RELATIVITY THEORY AND QUANTUM THEORY 2Qquantum theory were, the successes of equations like these made it evident that
such a theory had to exist. Every one of these successes was a slap in the face of
hallowed classical concepts. New inner frontiers, unexpected contraventions of
accepted knowledge, appeared in several places: the equipartition theorem of clas-
sical statistical mechanics could not be true in general (19b); electrons appeared
to be revolving in closed orbits without emitting radiation.
The old quantum theory spans a twenty-five-year period of revolution in phys-
ics, a revolution in the sense that existing order kept being overthrown. Relativity
theory, on the other hand, whether of the special or the general kind, never was
revolutionary in that sense. Its coming was not disruptive, but instead marked an
extension of order to new domains, moving the outer frontiers of knowledge still
farther out.
This state of affairs is best illustrated by a simple example. According to special
relativity, the physical sum (r(y,,i> 2 ) of two velocities w, and v 2 with a common
direction is given bya result obtained independently by Poincare and Einstein in 1905. This equation
contains the limit law, ff(v,,c) = c, as a case of extreme novelty. It also makes
clear that for any velocities, however small, the classical answer, a(vi,v 2 ) = vt +
r> 2 , is no longer rigorously true. But since c is of the order of one billion miles per
hour, the equation also says that the classical answer can continue to be trusted
for all velocities to which it was applied in early times. That is the correspondence
principle of relativity, which is as old as relativity itself. The ancestors, from Gal-
ileo via Newton to Maxwell, could continue to rest in peace and glory.
It was quite otherwise with quantum theory. To be sure, after the discovery of
the specific heat expression, it was at once evident that Eq. 2.3 yields the long-
known Dulong-Petit value of 6 calories/mole (20a) at high temperature. Nor did
it take long (only five years) before the connection between Planck's quantum
formula (Eq. 2.1) and the classical 'Ray leigh-Einstein-Jeans limit' (hv <C kT)
was established (19b). These two results indicated that the classical statistical law
of equipartition would survive in the correspondence limit of (loosely speaking)
high temperature. But there was (and is) no correspondence limit for Eqs. 2.2 and
2.4. Before 1925, nothing was proved from first principles. Only after the discov-
eries of quantum mechanics, quantum statistics, and quantum field theory did
Eqs. 2.1 to 2.4 acquire a theoretical foundation.
The main virtue of Eq. 2.5 is that it simultaneously answers two questions:
where does the new begin? where does the old fit in? The presence of the new
indicates a clear break with the past. The immediate recognizability of the old
shows that this break is what I shall call an orderly transition. On the other hand,
a revolution in science occurs if at first only the new presents itself. From that
moment until the old fits in again (it is a rule, not a law, that this always happens