Theory of the Brownian motion of a Planck radiator in black body radiation.---In the case of a classical resonator it is shown that the motion takes place even though the emission and absorption is not unidirectional provided the radiation is not strictly monochromatic. This theory is then extended to the case of a quantized atom. Interference between the waves emitted by the atom and the surrounding radiation provides for the recoil actions without the assumption of unidirectional quanta. Statistically these have the same effect as Einstein's unidirectional quanta. This theory removes the contradiction postulated by Einstein between the Rubinowicz-Sommerfeld considerations and the requirements of classical Brownian motion. It leaves the wave-theory of light intact and is in agreement with Bohr's principle of correspondence.
Theory of the Brownian motion of a Planck radiator in black body radiation.---In the case of a classical resonator it is shown that the motion takes place even though the emission and absorption is not unidirectional provided the radiation is not strictly monochromatic. This theory is then extended to the case of a quantized atom. Interference between the waves emitted by the atom and the surrounding radiation provides for the recoil actions without the assumption of unidirectional quanta. Statistically these have the same effect as Einstein's unidirectional quanta. This theory removes the contradiction postulated by Einstein between the Rubinowicz-Sommerfeld considerations and the requirements of classical Brownian motion. It leaves the wave-theory of light intact and is in agreement with Bohr's principle of correspondence.
The problem of emission by an atom is treated according to Schroedinger’s rules. The translational motion of the atom as a whole is taken into account. The charge-current density vector is shown to be propagating with the velocity of light in the direction of the emitted quantum. Only unidirectional quanta can be emitted according to the theory. The reason is that the charge-current wave radiates infinitely more intensely if it travels with light velocity than otherwise.It is shown that Gordon’s treatment of the Compton effect involves an analogous phenomenon. It is suggested that Schroedinger’s equations designed for the conservation of energy and momentum work out better when the translational motion of the atom as a whole is considered.
We argue that certain assumptions about the process of the emission of the quanta by their (oscillating) emitter provide for their changing (oscillatory) flux at any location. This mechanism underlying (such) wave phenomena is not based, both, on the newtonian notion of force and the field concept (of Faraday, Maxwell, Lorentz and Einstein). When applied to the case of thermal radiation, this emission origin for the wave of quanta is shown here to be consistent with the laws of the black body radiation. We conclude therefore also that a conceptual framework, which is not rooted in the notion of force and in the field concept, may provide a deterministic basis underlying the probabilistic methods of the quantum theory.
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.
It is suggested that, if the Wilson-Sommerfeld quantization postulate is modified such that phase integrals for nonignorable coordinates are placed equal to half-integers times Planck's constant while those for ignorable coordinates are placed equal to integers times Planck's constant, eigenvalues that are in much better agreement with quantum mechanics are obtained. Also there results a picture of the radiation process that is conceptually consistant with classical theory. It avoids the picture of an electron making many revolutions in a closed orbit without radiating. Some of the discussion is based upon developments in classical theory that have evolved since the Bohr-Sommerfeld theory was formulated. In addition, some of the effects of the uncertainty principle are made more apparent.
An attempt is made to present a consistent detailed theory of optical phenomena, based on the suggestion recently made by the author in collaboration with Bohr and Kramers. This suggestion is that atoms are radiating or absorbing continuously, during their stationary states, and that transitions influence radiation only in terminating the radiation characteristic of the old state, and substituting that of the new. The atoms, on the other hand, are supposed not to change their energy while radiating, but to change it discontinuously on transition. This necessitates giving up the detailed application of the conservation of energy in interaction between atoms and radiation. In the present paper, an additional suggestion is made, namely that resonance radiation is to be identified with the radiation carried out by the spherical wavelets which, by their interference with the external field, also produce absorption. This is practically a return to the classical picture of resonance radiation. Statement of the theory consists formally of two parts: the description of the behavior of atoms, and of radiation, when the two interact. The first involves the statement of the probabilities of transition of atoms, and is taken without change from Einstein. The probability of interruption of coherent vibrations is also discussed. The second requires the specification of the fields emitted by atoms in any steady state under the influence of any external field. These consist of spherical wavelets of the frequencies of the various quantum lines which the atom can emit or absorb in the stationary state in which it is. For emission frequencies, wavelets are emitted even in the absence of an external field; for absorption frequencies, external fields induce wavelets, similar to the wavelets of linearly bound electrons in electron theory, which on the one hand interfere with the external field to produce the phenomena of dispersion, etc., and on the other carry out the resonance radiation in all directions. Detailed descriptions of these fields are given. In a discussion of the theory, it is first shown that the assumptions which have been made about the field satisfy the correspondence principle, in that for large quantum numbers the field aproaches that which would be emitted classically on account of the interaction of an external field and a multiply periodic atom. On the other hand, it is shown that the field has a character essentially like that of classical electron theory, which is known to be in general agreement with experiments. Next, the energy and momentum relations at interaction of atoms and light are investigated, and it is shown that, although these quantities are not precisely conserved, still the assumptions as to atomic and radiation processes have been so made that they are conserved on an average over a great number of atomic processes. Finally the spectral resolution of emitted and absorbed radiation is considered; the theory gives a minimum breadth for the lines, depending on the finite length of wave trains resulting from the finite life in stationary states, and it is shown that Kirchhoff's law is obeyed, the emission and absorption lines being of the same breadth. By way of illustration, specific application of the theory is made to the simple examples of emission of light by bombardment of electrons at the resonance potential, resonance radiation, its quenching by presence of foreign gases, absorption, scattering, and disperison.
The conclusion of the Planck radiation law is proposed, which does not require the involvement of non-thermodynamic considerations. The conclusion is based on the concept of the wave nature of the radiation process and the existence of harmonics in oscillators. It is shown that the true radiation quantum is a wave that is discrete both in time and in space, and the Planck constant plays the role of the proportionality coefficient between the fluxes of radiant energy and traveling waves. The de Broglie relation is obtained as a consequence of the identity of the oscillation frequency of the oscillators to the flow of emitted waves. The proposed approach removes a number of contradictions of quantum theory with classical physics.