9780192806727.pdf

THE PHOTON 403

this result to energy fluctuations of blackbody radiation in a frequency interval

between v and v + dv. In order to understand how this refinement is made, con-

sider a small subvolume v of a cavity filled with thermal radiation. Enclose v with

a wall that prevents all frequencies but those in dv from leaving v while those in

dv can freely leave and enter v. We may then apply Eq. 21.1 with (E) replaced

by pvdv, so that (€^2 ) is now a function of v and T and we have

This equation expresses the energy fluctuations in terms of the spectral function

p in a way that is independent of the detailed form of p. Consider now the follow-

ing three cases.

1. p is given by the Rayleigh-Einstein-Jeans law (eq. 19.17). Then


2. p is given by the Wien law (Eq. 19.7). Then


3. p is given by the Planck law (Eq. 19.6). Then

(21.3)

(21.4)

(21.5)

(I need not apologize for having used the same symbol p in the last three equations
even though p is a different function of v and T in each of them.)*
In his discussion of Eq. 21.5, Einstein stressed that 'the current theory of radia-
tion is incompatible with this result.' By current theory, he meant, of course, the
classical wave theory of light. Indeed, the classical theory would give only the
second term in Eq. 21.5, the 'wave term' (compare Eqs. 21.5 and 21.3). About the
first term of Eq. 21.5, Einstein had this to say: 'If it alone were present, it would
result in fluctuations [to be expected] if radiation were to consist of independently
moving pointlike quanta with energy hi>.' In other words, compare Eqs. 21.4 and
21.5. The former corresponds to Wien's law, which in turn holds in the regime
in which Einstein had introduced the light-quantum postulate.
Observe the appearance of a new element in this last statement by Einstein.
The word pointlike occurs. Although he did not use the term in either of his 1909
papers, he now was clearly thinking of quanta as particles. His own way of refer-
ring to the particle aspect of light was to call it 'the point of view of the Newtonian
emission theory.' His vision of light-quanta as particles is especially evident in a
letter to Sommerfeld, also dating from 1909, in which he writes of 'the ordering
of the energy of light around discrete points which move with light velocity' [E4].

'Equations 21.3 and 21.4 do not explicitly occur in Einstein's own paper.

(21. 2)