l x x x i i I N T R O D U C T I O N T O V O L U M E 1 5 One major topic in the correspondence concerns a peculiar result following from the treatment of the harmonic oscillator, which serves as a model for black-body radiation in the new formalism. It was required that in the ground state a harmonic oscillator does not emit any radiation. From this it followed, within matrix mechan- ics, that a harmonic oscillator has a zero-point energy of . Einstein must have criticized this result, because both Heisenberg and Jordan agreed that it was prob- lematic. Heisenberg argued that the zero-point energy was “initially purely formal. In any event, its physical meaning has not yet been completely clarified” (Doc. 112). Jordan wrote that it is “actually just a formal quantity, without any di- rect physical meaning” (Doc. 132). While Einstein’s reply to them is unknown, it probably was similar to his comments to Ehrenfest two months later: “There can’t be any zero-point energy in cavity radiation. I deem the argument by Heisenberg, Born, and Jordan (fluctuations) as faulty, if only because the probability of large fluctuations... certainly does not come out correctly that way” (Doc. 194). The cal- culation and interpretation of the zero-point energy of a harmonic oscillator played a major role in almost all other exchanges as well (Docs. 119, 198, 199, 212, 247, 524). Other important topics were the interpretation of the canonical commutation relations (Docs. 194, 198), electron spin and thus half-integer quantum numbers (Docs. 112, 132, 199), and the classical limit of matrix mechanics. Einstein’s reception of matrix mechanics is expressed in several letters to friends and colleagues. In his Christmas greetings to Besso he wrote: “The most interesting thing that theory has produced recently is the Heisenberg-Born-Jordan theory of quantum states. Such a magic formula, in which infinite determinants (matrices) take the place of Cartesian coordinates. Highly ingenious, and sufficiently protect- ed from refutation by great complexity” (Doc. 138). To Hedwig Born, who had just returned from accompanying her husband on a lecture tour to the United States, Einstein expressed himself in a more positive vein: “The Heisenberg-Born ideas are keeping everyone breathless, the reflection and thinking of all theoretically in- terested people. In place of dull resignation, a unique tension has taken hold in us sluggish people” (Doc. 215). In letters to Lorentz and Zangger (Doc. 243) he was rather more outspoken. He wrote to Lorentz: “I have been quite occupied with Heisenberg-Born. With all due admiration of the intellect behind these papers, my instinct still balks at this kind of conception” (Doc. 218). Lorentz felt the same (Doc. 220). The flip side of the coin of what is today called quantum mechanics concerns the formulation of wave mechanics by Erwin Schrödinger (see Illustration 21). In the summer of 1924, Louis de Broglie had suggested in his dissertation that matter may 1 2 -- - hν