408 THE QUANTUM THEORY
October 1927 the fifth Solvay conference was held. Its subject was 'electrons et
photons.'
When Einstein introduced light-quanta in 1905, these were energy quanta sat-
isfying Eq. 21.13. There was no mention in that paper of Eqs. 21.15 and 21.14.
In other words, the full-fledged particle concept embodied in the term photon was
not there all at once. For this reason, in this section I make the distinction between
light-quantum ('E — hv only') and photon. The dissymmetry between energy and
momentum in the 1905 paper is, of course, intimately connected with the origins
of the light-quantum postulate in equilibrium statistical mechanics. In the statis-
tical mechanics of equilibrium systems, important relations between the overall
energy and other macroscopic variables are derived. The overall momentum plays
a trivial and subsidiary role. These distinctions between energy and momentum
are much less pronounced when fluctuations around the equilibrium state are con-
sidered. It was via the analysis of statistical fluctuations of blackbody radiation
that Einstein eventually came to associate a definite momentum with a light-quan-
tum. That happened in 1916. Before I describe what he did, I should again draw
the attention of the reader to the remarkable fact that it took the father of special
relativity theory twelve years to write down the relation p = hv/c side by side
with E = hv. I shall have more to say about this in Section 25d.
- Momentum Fluctuations: 1909. Einstein's first results bearing on the
question of photon momentum are found in the two 1909 papers. There he gave
a momentum fluctuation formula that is closely akin to the energy fluctuation
formula Eq. 21.5. He considered the case of a plane mirror with mass m and area
/ placed inside the cavity. The mirror moves perpendicular to its own plane and
has a velocity v at time t. During a small time interval from t to t + T, its momen-
tum changes from mv to mv — Pvr + A. The second term describes the drag
force due to the radiation pressure (P is the corresponding friction constant). This
force would eventually bring the mirror to rest were it not for the momentum
fluctuation term A, induced by the fluctuations of the radiation pressure. In ther-
mal equilibrium, the mean square momentum m^2 (v^2 ) should remain unchanged
over the interval T. Hence* (A^2 ) = 2mPr{v^2 ). The equipartition law applied to
the kinetic energy of the mirror implies that m(v^2 ) = kT. Thus
Einstein computed P in terms of p for the case in which the mirror is fully trans-
parent for all frequencies except those between v and v + dv, which it reflects
perfectly. Using Planck's expression for p, he found that
(21.16)
(21.17)
"Terms O(T ) are dropped, and (v A) =0 since v and A are uncorrelated.
