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Classical charged particles : foundations of their theory / F. Rohrlich
... The results here cannot be constrained by particle accelerator measurements of subatomic structure, just as such experiments cannot constrain general relativity or the Maxwell equations. Indeed, the validity of a classical theory of charged particles is confined only to results independent of elementary particle structure [10]. Certainly, the Maxwell equations and the Einstein equations describe macroscopic fields whose underlying reality is quantum, yet still yield testable predictions. ...
... So, too, do we apply the classical 5D theory, in the hopes that it can still yield testable predictions independent of atomic structure. Rohrlich [10] assures us that classical theories can yield valid descriptions of atomic systems in those cases where the result does not depend on assumptions of the atomic structure, and where the results are convergent. ...
... The equation of motion (15) has been studied by various researchers, including [13,18,19]. The term in brackets on the RHS of (15) that is quadratic in U α arises from the transformation of derivatives with respect to s, to derivatives with respect to τ, and using (10). This is indeed the form expected for a scalar field force [24]. ...
We present new results regarding the long-range scalar field that emerges from the classical Kaluza unification of general relativity and electromagnetism. The Kaluza framework reproduces known physics exactly when the scalar field goes to one, so we studied perturbations of the scalar field around unity, as is done for gravity in the Newtonian limit of general relativity. A suite of interesting phenomena unknown to the Kaluza literature is revealed: planetary masses are clothed in scalar field, which contributes 25% of the mass-energy of the clothed mass; the scalar potential around a planet is positive, compared with the negative gravitational potential; at laboratory scales, the scalar charge which couples to the scalar field is quadratic in electric charge; a new length scale of physics is encountered for the static scalar field around an electrically-charged mass, Ls=μ0Q2/M; the scalar charge of elementary particles is proportional to the electric charge, making the scalar force indistinguishable from the atomic electric force. An unduly strong electrogravitic buoyancy force is predicted for electrically-charged objects in the planetary scalar field, and this calculation appears to be the first quantitative falsification of the Kaluza unification. Since the simplest classical field, a long-range scalar field, is expected in nature, and since the Kaluza scalar field is as weak as gravity, we suggest that if there is an error in this calculation, it is likely to be in the magnitude of the coupling to the scalar field, not in the existence or magnitude of the scalar field itself.
... It is known that one has to deal with complex difference-differential equations when considering a relativistic classical dynamics of a system of interacting charges [1,2]. This is even more the case for scalar [2], gravitational [3] or non-Abelian [4] interactions where the dynamics is governed by integro-differential equations. ...
... A solution for this dynamics is obtained in terms of quadratures. This is done by means of projection operators built in terms of conserved canonical generators of O (1,4). The system of free particles as a time-asymmetric model is particularly considered. 2 Manifestly covariant test particle mechanics in de Sitter space ...
... 3 Action-at-a-distance dynamics of two particles in de Sitter space In the framework of Wheeler-Feynman electrodynamics [1,2,27,28] a system of charged point-like particles is described by the Tetrode-Fokker action-at-a-distance variational principle [7,8]. This formalism was generalized for a curved space-time by Hoyle and Narlikar [27] and others [28,29]. ...
The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant descriptions of the models within the Lagrangian and Hamiltonian formalisms with constraints are proposed. It is shown that the models are de Sitter-invariant and integrable. An explicit solution of equations of motion is derived in quadratures by means of projection operator technique.
... The history of CED teaches us that it can be accomplished, although this is far from a straightforward affair as prima facie may seem (cf. Rohrlich 1970;Landau and Lifshitz 1975, 77-80;Schwinger 1978). If one chooses for a Hamiltonian or for a Lagrangean approach to CED, energy conservation is automatically guaranteed as a consequence of the time-translation symmetry-an instance of Noether's Theorem. ...
... These binding forces accounted for a violation, in the models of Lorentz and Abraham, of the timehonored relation between force and power P, namely, (see F F 7 u p P Yaghjian 1992, 9-29). Seeming violations of energy and momentum conservation were avoided by redefining relativistic energy and momentum, suggestions which go back to E. Fermi in the 1920s (see Rohrlich 1970). ...
... The question how to derive equation (40) remained open for more than 30 years. The canonical monograph reviewing these and more theoretical investigations into the classical-electrodynamical behavior of electric charges until the mid-1960s was Rohrlich's (1965). The revised edition of this monograph had hardly appeared in 1990 when another monograph appeared on the subject written by the electrical engineer A. D. Yaghjian (1992 Dirac, and others through the looking glass, Yaghjian (1992) rediscovered the frequently tacitly made assumption of slowly varying electromagnetic fields in those derivations. ...
In a recent issue of this journal, M. Frisch claims to have proven that classical elec- trodynamics 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.
