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
[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
For the statistical equilibrium between one Bohr state and another, as Bose has
set forth, the relation
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
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]
Av Nv +
---- =
r s s r
[p. 393]
Av Nv +
----------------- -: 1
Av Nv +
Av Nv +
----------------- -
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