kind of traditional philosophical conception of scientific theorizing defended by Muller and Belot. *Received January 2007; revised October 2007. †To contact the author, please write to: Department of Philosophy, University of Maryland, Skinner Building, College Park, MD 20742; e-mail: [email protected]. (shrink)

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy–momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell’s equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell’s equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell’s equations to both operations, we obtained an additional symmetric term in the tensor, named as “compensating term”. Analyzing the structure of this “compensating term”, (...) we suggested a method of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any “runaway solutions”. It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov’s vector, defined in the paper. The problem of electromagnetic momentum is also examined. (shrink)

Classical electrodynamics—if developed consistently, as in Dirac's classical theory of the electron—is causally non‐local. I distinguish two distinct causal locality principles and argue, using Dirac's theory as my main case study, that neither can be reduced to a non‐causal principle of local determinism.

In classical electrodynamics, electromagnetic effects are calculated from solution of wave equation formed by combination of four Maxwell’s equations. However, along with retarded solution, this wave equation admits advanced solution in which case the effect happens before the cause. So, to preserve causality in natural events, the retarded solution is intentionally chosen and the advance part is just ignored. But, an equation or method cannot be called fundamental if it admits a wrong result (that violates principle of causality) (...) in addition to the correct result. Since it is the Maxwell’s form of equations that gives birth to this acausal advanced potential, we rewrite these equations in a different form using the recent theory of reaction at a distance (Biswaranjan Dikshit, Physics essays, 24(1), 4-9, 2011) so that the process of calculation does not generate any advanced effects. Thus, the long-standing causality problem in electrodynamics is solved. (shrink)

in Dirac's classical theory of the electron—is causally non-local. I distinguish two distinct causal locality principles and argue, using Dirac's theory as my main case study, that neither can be reduced to a non-causal principle of local determinism.

In previous work I have argued that classical electrodynamics is beset by deep conceptual problems, which result from the problem of self-interactions. Symptomatic of these problems, I argued, is that the main approach to modeling the interactions between charges and fields is inconsistent with the principle of energy–momentum conservation. Zuchowski reports a formal result that shows that the so-called ‘Abraham model' of a charged particle satisfies energy–momentum conservation and argues that this result amounts to a refutation of my (...) inconsistency claim. In this paper I defend my claims against her criticism and argue that she has succeeded neither in refuting my inconsistency argument nor in showing that the conceptual problems of classical electrodynamics have been solved. (shrink)

In this paper, I argue that the recent discussion on the time - reversal invariance of classical electrodynamics (see (Albert 2000: ch.1), (Arntzenius 2004), (Earman 2002), (Malament 2004),(Horwich 1987: ch.3)) can be best understood assuming that the disagreement among the various authors is actually a disagreement about the metaphysics of classical electrodynamics. If so, the controversy will not be resolved until we have established which alternative is the most natural. It turns out that we have a (...) paradox, namely that the following three claims are incompatible: the electromagnetic fields are real, classical electrodynamics is time-reversal invariant, and the content of the state of affairs of the world does not depend on whether it belongs to a forward or a backward sequence of states of the world. (shrink)

One of the most relevant features of quantum field theory is the phenomenon of pair production, the existence of which, first suggested by Dirac, was not even suspected in the older theories. On the other hand Feynman, in the spirit of his spatiotemporal approach to quantum mechanics, showed how a description of pair production could be given within classical relativistic kinematics; in fact, he actually exhibited world lines with the required properties in the framework of a nonlocal modification of (...) classical electrodynamics conceived by Bopp. In the present paper we show how classical world lines, just of the type required by Feynman to describe the phenomenon of pair production, naturally arise in classical electrodynamics. More precisely, we show that such world lines occur as solutions of the well-known Abraham-Lorentz-Dirac equation, which was originally designed to describe the motion of just a single point charge in self-interaction with the electromagnetic field. (shrink)