... Fortunately, there are known the equations of motion (and the above examples are based on them) derived via several ways regardless of the Larmor formula or energy balance condition [2,11,[15][16][17]. These are the Lorentz-Abraham-Dirac equation [18] or its nonrelativistic predecessor known as the Abraham-Lorentz equation [19] which both are widely accepted. ...
... (4. 16) In the limit Ω 3 → 0 the function Φ(t) reduces to 1/R(t); see (4.6). The Poisson equations (4.8) for this case take the form: ...
The formula for dipole radiation reaction torque acting on a system of charges, and the Larmor-like formula for the angular momentum loss by this system, differ in the time derivative term which is the analogue of the Schott term in the energy loss problem. In the well-known textbooks this discrepancy is commonly avoided via neglect of the Schott term, and the Larmor-like formula is preferred. In the present paper both formulae are used to derive two different equations of motion of a polarized spinning-top. Both equations are integrable for the symmetric top and lead to quite different solutions. That one following from the Larmor-like formula is physically unplausible, in contrast to another one. This result is accorded with the reinterpretation of Larmor's formula discussed recently in the pedagogical literature. It is appeared, besides, that the Schott term is of not only academic significance, but it may determine the behavior of polarized micro- and nanoparticles in nature or future experiments.
... where ǫ 0 ≡ Q/M is the charge-to-mass ratio of gravitational source, φ ≡− M/r is Newtonian potential, and ζ M ≡ 2aM (x × e 3 )/r 3 denotes the vector potential due to the source's rotation. The test particle is assumed to have a charge-to-mass ratio of ǫ 1 , and its motion is described by the geodesic equation [12] ...
... where ǫ 0 ≡ Q/M is the charge-to-mass ratio of gravitational source, φ ≡− M/r is Newtonian potential, and ζ M ≡ 2aM (x × e 3 )/r 3 denotes the vector potential due to the source's rotation. The test particle is assumed to have a charge-to-mass ratio of ǫ 1 , and its motion is described by the geodesic equation[12] ...
We first present the post-Newtonian dynamics for a charged particle in the gravitational field of a rotating, charged and massive body. Based on the particle dynamics, we further derive analytically the orbital precession of the particle via calculating the rate of change of the Runge-Lenz vector.
... Significant contributions were made, but a completely satisfactory treatment is yet to be developed (Parrot 1987). The starting point for the early investigations (Lorentz 1904;Abraham 1903) was an extended model for the point charge (more readily available accounts of these works can by found in Jackson 1973 andRohrlich 1959). The formula for the radiation reaction obtained from extended-particle models is in the form of a power series, with higher order terms dependent on some unverifiable form-factors. ...
... This very important contribution did not provide a satisfactory treatment of the diverging self-energy. More recent contributions were discussed by Rohrlich (1959) who showed the importance of incorporating an asymptotic boundary condition. Modern contributions include those of Barut (1990Barut ( , 1992, Ford andO'Connell (1991, 1993), Herdgen (1992), Ianconescu and Horwitz (1992), Bosanac (1994) and Gaftoi et al . ...
A new derivation for the radiation reaction on a point charge is presented. The field of the charge is written as a superposition of plane waves. The plane wave spectrum of the field consists of homogeneous plane waves which propagate away from the charge at the speed of light, and inhomogeneous plane waves which constitute the Coulomb field of the point charge. The radiation field is finite at the orbit of the point charge. The force acting on the charge due to this field is the well known Abraham-Lorentz radiation reaction.
... Now we turn to the long-time solutions of the field operators that we determined in section IV A. The long-time solution of the vector potential in (37) obviously is a solution of the following inhomogeneous wave equation: ...
... However, (56) is not a proper response function, since it has a pole near the very large positive imaginary frequency 3ic/(2Γ e ). This can be related to the need for the a-causal phenomenon called pre-acceleration to avoid so-called runaway solutions of the Abraham-Lorentz equation [37]. Although we know that in the damped-polariton theory only proper response functions can be found, we proceed like in the previous subsection and try to find coupling constants that in the optical regime give rise to the dielectric function (56). ...
The spontaneous-emission rate of a radiating atom reaches its time-independent equilibrium value after an initial transient regime. In this paper, we consider the associated relaxation effects of the spontaneous-decay rate of atoms in dispersive and absorbing dielectric media for atomic-transition frequencies near material resonances. A quantum mechanical description of such media is furnished by a damped-polariton model in which absorption is taken into account through coupling to a bath. We show how all field and matter operators in this theory can be expressed in terms of the bath operators at an initial time. The consistency of these solutions for the field and matter operators are found to depend on the validity of certain velocity sum rules. The transient effects in the spontaneous-decay rate are studied with the help of several specific models for the dielectric constant, which are shown to follow from the general theory by adopting particular forms of the bath coupling constant.
