J. H. Jeans, Nature, vol. 115, p. 364, 1925.
THE QUANTUM
condition of physics. . . . We find it hard to rest content with
the existence of unrelated absolute constants, such as Planck’s
constant and the size of an electron, which, so far as we can see,
might just as easily have had any different magnitude. To the
scientific mind such facts are a challenge, leading to a search for
some way of inter-relating them and making them seem less
accidental.”
The possibility of establishing a relationship between Planck’s
constant, h, and the electron charge, e, was suggested in 1911 by
Einstein, who pointed out that the product he (where c is the
velocity of light) has the same physical dimensions as the square
of an electric charge, when the charge is measured in electro
static units. Jeans commented on this at the Birmingham
meeting of the British Association in 1913, and in the first
edition of his Physical Society Report on Radiation and the
Quantum Theory (1914) wrote: “In point of fact, hc/2n, if
not exactly equal, is almost equal to (4ne) 2 , i.e. to the square
of the strength of a tube of force binding two electrons. This
suggests that the atomicity of h may be associated with the
atomicity of e.”
Various attempts have been made to establish a relation
between he and e 2 , and the more important of these will be
discussed in the present chapter, although it may be said at the
outset that no final and entirely satisfactory solution has yet
been reached. The problem may be attacked in two ways,
either by endeavouring to find an exact numerical relation
between the quantities involved, or by finding some hypothesis
of a physical nature which may serve to link together the two
types of atomicity.
Jeans * has given an illuminating account of the nature of
the atomicity demanded by the theory of electrons and by the
quantum theory.
“ Electric charges are a consequence of, or at least are
associated with, a curving or crumpling of space, but so far as
pure geometry goes there is no restriction on the extent of this
crumpling, so that our geometer, reasoning from geometry alone,
might expect to find charges of all possible amounts, whereas in
actual fact electric charges occur only in multiples of a definite
unit, the charge of an electron. It is clear, then, that there
is something more than geometry underlying the phenomena
of Nature; the whole phenomenal universe may be geometry
with restrictions if we like, but not merely the geometry
which is obtained by generalizing the geometry of Euclid
until we can generalize no further. Space can be crumpled up