Richard T Hammond
The problem of self forces and radiation reaction is solved by conservation of energy methods. The longstanding problem of constant acceleration is solved, and it is shown that the self force does indeed affect the particle's motion, as expected on physical grounds. The relativistic generalization is also presented.
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We study radiation reaction in a Lorentz violating electrodynamics [1]. We explore the possible modification whatsoever present in the radiation reaction force experienced by an accelerating charge in the modified Maxwell theory. However it turns out that radiation reaction receives no change due to Lorentz violation whereas electromagnetic mass manifests anisotropy.
The self force of electrodynamics is derived from a scalar field. The resulting equation of motion is free of all of the problems that plague the Lorentz Abraham Dirac equation. The age-old problem of a particle in a constant field is solved and the solution has intuitive appeal.
I show that the main statement of [Phys. Rev. Lett. 105, 094802 (2010), arXiv:1005.2617] is wrong. Other inconsistences of this Letter are also discussed.
We study the radiation reaction acting on an accelerating charge moving in noncommutative spacetime and obtain an expression for it. Radiation reaction, due to a nonrelativistic point charge, is found to receive a small noncommutative correction term. The Abraham-Lorentz equation for a point charge in noncommutative spacetime suffers from the pre-acceleration and the runaway problems. We explore as an application the radiation reaction experienced by a charge which undergoes harmonic oscillations in a noncommutative plane.
We reply to P. Forgács, T. Herpay, and P. Kovács (arXiv: 1202.6289).
In classical electrodynamics for rotating with variable angular velocity charged rigid sphere are found: the exact values of electromagnetic fields, the flux of radiating energy and the exact integral equation of rotation including the terms of self-rotation. The analysis of this eq. shows that on one hand, there is no "runaway" solutions, peculiar to the Lorentz-Dirac eq. of radiating point particle, on the other hand, there appear new problems, among them is the nonexistence of solution for some external moments of force.
The energy-impulse flow of electromagnetic field, produced by the arbitrary moving charged particle, through the sphere of large radius is calculated. The result formulae are used in problem of radiation produced by hyperbolically moving particle and the problem of the synchrotron radiation energy loss. The energy-impulse radiated by a moving charged particle is shown to be not an invariant 4-tensor, for this reason calculation methods based on change of reference frame are not correct.
Flaws and ambiguities are pointed out upon examining the comment attempting to solve a problem as raised recently --- the currently accepted formulation of electromagnetic radiation of an accelerated charge violates the principle of conservation of energy. This problem is not solved by the comment, due to a misunderstanding in the meaning of the total radiated power crossing a sphere. An experiment is suggested to determine whether on not the currently accepted formulation is valid.
The region very close to an electron ($r << r_0 = e^2/mc^2 \approx 2.8\times 10^{-13}$ cm) is, according to quantum electrodynamics, a seething maelstrom of virtual electron-positron pairs flashing in and out of existence. To take account of this well-established physical reality, a phenomenological representation for vacuum polarization is introduced into the framework of classical electrodynamics. Such a model enables a consistent picture of classical point charges with finite electromagnetic self-energy. It is further conjectured that the reaction of a point charge to its own electromagneti…
On simple example is shown that a model of mechanically extended source of radiation in classical electrodynamics indeed has some problems with radiation reaction force. So one cannot, in general case, state, that the present situation with classical dynamics of mechanically extended sources of radiation is "very satisfactory".
Relativistic hydrogen in classical electrodynamics with classical zero-point radiation
本文研究了经典电动力学中包含经典电磁零点辐射对氢原子基态和共振激发态的影响，提出与玻尔-索末菲理论相似的整数作用变量。
In this paper we propose an approach to the problem of two body motion in classical electrodynamics that takes into account the electromagnetic radiation and the radiation reaction forces. The resulting differential equations are solved numerically.
The aim of this paper is to investigate the fundamental problems of retardation and radiation caused by non-uniformly moving point sources using the theories of electrodynamics and elastodynamics. This paper investigates and compares the retarded electromagnetic fields and the retarded elastodynamic fields. For the non-uniform motion of a general point source, the Liénard-Wiechert type potentials and the radiation and nonradiation fields are derived for a point charge and for a point force.
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 that 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.