... In sec. 3 and 4, I turn to two considerably more complicated examples, both in terms of the physics involved and in terms of their history. From a relativistic point of view, both examples revolve around the transformation properties of the four-momentum of spatially extended systems (Rohrlich, 1960Rohrlich, , 1965). Sec. 3 deals with the velocity dependence of electron mass measured in a series of experiments by Kaufmann and others in the first two decades of the 20th century (Janssen and Mecklenburg, 2007). ...
... This alternative definition was first proposed by Fermi (1921 Fermi ( , 1922 ), forgotten , rediscovered several times, and finally broadly disseminated by Rohrlich (1960 Rohrlich ( , 1965). Some of the discussion in the literature over which of these two definitions is preferable may suggest that one is right and the other is wrong. ...
Special relativity is preferable to those parts of Lorentz's classical ether theory it replaced because it shows that various phenomena that were given a dynamical explanation in Lorentz's theory are actually kinematical. In his book, Physical Relativity, Harvey Brown challenges this orthodox view. I defend it. The phenomena usually discussed in this context in the philosophical literature are length contraction and time dilation. I consider three other phenomena in the same class, each of which played a role in the early reception of special relativity in the physics literature: the Fresnel drag effect, the velocity dependence of electron mass, and the torques on a moving capacitor in the Trouton–Noble experiment. I offer historical sketches of how Lorentz's dynamical explanations of these phenomena came to be replaced by their now standard kinematical explanations. I then take up the philosophical challenge posed by the work of Harvey Brown and Oliver Pooley and clarify how those kinematical explanations work. In the process, I draw attention to the broader importance of the kinematics–dynamics distinction.
... There were many attempts to overcome these difficulties. One of them consists in using the Lorentz–Dirac equation, see [2],[4],[9]. Here, an effective force by which the retarded solution computed for a given particle trajectory acts on that particle is postulated (the remaining field is finite and acts by the usual Lorentz force). ...
... The spherical coordinates related to z l are called r, θ, φ. The Born solution of Maxwell equations with a delta-like source carried by the particle (cf. [9],[10], Section 3.3 of [8] and [11]) reduces in these coordinates to the following time–independent expression: ...
We define and compute the renormalized four-momentum of the composed physical system: classical Maxwell field interacting with charged point particles. As a ‘reference’ configuration for the field surrounding the particle, we take the Born solution. Unlike in the previous approach [Commun. Math. Phys. 198 (1998) 711; Gen. Relat. Grav. 26 (1994) 167; Acta Phys. Pol. A 85 (1994) 771], based on the Coulomb ‘reference’, a dependence of the four-momentum of the particle (‘dressed’ with the Born solution) upon its acceleration arises in a natural way. This will change the resulting equations of motion. Similarly, we treat the angular momentum tensor of the system.
... P is here a preselected point. So, a gravitational theory with torsion is not a covering theory for SRT [54] and violates EEP (Strictly speaking, it violates LLI). A correct relativistic theory of gravity should be a covering theory for the both theories, SRT and Newton's theory of gravity. ...
... In a Riemann-Cartan spacetime we have geodesics and autoparallells (paths). Hamiltonian Principle demands geodesics as trajectories for the test particles [54]. Then, what about the physical meaning of the autoparallells? ...
It is known that General Relativity ({\bf GR}) uses a Lorentzian Manifold
$(M_4;g)$ as a geometrical model of the physical spacetime. The metric $g$ is
required to satisfy Einstein's equations. Since the 1960s many authors have
tried to generalize this model by introducing torsion. In this paper we discuss
the present status of torsion in a theory of gravity. Our conclusion is that
the general-relativistic model of the physical spacetime is sufficient for the
all physical applications and it seems to be the best satisfactory.
... Then, using the example of a stationary atom, we showed how, in this case, the absence of radiation at a far-away observation point where a probe (or detector-note the so-called Unruh-DeWitt 'detector' [1,3] is an emitter in the present context) is located is actually a result of complex cancellations of the interference between emitted radiation from the atom's idf and the local fluctuations in the free field. By this, we pointed out that the entity which enters into the duality relation with vacuum fluctuations is not radiation reaction (in the quantum optics literature, e.g., [4][5][6][7], the relation between quantum fluctuations and radiation reaction is often mentioned without emphasizing the difference between classical radiation reaction [8,9] and quantum dissipation, which exist at two separate theoretical levels; only quantum dissipation enters in the fluctuations-dissipation relation with quantum fluctuations, not classical radiation reaction), which can exist as a classical entity, but quantum dissipation [10,11]. In the second paper [12], we considered the idf of the atom interacting with a quantum scalar field initially in a coherent state. ...
