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THE QUANTUM [xvii. 5
and by others.* It has been shown by Ehrenfest and Uhlenbeckf
that a graphical representation of the phase waves of de Broglie
may be obtained in the five-dimensional universe.
A remarkable result which indicates an inner unity between
the quantum theory and gravitational relativity has been
announced by Wiener and Struik.J The connecting link is the
wave theory of Schrodinger. If we define the gravitational field
in the proper invariantive manner in terms of a wave equation,
the quantization of this equation follows from the gravitational
field equations. The equation also defines an electromagnetic
potential, to which most of Weyl’s considerations apply.
The fundamental equation of these authors can be rendered
homogeneous by means of a suitable substitution, and a treat
ment of their theory is then obtained analogous to that of Klein.
“ The fifth dimension turns out to be a mere mathematical
convention that can be compared to the introduction of homo
geneous co-ordinates in other parts of mathematics.”
One test of a scientific theory is its comprehensiveness, and
the wide sweep of the new quantum mechanics is shown not only
in the various ways of formulating it in mathematical language,
but also in the physical ideas that may be associated with it.
It is probable that the views of the quantum suggested by
Whittaker and by the present writer, in which its magnetic
aspects are emphasized, may be simply related to the new theory.
In a recent paper Whittaker has described a simple light quantum
in which a disembodied magnetic molecule, travelling with the
speed of light, forms a singularity on the wave front and confers
upon it the desired quantum properties. It may be suggested
that such a quantum is related to a quantum magnetic tube on
the one hand, and to Schròdinger’s wave mechanics on the other.
5. Statistical Methods and the Quantum Theory
The application of probability methods in quantum theory
has attracted considerable attention since the publication of an
important paper by Einstein § in 1917. He showed that Planck’s
radiation law could be derived by considering the probability
of transitions between different stationary states, assuming Bohr’s
frequency condition to hold for the radiation emitted or absorbed
in a transition. He considered an enclosure containing a gas,
* Klein, Zeits. f. Physik, voi. 37, p. 895, 1926 ; Fock, Zeits. f. Physik,
voi. 39, p. 226, 1926 ; Gamow and Iwanenko, Zeits. f. Physik, voi. 39,
p. 865, 1926; Iwanenko and Landau, Zeits. f. Physik, voi. 40, p. 161, 1926.
f Ehrenfest and Uhlenbeck, Zeits. f. Physik, voi. 39, p. 495, 1926.
j Wiener and Struik, Nature, voi. 119, p. 853, 1927.
§ Einstein, Phys. Zeits., voi. 18, p. 122, 1917. See Birtwistle, Quantum
Theory, p. 36.