Mathias Frisch provides the first sustained philosophical discussion of conceptual problems in classical particle-field theories. Part of the book focuses on the problem of a satisfactory equation of motion for charged particles interacting with electromagnetic fields. As Frisch shows, the standard equation of motion results in a mathematically inconsistent theory, yet there is no fully consistent and conceptually unproblematic alternative theory. Frisch describes in detail how the search for a fundamental equation of motion is partly driven by pragmatic considerations (...) (like simplicity and mathematical tractability) that can override the aim for full consistency. The book also offers a comprehensive review and criticism of both the physical and philosophical literature on the temporal asymmetry exhibited by electromagnetic radiation fields, including Einstein's discussion of the asymmetry and Wheeler and Feynman's influential absorber theory of radiation. Frisch argues that attempts to derive the asymmetry from thermodynamic or cosmological considerations fail and proposes that we should understand the asymmetry as due to a fundamental causal constraint. The book's overarching philosophical thesis is that standard philosophical accounts that strictly identify scientific theories with a mathematical formalism and a mapping function specifying the theory's ontology are inadequate, since they permit neither inconsistent yet genuinely successful theories nor thick causal notions to be part of fundamental physics. (shrink)

This paper follows up a debate as to whether classical electrodynamics is inconsistent. Mathias Frisch makes the claim in Inconsistency, Asymmetry and Non-Locality ([2005]), but this has been quickly countered by F. A. Muller ([2007]) and Gordon Belot ([2007]). Here I argue that both Muller and Belot fail to connect with the background assumptions that support Frisch's claim. Responding to Belot I explicate Frisch's position in more detail, before providing my own criticisms. Correcting Frisch's position, I find that (...) I can present the theory in a way both authors can agree upon. Differences then manifest themselves purely within the reasoning methods employed. Introduction Features of the Theory Frisch's Inconsistency Claim Defending Frisch 4.1 Muller 4.2 Belot Difficulties for Frisch and a Compromise Conclusion CiteULike Connotea Del.icio.us What's this? (shrink)

I have argued that the standard ways of modeling classical particle-field interactions rely on a set of inconsistent assumptions. This claim has been criticized in (Muller forthcoming). In this paper I respond to some of Muller's criticism.

The usual action integral of classical electrodynamics is derived starting from Lanczos’s electrodynamics – a pure field theory in which charged particles are identified with singularities of the homogeneous Maxwell’s equations interpreted as a generalization of the Cauchy–Riemann regularity conditions from complex to biquaternion functions of four complex variables. It is shown that contrary to the usual theory based on the inhomogeneous Maxwell’s equations, in which charged particles are identified with the sources, there is no divergence in (...) the self-interaction so that the mass is finite, and that the only approximations made in the derivation are the usual conditions required for the internal consistency of classical electrodynamics. Moreover, it is found that the radius of the boundary surface enclosing a singularity interpreted as an electron is on the same order as that of the hypothetical “bag” confining the quarks in a hadron, so that Lanczos’s electrodynamics is engaging the reconsideration of many fundamental concepts related to the nature of elementary particles. (shrink)

It is common in the literature on classical electrodynamics and relativity theory that the transformation rules for the basic electrodynamical quantities are derived from the pre-assumption that the equations of electrodynamics are covariant against these---unknown---transformation rules. There are several problems to be raised concerning these derivations. This is, however, not our main concern in this paper. Even if these derivations were completely correct, they leave open the following fundamental question: Are the so-obtained transformation rules indeed identical with (...) the true transformation rules of the fundamental electrodynamical quantities? In other words, is it indeed the case that the values calculated from the quantities in one inertial frame by means of the transformation rules we derived are equal to the values of the same quantities obtained by the same operations with the same measuring equipments when they are co-moving with the other inertial frame? This is of course an empirical question. In this paper, we will investigate the problem in a purely theoretical framework by applying what J. S. Bell calls “Lorentzian pedagogy”---according to which the laws of physics in any one reference frame account for all physical phenomena. We will show that the transformation rules of the electrodynamical quantities are indeed identical with the ones obtained by presuming the covariance of the equations of electrodynamics, and that the covariance is indeed satisfied. Beforehand, however, we need to clarify the operational definitions of the fundamental electrodynamical quantities. As we will see, these semantic issues are not as trivial as one might think. (shrink)

We present a description of the Stern–Gerlach type experiments using only the concepts of classical electrodynamics and the Newton’s equations of motion. The quantization of the projections of the spin (or the projections of the magnetic dipole) is not introduced in our calculations. The main characteristic of our approach is a quantitative analysis of the motion of the magnetic atoms at the entrance of the magnetic field region. This study reveals a mechanism which modifies continuously the orientation of (...) the magnetic dipole of the atom in a very short time interval, at the entrance of the magnetic field region. The mechanism is based on the conservation of the total energy associated with a magnetic dipole which moves in a non uniform magnetic field generated by an electromagnet. A detailed quantitative comparison with the (1922) Stern–Gerlach experiment and the didactical (1967) experiment by J.R. Zacharias is presented. We conclude, contrary to the original Stern–Gerlach statement, that the classical explanations are not ruled out by the experimental data. (shrink)