In this third of a series on quantum radiation, we further explore the feasibility of using the memories (non-Markovianity) kept in a quantum field to decipher certain information about the early universe. As a model study, we let a massless quantum field be subjected to a parametric process for a finite time interval such that the mode frequency of the field transits from one constant value to another. This configuration thus mimics a statically-bounded universe, where there is an ‘in’ and an ‘out’ state with the scale factor approaching constants, not a continuously evolving one. The field subjected to squeezing by this process should contain some information of the process itself. If an atom is coupled to the field after the parametric process, its response will depend on the squeezing, and any quantum radiation emitted by the atom will carry this information away so that an observer at a much later time may still identify it. Our analyses show that (1) a remote observer cannot measure the generated squeezing via the radiation energy flux from the atom because the net radiation energy flux is canceled due to the correlation between the radiation field from the atom and the free field at the observer’s location. However, (2) there is a chance to identify squeezing by measuring the constant radiation energy density at late times. The only restriction is that this energy density is of the near-field nature and only an observer close to the atom can use it to unravel the information of squeezing. The second part of this paper focuses on (3) the dependence of squeezing on the functional form of the parametric process. By explicitly working out several examples, we demonstrate that the behavior of squeezing does reflect essential properties of the parametric process. Actually, striking features may show up in more complicated processes involving various scales. These analyses allow us to establish the connection between properties of a squeezed quantum field and details of the parametric process which performs the squeezing. Therefore, (4) one can construct templates to reconstitute the unknown parametric processes from the data of measurable quantities subjected to squeezing. In a sequel paper these results will be applied to a study of quantum radiations in cosmology.
... The motion of accelerated charged body constitutes an interesting theoretical problem and has a long-standing history [56]. Starting with the seminal works of Lorentz, Abraham and Poincaré in the Newtonian case [57], the contributions from Dirac [58], Landau [59], Dewitt, and Brehme for the relativistic domain have made remarkable expansion of the field [60]. ...
We investigate resonance crossings of a charged body moving around a Kerr black hole immersed in an external homogeneous magnetic field. This system can serve as an electromagnetic analogue of a weakly non-integrable extreme mass ratio inspiral (EMRI). In particular, the presence of the magnetic field renders the conservative part of the system non-integrable in the Liouville sense, while the electromagnetic self-force causes the charged body to inspiral. By studying the conservative dynamics, we show the existence of an approximate Carter-like constant and discuss how resonances grow as a function of the perturbation parameter. Then, we apply the electromagnetic self-force to investigate crossings of these resonances during an inspiral. Averaging the energy and angular momentum losses during crossings allows us to employ an adiabatic approximation for them. We demonstrate that such adiabatic approximation provides results qualitatively equivalent to the instantaneous self-force evolution, which indicates that the adiabatic approximation may describe the resonance crossing with sufficient accuracy in EMRIs.
... The difference between (22) and (23) is easily overlooked if one adopts a passive interpretation of Lorentz transformations, in which case one is tempted to let Λ act on any geometric structure that appears in one's formulae ("anything that has indices on it is transformed"). This confusion has led to several fake-resolutions of the transformation problem in the classic literature, like e.g. in [21] and [22]. ...
The energy-momentum tensor for a particular matter component summarises its local energy-momentum distribution in terms of densities and current densities. We re-investigate under what conditions these local distributions can be integrated to meaningful global quantities. This leads us directly to a classic theorem by Max von Laue concerning integrals of components of the energy-momentum tensor, whose statement and proof we recall. In the first half of this paper we do this within the realm of Special Relativity and in the traditional mathematical language using components with respect to affine charts, thereby focusing on the intended physical content and interpretation. In the second half we show how to do all this in a proper differential-geometric fashion and on arbitrary space-time manifolds, this time focusing on the group-theoretic and geometric hypotheses underlying these results. Based on this we give a proper geometric statement and proof of Laue's theorem, which is shown to generalise from Minkowski space (which has the maximal number of isometries) to space-times with significantly less symmetries. This result, which seems to be new, not only generalises but also clarifies the geometric content and hypotheses of Laue's theorem. A series of three appendices lists our conventions and notation and summarises some of the conceptual and mathematical background needed in the main text.
... This was explained since the beginning of special relativity by Fermi [40]. Synge [41], Gamba [23], Nakamura [19,20] and Rohrlich [15,42] recovered Fermi's idea, and a covariant volume was defined. The choice of the volume does not have to correspond to the volume of a system in its rest frame [21,22]. ...
The Lorentz transformations are obtained by assuming that the laws of classical thermodynamics are invariant under changes of inertial reference frames. As Maxwell equations are used in order to deduce a wave equation that shows the constancy of the speed of light, by means of the laws of classical thermodynamics, the invariance of the Carnot cycle is deduced under reference frame changes. Starting with this result and the blackbody particle number density in a rest frame, the Lorentz transformations are obtained. A discussion about the universality of classical thermodynamics is given.
