l x v i i i I N T R O D U C T I O N T O V O L U M E 1 4 Neither Bose nor Einstein may initially have realized how profoundly innovative their respective derivations would turn out to be. It was perhaps pointed out to Ein- stein after publication of the two papers that the use of the statistical procedure in the derivation implied a nontrivial fundamental assumption. In the case of a mate- rial gas, that assumption was particularly puzzling. As became clear in correspon- dence with Otto Halpern (Docs. 216, 308, 309), a distribution of light quanta or gas molecules over cells of phase space leaves open the question which configurations are to be considered equally probable. In the case of independent particles, config- urations in which two particles exchange places over different cells are considered to be different. In Bose’s and Einstein’s counting, however, it only mattered how many particles would sit in each cell. In the latter case, the particles were in effect indistinguishable, a feature that had been noted before in the case of distributing vibration modes (hν-quanta) over resonators but was an entirely new and non-clas- sical assumption for material particles. The difference between the two ways of counting effectively resulted in a higher probability of configurations in which many particles share the same cell. It is as if the Bose-Einstein counting indicated a kind of attractive interaction between particles of the same energy and momen- tum. In his response to Halpern (Doc. 309), Einstein states that the decision be- tween the two alternatives can only be made by experience. Einstein’s correspondence with Ehrenfest provides some clues about his devel- oping thoughts on the quantum theory of the ideal gas and his confidence in the the- ory. In July 1924, he had praised Bose’s work: “The Indian Bose gave a beautiful derivation of Planck’s law and of its constant, on the basis of the loose light quanta. The derivation is elegant but its nature remains dark. I applied his theory to the ideal gas. A rigid theory of ‘degeneracy.’ No zero point energy, and at the top no energy defect. God knows if this is so. The theory does not account for the deviations from the law of corresponding states” (Doc. 285). That same month, as a brief detour, he returned to an earlier interest in the mech- anism of the radiometer. Already in 1919 he had offered the subject to his cousin Edith Einstein as a theme for her doctoral dissertation, and had helped her through- out her travails in wrestling with it. In 1922 he presented a short note on the subject to the Prussian Academy (Vol. 13, Doc. 339, and Vol. 13, Introduction, p. lxxiii), and now that his cousin’s dissertation had been published, Einstein too published a paper, “On the Theory of Radiometer Forces,” submitted in July 1924 (Einstein 1924k [Doc. 290]). It is likely that Einstein was made aware of the “counting” implications of the ideal gas paper by Ehrenfest, an expert on statistical physics and author of studies that had explicitly investigated the statistical assumptions in derivations of Planck’s formula.[38] They probably discussed these issues when Einstein visited Leyden in