3 3 6 D O C U M E N T 2 1 6 F E B R U A R Y 1 9 2 4 an der Grösse dieser mittleren Kraft nicht zweifeln lässt,[11] so kann man deren Kenntnis unbedenklich verwerten, und erhält so mehr als die Gleichung (7), näm- lich eine Aussage über die Impuls-Eigenschaften der Elementarvorgänge. Dies wird durch Ihre Ausführungen verdunkelt. Indem ich hoffe, dass Sie selbst Ihre Behauptungen richtig stellen werden bin ich mit vorzüglicher Hochachtung Ihr A. Einstein ALSX. [12 118].The letter is addressed “Herrn Dr. Otto Halpern, Wien, Boltzmanngasse 3.” [1]Halpern (1899–1982) was Assistent at the University of Vienna. [2]Halpern 1923. [3]At issue is the question whether or not the existence of selectively reflecting mirrors, i.e., mirrors that totally reflect radiation in a certain frequency interval but are transparent for all other frequencies, is compatible with the second law of thermodynamics. Halpern describes a thought experiment involving such mirrors, in which heat is fully transformed into work, thus violating the second law. One step in the experiment involves a closed vessel, filled with equilibrium black-body radiation, which is divided into two parts by a mirror that only reflects radiation in the interval . Below the mirror, all frequencies are present above it, the frequencies between and are absent. When the mirror is moved upward, work is done by the radiation in the interval through reflection at the mirror’s underside. As a consequence, the reflected radiation has decreased in frequency. In the end, Halpern argues, below the mirror all radiation in the interval will have disappeared. Ein- stein’s comments refer to this reasoning. [4]Halpern admitted his error and thanked Einstein in Halpern 1924b. [5]Halpern 1924a. [6]In Bohr 1923, Niels Bohr had raised some objections to Einstein’s treatment of radiation pro- cesses in Einstein 1917c, the republication of Einstein 1916n (Vol. 6, Doc. 38 see also Einstein and Ehrenfest 1923 [Doc. 129] for a brief recapitulation of the argument of this paper). In this paper Ein- stein considered emission and absorption processes for atoms in a radiation field, distinguishing between spontaneous emission of radiation and induced emission and absorption. For equilibrium between states 1 and 2, Einstein derived the following equation: , (1) where the coefficients A determine spontaneous emission, the B’s induced emission and absorption, ρ being the energy density of the radiation field, and the weight factors occurring in the Boltzmann distribution of the atomic states . Bohr’s “second objection” (Halpern’s terminology) is the claim that it follows from the correspon- dence principle that the coefficients A are not necessarily independent of ρ. [7]Eq. (3) is . Einstein derived it from equation (1) above by assuming that, for increasing temperature, tends to infinity, whereas A is independent of the temperature. According to Halpern, Bohr’s objection invalidates Einstein’s derivation. [8]On p. 155, Halpern argues that an atom suffers a recoil when it emits a light quantum. As a con- sequence, the frequency of the emitted radiation is smaller than , so that the Bohr fre- quency condition does not hold. [9]On p. 157, Halpern derives a relation that has the same form as (1) above, but where instead of the ε’s the total energy appears, i.e., the internal and kinetic energy. Halpern’s reasoning is similar to the argument on p. 304 of Einstein and Ehrenfest 1923 (Doc. 129). [10]See Einstein 1917c, sec. 4, for the earlier treatment of the Brownian motion of an atom in a radi- ation field. [11]At this point in the original text, Einstein indicates a footnote: “Man kann sie einfach nach der klassischen Theorie berechnen. Die Impuls-Eigenschaften der Elementarvorgänge gehen in diese Rechnung nicht ein.” ν1, ν2) ( ν1 ν2 ν1, ν2) ( ν1, ν2) ( p1e ε1 kT( ----- -– A1 2 B1 2ρ) + p2e ε kTB2 -----2 -– 1ρ = pi εi p1B1 2 p2B2 1 = Bρ ε1 ε2) – ( h ⁄