where Ne is the charge of the particle considered and e is the charge of the
electron. Now, Klein argued [K4], since nature tells us that N is an integer,
'[Eq. 17.12] suggests that the atomicity of electricity may be interpreted as a
quantum theoretical law. In fact, if the five-dimensional space is assumed to be
closed in the direction of x^5 with a period /, and if we apply the formalism of
quantum mechanics to our geodesies, we shall expect /> 5 to be governed by the
following rule:Klein conjectured that '[the] smallness [of /] may explain the nonapp .-arance
of the fifth dimension in ordinary experiments as the result of averaging over
the fifth dimension.'* This same suspicion that there might be some reality to
the fifth dimension was also on Einstein's mind when, in the late 1930s, he*In those years immediately following the discovery of quantum mechanics, there were also quite
different speculations to the effect that the fifth dimension had something to do with the new mechan-
ics. For example, it was suggested that 755 should be taken as a scalar field (rather than as a constant)
which might play the role of the Schroedinger wavefield [Gl].
George Uhlenbeck told me, 'I remember that in the summer of 1926, when Oskar Klein told us
of his ideas which would not only unify the Maxwell with the Einstein equations but also bring in
the quantum theory, I felt a kind of ecstasy! Now one understands the world!'
such that /J 5 is constant along a geodesic. For i = 1,... , 4, the corresponding
equations of motion yield Kaluza's result for the geodesic motion in a gravi-
tational-electromagnetic field (see, e.g., Pauli's review article [PI]) provided
one chooses(17.12)(17.11)
(17.10)
332 THE LATER JOURNEY[K5]. In particular he noted that the Lagrangian L for a particle with mass
m(where ds is given by Eq. 17.1 and where dr is the differential proper time)
leads to five conjugate momenta p^.Thus a length / enters the theory given by