Abstract The classical theory of radiation was able to explain satisfactorily the relationship between the dispersion of refraction and coherent light scattering. However, in the 1920s the old quantum theory encountered difficulties in explaining these phenomena and these were only fully overcome 20 years later.
Abstract It is commonplace to recount the history of quantum physics on the basis of phenomena that have found no satisfactory explanation in the context of so‐called classical physics. This is the case of, for example, blackbody radiation, the photoelectric effect, specific heats, and series of spectral lines. This story goes in another direction: new knowledge about quantum physics not only emerged from the need to explain new phenomena that conflicted with old theoretical structures, but also from the attempts to provide a quantum explanation of phenomena, like optical dispersion, which for a long time had found a very convincing explanation in old physical models, such as the resonance model. The boundary between classical and quantum domains of knowledge was not fixed a priori, but historically negotiated in the context of specific problems, including the problem of optical dispersion.
This chapter provides a basis for an insight into the nature of quantum effects. The Newtonian approach cannot explain diffraction phenomena. The wave theory of the nature of light proposed by Huygens was able to account for these phenomena as well as for geometric optics. Planck was not only able to overcome the difficulties encountered by his predecessors, but included their findings as special cases of his analysis. Planck considered that the radiating surface was composed of electric dipole oscillators, and that a relationship should exist between the energy of the radiation and the frequency of the oscillators. According to classical theory a continuous spectrum is expected when matter is excited by an arc, or spark, as in spectroscopy. It is found experimentally that only “lines”, or discrete radiations, occur when the light is diffracted. Bohr’s revolutinary ideas provided a significant portion of the bases for the modern understanding of spectra and, consequently, of atomic structure.
Abstract It will probably be agreed that among all the recent developments of the quantum theory, one of the least satisfactory is the theory of radiation. The present paper is intended as a preliminary to a new line of attack on the subject. It was begun some time ago, but owing to lack of success in carrying it to a conclusion, its publication has been much delayed. In the meantime other papers have appeared, which in some respects follow the same train of thought. The authors of these works have carried their methods further in some directions than I have attempted, but there is still perhaps room for the discussion of a number of questions from the rather different point of view adopted here. 1. The main principle of the present work is the idea that, since matter and light both possess the dual characters of particle and wave, a similar mathematical treatment ought to be applied to both, and that this has not yet bee done as fully as should be possible. Whereas we have a fairly complete calculus for dealing with the behaviour of any number of electrons or atoms, for photons the existing processes are much less satisfactory. The central difficulty, which makes it hard to apply the ordinary methods of wave mechanics to light, is the fact that (at least according to our present ideas) photons can be created and annihilated, and to represent this in a wave system we have to be able to think of a medium suddenly coming into existence and then going out again, when the light that it was carrying is absorbed. Such behaviour is a grave difficulty in the way of allowing us to think of the photon as a wave, and tends to make us think with more favour of its particle aspect, until we recall that after all it is quite unlike any known particle to come into existence and later to disappear without trace. The theories at present current, such as that of Heisenberg and Pauli, avoid these difficulties because they are mainly formal generalisations of the classical theory; this frees them from the above difficulties, but they pay for it in being highly abstract, and, as it has turned out, rather unsuccessful.
Ever splitting the light! How often do they strive to divide that which, despite everything, would always remain single and whole. Goethe (quoted in Zajonc 1993) Introduction The use of electromagnetic wave theory and geometrical optics to describe propagation of light is satisfactory when there is no exchange of energy between radiation and matter. All observable characteristics – direction of propagation, polarization, diffraction, interference, the energy of radiation, and so forth – are accurately described by one of these so-called classical theories. However, with the exception of absorption by lossy media (eqn. 4.36) or the effects of dispersion (eqn. 4.22), classical theories fail to give reasons for many phenomena that have practical consequences in modern technology and that involve interaction between radiation and matter. Even the partially successful descriptions of dispersion or loss cannot explain the existence of the multitude of spectrally distinct absorption lines; cannot predict the wavelengths for absorption or the wavelengths for anomalous dispersion; cannot account for all the absorbed energy; and, most importantly, cannot predict or describe the effect of optical gain, which is closely related to absorption. Thus, the principles of operation of many important devices of modern optics such as lasers, photodiodes, electronic cameras, and television screens cannot be explained by classical theories. Even the emission by the sun or an incandescent lamp are beyond the scope of these theories. It is evident therefore that a new, modern theory is necessary – one that is either more complete than, or simply complements, the classical theories.
Abstract This chapter covers the history of dispersion theory starting from the classical theories of the late nineteenth century, involving charged harmonic oscillators with resonance frequencies at the absorption frequencies of the dispersing materials to account for anomalous dispersion, the phenomenon that the index of refraction decreases rather than increases with frequency around the absorption frequencies. It then covers dispersion theories formulated in the context of the old quantum theory, in which the link between radiation frequencies and orbital frequencies is severed. Drawing on these efforts, especially by Ladenburg and Reiche in the early 1920s, and using Bohr’s correspondence principle and other ingredients of the old quantum theory, Kramers found a successful quantum formula in late 1923. He only published a full treatment of his new dispersion theory in a paper with Heisenberg in early 1925. This paper played a key role in laying the foundations of matrix mechanics.
From a historical point of view, a distinction can be drawn between ‘old quantum theory’ and the full quantum theory that we now use. Old quantum theory was in essence a patchwork, cobbled together by incorporating some quantum ideas into essentially classical physics. The work of Planck, Einstein, Bohr, and Sommerfeld can be bracketed as old quantum theory. This classification is not meant to undermine the tremendous achievement that old quantum theory represents, but simply to underline its standing as a stage on the way to a fully formed quantum theory, which emerged from the work of Heisenberg, Schrodinger, Born, and Dirac. The development of the photon concept is a key example of a radically new idea gradually gaining acceptance. The process works via a growing realization that more and more things can be explained in the context of the photon model.