Abstract
The theory of electrodynamics of radiating charges is reviewed with special emphasis on the role of the Schott energy for the conservation of energy for a charge and its electromagnetic field. It is made clear that the existence of radiation from a charge is not invariant against a transformation between two reference frames that has an accelerated motion relative to each other. The questions whether the existence of radiation from a uniformly accelerated charge with vanishing radiation reaction force is in conflict with the principle of equivalence and whether a freely falling charge radiates are reviewed. It is shown that the resolution of an electromagnetic “perpetuum mobile paradox” associated with a charge moving geodetically along a circular path in the Schwarzschild spacetime requires the so-called tail terms in the equation of motion of a charged particle.
Highlights
The nonrelativistic version of the equation of motion of a radiating charged particle was discussed already more than a hundred years ago by Lorentz 1, m0a fext m0τ0da dT q2 τ0 6πε0m0c3, 1.1 where a is the ordinary Newtonian acceleration of the particle
The time τ0 is of the same order of magnitude as the time taken by light to move a distance equal to the classical electron radius, that is, τ0 ≈ 10−23 seconds
Equation 2.18 can be written as ES ΔEbcur − Eb C, 2.19 which leads to the following interpretation: the Schott energy is the difference between the bound field energy of an accelerated charged particle if the particle had moved with its current velocity for its entire history and the actual bound field energy of the particle
Summary
The nonrelativistic version of the equation of motion of a radiating charged particle was discussed already more than a hundred years ago by Lorentz 1 , m0a fext m0τ0da dT. In the 4-vector notation invented by Minkowski in 1908, and referring to an inertial frame in flat spacetime, the equation of motion of a radiating charged particle takes the form. FAμ ≡ m0τ0 Aμ − g2Uμ , g2 AαAα, 1.6 is called the Abraham 4-force, g is the proper acceleration of the charged particle with respect to an inertial frame, and. Gal’tsov and Spirin 4 have reviewed and compared two different approaches to radiation reaction in the classical electrodynamics of point charges: a local calculation of the self-force, using the equation of motion and a global calculation consisting in integration of the electromagnetic energy-momentum flux through a hypersurface encircling the worldline. In an inertial reference frame the Abraham 4-force may be written as FAμ m0τ0γ v · g , g , 1.11 where the vector g is the proper acceleration of the charged particle with respect to an inertial frame.
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