Is it a "conceptual truth" or only a logically contingent fact that, in any given kind of case, an event x which asymmetrically causes ("produces") an event y likewise temporally precedes y or at least does not temporally succeed y? A bona fide physical example in which the cause retroproduces the effect would show that backward causation is no less conceptually possible than forward causation. And it has been claimed ([9], p. 151; [4], p. 41) that in Dirac's classical (...) electrodynamics (relativistic and non-relativistic), the preacceleration of charged particles before any forces are applied to them furnishes a genuine case of retrocausation by later forces. An exposition of the pertinent physics furnishes the basis for arguing the following: Whereas the non-zero acceleration of a neutral NEWTONIAN mass particle is, of course, causally connected as such to the simultaneously applied non-zero force, the non-zero acceleration of a DIRACIAN charged particle is not causally connected at all as such to the applied forces. A fortiori, in Dirac's electrodynamics, the applied forces do not qualify asymmetrically as the causes of a non-zero acceleration as such; nor does a non-zero acceleration as such qualify as an effect produced by forces. This is shown by means of two considerations as follows: (1) In Dirac's theory, no functional dependence of the value of a non-zero acceleration on the weighted time-average of the forces is vouchsafed as a matter of physical LAW alone without any value of a constant of integration, just as no Newtonian law(s) alone can guarantee a functional dependence of the non-zero value of the velocity of a Newtonian mass particle on the applied forces. Instead, both functional dependencies alike are vouchsafed only with the crucial aid of some de facto boundary condition pertaining to either the past or to the furute, so that (2) Non-zero preaccelerations of Diracian charged particles can no more be causally attributed as such to the retrocausal action of later forces than non-zero "prevelocities" of Newtonian mass particles can be held to be caused as such by later applied forces. The retrocausal interpretation of Dirac's preaccelerations is just as invalid as the retrocausal interpretation of Newtonian prevelocities. (shrink)

We present a new formalism for the microscopic classical electrodynamics of point charges in which the dynamic absence of self-interactions is enforced by the action principle, without eliminating the field degrees of freedom. In this context, free local radiation fields are dynamically prohibited. Instead radiation is carried by charge-field functionals of the current which have a negative parity under mathematical time reversal. This leads to the dynamic requirement of a physical time arrow in the equations of motion in (...) order to preserve the overall mathphysical time-reversal symmetry of the formalism. Since this physical time arrow emerges electrodynamically without the need of external thermodynamic or cosmological criteria, it offers a dynamical explanation for the origin of irreversibility in classical electrodynamic measurement processes. “Science, like the arts, admits aesthetic criteria; it seeks theories that display ‘a proper conformity of the parts to one another and to the whole’ while still showing some strangeness in their proportion”—S. Chandrasekar. (shrink)

In this article, I present a case study of underdetermination in nineteenth-century electrodynamics between a pure field theory and a formulation in terms of action at a distance. A particular focus is on the question if and how this underdetermination is eventually resolved. It turns out that after a period of overt underdetermination, during which the approaches are developed separately, the two programmes are merged. On the basis of this development, I argue that the original underdetermination survives in hidden (...) form in ontological and methodological redundancies of the subsequent particle–field electrodynamics. Implications regarding criteria for theory choice and the realism debate are briefly addressed. (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)

It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a classical ontology, can be traced to the fact that classical electrodynamics of interacting particles has never been given a consistent definition. Once this is done, our conjecture follows rather naturally, including a purely classical explanation of photon related phenomena. Our (...) analysis entirely rests on the block-universe view entailed by relativity theory. (shrink)

Dirac's classical electrodynamics countenances "preaccelerations" of charged particles at a time t as mathematical functions of external forces applied after the time t. These preaccelerations have been interpreted as evidence for physical retrocausation upon assuming that, in electrodynamics no less than in Newton's second law, external forces sustain an asymmetric causal relation to accelerations. And this retrocausal interpretation has just been defended against the critiques in (Grunbaum 1976), (Grunbaum and Janis, 1977 and 1978) by appeal to the (...) formal assimilation of the electrodynamic laws of motion to Newton's second law. It is argued below that this latest defense of the retrocausal interpretation is even more ill-founded than the prior ones in the literature. (shrink)

