6 4 6 D O C . 4 2 5 R E M A R K O N J O R D A N ’ S P A P E R Published in Zeitschrift für Physik 31 (1925): 784–785. Received 22 January 1925, published February–April 1925. An ADft is also available [1 048]. [1]Jordan 1924, based on Pascual Jordan’s doctoral dissertation at the University of Göttingen. Ein- stein had concluded in his early work on radiation theory that emission and absorption of radiation are always accompanied by momentum transfer (directed radiation) see Einstein 1916n (Vol. 6, Doc. 38). [2]As §6 of the paper deals with the Compton effect, Einstein presumably refers to the concluding §8, in which Jordan discusses the differences between his and Einstein’s work. He argues that in Ein- stein’s 1916 calculation it is shown that the assumption of directed radiation is consistent with the existence of thermal equilibrium between matter and radiation, not the other way around. He also claims that the hypothesis of directed radiation is already implied in Einstein’s assumption that the radiation emitted and absorbed by atoms is monochromatic. Finally, Jordan points out that in Ein- stein’s treatment, the atoms are supposed to be at rest and that the influence of a translation is only considered in an unsystematic way. [3]In §5 of his paper, Jordan sketches a theory of radiation based on the following assumptions: 1. In each atomic emission process, radiation is emitted in all directions, in such a way that in the direction the radiation has frequency ν and energy (Jordan’s equa- tion [12]). Here σ is a function of angles θ and ϕ the frequency ν is also a function of θ and ϕ, but it is possible to choose a coordinate system in which ν becomes independent of these angles, so that the radiation is monochromatic. In this system, the Bohr frequency rule holds, because of the condition that Jordan imposes on σ (Jordan’s equation [13]). 2. The probabilities and for the transition between two given atomic states, by emission and absorption, respectively, and in the presence of a radiation field with energy density are given by and , with and b a factor that is determined by the transition under consideration (Jordan’s equations [18] and [18′]). These probabilities generalize expressions derived by Einstein in his 1916 papers on the quantum theory of radiation (Einstein 1916j and 1916n [Vol. 6, Docs. 34 and 38]) see also the simplified treat- ment in §1 of Einstein and Ehrenfest 1923 (Doc. 129). In fact, as Jordan points out, Einstein’s results, including the existence of directed radiation, are recovered if one puts σ everywhere equal to zero ex- cept in one particular direction. Jordan also derives Planck’s radiation law for the case of thermal equilibrium between matter and radiation. dω sinθdθdϕ = dE hσνdω = dω ³σ 1 = We Wa ρν We bexp[ αν3 ρν)dω] + log( ³σ = Wa bexp[ logρνdω] ³σ = α 8πh c3 --------- -=