scholarly journals Is Classical Electrodynamics an Inconsistent Theory?

2007 ◽  
Vol 37 (2) ◽  
pp. 263-282 ◽  
Author(s):  
Gordon Belot
Keyword(s):  
Electromagnetic Field ◽  
Classical Theory ◽  
Classical Electrodynamics ◽  
Recent Book ◽  
Charged Matter ◽  
Inconsistent Theory ◽  
Electrically Charged

Classical Electrodynamics is a classical theory treating Systems comprising an electromagnetic field and electrically charged matter. In a recent book Mathias Frisch argues that this theory is inconsistent within its intended domain of application and that a number of interesting methodological morals follow from this conclusion (2005,33-5; all citations of Frisch refer to this work).

A new classical theory of electrons

1951 ◽  
Vol 209 (1098) ◽  
pp. 291-296 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Classical Theory ◽  
Physical Significance ◽  
Gauge Transformations

In the theory of the electromagnetic field without charges, the potentials are not fixed by the field, but are subject to gauge transformations. The theory thus involves more dynamical variables than are physically needed. It is possible by destroying the gauge transformations to make the superfluous variables acquire a physical significance and describe electric charges. One gets in this way a simplified classical theory of electrons, which appears to be more suitable than the usual one as a basis for a passage to the quantum theory.

scholarly journals Relativistic quantum mechanics

1932 ◽  
Vol 136 (829) ◽  
pp. 453-464 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Theory ◽  
Correspondence Principle ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Relativistic Quantum Mechanics ◽  
Classical Electrodynamics ◽  
Quantum Phenomena

The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approxi­mation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.

Electromagnetism and special relativity

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Electromagnetic Field ◽  
Special Relativity ◽  
Point Charge ◽  
Reference Frames ◽  
Classical Electrodynamics ◽  
Covariant Form ◽  
Field Tensor ◽  
Electromagnetic Field Tensor ◽  
Preferred Reference Frame ◽  
Physical Quantities

In 1905, when Einstein published his theory of special relativity, Maxwell’s work was already about forty years old. It is therefore both remarkable and ironic (recalling the old arguments about the aether being the ‘preferred’ reference frame for describing wave propagation) that classical electrodynamics turned out to be a relativistically correct theory. In this chapter, a range of questions in electromagnetism are considered as they relate to special relativity. In Questions 12.1–12.4 the behaviour of various physical quantities under Lorentz transformation is considered. This leads to the important concept of an invariant. Several of these are encountered, and used frequently throughout this chapter. Other topics considered include the transformationof E- and B-fields between inertial reference frames, the validity of Gauss’s law for an arbitrarily moving point charge (demonstrated numerically), the electromagnetic field tensor, Maxwell’s equations in covariant form and Larmor’s formula for a relativistic charge.

Classical electrodynamics: the equation of motion

1974 ◽  
Vol 76 (1) ◽  
pp. 359-367 ◽  
Author(s):  
P. A. Hogan
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Scalar Field ◽  
World Line ◽  
External Electromagnetic Field ◽  
Equation Of Motion ◽  
The Self ◽  
Classical Electrodynamics ◽  
Field Equations ◽  
The World

In this paper we derive the Lorentz-Dirac equation of motion for a charged particle moving in an external electromagnetic field. We use Maxwell's electromagnetic field equations together with the assumptions (1) that all fields are retarded and (2) that the 4-force acting on the charged particle is a Lorentz 4-force. To define the self-field on the world-line of the charge we utilize a contour integral representation for the field due to A. W. Conway. This by-passes the need to define an ‘average field’. In an appendix the case of a scalar field is briefly discussed.

A Proposed Experiment of Direct Detecting of the Vector Potential within Classical Electrodynamics

1997 ◽  
Vol 11 (12) ◽  
pp. 531-540
Author(s):  
V. Onoochin
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Charged Particle ◽  
Vector Potential ◽  
Energy Exchange ◽  
Short Pulse ◽  
Classical Electrodynamics ◽  
Direct Influence ◽  
Ultra Short Pulse ◽  
The Magnetic Field

An experiment within the framework of classical electrodynamics is proposed, to demonstrate Boyer's suggestion of a change in the velocity of a charged particle as it passes close to a solenoid. The moving charge is replaced by an ultra-short pulse (USP), whose characteristics should depend on the current in the coil. This dependence results from the exchange of energy between the electromagnetic field of the pulse and the magnetic field within the solenoid. This energy exchange could only be explained, by assuming that the vector potential of the solenoid has a direct influence on the pulse.

Classical electrodynamics of spinning particles

1984 ◽  
Vol 62 (10) ◽  
pp. 943-947
Author(s):  
Bruce Hoeneisen
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Wave Equations ◽  
Dipole Moments ◽  
Equations Of Motion ◽  
Radiation Reaction ◽  
Classical Electrodynamics ◽  
Electric Dipole Moments ◽  
Gauge Invariant ◽  
Intrinsic Angular Momentum

We consider particles with mass, charge, intrinsic magnetic and electric dipole moments, and intrinsic angular momentum in interaction with a classical electromagnetic field. From this action we derive the equations of motion of the position and intrinsic angular momentum of the particle including the radiation reaction, the wave equations of the fields, the current density, and the energy-momentum and angular momentum of the system. The theory is covariant with respect to the general Lorentz group, is gauge invariant, and contains no divergent integrals.

X.—The Reciprocity Theory of Electrodynamics

1951 ◽  
Vol 63 (2) ◽  
pp. 105-138
Author(s):  
H. S. Green ◽  
K. C. Cheng
Keyword(s):  
Electromagnetic Field ◽  
Quantum Electrodynamics ◽  
Lagrangian Function ◽  
Classical Electrodynamics ◽  
Previous Communication

SynopsisThis paper represents the application of the Principle of Reciprocity, formulated in a previous communication, to the outstanding problems of classical and quantum electrodynamics.The first step consists in the formulation of a reciprocally invariant Lagrangian function for a system of electrons in interaction with the electromagnetic field. A study is made of the unaccelerated motion of an electron, and this is subsequently extended to embrace the problem of an electron in arbitrary motion. It is found that the usual difficulties of classical electrodynamics do not appear. The methods of the earlier paper are applied to the derivation of the Hamiltonian energy of electron and field, and this enables a quantized formulation of the theory to be given, which also does not lead to the usual divergence difficulties.

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