... Moreover, action (2.1) is invariant under (global) transformations of the Poincaré group; this invariance results in the conservation of the symmetric energy-momentum tensor [6]: ...
The procedure of reducing canonical field degrees of freedom for a sys-tem of charged particles plus field in the constrained Hamiltonian formal-ism is elaborated up to the first order in the coupling constant expansion. The canonical realization of the Poinca e algebra in the terms of particle variables is found. The relation between covariant and physical particle variables in the Hamiltonian description is written. The system of particles interacting by means of scalar and vector massive fields is also considered. The first order approximation in ¡ £ ¢ ¥ ¤ is examined. An application to calcu-lating the relativistic partition function of an interacting particle system is discussed.
... A covariant theory must have well-defined quantities when finite size systems are considered and different inertial systems are involved as the volume and any quantity derived by an integration over a volume of a vector or a tensor, as the total momentum. Fermi [33], Synge [34], Rohrlich [35], Gamba [36] and Nakamura [14] have showed the correct form of defining those physical quantities without ambiguities. ...
Based on a covariant theory of equilibrium Thermodynamics, a Statistical Relativistic Mechanics is developed for the non-interacting case. Relativistic Thermodynamics and Jüttner Relativistic Distribution Function in a moving frame are obtained by using this covariant theory. A proposal for a Relativistic Statistical Mechanics is exposed for the interacting case.
... Since these equations are of second order in time derivatives, contrary to the Lorentz-Dirac equation (3.15) their solutions entail no unphysical properties, e.g. causality violation in terms of a pre-acceleration, see for example [14]. ...
We derive the classical dynamics of massless charged particles in a rigorous
way from first principles. Since due to ultraviolet divergences this dynamics
does not follow from an action principle, we rely on a) Maxwell's equations, b)
Lorentz- and reparameterization-invariance, c) local conservation of energy and
momentum. Despite the presence of pronounced singularities of the
electromagnetic field along Dirac-like strings, we give a constructive proof of
the existence of a unique distribution-valued energy-momentum tensor. Its
conservation requires the particles to obey standard Lorentz equations and they
experience, hence, no radiation reaction. Correspondingly the dynamics of
interacting classical massless charged particles can be consistently defined,
although they do not emit bremsstrahlung end experience no self-interaction.
... Eqs. (43) and (45) lead to the classical expression for the radiation reaction [46] [47]. We have shown in Theorem 9 that the quantum radiation reaction has a classical limit for a sufficiently small time. ...
We express the unitary time evolution in nonrelativistic regularized quantum electrodynamics at zero and positive temperature by a Feynman integral defined in terms of a complex Brownian motion. An average over the quantum electromagnetic field determines the form of the quantum mechanics in an environment of a quantum black body radiation. In this nonperturbative formulation of quantum electrodynamics we prove the existence of the classical limit ℏ→0. We estimate an error to some approximations commonly applied in quantum radiation theory. © 1998 American Institute of Physics.
... Moreover, action (1) is invariant under (global) transformations of the Poincaré group; this invariance results in the conservation of the symmetric energy-momentum tensor [4]: ...
The canonical realization of the Poincaré group for the systems of the pointlike particles coupled with the electromagnetic, massive vector and scalar fields is constructed. The reduction of the canonical field degrees of freedom is done in the linear approximation in the coupling constant. The Poincaré generators in terms of particle variables are found. The relation between covariant and physical particle variables in the Hamiltonian description is written. The approximation up to c −2 is examined.
... Usually, an interaction within a system of N charged particles is described by means of the electromagnetic field with its own degrees of freedom represented by the 4-potential A µ (x), x ∈ M 4 , over the Minkowski space-time 1 [1,2,3]. ...
The procedure of reducing of canonical field degrees of freedom for a system of charged particles plus electromagnetic field in the constraint Hamiltonian formalism is developed up to the first order in the coupling constant expansion. The canonical realization of the Poincaré algebra in the terms of physical variables is found. The relation between covariant and physical particle variables in the Hamiltonian description is studied.
... The consequences are as follows. Mixing classical mechanics with field theory models leads to the inconsistency as the one for the Lorentz-Abraham-Dirac equation which leads to the self acceleration of point-like charged particle which interacts with its own electromagnetic field [10]. From the other side combining quantum (wave) mechanics with classical electrodynamics is more promising. ...
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction of a self-consistent field theory, which joins the quantum theory and classical field theory, is proposed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
... It is in particular feature b) that turns classical Electrodynamics of point–particles into an internally inconsistent theory. Nevertheless, from an experimental point of view equation (1.5) describes correctly the emission of four–moment due to radiation, up to the quantum energy scale, i.e. for wavelengths λ ≫ /Mc [22], and therefore an independent criterion to establish its " validity " should be pursued. One of the purposes of the present paper is to provide such a general and feasible criterion, that applies to a generic brane in arbitrary dimensions. ...
