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THE QUANTUM [ X i. 2
able of separate existence, as Lucretius held) is raised to a natural
and necessary consequence of the new standpoint. We may
even reverse the argument, and derive from the ascertained
atomic constitution of matter a philosophical necessity for the
assumption of a plenum, in which the ultimate atoms exist as
the nuclei which determine its strains and motions.” To this
passage Larmor appends a suggestive footnote. “ It is perhaps
not superfluous to point out the argument here involved against
any tendency we might have to assign to the aether itself an
atomic structure.”
It is to be remembered that these passages were written
before the development of the principles of relativity, and no
doubt their author would at the present time express them
differently.
A very interesting discussion of the question of continuity
in relation to sub-atomic phenomena is to be found in Emile
Borel’s stimulating volume on Space and Time* He propounds
the question, whether, seeing that the motion of a solid body
on which our geometry is based fails us completely on the sub
atomic scale, we should not try to construct an entirely different
geometry of a discontinuous character. He suggests that this
might be a way of attacking the difficulties raised by the theory
of quanta.
“ Following up a suggestion made by Riemann, to which,
however, he did not seem to attach much importance, we might
also ask whether the property which space seems to possess, of
being in a sense the more certainly Euclidean the smaller the
region is which we consider, does not disappear when we reach
atomic or sub-atomic dimensions. Very small regions may have,
as it were, a granular structure, and the Euclidean properties
only hold good as averages.”
One possible way of describing the discontinuity required by
the quantum theory is to make the hypothesis that time itself
is discontinuous, “ Thus the universe would jump suddenly from
one state to another, but in the interval between it would stand
at rest. The different instants during which it stayed in the
same state could not be distinguished from one another, so that
we should be led to the discontinuous variation of time, to the
atom of time” (Poincare).
If, however, we adopt the view held by some supporters of
the theory of relativity, that time ought not to be separated
from space, we are led to the hypothesis that the space-time
world is not a true continuum. With regard to such a sugges
tion Jeans f remarks : “ The only type of atomicity which rela-
* Borel, Space and Time (Blackie, 1926).
t J. H. Jeans, Atomicity and Quanta, pp. 8, 55, 1926.