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XIII. i]
173
qualitatively in all the ways known to geometry but not quan
titatively; the uniformity of the electronic charge must in
some way represent an absolute restriction on the measure of
the crumpling.
“ Each particle of matter—each electron let us say—occupies
one point of space at any one instant of time, and the succession
of these points will form a line in the four-dimensional space-
time continuum—the * world-line ’ of the electron. In the
neighbourhood of this world-line there is a deformation of
the continuum due to the existence of the electron.
“ The near approach of two electrons or of any two charged
particles is represented by a near approach of their world-lines
in the four-dimensional continuum. Each world-line is sur
rounded by its associated deformation, and in regions in which
the world-lines are near to one another the adjacent regions of
the continuum will be doubly deformed.
“ A priori there are two possibilities open. The first is that
the two deformations are merely additive, just as, when two
ships approach, each making its own wash (or deformation of
the surface of the sea), the height of wash at any point is the sum
of the heights of the washes made by the two ships independently.
The second possibility is that, as there have been found to be
restrictions on the amount of deformation associated with the two
separate world-lines, there may be a further restriction on the
deformation arising from their combination.
“ In actual fact the former alternative appears to prevail
when one or both of the charged particles are ‘ free ’ electrons,
but the latter alternative when they are ‘ bound ’ together;
that is, when they are permanently describing orbits about one
another. It is these latter restrictions that have given rise to
the theory of quanta. Just as the restrictions associated with
single world-lines give rise to an atomic constant e, the charge
on an electron, so the restrictions associated with pairs of world
lines give rise to a second atomic constant. This is generally
taken to be h, Planck’s constant, but in many respects it is more
appropriate to regard the product he as the second constant,
where c is the velocity of light. It is significant that he is of the
same physical dimensions as e 2 and so may be regarded as being
the same thing as e 2 except for a numerical multiplier. Thus
while the restrictions connected with one world-line introduce e,
those connected with two world-lines, depending only on e 2 ,
introduce no essentially new constant, whence it may reasonably
be suspected that the two sets of restrictions are merely different
aspects of one and the same set. It looks as though the atomicity
of the quantum theory is only another aspect of the atomicity
of electric charges.”