We construct for the first time an energy-momentum tensor for the electromagnetic field of a p-brane in arbitrary dimensions, entailing finite energy-momentum integrals. The construction relies on distribution theory
and is based on a Lorentz-invariant regularization, followed by the subtraction of divergent and finite counterterms supported
on the brane. The resulting energy-momentum tensor turns out to be uniquely determined. We perform the construction explicitly
for a generic flat brane. For a brane in arbitrary motion our approach provides a new paradigm for the derivation of the,
otherwise divergent, self-force of the brane. The so derived self-force is automatically finite and guarantees, by construction,
energy-momentum conservation.
Keywordsp-branes–Space-Time Symmetries–Bosonic Strings
... II; [28], pp. 303-19; [48], chapter 2. 22 With minor changes, we use the Wikipedia translation [31]. ...
The unification of electricity and magnetism achieved by special relativity
has remained for decades a model of unification in theoretical physics. We
discuss the relationship between electric and magnetic fields from a classical
point of view, and then examine how the four main relevant authors (Lorentz,
Poincar\'e, Einstein, Minkowski) dealt with the problem of establishing the
transformation laws of the fields in different inertial systems. We argue that
Poincar\'e's derivation of the transformation laws for the potentials and the
fields was definitely less arbitrary than those of the other cited authors,
contrast this with the fact that here, as in other instances, Poincar\'e's
contribution to relativity was belittled by authoritative German physicists in
the first two decades. In the course of the historical analysis a number of
questions which are of contemporary foundational interest concerning
relativistic electromagnetism are examined, with special emphasis on the role
of potentials in presentations of electromagnetism, and a number of errors in
the historical and foundational literature are corrected.
Resumo Atualmente o conceito de potencial vetor é geralmente tratado nos livros-texto e ensinado nos cursos universitários de eletromagnetismo como um artifício matemático para o cálculo dos campos elétrico e magnético. Po-rém, a investigação histórica da origem e desenvolvimento deste conceito, principalmente nos trabalhos de Michael Faraday e James Clerk Maxwell, nos deu indícios de que estes cientistas atribuíam significados físicos e análogos mecânicos a grandezas que atualmente recebem a de-nominação de potencial vetor. No contexto no qual estes cientistas traba-lhavam, segunda metade de século XIX, a comunidade científica conside-rava que os fenômenos eletromagnéticos ocorriam em um éter com pro-priedades mecânicas e que as grandezas eletromagnéticas deveriam ter análogos mecânicos. No final deste mesmo século, alguns físicos, entre eles, Oliver Heaviside e Heinrich Hertz, reformularam a teoria de Maxwell, abandonando a interpretação física dada por Maxwell ao po-tencial vetor. Neste trabalho, discutimos sinteticamente como se deu esse processo de mudança. Para isso, realizamos um estudo histórico pautado em fontes primárias e secundárias sobre o assunto e, por último, investi-gamos a abordagem usada em alguns livros-texto de eletromagnetismo no ensino deste conceito. Apresentamos ainda, indícios de que o abandono + A historical analysis of the construction of physical meanings to the concept of vector potential in classical electromagnetism
German translation by H. Härtel of the book The Electric Force of a Current: Weber and the Surface Charges of Resistive Conductors Carrying Steady Currents (Apeiron, Montreal, 2007).
This chapter marks the beginning of an itinerary that will take us to the quantum theory of matter. All along this exciting journey we will be accompanied by the zero-point radiation field introduced in Chap. 3, considered as a real, fluctuating field in permanent interaction with matter. Our point of departure is the (nonrelativistic) Abraham-Lorentz!equationAbraham-Lorentz equation governing the particle motion under the action of this field plus an arbitrary external (binding, conservative) force. A statistical treatment leads to a generalized phase-space Fokker-Planck equation!and laws of evolutionFokker-Planck equation. In the transition to configuration space through a partial averaging, a hierarchy of equations is obtained for the local moments of the momentum. When a balance is eventually reached in the mean between the energy lost by the particle through radiation reaction Radiation reactionand the energy gained by it from the background field, any remaining effect of the radiation terms becomes negligible. In this (time-asymptotic) limit, theFokker-Planck equation!generalized generalized Fokker-Planck equation!and laws of evolutionFokker-Planck equation transforms into a true Fokker-Planck equationFokker-Planck equation, describing a Markov processMarkov process. Further, in the Approximation!radiationlessradiationless approximationRadiationless approximation
Linear sed!radiationless approximation the first two equations of the hierarchy decouple from the rest and are shown to be equivalent to Schrödinger’s equation. The main lessons and implications of these results are discussed. In particular, an explanation is given for the impossibility to go back from the Schrödinger description Quantum regime!and Schrödinger descriptionand retrieve a fullDetailed energy balance!and Schrödinger equation phase-space description that is consistent with quantum mechanics.