Energy-momentum conservation of classical axion-electrodynamics is carefully analyzed in the Hamiltonian formulation of the theory. The term responsible for the energy transfer between the electromagnetic and the axion sectors is identified. As a special application the axion-to-light Primakoff-process in the background of a static magnetic field is worked out and the radiative self-damping of the axion oscillations is characterized quantitatively. The damping time turns out comparable to the age of the Universe in the preferred axion mass range.
We consider a self-action problem for an electric charge arbitrarily moving in flat spacetime of three dimensions. Its electromagnetic field satisfies the Maxwell equations in Minkowski space of three dimensions. In this space electromagnetic waves propagate not just at a speed of light, but also at all speeds smaller than or equal to the speed of light. The massive particle may "fill" its own field, which acts on it just like an external one. The radiation reaction is determined by Lorentz force of point-like charge acting upon itself plus non-local term which provides finiteness of the self-…
Classical linear oscillator in classical electrodynamics with classical zero-point radiation
研究经典线性振子在小振幅极限下的相对论近似，发现其基态能量与辐射损耗平衡，共振激发态中辐射能量与零点辐射能量平衡。
Using the canonical formalism, Compagno and Persico [J. Phys. A: Math. Gen. 35 (2002) 3629--45] have calculated the 'radiation-reaction' force on a uniform spherical charge moving rigidly, slowly and slightly from its position at the time when the transverse electric field is assumed to vanish. This force is shown to result in the same time-averaged self-force as that which has been obtained by different means for the test charge of a Bohr--Rosenfeld field-measurement procedure and which Compagno and Persico claimed to be incorrect.
A self-action problem for a pointlike charged particle arbitrarily moving in flat spacetime of three dimensions is considered. Outgoing waves carry energy-momentum and angular momentum; the radiation removes energy and angular momentum from the source which then undergoes a radiation reaction. We decompose Noether quantities carried by electromagnetic field into bound and radiative components. The bound terms are absorbed by individual particle's characteristics within the renormalization procedure. Radiative terms together with already renormalized 3-momentum and angular momentum of pointlike…
The idea about a quantum nature of Planck's blackbody radiation law is deeply rooted in minds of most physicists. Einstein's work, in which the coefficients of spontaneous and induced emission were introduced, has always been regarded as a proof that quantum energy discreteness of an atom plays a crucial role in the derivation of this law. In our paper we avoid this standpoint. It may be shown that the de Broglie wave assigned to every material particle is a result of interaction of the particle with zero-point vibrations of electromagnetic ground field. The energetic spectrum of a harmonic os…
We introduce an effective field theory approach that describes the motion of finite size objects under the influence of electromagnetic fields. We prove that leading order effects due to the finite radius $R$ of a spherically symmetric charge is order $R^2$ rather than order $R$ in any physical model, as widely claimed in the literature. This scaling arises as a consequence of Poincaré and gauge symmetries, which can be shown to exclude linear corrections. We use the formalism to calculate the leading order finite size correction to the Abraham-Lorentz-Dirac force.
The direct interaction theory of electromagnetism, also known as Wheeler-Feynman electrodynamics, is often misinterpreted and found unappealing because of its reference to the absorber and, more importantly, to the so-called absorber condition. Here we remark that the absorber condition is indeed questionable and presumably not relevant for the explanation of irreversible radiation phenomena in our universe. What is relevant and deserves further scrutiny is the emergent effective description of a test particle in an environment. We therefore rephrase what we consider the relevant calculation b…
Energy equipartition is appropriate only for nonrelativistic classical mechanics, but has only limited relevance for a relativistic theory such as classical electrodynamics. In this article, we discuss harmonic-oscillator thermal equilibrium from three different perspectives. First, we contrast the thermal equilibrium of nonrelativistic mechanical oscillators (where point collisions are allowed and frequency is irrelevant) with the equilibrium of relativistic radiation modes (where frequency is crucial). The Rayleigh-Jeans law appears from applying a dipole-radiation approximation to impose th…
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 g…
