D O C U M E N T 4 7 3 F E B R U A R Y 1 9 2 7 7 4 3 sind die Einheiten freilich ganz anders: die Rolle, welche ich den kosmologischen Gliedern zuwies, wird von der Materie übernommen.[9] Wir müssen warten, wel- chen Pakt die Quantenmechanik mit der Feldtheorie schließt. Ich selber bin jetzt ganz wo anders beschäftigt aber die neue Quantenmechanik hat mich doch mäch- tig gepackt. Wie stehen Sie zu dem Kampf zwischen Schrödingers sehr konkret- kausaler Auffassung und der prinzipiell statistischen von Heisenberg-Born- Pauli?[10] Ich neigte von vornherein entschieden zu der letzteren, hatte aber damit in Zürich einen schweren Stand. Mit herzlichem Gruß und Handschlag Ihr H. Weyl. NB: Soll ich die Korrektur zurückschicken? ALS. [24 086]. [1]The galleys of Einstein and Grommer 1927 (Doc. 443). Gustav Herglotz. [2]Bach and Weyl 1922. [3]Weyl 1922. [4]Square brackets here and in the remainder of the letter are in the original. [5]Weyl 1923. [6]Weyl 1921b. [7]Mie 1923. [8]Weyl proposes a new application of a key aspect of the unified field theory he published in 1918, now called gauge invariance (Weyl 1918). The same idea was published several months later, appar- ently independently, by Fritz London (London 1927). Weyl probably raised the idea with Einstein in riposte to Einstein’s old objection to his theory of 1918 (see Einstein 1918g, [Vol. 7, Doc. 8]). At the time, Einstein had pointed out that the scale change in the metric components produced by the φ factor would mean that moving rods would change their lengths if they followed different paths through space (because φ represents components of the electromagnetic potential, which is position- dependent). Thus two rods of the same original length would arrive at a new position with different lengths if they traveled by different paths. This scale change of the original theory now becomes merely a phase change in the new theory, because the exponential factor is now imaginary in Weyl’s modification. Weyl himself used this new approach in his 1929 paper, which is widely credited with the inauguration of modern gauge theory (e.g., by O’Raifeartaigh 1997). [9]This is a comment that Weyl repeated in a 1955 postscript to his 1918 paper (reprinted in O’Rai- feartaigh 1997, p. 37). It is an issue raised earlier by Erwin Schrödinger (Schrödinger 1922), concern- ing the actual value that Weyl’s scale factor should have, based on fundamental considerations. The two possibilities proposed by Schrödinger are to identify a quantity with units of action (Joule sec- ond), either based on Plank’s constant or the ratio of the electron charge to the speed of light squared. Schrödinger rejected the latter because it is too large. Weyl originally left this point open, presumably because he expected the scale to be set by some unknown property of the universe as a whole. Since the relevant quantity with units of action turned out to be Planck’s constant, he concluded that the scale was instead set by the fundamental nature of matter in the quantum theory, rather than by cos- mological considerations, as he had originally imagined when framing his idea as a unified field theory. [10]Erwin Schrödinger’s wave mechanics and the quantum mechanics of Werner Heisenberg, Max Born, and Wolfgang Pauli.
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