I would like to describe some calculationstl(1,2) which E. J. Moniz and I carried out for the purpose of understanding more clearly the relationship between classical and quantum electrodynamics, particularly in regard to their treatment of radiation reaction. Let us begin by reviewing some of the questions of interest here.
This book has two principal aims: to investigate the conceptual structure of classical electrodynamics, and show that investigating a particular scientific theory can shed light on concerns in the general philosophy of science. It focuses on two basic issues on the interaction between charged particles and classical fields. First, what is the equation of motion of a charged particle interacting with an electromagnetic field? Second, how does the presence of charged particles or sources affect the total field? The book is divided into two parts. Part I focuses on particles - different particle equations of motion and their properties. Part II focuses on fields and their symmetry properties in the presence of particles. © 2005 by The American Philological Association. All rights reserved.
Maxwell's stress equation for electrostatics identifies a tensile stress in the direction of the electric field and a pressure normal to this direction. For an isolated, spherically symmetric static charge distribution, Maxwell's stress equation may be recast to eliminate the stress normal to the electric field and establish a stress only aligned with the electric field. The remaining stress is identified as an external omnidirectional Poincaré stress, inwardly directed towards the charge distribution. The Poincaré stress is modeled as a mean valued, continual exchange of bosons between the charge distribution and the distant matter of the universe. For two separated, spherically symmetric static charge distributions, Maxwell's stress equation may be recast to develop a line stress that only exists on the straight path between the two charge distributions. The line stress is identified as a Coulomb stress modeled as a mean valued, continual exchange of photons back and forth between two like-charge distributions.
The subject, which is treated in this report, combines in one bundle some questions of complex analysis, geometry and probability theory. Our purpose is to give a review of open problems and known results. First investigations in geometric probability theory start from the well known Buffoons needle problem and related Bertrand paradoxes. Further, the paper introduces original conjectures and results of the present author. See also the author’s paper in [ibid. 60, No. 3, 73–80 (2010; Zbl 1241.52005)].
The Hamiltonian formulation of relativistic system of charged particles plus electromagnetic field in the Dirac instant and front forms of dynamics is considered. The canonical realization of the Poincaré algebra in the terms of gauge-invariant variables is found. The procedure of elimination of the field degrees of freedom within the framework of the Dirac constraint theory is elaborated up to the first order in the coupling constant. The Poincaré generators in the terms of particle variables are obtained. The relations between the instant form generators and front form ones are examined. The instant form Hamiltonian in the weak-relativistic approximation results in the Darwin Hamiltonian.
The orbital precession of a charged test body interacting with a charged and massive body, fixed
in the origin, is obtained by means of an approximate solution to the motion equations for such a system.
Once the precession is known, in order to fit the Mercury perihelion precession uncertainty, some analysis
regarding the possible charges for the Sun and Mercury is made.
Our purpose in this paper is to provide theframework for a generalization of classical mechanicsand electrodynamics, including Maxwell's theory, whichis simple, technically correct, and requires noadditional work for the quantum case. We first show thatthere are two other definitions of proper-time, eachhaving equal status with the Minkowski definition. Weuse the first definition, called the proper-velocity definition, to construct a transformationtheory which fixes the proper-time of a given physicalsystem for all observers. This leads to a new invariancegroup and a generalization of Maxwell's equations left covariant under the action of this group.The second definition, called the canonical variablesdefinition, has the unique property that it isindependent of the number of particles. This definition leads to a general theory of directlyinteracting relativistic particles. We obtain theLorentz force for one particle (using its proper-time),and the Lorentz force for the total system (using theglobal proper-time). Use of the global proper-time tocompute the force on one particle gives the Lorentzforce plus a dissipative term corresponding to thereaction of this particle back on the cause of itsacceleration (Newton's third law). The wave equation derivedfrom Maxwell's equations has an additional term, firstorder in the proper-time. This term arisesinstantaneously with acceleration. This shows explicitly that the longsought origin of radiationreaction is inertial resistance to changes in particlemotion. The field equations carry intrinsic informationabout the velocity and acceleration of the particles in the system. It follows that our theory isnot invariant under time reversal, so that the existenceof radiation introduces an arrow for the (proper-time ofthe) system.
By using the concept of volume introduced by Nakamura in relativistic thermodynamics, a relativistic thermodynamical theory is proposed. A comparison is presented between the new theory, the van Kampen covariant theory and the Rohrlich proposal. A relativistic thermometer is proposed by using the Unruh–DeWitt detector.
This paper deals with the motion of a point test charge in an external electromagnetic field with the effect of electromagnetic radiation reaction included. The equation of motion applicable in a general Riemannian space-time is written as the geodesic equation of an affine connection. The connection is the sum of the Christoffel connection and a tensor which depends on, among other things, the external electromagnetic field, the charge and mass of the particle and the Ricci tensor. The affinity is not unique; a choice is made so that the covariant derivative of the metric tensor with respect to the connection vanishes. The special cases of conformally flat spaces and the space of general relativity are discussed.
