2 0 0 D O C U M E N T 1 1 2 N O V E M B E R 1 9 2 5 man sich nicht genau auf die prinzipiell beobachtbaren Grössen besinnt dass man dabei die Anschaulichkeit so ganz verliert, ist mir auch sehr schlimm vorgekom- men und ich hab mich eine Zeit lang garnicht getraut, das Zeug zu publizieren. Aber ich hab mein Gewissen wieder damit getröstet, dass es ja sicher keine Atome gäbe, wenn unsere Raum-Zeitbegriffe in sehr kleinen Räumen auch nur annähernd richtig wären. Freilich bin ich über den jetzigen Zustand der Theorie auch noch sehr unglücklich, weil alles so unfertig ist und eine Präzisierung der wirklich bei den Atomen herrschenden Raum-Zeitverhältnisse nicht gelingen will. Das beste an der Theorie ist wohl bis jetzt die von Born u. Jordan gemachte Mathematik dazu. Aber entschuldigen Sie, wenn ich Sie mit so unfertigem Zeug so lange aufgehal- ten hab. Mit vielen Grüssen von Hrn Prof. Franck[9] bin ich Ihr aufrichtig ergebener W. Heisenberg. ALS. [12 170]. Cropped. There are perforations for a loose-leaf binder at the left margin of the document. [1]See Doc. 132 for Jordan’s own reply to Einstein’s letter. [2]To account for rotational spectra of diatomic molecules such as HCl, in the old quantum theory the rigid rotator was quantized with half-integer quantum numbers (see, e.g., Sommerfeld 1924, p. 712). In Heisenberg 1925, the paper enclosed in this letter, Heisenberg derives an expression for the energy of a rigid rotator that is proportional to , with n an integer (p. 891). Because the term ¼ does not affect the energy differences, and thus the frequencies of spectral lines, Heisen- berg concluded that he had reproduced the old result with half-integer quantum numbers. Heisen- berg’s result is incorrect: a later corrected calculation (see Mensing 1926) gives the result that the energy is proportional to , thus explaining the success of half-integer quantization in the case of the rigid rotator. [3]The manuscript of Born, Heisenberg, and Jordan 1926, which was received by Zeitschrift für Physik on the date of this letter. The earlier version of the section on fluctuations, to which Einstein had apparently raised objections, was sent to him by Pascual Jordan enclosed in Doc. 98. [4]The result that a harmonic oscillator has a zero-point energy of followed from Heisen- berg’s requirement that it should have a ground state from which no radiation is emitted. [5]Elsewhere, Heisenberg and his coauthors used the term “kinematics” rather than “geometry.” In the conclusion of Born, Heisenberg, and Jordan 1926 the authors emphasize that “the fundamental difference of the theory proposed here and that used hitherto does not lie in a difference in mechanical laws, but in the kinematics that is characteristic of the new theory” (“liegt der wesentliche Unterschied der hier versuchten Theorie von der bisherigen nicht in einer Verschiedenheit der mechanischen Gesetze, sondern in der für diese Theorie charakteristischen Kinematik” p. 615). See also Doc. 119 for a comment by Heisenberg on the use of the terms “geometry” and “kinematics.” [6]Perhaps a reference to Walther Nernst’s idea that the ether was endowed with an enormous amount of zero-point energy (see, e.g., Nernst 1922). [7]In chap. 4, the final chapter of Born and Jordan 1925b, “Bemerkungen zur Elektrodynamik” (“Comments on Electrodynamics”), the authors give a formula for the radiation of a dipole involving a double sum over all its possible transitions. Then they rewrite this sum, restricting it to downward transitions, at the same time emphasizing the preliminary character of their considerations. Jordan later disavowed the whole chapter in a letter of 10 April 1962 to Bartel L. van der Waerden (see Doc. 98, note 3). Accordingly, the chapter was not included in the English translation of the paper in the anthology Waerden 1967. [8]See Pauli 1926. [9]James Franck. n ½+ ( )2 ¼+ n ½+ ( )2 ¼– ½hν