It is common in the literature on classical electrodynamics and relativity theory that the transformation rules for the basic electrodynamical quantities are derived from the hypothesis that the relativity principle applies to Maxwell's electrodynamics. As it will turn out from our analysis, these derivations raise several problems, and certain steps are logically questionable. This is, however, not our main concern in this paper. Even if these derivations were completely correct, they leave open the following questions: Is the (...) RP a true law of nature for electrodynamical phenomena? Are, at least, the transformation rules of the fundamental electrodynamical quantities, derived from the RP, true? Is the RP consistent with the laws of ED in a single inertial frame of reference? Are, at least, the derived transformation rules consistent with the laws of ED in a single frame of reference? Obviously, and are empirical questions. In this paper, we will investigate problems and. Abstract First we will give a general mathematical formulation of the RP. In the second part, we will deal with the operational definitions of the fundamental electrodynamical quantities. As we will see, these semantic issues are not as trivial as one might think. In the third part of the paper, applying what J. S. Bell calls “Lorentzian pedagogy”---according to which the laws of physics in any one reference frame account for all physical phenomena---we will show that the transformation rules of the electrodynamical quantities are identical with the ones obtained by presuming the covariance of the equations of ED, and that the covariance is indeed satisfied. Abstract As to problem, the situation is much more complex. As we will see, the RP is actually not a matter of the covariance of the physical equations, but it is a matter of the details of the solutions of the equations, which describe the behavior of moving objects. This raises conceptual problems concerning the meaning of the notion “the same system in a collective motion”. In case of ED, there seems no satisfactory solution to this conceptual problem; thus, contrary to the widespread views, the question we asked in the title has no obvious answer. (shrink)

It is common in the literature on classical electrodynamics (ED) and relativity theory that the transformation rules for the basic electrodynamical quantities are derived from the hypothesis that the relativity principle (RP) applies to Maxwell’s electrodynamics. As it will turn out from our analysis, these derivations raise several problems, and certain steps are logically questionable. This is, however, not our main concern in this paper. Even if these derivations were completely correct, they leave open the following questions: (...) (1) Is the RP a true law of nature for electrodynamical phenomena? (2) Are, at least, the transformation rules of the fundamental electrodynamical quantities, derived from the RP, true? (3) Is the RP consistent with the laws of ED in a single inertial frame of reference? (4) Are, at least, the derived transformation rules consistent with the laws of ED in a single frame of reference? Obviously, (1) and (2) are empirical questions. In this paper, we will investigate problems (3) and (4). First we will give a general mathematical formulation of the RP. In the second part, we will deal with the operational definitions of the fundamental electrodynamical quantities. As we will see, these semantic issues are not as trivial as one might think. In the third part of the paper, applying what J. S. Bell calls “Lorentzian pedagogy”—according to which the laws of physics in any one reference frame account for all physical phenomena— we will show that the transformation rules of the electrodynamical quantities are identical with the ones obtained by presuming the covariance of the equations of ED, and that the covariance is indeed satisfied. As to problem (3), the situation is much more complex. As we will see, the RP is actually not a matter of the covariance of the physical equations, but it is a matter of the details of the solutions of the equations, which describe the behavior of moving objects. This raises conceptual problems concerning the meaning of the notion “the same system in a collective motion”.. (shrink)

A new scheme is proposed in order to deduce an equation of motion for a spinless charged point particle leading to an equivalent Landau–Lifshitz equation of motion. Consequently Larmor’s formula must be substituted by a new expression for the large distance radiation rate of energy. A constraint appears on the applicability of the Maxwell electromagnetic tensor. The particular case of a sudden force is analyzed in order to show the physical results predicted by the new model. A geometrical rearrangement of (...) the energy explains the balance. (shrink)