We derive a generalization of the prolongation formula for tensor-valued functions, by taking into account the natural action of diffeomorphisms on tensor fields. This differs from the usual procedure, where such fields are viewed as defining 'multi-component scalars'; it replaces the ordinary derivative in the expression of the 'characteristic' by a Lie derivative. The resulting version of Noether's theorem takes a form more familiar to theoretical physicists. A very simple proof of the conformal invariance of the Maxwell Lagrangian also follows from this procedure. The Eshelby tensor is also readily obtained, as a further illustration of the practical use of this new prolongation formula.
Classical electrodynamicsÐif developed consistently, as in Dirac's classical theory of the electronÐis 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.
Starting from a Lagrangian treatment of classical electrodynamics and using simple heuristic arguments, an effective generalization of the Darwin Lagrangian for point charges moving with arbitrary velocities (vc) is obtained. In addition, another, the simplesta priori Lagrangian (preserving the most important features of standard classical theory) is proposed.
The Einstein-Maxwell field equations for charged dust corresponding to static axially-symmetric metric of Levi-Civita have been studied. It has been shown that when the metric potentialsg
ij are functions of only one of the coordinates, viz.,r, the interior charged dust becomes purely of electromagnetic origin, in the sense that the physical quantities like the energy density, the effective gravitational mass, etc., are dependent only on the charge density and vanish when this charge density vanishes. Such models are known as electromagnetic mass models in the classical electrodynamics. An interior charged dust solution corresponding to this case has been obtained which, in a sense, represents an infinite dust distribution of electromagnetic origin. In the second case, viz., when the metric potentials are functions of the coordinatesr andz both, it has been shown that some of the situations correspond to electromagnetic mass models. An example to illustrate this case has been obtained. This represents the source of the Reissner-Nordstrm-Curzon field (an analogue of the Reissner-Nordstrm solution obtained by Curzon) which according to Curzon describes the exterior field of an electron.
Three interpretations of quantum mechanics are re-examined: the orthodox or «Copenhagen» interpretation, the expanding-worlds
interpretation and the interpretation that is generally named statistical. It is concluded that the first two interpretations
introduce unnecessary conceptual difficulties, and that it is consequently preferable to accept the statistical interpretation.
Si sono riesaminate tre interpretazioni della meccanica quantistica: l’interpretazione ortodossa o di «Copenhagen”, l’interpretazione
dei mondi in espansione e l’interpretazione che generalmente è chiamata statistica. Si conclude che le prime due interpretazioni
introducono difficoltà concettuali non necessarie, e che di conseguenza è preferibile accettare l'interpretazione statistica.
Заново исследуются три интерпретации квантовой механики: ортодоксаьная или “копенгагенская» интерпретация, интерпретация расширяющегося
мира и интерпретация, которая обычно называется статистической. Отмечается, что первые две интерпретации неизбежно приводят
к умозрительным трудностям, и поетому статистуческая интерпретация является предпочтительной.
Many have noted the irony of the English title, The Logic of Scientific Discovery, of Karl Popper’s expanded translation of his Logik der Forschung (1934). Given Popper’s use of the distinction between context of discovery and context of justification (the DJ distinction),
there is no such thing as a logic (or method or even rationality) of discovery. Yet the book is nearly 500 pages long!1 But instead of once again looking at how the DJ distinction discouraged attention to what Popper termed “the initial stage,
the act of conceiving or inventing a theory” (Popper 1959, p. 31), I shall examine the privileged context of justification.
We have calculated the decay rate and the frequency shift of the harmonic oscillator located within the cavity between the perfect conductor and a nondispersive lossless dielectric. The cavity-induced change in the decay rate is completely different from the one caused by the ordinary cavity consisting of two perfectly conducting mirrors, whereas modifications of the frequency shift are quite similar in both cases. We have obtained also the radiation pattern of light emitted by the point-like source (atom) located in the cavity. The pattern reveals a resonant character with several sharply outlined maxima if only the dielectric refractive index is not too small.
We consider the system of a point particle, accelerated through a confining potential, and interacting with a scalar wave field. We prove that the periodic solutions of the linearized system (which has an eigenvalue embedded in the continuous spectrum) do not survive perturbation through the nonlinearity, if some "mode" of the wave field does not couple to the particle.
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a novel trajectory-adapted coordinate system, which simplifies considerably the equations. The solution is given in terms of a series, where a new family of special functions arises in a natural way. Singular behaviour of the field near to the particle may be analyzed this way up to an arbitrary order. Application to the self-interaction problems in classical electrodynamics is discussed.
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