Relativistic Electrodynamics
The origin of Relativity Theory is strongly tied to electrodynamics, and also the wealth of applications makes relativistic electrodynamics an important part of Einstein's theory. Quantum electrodynamics, which unites Relativity, electrodynamics and quant
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Relativistic Electrodynamics
The origin of Relativity Theory is strongly tied to electrodynamics, and also the wealth of applications makes relativistic electrodynamics an important part of Einstein's theory. Quantum electrodynamics, which unites Relativity, electrodynamics and quantum theory, is perhaps the most precise physical theory we have, and its successes dominated our thinking about elementary particles during the period 19451960. Its predictions about the magnetic moments of the electron and the muon, accurate to eight decimal places, and the calculations of the spectral lines of hydrogen with a similar precision are at the same time our best confirmations of Relativity and of electrodynamics. They also show that the relativistic space-time concept is valid down to distances of about 10- 15 cm. We shall here only touch upon some of the most important aspects of relativistic electrodynamics, leaving aside numerous applications of the theory, for which we refer the reader to, e.g., Jackson (1999) or Landau and Lifshitz (1961). The formal development of the theory will be supplemented in this chapter by the introduction of the tensor concept.
5.1
Forces
In the last chapter we wrote down the relativistic version F = ma of Newton's basic law of dynamics. However, for this equation to have physical content it is necessary to specify the four-force F occurring therein. What can be inserted for it? On the phenomenological level of macrophysics, F could be a pressure or frictional force as in relativistic hydrodynamics, which will be sketched in chap. 10; for relativistic continuum mechanics see, e.g., Schwartz (1968). The domain of applicability of such theories is, however, quite narrow (except in astrophysical or cosmological situations, where general-relativistic versions are needed, however), since fluid flow and other macroscopic processes hardly ever reach ('relativistic') velocities close to c(= 1). If we now turn to microphysics, we there encounter four kinds of interactions: electrodynamics gravitation
strong interactions weak interactions.
The interactions on the left are characterized by infinite range and may be described classically by fields of (velocity-dependent) forces. The interactions on the right become pronounced only when particles approach each other closer than about 10- 13 cm. At these short distances, however, the classical orbit concept becomes meaningless, so that a particle's acceleration cannot be defined. Consequently, in the processes illustrated in Fig. 4.6 it is not possible to use cassical concepts like force and acceleration, and one can measure and calculate only interaction cross sections, i.e., probabilities for particle scattering, production, decay, etc. R. U. Sexl et al., Relativity, Groups, Particles © Springer-Verlag Wien 2001
5 Relativistic Electrodynamics
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Among the two classical forces, gravitation turns out to require a special treatment also, since gravitational fields change the space-time structure: this is the subject of General Relativity.1 Thus the
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