Chapter 4 presents the joining of quantum theory to electromagnetism and radiation associated with Dirac, particularly noting the variety of photons that are consistent with the choice of radiation field modes that still form the working definition of photons for many physicists, and which ofiers a possible resolution to the seeming paradox of wave-particle duality.
Chapter 4 presents the joining of quantum theory to electromagnetism and radiation associated with Dirac, particularly noting the variety of photons that are consistent with the choice of radiation field modes that still form the working definition of photons for many physicists, and which ofiers a possible resolution to the seeming paradox of wave-particle duality.
This book describes the changing views of the physics community toward photons, and how photons are viewed today in several contexts. The first portion, a ninechapter Memoir with few equations and many definitions, explains the changing view of physicists toward radiation and its wave-particle photons, written for those with interest but possibly without technical background. It gives operational definitions that have been used for photons and their association with quantum-state manipulations that include Quantum Information, astronomical sources and crowds of photons, the boxed fields of cavity Quantum Electrodynamics It defines, qualitatively, the historical photons of Planck, Einstein, Compton, and Bohr, the later photons of Dirac, Feynman, and Glauber, and the photon constituents of the Standard Model of Particle Physics. It points to contemporary photons as causers of change to atoms, as carriers of messages, and as subject to controllable creation and alteration. A second portion, of three tutorial appendices, explains the mathematical background of quantum theory and radiation needed by those whose profession involves photonics and who therefore want more detailed understanding of the Memoir portion: quantum theory and the Schrodinger equation for quantum-state manipulation; Maxwell equations for electromagnetism with wave modes that become photons through a quantization postulate, possibly exhibiting quantum entanglement; and the coupling of atoms and fields to create quasiparticles that are seen as slow and stored light pulses. As with other Memoirs, the present book has idiosyncrasies of the author. Most notably, on the opening page of each chapter, and at the end of the book, is a cartoon drawn by the author, as a grad student, that reflects the changing views of a PhD aspirant toward the grad school experience as he progressed through the graduate school of MIT in the 1950s.
Light occupies a special position in our attempts to understand nature both classically and quantum mechanically. We recall that Newton, who made so many fundamental contributions to optics, championed a particle description of light and was not favorably disposed to the wave picture of light. However, the beautiful unification of electricity and magnetism achieved by Maxwell clearly showed that light was properly understood as the wave-like undulations of electric and magnetic fields propagating through space. The central role of light in marking the frontiers of physics continues on into the twentieth century with the ultraviolet catastrophe associated with black-body radiation on the one hand and the photoelectric effect on the other. Indeed, it was here that the era of quantum mechanics was initiated with Planck's introduction of the quantum of action that was necessary to explain the black-body radiation spectrum. The extension of these ideas led Einstein to explain the photoelectric effect, and to introduce the photon concept. It was, however, left to Dirac to combine the wave-and particlelike aspects of light so that the radiation field is capable of explaining all interference phenomena and yet shows the excitation of a specific atom located along a wave front absorbing one photon of energy. In this chapter, following Dirac, we associate each mode of the radiation field with a quantized simple harmonic oscillator, this is the essence of the quantum theory of radiation.
Having just described electromagnetic radiation as a wave, it may seem a bit peculiar to embark on a particle description of that radiation. Perhaps it will help to recall from Chapter 2 that our perception of something depends in part on the means we use to perceive it and that we used a specific experiment (interference) to define the wave property. There is no reason to believe that one human-invented experiment is the only one that can be used to describe electromagnetic radiation. In fact, the Einstein photoelectric effect, described next, is consistent with light being a particle.
The fundamental fact for quantum physics which has emerged from experimental investigations in the field is a double duality of wave and particle concepts. The wave theory of light, firmly grounded by the wave explanations of interference and diffraction and by Maxwell’s electromagnetic theory of light waves, is now recognized as giving but one aspect of the nature of radiation. The corpusclar aspect of radiation is revealed in the photoelectric effect and in the Compton effect. In these effects Planck’s constant appears as a universal constant which connects the wave and particle modes of description of the same radiation.
The idea of the photon has stirred the imaginations of physicists ever since 1905 when Einstein originally proposed the use of light quanta to explain the photoelectric effect. This concept is formalized in the quantum theory of radiation, which has had unfailing success in explaining the interaction of electromagnetic radiation with matter, seemingly limited only by the ability of physicists to perform the indicated calculations. Nevertheless, it has its conceptual problems—various infinities and frequent misinterpretations. Consequently an increasing number of workers are asking, “to what extent is the quantized field really necessary and useful?” In fact the experimental results of the photoelectric effect were explained by G. Wentzel in 1927 without the quantum theory of radiation. Similarly most electro-optic phenomena such as stimulated emission, reaction of the emitted field on the emitting atom, resonance fluorescence, and so on, do not require the quantization of the field for their explanation. As we will see, these processes can all be quantitatively explained and physically understood in terms of the semiclassical theory of the matter–field interaction in which the electric field is treated classically while the atoms obey the laws of quantum mechanics. The quantized field is fundamentally required for accurate descriptions of certain processes involving fluctuations in the electromagnetic field: for example, spontaneous emission, the Lamb shift, the anomalous magnetic moment of the electron, and certain aspects of blackbody radiation. (The Compton effect also fits here, but see later under references 8b and c.) Here we will outline how the photon concept originated and developed, where it is not required and is often misused, and finally where it plays an essential role in the understanding of physical phenomena. In our discussion we will attempt to give a logically consistent definition of the word “photon”—a statement far more necessary than one might think, for so many contradictory uses exist of this elusive beast. In particular consider the original coining of the word by G. N. Lewis: “[because it appears to spend] only a minute fraction of its existence as a carrier of radiant energy, while the rest of the time it remains an important structural element within the atom…, I therefore take the liberty of proposing for this hypothetical new atom which is not light but plays an essential part in every process of radiation, the name photon!” (our exclamation point). Clearly the present usage of the word is very different.
For many years the physical interpretation of quantum theory has been dominated by the “wave-particle duality” attitude of the “Copenhagen school.” This point of view is eloquently described in Bohr's collection of essays on the subject. Despite persistent concerns with apparent paradoxes and limitations to this interpretation (as exemplified by Schrodinger's cat, the paradox of Einstein, Podolsky and Rosen, among others), the Copenhagen view persists de facto in the daily life of the modern physicist. Traditional quantum theory has so successfully explained such a vast amount of data in atomic and molecular physics, solid state physics (and to a lesser extent, elementary particle physics) that little doubt can exist concerning its essential validity. As a consequence of the overwhelming practical success of the “Copenhagen interpretation, ” the latter has acquired the status of dogma. For many years, therefore, most physicists have found it expedient to relegate the puzzling aspects of the theory to philosophers, and mathematicians. Nevertheless, a persistent interest in this subject has produced a significant and fascinating literature, reviewed by Jammer. In recent years, concerns over the proper meaning to be ascribed to quantum theory have produced an increasingly deep and incisive series of investigations. These investigations fall generally into two categories: either (1) discussion of the philosophical content of the theory, or (2) analyses of the mathematical variants of the theory and their connection with differing interpretational schemes. Physicists tend to be detached from a commitment to philosophical issues, because of their realization of the transient character of the meanings attached to theories of the day. As a simple illustration of this we can mention the profound differences between nonrelativistic and relativistic quantum mechanics.