Radiation force in Abraham-Lorentz-Dirac equation is revisited for possible signature of irreversible action in the dynamics. The analysis shows that the classical electron can dissipate out a certain fraction of field energy that distinguishes itself from the well known Larmor radiation loss. The thermal power loss is shown to follow bi-quadratic acceleration functionality, which is akin to the characteristics of Hawking-Unruh radiation emission from warm surrounding field of a non-inertial observer. Reversibility in nonstationary evolution is possible at the expense of power from concerned e…
Radiation reaction (but, more generally, fluctuations and dissipation) occurs when a system interacts with a heat bath, a particular case being the interaction of an electron with the radiation field. We have developed a general theory for the case of a quantum particle in a general potential (but, in more detail, an oscillator potential) coupled to an arbitrary heat bath at arbitrary temperature, and in an external time-dependent $c$-number field. The results may be applied to a large variety of problems in physics but we concentrate by showing in detail the application to the blackbody radia…
A self-action problem for a point-like charged particle arbitrarily moving in flat space-time of six dimensions is considered. A consistent regularization procedure is proposed which relies on energy-momentum and angular momentum balance equations. Structure of the angular momentum tensor carried by the retarded "Liénard-Wiechert" field testifies that a point-like source in six dimensions possesses an internal angular momentum. Its magnitude is proportional to the square of acceleration. It is the so-called {\em rigid} relativistic particle; its motion is determinated by the higher-derivative …
Magnetic Field Applied to the Classical Hydrogen Atom Treated in Classical Electrodynamics with Classical Zero-Point Radiation
研究外加磁场下经典氢原子与经典零点辐射的共振条件，解释斯特恩-格拉赫实验和塞曼效应。
Stochastic electrodynamics is the classical electrodynamic theory of interacting point charges which includes random classical radiation with a Lorentz-invariant spectrum whose scale is set by Planck's constant. Here we give a cursory overview of the basic ideas of stochastic electrodynamics, of the successes of the theory, and of its connections to quantum theory.
Hydrogen Molecular Ion and Molecule in Classical Electrodynamics with Classical Zero-Point Radiation
本文采用含经典零点辐射的经典电动力学近似计算，得出氢分子离子结合能2.1eV、质子间距0.916Å，氢分子结合能4.6eV、质子间距0.6Å，揭示其结合特性。
Remarks on classical pseudo-electrodynamics
本文研究了伪电动力学中的守恒定律与辐射场，通过无穷小变换下的作用量对称性推导出相关张量，分析了1+2维电偶极子辐射，并提出引入磁单极子的方法。
Here we discuss blackbody radiation within the context of classical theory. We note that nonrelativistic classical mechanics and relativistic classical electrodynamics have contrasting scaling symmetries which influence the scattering of radiation. Also, nonrelativistic mechanical systems can be accurately combined with relativistic electromagnetic radiation only provided the nonrelativistic mechanical systems are the low-velocity limits of fully relativistic systems. Application of the no-interaction theorem for relativistic systems limits the scattering mechanical systems for thermal radiati…
Classically encountered problem of acceleration runaway in radiative motion of a charged-particle is addressed by considering the criterion of minimum radiation loss under optimum displacement in variationally referred dynamic course in between a pair of arbitrarily selected space-like surfaces having time-like separation. Using the criterion, analysis made by involving a family of infinitesimally differed paths reveals that for attaining stationary action of the dynamic course it is necessary to involve orchestrated displacement of the path family. Dynamics that generally follows from such an…
A generalization of the force approach to radiation reaction is given, taken into consideration an arbitrary motion of the charged particle . The expression obtained brings about the expression already given for the linear an the circular acceleration cases.
Abraham Lorentz (AL) formula of Radiation Reaction and its relativistic generalization, Abraham Lorentz Dirac (ALD) formula, are valid only for periodic (accelerated) motion of a charged particle, where the particle returns back to its original state. Thus, they both represent time averaged solutions for radiation reaction force. In this paper, another expression has been derived for radiation reaction following a new approach, starting from Larmor formula, considering instantaneous change (rather than periodic change) in velocity, which is a more realistic situation. Further, it has been also…
On the model of moving rigid charged body is shown that the Lorentz-Dirac approach to radiation reaction in classical electrodynamics does not work for trajectories of body close to the light cone.
The difficulty of usual approach to radiation reaction is pointed out , and a possible approach based on the force acting to the charged particle which produces the acceleration itself, is presented. This approach brings about an expression such that acceleration is zero whenever the external force is zero.
