Pauli’s objection to Weyl and the origins of the divide between Anschaulichkeit and Beobachtbarkeit

Johanna Wolff

Dept. of Philosophy, University of Hong Kong

During the heated debate between developers of matrix mechanics (Heisenberg, Born, Jordan) and the supporters of wave mechanics (Schrödinger, Einstein) around 1926-7, Beobachtbarkeit (observability) and Anschaulichkeit (visualizability) emerged as the respective rallying cries for the two camps. This divide between Beobachtbarkeit and Anschaulichkeit turned into a philosophical debate over the foundations of quantum mechanics, and has often been interpreted as a debate over realism (or perhaps Kantianism) on the one hand, and empiricism (or positivism) on the other. What I hope to show in this talk is that the debate is not so much a debate over the appropriate epistemology of physics; instead it concerns the appropriate metaphysics of quantum mechanics. More specifically, we should understand the debate as one over the nature of physical quantities: must they be continuous or may they be discrete? To make the case for this reading of the debate over quantum mechanics, I will show how the division between Anschaulichkeit and Observability emerges very clearly in a criticism Wolfgang Pauli puts forward against Hermann Weyl’s 1918 unified field theory. There Pauli criticizes Weyl’s use of the idea of the electric field inside an electron. The field strength of the electric field inside the electron is unobservable, Pauli says, since to measure the electric field strength, one needs a test-body, but the smallest available test-body was the electron itself. Pauli was likely inspired to criticize Weyl’s theory in this way by Einstein’s argument in his 1905 paper on special relativity, which Pauli knew very well. Neither Weyl himself, nor, interestingly, Einstein, seem to have been very impressed with Pauli’s objection, suggesting that the problem was merely a practical one: that of finding either a smaller test-body, or, more plausibly, a different way of measuring the electric field. Following this rejection of Pauli’s objection to Weyl, Einstein would go on to dismiss Heisenberg’s appeal to observability and Bridgman’s operationalism. Einstein hence seems to have turned against his earlier methodological commitments, which has sometimes been interpreted as a turn to “realism”. But what prompted this turn? I suggest that the real concern for Einstein is that the idea of continuity is under threat by the appeal to observability, and that Pauli’s argument marks the first employment of this idea. Unsurprisingly, Born and other physicists who favored discrete theories embraced Pauli’s objection. Beobachtbarkeit could be appealed to by those who felt that discreteness was a key feature of quantum phenomena. This suggests that Pauli’s objection marks the origin of the divide between Anschaulichkeit and Beobachtbarkeit, as well as setting the stage for the more explicit fight over wave mechanics vs matrix mechanics less than ten years later.