378 THE QUANTUM THEORYIn other words, the light-quantum hypothesis is an assertion about a quantum
property of free electromagnetic radiation; the heuristic principle is an extension
of these properties of light to the interaction between light and matter. That,
indeed, was a revolutionary step.
I shall leave Einstein's applications of the heuristic principle to Section 19e and
shall describe next how, in 1906, Einstein ceased assiduously avoiding Planck's
equation (Eq. 19.11) and embraced it as a new hypothesis.19d. Einstein on Planck: 1906
In 1906 Einstein returned once more to Planck's theory of 1900. Now he had
much more positive things to say about Planck's radiation law. This change in
attitude was due to his realization that 'Planck's theory makes implicit use of the... light-quantum hypothesis' [E8]. Einstein's reconsideration of Planck's reason-
ing and of its relation to his own work can be summarized in the following way:
- Planck had used the p- U relation, Eq. 19.11, which follows from classical
mechanics and electrodynamics. - Planck had introduced a quantization related to U, namely, the prescription
U = Phv/N(sce Eqs. 19.12-19.15). - If one accepts step 2, which is alien to classical theory, then one has no reason
to trust Eq. 19.11, which is an orthodox consequence of classical theory. - Einstein had introduced a quantization related to p: the light-quantum hypoth-
esis. In doing so, he had not used the p- U relation (Eq. 19.11). - The question arises of whether a connection can be established between
Planck's quantization related to U and Einstein's quantization related to p.
Einstein's answer was that this is indeed possible, namely, by introducing a
new assumption: Eq. 19.11 is also valid in the quantum theory! Thus he proposed
to trust Eq. 19.11 even though its theoretical foundation had become a mystery
when quantum effects are important. He then re-examined the derivation of
Planck's law with the help of this new assumption. I omit the details and only
state his conclusion. 'We must consider the following theorem to be the basis of
Planck's radiation theory: the energy of a [Planck oscillator] can take on only those
values that are integral multiples of hv; in emission and absorption the energy of
a [Planck oscillator] changes by jumps which are multiples of hv.' Thus already
in 1906 Einstein correctly guessed the main properties of a quantum mechanical
material oscillator and its behavior in radiative transitions. We shall see in Section
19f that Planck was not at all prepared to accept at once Einstein's reasoning,
despite the fact that it lent support to his own endeavors. As to Einstein himself,
his acceptance of Planck's Eq. 19.11, albeit as a hypothesis, led to a major advance
in his own work: the quantum theory of specific heats, to be discussed in the next
chapter.