The radiation reaction problem for an electric charge moving in flat space-time of three dimensions is discussed. The divergences stemming from the pointness of the particle are studied. A consistent regularization procedure is proposed, which exploits the Poincaré invariance of the theory. Effective equation of motion of radiating charge in an external electromagnetic field is obtained via the consideration of energy-momentum and angular momentum conservation. This equation includes the effect of the particle's own field. The radiation reaction is determined by the Lorentz force of point-like…
The Lorentz-Abraham-Dirac equations (LAD) may be the most commonly accepted equation describing the motion of a classical charged particle in its electromagnetic field. However, it is well known that they bare several problems. In particular, almost all solutions are dynamically unstable, and therefore, highly questionable. The question remains whether better equations of motion than LAD can be found to describe the dynamics of charges in the electromagnetic fields. In this paper we present an approach to derive such equations of motions, taking as input the Maxwell equations and a particular …
Equation of motion of Sommerfeld sphere in the one-dimensional potential hole, produced by two equal charges on some distance from each other, is numerically investigated. Two types of solutions are found: (i) damping oscillations, (ii) oscillations without damping (radiationless motion). Solutions with growing amplitude ("climbing-up-the-wall solution") for chosen initial conditions were not founded.
Scalar-Longitudinal Radiation in Extended Electrodynamics with Multipole Theory and a Compensated Source Model
本文基于多极理论与补偿源模型，研究扩展电动力学（EED）的标量-纵向辐射，推导其全阶多极通量公式，发现补偿极化载流子可激发该通道，结果为EED的条件预测，不违背经典电动力学电荷守恒。
We study a system of a finite size charged particle interacting with radiation field by exploiting the Hamilton's principle for non-conservative system introduced recently by Galley[1]. The said formulation leads to the equation of motion of the charged particle that turns out to be the same as obtained by Jackson[3]. We show that radiation reaction stems from the non-conservative piece of the effective Lagrangian. We notice that a charge interacting with radiation field modeled as heat bath affords a way to justify that radiation reaction is a non-conservative force. The topic is suitable for…
The radiation reaction fields are calculated for an accelerated changing dipole in scalar and electromagnetic radiation fields. The acceleration reaction is shown to alter the damping of a time varying dipole in the EM case, but not the scalar case. In the EM case, the dipole radiation reaction field can exert a force on an accelerated monopole charge associated with the accelerated dipole. The radiation reaction of an accelerated charge does not exert a torque on an accelerated magnetic dipole, but an accelerated dipole does exert a force on the charge. The technique used is that originally d…
It is shown that the well-known disparity in classical electrodynamics between the power radiated in electromagnetic fields and the power-loss, as calculated from the radiation reaction on a charge undergoing a non-uniform motion, is successfully resolved when a proper distinction is made between quantities expressed in terms of a "real time" and those expressed in terms of a retarded time. It is shown that the expression for the real-time radiative power loss from a charged particle is somewhat different from the familiar Larmor's formula, or in a relativistic case, from Liénard's formula.
The Abrahamn Lorentz radiation reaction force term, with da/dt, derived in text books is shown to be incomplete. We show that, with the addition of a term, the classical radiation reaction force can be generalized to the relativistic force expression. This addition is the Poynting Robertson term, seen mostly in astrophysics and usually missing from texts in electromagnetism. With this term added, it takes into account the rate of change of mass dm/dt of the particle and makes the generalization to the relativisitic formula for force very straight forward.
We consider the 1-D motion of an electron under a periodic force and taking into account the effect of radiation reaction dissipation force on its motion, using the formulation of the radiation reaction force as a function of the external force. Two cases are considered: a simple sinusoidal time depending force, and sinusoidal electromagnetic force with position and time dependence. We found that the difference of the normalized (with respect the speed of light) velocities, with and without radiation reaction, are quite small between $10^{-31}$ to $10^{-14}$ for intensities on the electric fie…
The usual radiation self-force of a point charge is obtained in a mathematically exact way and it is pointed out to that this does not call forth that the spacetime motion of a point charge obeys the Lorentz--Abraham--Dirac equation.
