8 1 4 D O C . 5 1 6 S C H R Ö D I N G E R ’ S W A V E M E C H A N I C S Herr Grommer[9] hat darauf aufmerksam gemacht, dass diesem Einwand Rech- nung getragen werden könnte durch eine Abänderung des dargelegten Schemas, in welcher nicht der Skalar ψ selbst sondern der Skalar zur Definition der Hauptrichtungen herangezogen wird.[10] Die Durchführung hat keine Schwierig- keit, soll aber erst dann gegeben werden, wenn sie sich an Beispielen bewährt hat. ADft. [2 100]. [1]This manuscript was submitted for publication at the meeting of the Prussian Academy of 5 May 1927. Proofs were prepared, sent to Einstein, together with the manuscript, and returned with a note added to the manuscript. After the paper was partially typeset in final form (the still existing typeset part corresponds to the first page of the transcription presented here) Einstein retracted the paper in a telephone call. A note by the printer (or editor) dates this call at 21 May 1927. See Kirsten and Treder 1979a, pp. 134–135, for the history of the manuscript and Belousek 1996 and Holland 2005 for a detailed analysis of its contents. See also the Introduction, sec. IX, for a discussion. [2]Dated from the date of submission. [3]Werner Heisenberg begins his first paper on matrix mechanics (Heisenberg 1925) by denying that it is possible to associate an electron with a point in space and describe its position as evolving in time. This line of thought culminated in the publication of the uncertainty relations in Heisenberg 1927, the manuscript of which Einstein had received attached to a letter from Niels Bohr dated 13 April 1927 (Doc. 513). In the context of wave mechanics, Born 1926a, 1926b had introduced the idea that Schrödinger’s wave function represents the probability distribution of where a given elec- tron might be found Born also stated that he was inclined to give up the idea of a fully deterministic description of a quantum system. Einstein had resisted this line of thought most clearly in Doc. 426. [4]For more details, see Schrödinger 1926d, p. 491. The mass is put equal to 1. [5]Einstein further explores Schrödinger’s idea of using the methods of Riemannian geometry in understanding the structure of configuration space. Belousek 1997, p. 443, points out that Schrödinger developed but never published a tensorial version of classical mechanics, based on Heinrich Hertz’s insight of an analogy between the mechanics of point particles and the geometry of higher-dimensional spaces. The connection is made in Hertz 1894, which Einstein studied as a student. However, in the present document, what Einstein calls “the tensor of ψ−curvature” is actually the covariant Laplacian of the scalar field ψ, rather than the curvature tensor compatible with the metric defined in eq. (2). [6]Using the method of Lagrange multipliers, Einstein adds and , multiplied by the new variable λ, and then takes derivatives with respect to λ and to to find an extremum of . Belousek 1997 argues that the principal directions constitute “hidden variables” in the modern sense, and gives a detailed comparison of how Einstein’s “hidden variables” compare espe- cially to those of De Broglie-Bohm theory. See the Introduction, sec. IX, for further discussion. [7]Walther Bothe. [8]In Doc. 256, Einstein had written to Schrödinger expressing the worry that this requirement of “system additivity” was violated in Schrödinger’s theory but at the time Einstein was under the false impression that the Schrödinger equation was a different, nonlinear equation. Einstein realized his mistake and pointed it out to Schrödinger in Doc. 261, but the latter answered before receiving the postcard, in Doc. 264, and in Doc. 267 Einstein ended up convinced that Schrödinger’s theory does obey system additivity and points out that this is a major advantage that wave mechanics has as com- pared to matrix mechanic. Howard 1990, pp. 90–91, interprets this addendum to the present document as the clearest early manifestation of Einstein’s worries about the nonseparability of quantum mechanics, which would be the central point of Einstein, Podolsky, and Rosen 1935. [9]Jakob Grommer. [10]Belousek 1997, p. 442, quotes James T. Cushing as having suggested that Grommer’s idea might have rested on the fact that , and that the modification sug- gested might hence render diagonal for . See the Introduction, sec. IX, for further discussion. χ lgψ = ψA 1 gμνAμAν – Aμ ψA λ(a)} { ψ1 ψ2) ⋅ log( logψ1 logψ2 += ψμν Σ