412 THE QUANTUM THEORYunderstood as yet' [E15]. It is believed by nearly all of us that the joke was under-
stood soon after 1925, when it became possible to calculate Einstein's Amn and
fimn from first principles. As I shall discuss later, Einstein eventually accepted
these principles but never considered them to be first principles. Throughout the
rest of his life, his attitude was that the joke has not been understood as yet. One
further example may show how from 1917 on he could not make his peace with
the quantum theory. In 1920 he wrote as follows to Born:
That business about causality causes me a lot of trouble, too. Can the quantum
absorption and emission of light ever be understood in the sense of the complete
causality requirement, or would a statistical residue remain? I must admit that
there I lack the courage of a conviction. However, I would be very unhappy to
renounce complete causality. [E16]21e. An Aside: Quantum Conditions for Nonseparable Classical Motion
In May 1917, shortly after Einstein finished his triple of papers on the quantum
theory of radiation, he wrote an article on the restrictions imposed by the 'old'
quantum theory on classically allowed orbits in phase space [El7], to which he
added a brief mathematical sequel a few months later [E18]. He never returned
to this subject nor, for a long time, did others show much interest in it. However,
recently the importance and the pioneering character of this work has been rec-
ognized by mathematicians, quantum physicists, and quantum chemists. The only
logic for mentioning this work at this particular place is that it fits with the time
sequence of Einstein's contributions to quantum physics.
What Einstein did was to generalize the Bohr-Sommerfeld conditions for a
system with / degrees of freedom. These conditions are Jp,<^<?, = nth, i =
1, ... , I, where the (?, are the coordinates, the p{ their conjugate momenta, and
the n, the integer quantum numbers. These conditions had been derived for the
case where one can find a coordinate system in which the classical motion is sep-
arable in the coordinates. Thus, the conditions, if at all realizable, depend on the
choice of a suitable coordinate system. Einstein found a coordinate-invariant gen-
eralization of these conditions which, moreover, did not require the motion to be
separable, but only to be multiply periodic. The generalization of this result has
become a problem of interest to mathematicians. Its relevance to modern physics
and chemistry stems from the connection between the orbits of the old quantum
theory and the semiclassicai (WKB) limit of quantum mechanics. For example,
a semiclassicai treatment of the nuclear motion in a molecule can be combined
with a Born-Oppenheimer treatment of the electronic motion. For references to
recent literature, see, e.g., [B2] and [Ml].21f. The Compton Effect
I return to the photon story and come to its denouement.
Since, after 1917, Einstein firmly believed that light-quanta were here to stay,