The thermodynamic behavior is analyzed of a single classical charged particle in thermal equilibrium with classical electromagnetic thermal radiation, while electrostatically bound by a fixed charge distribution of opposite sign. A quasistatic displacement of this system in an applied electrostatic potential is investigated. Treating the system nonrelativistically, the change in internal energy, the work done, and the change in caloric entropy are all shown to be expressible in terms of averages involving the distribution of the position coordinates alone. (...) A convenient representation for the probability distribution is shown to be the ensemble average of the absolute square value of an expansion over the eigenstates of a Schrödinger-like equation, since the heat flow is shown to vanish for each hypothetical “state.” Subject to key assumptions highlighted here, the demand that the entropy be a function of state results in statistical averages in agreement with the form in quantum statistical mechanics. Examining the very low and very high temperature situations yields Planck's and Boltzmann's constants. The blackbody radiation spectrum is then deduced. From the viewpoint of the theory explored here, the method in quantum statistical mechanics of statistically counting the “states” at thermal equilibrium by using the energy eigenvalue structure, is simply a convenient counting scheme, rather than actually representing averages involving physically discrete energy states. (shrink)

A new scheme is proposed in order to deduce an equation of motion for a spinless charged point particle leading to an equivalent Landau–Lifshitz equation of motion. Consequently Larmor’s formula must be substituted by a new expression for the large distance radiation rate of energy. A constraint appears on the applicability of the Maxwell electromagnetic tensor. The particular case of a sudden force is analyzed in order to show the physical results predicted by the new model. A geometrical rearrangement of (...) the energy explains the balance. (shrink)

It is shown that a newly derived “exact expression” for radiation of an accelerated charge in the recent literature is simply incorrect, having arisen because of a wrong relativistic transformation of the distance parameter. The ensuing claim that the newly derived expression alone satisfies the energy conservation for the electromagnetic radiation, is based on a wrong reasoning where a proper distinction between the time during which the radiation is received and the time for emission (retarded time of the charge) was (...) not maintained. (shrink)

The present expression of radiation of an accelerated point charge is only approximately valid. The exact expression of radiation of an accelerated point charge is derived based on special relativity, and using the Larmor formulation for the radiation of an charged particle being accelerated, but instantaneously at rest. The totaled radiation power obtained by the exact expression is the same as Liénard’s generalization of the Larmor formula.

The reason for the arrow of time in electromagnetic radiation is explicated.

A detailed analysis is made of Grunbaum's claim that the Abraham-Lorentz (AL) and Dirac-Lorentz (DL) equations have no bearing on causality. It is pointed out that (a) both equations are derived from F = ma, and thus should obey the same causality conditions as Newton's law, (b) independently of what boundary conditions are imposed, non-causal behavior is always along the same straight line as the force, (c) the distinction in status between laws and boundary conditions which Grunbaum imposes is one (...) which is not always useful, especially since what is a law in one formulation of the theory can become a boundary condition in another, and thus it is argued that a complete theory must be such that laws and boundary conditions form a coherent whole, (d) the asymptotic boundary conditions that are applied are in agreement with experiment, (e) the AL equation is such that if the "effect," the acceleration as function of time, is known, then the "cause," the force, can be determined. In addition, it is noted that in the DL equation the acceleration at times later than t influences the acceleration at t. Finally, it is pointed out that electrodynamics is indeed a causal field theory, and that retrocausality is due to the transition from a field description to a particle description. (shrink)

Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as a more fundamental theory, but as an upgrade of classical electrodynamics, which permits an (...) extension of classical theory to the description of phenomena that, while being related to the conceptual framework of the classical theory, cannot be addressed from the classical theory. (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)

We explore certain difficulties in the covariant classical mechanics associated with off-shell electrodynamics, through an examination of the classical Coulomb problem. We present a straightforward solution of the classical equations of motion for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution reveals the essential difficulties in the formalism at the classical level. We then offer a new (...) model of the particle, as a certain distribution of events on the worldline, which eliminates these difficulties and permits comparison of classical off-shell electrodynamics with the standard Maxwell theory In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions—they are seen to coincide when λ > 10–6 sec, providing an initial estimate of this parameter. (shrink)

We explore certain difficulties in the covariant classical mechanics associated with off-shell electrodynamics, through an examination of the classical Coulomb problem. We present a straightforward solution of the classical equations of motion for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution reveals the essential difficulties in the formalism at the classical level. We then offer a new (...) model of the particle, as a certain distribution of events on the worldline, which eliminates these difficulties and permits comparison of classical off-shell electrodynamics with the standard Maxwell theory In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions—they are seen to coincide when λ > 10–6 sec, providing an initial estimate of this parameter. (shrink)