14 Introduction to the Classical andQuantum Theory of Radiation byAccelerating Charges

14 Introduction to the Classical and Quantum Theory of Radiation by Accelerating Charges In Part I, Chapters 1–13, we dealt with the polarization of the optical field and the phenomenological interaction of polarized light with optical components, namely, polarizers, retarders, and rotators All this was accomplished with only the classical theory of light By the mid-nineteenth century Fresnel’s theory of light was a complete triumph The final acceptance of the wave theory took place when Stokes showed that the Fresnel–Arago interference laws could also be explained and understood on the basis of classical optics Most importantly, Stokes showed that unpolarized light and partially polarized light were completely compatible with the wave theory of light Thus, polarized light played an essential role in the acceptance of this theory We shall now see how polarized light was again to play a crucial role in the acceptance of an entirely new theory of the optical field, namely, Maxwell’s theory of the electrodynamic field In spite of all of the successes of Frensel’s theory there was an important problem that classical optics could not treat We saw earlier that the classical optical field was described by the wave equation This equation, however, says nothing about the source of the optical field In 1865 James Clerk Maxwell introduced a totally new and unexpected theory of light Maxwell’s new theory was difficult to understand because it arose not from the description of optical phenomena but from a remarkable synthesis of the laws of the electromagnetic field This theory was summarized by expressing all of the known behavior of the electromagnetic field in the form of four differential equations In these equations a source term existed in the form of a current j(r, t) along with a new term postulated by Maxwell, namely, the displacement current @D(r, t)/@t After Maxwell had formulated his equations, he proceeded to solve them He was completely surprised at his results First, when either the magnetic or electric field was eliminated between the equations, he discovered that in free space the electromagnetic field was described by the wave equation of classical optics The next result surprised him even more It appeared that the electromagnetic field propagated at the same speed as light This led him to speculate that, perhaps, Copyright © 2003 by Marcel Dekker, Inc All Rights Reserved the optical field and the electromagnetic field were actually manifestations of the same disturbance, being different only in their frequency (wavelength) Maxwell died in 1879 Nearly 10 years later Heinrich Hertz (1888) carried out a set of very sophisticated and brilliant experiments and confirmed Maxwell’s theory In spite of Hertz’s verification, however, Maxwell’s theory was not immediately adopted by the optics community There were several reasons for this One reason was due to the simple fact that Hertz confirmed Maxwell’s theory not at optical wavelengths but at millimeter wavelengths For the optical community this was not enough In order for them to accept Maxwell’s theory, it would have to be proved at optical wavelengths Another reason for the slow acceptance of Maxwell’s theory was that for 30 years after the publication of Maxwell’s theory in 1865 nothing had been found which could clearly differentiate between the classical wave theory and Maxwell’s theory Nothing had appeared in optics which was not known or understood using Fresnel’s theory; no one yet understood exactly what fluorescence or the photoelectric effect was There was, however, one very slim difference between the two theories Maxwell’s theory, in contrast to Fresnel’s theory, showed that in free space only transverse waves existed It was this very slim difference that sustained the ‘‘Maxwellians’’ for several decades A third important reason why Maxwell’s theory was not readily embraced by the optics community was that a considerable effort had to be expended to study electromagnetism–a nonoptical subject–in order to understand fundamental optical phenomena Furthermore, as students to this day know, a fair degree of mathematical training is required to understand and manipulate Maxwell’s equations (this was especially true before the advent of vector analysis) It was, therefore, very understandable why the optics community was reluctant to abandon a theory that explained everything in a far simpler way and accounted for all the known facts In 1896, less than a decade after Hertz’s experiments, two events took place which overthrew Fresnel’s elastic theory of light and led to the complete acceptance of Maxwell’s theory The first was the discovery by J J Thomson of the electron, the long-sought source of the optical field, and the second was the splitting of unpolarized spectral lines which became polarized when an electron was placed in a magnetic field (the Lorentz–Zeeman effect) In this part we shall see how polarized light played a crucial role in the acceptance of Maxwell’s theory We shall use the Stokes parameters to describe the radiation by accelerating electrons and see how the Stokes parameters and the Stokes vector take on a surprising new role in all of this In the final chapter of this part we shall show that the Stokes vector can be used to describe both classical and quantum radiating systems, thereby providing a single description of radiation phenomena REFERENCES Books Maxwell, J C., A Treatise on Electricity and Magnetism, 3rd ed., Clarendon Press, Oxford, 1892 Hertz, H., Electric Waves, Macmillan, London, 1893 Lorentz, H A., The Theory of the Electron, Dover, New York, 1952 Copyright © 2003 by Marcel Dekker, Inc All Rights Reserved 4 10 Born, M and Wolf, E., Principles of Optics, 3rd ed., Pergamon Press, New York, 1965 Whittaker, E., A History of the Theories of Aether and Electricity, Philosophical Society, New York, 1951, Vol I Sommerfeld, A., Lectures on Theoretical Physics, Vols I–V, Academic Press, New York, 1952 Stratton, J A., Electrodynamic Theory, McGraw-Hill, New York, 1941 Feuer, L S., Einstein and the Generations of Science, Basic Books, New York, 1974 Jammer, M., The Philosophy of Quantum Mechanics, Wiley, New York, 1974 Schwinger, J., Einstein’s Legacy, Scientific American Books, Inc., New York, 1986 Copyright © 2003 by Marcel Dekker, Inc All Rights Reserved