376 THE QUANTUM THEORY
19c. The Light-Quantum Hypothesis and the Heuristic PrincipleI mentioned in Chapter 3 that the March paper was Einstein's only contribution
that he himself called revolutionary. Let us next examine in detail what this rev-
olution consisted of.
In 1905, it was Einstein's position that Eq. 19.6 agreed with experiment but
not with existing theory, whereas Eq. 19.17 agreed with existing theory but not
with experiment. He therefore set out to study blackbody radiation in a new way
'which is not based on a picture of the generation and propagation of radiation'—
that is, which does not make use of Planck's equation (Eq. 19.11). But then some-
thing had to be found to replace that equation. For that purpose, Einstein chose
to reason 'im Anschluss an die Erfahrung,' phenomenologically. His new starting
point was the experimentally known validity of Wien's guess (Eq. 19.5) in the
region of large (3v/T, the Wien regime. He extracted the light-quantum postulate
from an analogy between radiation in the Wien regime and a classical ideal gas
of material particles.
Einstein began by rederiving in his own way the familiar formula for the finite
reversible change of entropy S at constant T for the case where n gas molecules
in the volume v 0 are confined to a subvolume v:
(19.20)Two and a half pages of the March paper are devoted to the derivation and dis-
cussion of this relation. What Einstein had to say on this subject was described
following Eq. 4.15.
Now to the radiation problem. Let
volume in the frequency interval between v and v + dv. Then (p is again the
spectral density)
(19.21)Assume that Wien's guess (Eq. 19.5) is applicable. Then
(19.22)Let the radiation be contained in a volume v. Then S(v,v,T} = fyvdv and E(v,
v, T) = pvdv are the total entropy and energy in that volume in the interval v to
v + dv, respectively. In the Wien regime, S follows trivially from Eq. 19.22 and
one finds that
(19.23)
Compare Eqs. 19.23 and 19.20 and we have Einstein's