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physica status solidi (a)

Spontaneous emission revisited

Albert Rose

Published Sep 16, 1980• 1 citation
Publisher

Abstract

The cause of spontaneous emission is frequently assigned to the presence of zero-point energy in the radiation field. As such it would have no classical equivalent since zero-point energy does not exist classically. It is argued that spontaneous emission is not caused by zero-point energy but rather by an essentially classical interaction between the excited electron and its surrounding medium.

DOI
10.1002/pssa.2210610115

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The cause of spontaneous emission is frequently assigned to the presence of zero-point energy in the radiation field. As such it would have no classical equivalent since zero-point energy does not exist classically. It is argued that spontaneous emission is not caused by zero-point energy but rather by an essentially classical interaction between the excited electron and its surrounding medium.
The usual computation of the spontaneous emission uses a mixture of classical and quantum postulates. A purely classical computation shows that a source of electromagnetic field absorbs light in the eigenmode it is able to emit. Thus in an excitation by an other mode, the component of this mode on the eigenmode is absorbed, while the remainder is scattered. This loss of energy does not apply to the zero point field which has its regular energy in the eigenmode, so that the zero point field seems more effective than the other fields for the stimulation of light emission.
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 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.