D O C . 3 0 5 C O M M E N T O N B O S E 4 7 9
Published in Zeitschrift für Physik 27 (1924): 392–393. A manuscript entitled “Bemerkung zu vorste-
hender Arbeit” is also available ([1 044]). It carries a date stamp of “19. 8. 24.” and an editor’s remark
that the manuscript is to be published following Bose 1924b, received on 12 August 1924.
Einstein’s criticism pertains to the second part of Bose’s paper (Bose 1924b). In a first part, Bose
had criticized existing derivations of Planck’s law (specifically referring to Debye 1910, Einstein
1916n [Vol. 6, Doc. 38], Pauli 1923, and Einstein and Ehrenfest 1923 [Doc. 129]), arguing that all
derivations depended on specific hypotheses about the mechanism of radiative energy transfer
between the radiation field and a gas of material particles. In order to remedy this defect, he had pro-
posed to consider the equilibrium between radiation field and material gas as a problem in statistical
mechanics, based on assumptions about the thermodynamic probabilities of both radiation field and
material gas. For the radiation he referred to an earlier paper of his own (which is cited as “to appear
in Phil. Mag,” but which is probably Bose 1924a (see Docs. 278, and 261, note 2). For the material
gas he assumed a Maxwellian distribution, generalized to cover the case of both classical molecules
and Bohr atoms. Maximizing the joint probability of the composite system, Bose obtained general
conditions that were independent of any assumptions about the specific mechanisms of radiative
energy transfer underlying the thermodynamic equilibrium and therefore included Pauli’s hypotheses
as well as the one employed by Einstein and Ehrenfest as special cases.
Only in the second part of his paper did he criticize Einstein’s theory of negative absorption (i.e.,
induced emission) and advanced his own proposal, according to which there is only spontaneous
emission and induced absorption, the latter with a coefficient that depends explicitly on the radiation
In this relation, denotes the number of light quanta in the spectral range ;
, with c the velocity of light and V the spatial volume, was interpreted by Bose as
the number of elementary cells in the six-dimensional phase space of the quanta; and denote
arbitrary distributions of quanta.
Bose had criticized Einstein’s notion of induced emission as an ad hoc assumption, and instead
argued for his own hypothesis by pointing out that in quantum theory energy transfer will only take
place with a certain finite probability even if a light quantum and a material particle actually collide,
reflecting the inherent stability of Bohr orbits.
Planck 1923, especially §157, pp. 172–176. Einstein had recently reviewed this book (see Ein-
stein 1924h [Doc. 281]).
For further discussion of Bose’s paper and a critical assessment of Einstein’s counterarguments,
see Ghose 1994, pp. 56–62.
Nνdν ν ν , dν +