QUANTUM THEORY, THE. As recently as the opening years of the present century the vast majority of physicists still regarded Newton's dynamical laws as something established for all time. And they were not without solid grounds for this faith. Many phenomena were indeed known, chiefly those which may be classed under the heading radiation, e.g., black body radiation and line spectra, which refused to accommodate themselves to any sort of theory founded on Newtonian principles; but it was generally believed that such phenomena would, sooner or later, be completely accounted for without any departure from the classical principles of physics. Even the theory of relativity developed by Lorentz, Einstein, Minkow ski and their successors was regarded only as a widening or generalization of the Newtonian basis of physics. It was the culmination of classical physical theory. These phenomena we now believe, cannot be accounted for on the basis of the classi cal physical theory, whether Newtonian or Einsteinian. The first act of sacrilege was committed by Max Planck, until recently professor of theoretical physics in the University of Berlin, about the end of the year 1900, when he initiated the quantum theory. One of the prob lems engaging the attention of physicists during the closing years of last century was that of the radiation from a black body; a body, the surface of which absorbs all the radiation of any wave-length whatever that may fall on it. The radiation emitted by a black body at some definite temperature is like that inside a vacuous enclosure the walls of which are at this definite temperature. (The terms vacuous and empty as used in this article mean not containing atoms or molecules.) The character of black body radiation is determined solely by the temperature of the walls of the enclosure, and is independent of the nature of the mate rials of which they are made. Now the feature of this type of radiation which puzzled the physicists of the period immediately preceding the present century was the way in which the radiant energy was distributed among the different wave-lengths. The actual law of distribution is illustrated by the full line in fig. I. The distribution deduced from Lord Rayleigh's formula is shown by the broken line in fig. 1. The figure illustrates the wide diver gence of the theoretical from the actual distribution in the region of very short waves.
Planck convinced himself that Rayleigh's deduction, confirmed by J. H. Jeans, was sound, and he therefore drew the inference that the premises on which it was based, i.e., Newtonian dynamical
principles, were faulty. In the year 1896, W. Wien, then a pro fessor in Wurzburg, found a formula which represented the ob servational data very well for small values of the product of wave-length and absolute temperature. Planck had for his guid ance the formulae of Rayleigh and Wien, and also the ideas of Ludwig Boltzmann about the relation be tween entropy and probability. His first success was the discovery by a method of trial and error, of a formula which interpolated between those of Rayleigh and Wien, and which represents the facts of black body radiation exceedingly well for all ranges of wave-lengths and tempera tures over which observations have been made. A little later he succeeded in giving this formula a theoretical basis and it is here where the first mention of the quan tum theory appears.
The essential feature of the innovation which Planck introduced may be described with the aid of a simple illustration. Let us consider a pendulum, the bob of which is vibrating in a vertical plane, with not too large an amplitude. The centre of gravity of the bob will move backwards and f or wards along a short arc of a circle. Represent its distance at any instant from the central position by the letter q and the momen tum of the bob, i.e., the product of its mass and velocity, by the letter p. If we exhibit the relation between p and q graphically (fig. 2) we obtain a closed curve, on account of the periodicity of the motion. Newton's laws of motion require the shape of this curve to be an ellipse, and further, that the energy of the pendulum bob shall be equal to the product of the area of the ellipse and the frequency, i.e., the number of complete oscillations made by the pendulum in the unit time. Therefore where E is the energy, A is the area of the ellipse and v is the frequency. We are assuming, of course, that the pendulum is not subjected to damping influences and after being set in motion is not further interfered with. The constant A is called the action of the pendulum corresponding to its period of motion and has the dimensions of the product of energy and time. It seems self-evident that, provided we keep within a certain upper limit, the action A may have any value whatever. It merely depends on the energy with which the motion is initiated, and Newton's laws of motion impose no restrictions on the values of the con stant A.