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Soviet Physics Uspekhi

The nature of spontaneous radiation

Виталий Л. Гинзбург

Published Aug 31, 1983• 35 citations
Publisher

Abstract

The nature of spontaneous radiation is discussed in its technical and historical aspects. The point of view encountered in the literature according to which spontaneous radiation is induced radiation produced by the zero-point (vacuum) oscillations of the electromagnetic field is criticized. Spontaneous radiation is not a purely quantum effect since it occurs also in the classical region (and in this case it is described by classical electrodynamics).

DOI
10.1070/pu1983v026n08abeh004484

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The nature of spontaneous radiation is discussed in its technical and historical aspects. The point of view encountered in the literature according to which spontaneous radiation is induced radiation produced by the zero-point (vacuum) oscillations of the electromagnetic field is criticized. Spontaneous radiation is not a purely quantum effect since it occurs also in the classical region (and in this case it is described by classical electrodynamics).
This chapter reviews the classical description of radiation. It describes how classical electromagnetic radiation interacts with a quantum mechanical particle. The general rule is that, even though the wave functions and the electromagnetic potentials change with the gauge, all physically observable quantities are independent of the gauge. The chapter also describes the process of the absorption of light by a system in terms of the effect of an external classical electromagnetic field on the system. The total emission rate is the sum of the induced and the spontaneous rates. Spontaneous emission is just the quantum mechanical version of the classical phenomenon of radiation from an accelerating charge. A very important consequence of the fact that the electromagnetic field is quantized is that there are vacuum fluctuations of the field, analogous to the zero point motion of a harmonic oscillator. Einstein gave a simple statistical argument to determine the rate at which spontaneous emission takes place.
It is pointed out that induced radiation effects cannot be purely quantum in nature and that they must be present in the classical theory of radiation processes. The classical theory is usually built on the example of the harmonic oscillator. Several effects arising from the interaction of the oscillators with the field disappear when harmonic oscillators are considered. This is particularly true when one is concerned with radiation processes induced by the field. In addition, the interaction between the field and the radiation of nonlinear oscillators (their frequencies depend on the energy) was not previously considered from the standpoint of the classical theory. Because of these reasons and because of the interest in the problem of quantum generators the question of the role of induced radiation in classicai theory was examined. The theory is described, and some specific properties of the classical system are contrasted with those of the quantum system. The description includes a discussion of spontaneous radiation processes and both harmonic and anharmonic oscillators are considered. The limiting transition from quantum to classical theory is discussed, and a detailed comparison of the two more » theories is made. An ensemble of oscillators distributed in energy is discussed in the classical theory. It is shown, for certaln determined conditions, that classical systems do not absorb but rather enhance incident radiation. (TTT) « less
The idea about a quantum nature of Planck's blackbody radiation law is deeply rooted in minds of most physicists. Einstein's work, in which the coefficients of spontaneous and induced emission were introduced, has always been regarded as a proof that quantum energy discreteness of an atom plays a crucial role in the derivation of this law. In our paper we avoid this standpoint. It may be shown that the de Broglie wave assigned to every material particle is a result of interaction of the particle with zero-point vibrations of electromagnetic ground field. The energetic spectrum of a harmonic oscillator is obtained from this fact within classical physics which coincides with the quantum result. Thus, it is explained here how the energy discreteness came into existence in stochastic electrodynamics (SED) --- the classical electrodynamics with classical electromagnetic zero-point radiation. Next we reconsider the Einstein work from the viewpoint of SED and derive the Planck formula.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.
The role of vacuum fluctuations and radiation reaction in the process of spontaneous emission is examined with particular reference to the Heisenberg picture of quantum electrodynamics. In this picture the radiation reaction is found to be responsible for spontaneous emission if the equations are ordered normally. However, in the case of nonnormally ordered equations there appears to be an explicit contribution to the observable effects from vacuum fluctuations as well. We point out that this contribution from the vacuum field is an artifact of the approximation methods employed for eliminating the free-field variables from the nonnormally ordered equations These approximations are the same as those used in the master-equation approach, in which spontaneous emission appears to be due solely to the vacuum fluctuations. We show that the vacuum field does not contribute explicitly in any ordering if it is eliminated nonperturbatively and the approximation methods are invoked only after its elimination from the equations of motion.