In the present case, the outstanding names connected with the problem of radiation are those of Boltzmann, Wien, Rayleigh, Jeans and Planck, all of them theoretical physicists. Their object was to co-ordinate the facts of radiation with what little was known of the phenomenon of light emission. This task involved mathematical calculations which we should be unjustified in criticising unless we possessed an extensive knowledge of mathematics; hence we may assume that this part of the work is not disputed by the critic.
As a result of these calculations, it was found to be quite impossible to reconcile the existence of the facts disclosed by experiment with any continuous emission theory of light. Whenever it was assumed that the atoms in the heated enclosure emitted their radiations continuously, it always followed that, for any given temperature, the maximum intensity of the radiations should be found in the infinitely high frequencies, and not in the visible spectrum; whence it followed that a heated enclosure could never emit visible light. This was, of course, contrary to common experience. The literature on the subject extends over a number of years. Various explanations of the discrepancy between theory and experience were suggested, but for one reason or another none was found satisfactory.
Then Planck noticed that if, contrary to all previous opinion, we assumed that the atoms in the heated enclosure emitted their radiations by discrete quanta, it was possible to obtain a mathematical formula of radiation in perfect agreement with experiment. According to Planck’s calculations, it was necessary to assume that light was emitted in bundles, or quanta, possessing an energy
. In his expression,
represents a universal constant called Planck’s constant, and
represents the frequency of the light. Obviously, the greater the frequency of the light, the greater the value of its quantum of energy. These discontinuities in the light-energy emission necessitated the introduction of probability and entropy considerations into the theoretical treatment. Inasmuch as entropy is an abstruse concept drawn from thermodynamics, we see that the facts entering indirectly into the problem of radiation were considerably increased in number. Obviously, it would be quite impossible either to justify or to criticise Planck’s hypothesis by any general line of talk, for without the aid of the mathematical instrument, and a knowledge of thermodynamics and mechanics, no conceivable connection could be seen to exist between a discontinuous emission and the facts disclosed by experiment; hence the necessity of the hypothesis could not be gauged.
Thus far, however, nothing very revolutionary appeared to be involved. All we had to do was to assume that the emission of light by a heated atom was due to the breaking up of some intra-atomic structure. Nevertheless, on deeper investigation, even assuming Planck’s emission theory to be correct, a number of theoretical difficulties were noted. These are of so technical a nature that we shall not dwell on them. Suffice it to say that they relate in a general way to the exchange of energy between the various atoms and to the conditions of equilibrium. The names of Poincaré, Lorentz and Einstein are encountered at this stage, and the final result was that somewhere, somehow, discontinuities had to be introduced.