34 
Proceedings of the Royal Society of Edinburgh. [Ses§. 
III. — -ZEther and the Quantum Theory. By H. Stanley Allen, 
M.A., D.Sc. 
(MS. received October 30, 1920. Read November 22, 1920.) 
§ 1. Extreme supporters of the principle of relativity find no place for an 
aether. Thus Lord Haldane in discussing the theory of Einstein writes : 
Space, as a physical thing with unvarying geometrical properties, is to be 
banished, just for the same sort of reasons as the aether was banished 
before it. Only observable things are to be recognised as real in the new 
system of modern physicists.” On the other hand, many followers of 
Faraday and Maxwell have regarded aether as the primary real substance ; 
all mass, momentum, or energy being mass, momentum, or energy of the 
aether. Without entering into a discussion of the significance of physical 
“ reality,” we may, with most physicists, agree to use the concept of aether 
as giving a model, inadequate though it is at present, for the interpretation 
of physical phenomena. 
§ 2. During the present century it has been recognised that certain 
classes of observations cannot be explained on the basis of Newtonian 
mechanics, and a new theory has been developed which has proved 
extraordinarily fertile. “ The quantum theory is believed to have disclosed 
in nature a certain atomicity of a kind unsuspected by the older mechanics.” 
The theory centres round the idea of spasmodic interchanges, losses or 
gains of energy of amount hv, where h is Planck’s constant, and ;/ is a 
frequency (number of oscillations per second). According to Poincare, the 
hypothesis of quanta is the only one leading to the law of Planck which 
represents the distribution of energy between different wave-lengths in 
“ black-body ” radiation. In his invaluable report on Radiation and the 
Quantum Theory, Jeans has pointed out that if the aether is part of the 
dynamical system, then the energy in the aether must be treated as part 
of the energy of the system, and to arrive at Planck’s formula it would 
appear to be necessary to suppose that the vibrations in the # aether 
themselves gain or lose energy by whole quanta. The assumptions 
underlying the quantum theory have been stated in somewhat different 
forms by various theoretical physicists. For our present purpose we may 
adopt the hypotheses proposed by W. Wilson,* as these have been employed 
* W. Wilson, Phil. Mag ., vol. xxix, p. 795 (1915) ; vol. xxxi, p. 156 (1916). 