Up until now, a consistent causal theory of point charged particles (for example electrons) interacting with electromagnetic field is not known. The well-known problem is that the standard Lorentz force alone (in the case of point particles) does not lead to a theory in which momentum and energy are conserved. The need of radiation reaction force (or self-force) thus arises. The well known candidate for such force, the Lorentz-Abraham-Dirac reaction force, gives non-causal particle behavior, i.e., the particle starts to move before the arrival of external electromagnetic fields. Alternative, c…
Radiation-Reaction on the Straight-Line Motion of a Point Charge accelerated by a constant applied Electric Field in an Electromagnetic Bopp-Landé-Thomas-Podolsky vacuum
本文研究BLTP电动力学中点电荷在恒定电场作用下沿直线运动的辐射反应问题，揭示其在短时间内的物理合理性及长时间行为的非物理性。
The emission of radiation from an accelerated charge is analyzed. It is found that at zero velocity, the radiation emitted from the charge imparts no counter momentum to the emitting charge, and no radiation reaction force is created by the radiation. A reaction force is created by the stress force that exists in the curved electric field of the charge, and the work done in overcoming this force is the source of the energy carried by the radiation.
Radiation reaction on an accelerating point charge
针对加速点电荷因电磁辐射导致加速度降低的问题，研究推导了加速度与速度平行时辐射反作用带来的加速度降幅，发现该效应可忽略。
Time-Symmetric Action-at-a-Distance Electrodynamics and the Principle of Action and Reaction for Particles at Relative Rest
本文探讨了时间对称的作用于距离的电磁相互作用理论，通过在平坦共形空间中的对称操作证明了静止粒子的动量与反作用原理。
Nonlocal electrodynamics is a formalism developed to include nonlocal effects in the measurement process caused by the non-inertial state of the observers. This theory modifies Maxwell's electrodynamics by eliminating the hypothesis of locality that assumes an accelerated observer simultaneously equivalent to a comoving inertial frame of reference. In this scenario, the transformation between an inertial and accelerated observer is generalized which affects the properties of physical fields. In particular, we analyze how an uniformly accelerated observer perceives a homogeneous and isotropic b…
Equation of motion of Sommerfeld sphere in the field of Coulomb center is numerically investigated. It is shown that contrary to Lorentz-Dirac equation in the attractive case there are physical solutions. In the repulsive case sphere gains less energy then that should be according to relativistic equation of motion of point charge without radiation force.
Classical Radiation Reaction in Red-Shifted Harmonics
本文研究有限电磁平面波与电子在Landau-Lifshitz辐射反作用力下的碰撞，推导局部单色近似并计算能谱与横向动量谱，揭示谐波特征红移现象，并提出预测谐波边缘移动的简单公式，为实验验证辐射反作用提供依据。
We discuss radiation reaction effects on charges propagating in ultra-intense laser fields. Our analysis is based on an analytic solution of the Landau-Lifshitz equation. We suggest to measure radiation reaction in terms of a symmetry breaking parameter associated with the violation of null translation invariance in the direction opposite to the laser beam. As the Landau-Lifshitz equation is nonlinear the energy transfer within the pulse is rather sensitive to initial conditions. This is elucidated by comparing colliding and fixed target modes in electron laser collisions.
The influence of radiation reaction (RR) on multiphoton Thomson scattering by an electron colliding head-on with a strong laser beam is investigated in a new regime, in which the momentum transferred on average to the electron by the laser pulse approximately compensates the one initially prepared. This equilibrium is shown to be far more sensitive to the influence of RR than previously studied scenarios. As a consequence RR can be experimentally investigated with currently available laser systems and the underlying widely discussed theoretical equations become testable for the first time.
We propose a new method of detecting radiation reaction effects in the motion of particles subjected to laser pulses of moderate intensity and long duration. The effect becomes sizeable for particles that gain almost no energy through the interaction with the laser pulse.
As it is known a model of a charged particle with finite size is a good tool to consider the effects of self- action and backreaction, caused by electromagnetic radiation. In this work the "size" of a charged particle is induced by its stochastic Brownian vibration. Appropriate equation of particle's motion with radiation force is derived. It is shown that the solutions of this equation correctly describe the effects of radiation reaction.
We present a first-principles' prediction that two charged particles of masses M_1 and M_2 separated R apart in a dielectric vacuum act on each other always an attractive force in addition to other known forces in between. This component attractive force on one charge results as the Lorentz force in the radiation depolarization- and magnetic- fields of the other charge, being an attractive radiation force, and is in addition to the ordinary repulsive radiation force. The exact solution for the attractive radiation force is F_g=G' M_1M_2/R^2, an identical formula to Newton's law of gravitation.…
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