3 0 8 D O C . 3 0 5 C O M M E N T O N B O S E
305. Comment on Satyendra Nath Bose, “Heat
Equilibrium in a Radiation Field in the Presence of
Matter”
[Einstein 1924l]
Received 19 August 1924
Published August–September 1924
In: Zeitschrift für Physik 27 (1924): 392–393.
I consider Bose’s hypothesis about the probability of radiative elementary pro-
cesses as not valid for the following
reasons.[1]
For the statistical equilibrium between one Bohr state and another, as Bose has
set forth, the relation
.[2]
applies.
Hence it follows that the probabilities for the transitions and on the
left-hand and the right-hand sides of this equation must be proportional to each oth-
er. The transitional probabilities for one molecule must therefore (if, for the sake of
simplicity, we set the statistical weights of both states equal to 1) behave as
. More than that cannot be gathered from this information about the
thermal equilibrium. According to the hypothesis posited by me, these probabilities
Nv (that is, the radiation density) or , should be proportional, according to
Bose’s hypothesis, or
1.[3]
According to the latter hypothesis, the external radiation certainly can effectuate
a transition from the state Zr of smaller energy to the state Zs of higher energy, but
not conversely a transition from Zs to Zr. This, however, contradicts the legitimately
generally acknowledged principle that the classical theory must be a limiting case
of quantum theory. For, according to the latter, a radiation field can transfer both
positive as well as negative energy onto a resonator (depending on the phase),
[p. 392]
nr
gr
---------------------
Nv
Av Nv +
-
ns
gs
---- =
r s → s r →
[p. 393]
Nv
Av Nv +
----------------- -: 1
Av Nv +
Nv
Av Nv +
----------------- -