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The prime number 137 had continuously occupied Pauli's mind. It is an approximate value for a constant appearing in the fine structure theory of atomic spectra which in its theoretical expression ties together electromagnetism, relativity and quantum theory. Pauli saw the fine structure theory of spectra as a key in understanding the deepest contemporary problems of theoretical physics. For that reason the number 137 possessed a mysterious attraction for him. .K. V. Laurikainen
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In his first philosophical lecture on modern physics that Pauli gave in November 1934 to the Zurich Philosophical Society he said that only a formulation of quantum theory would be satisfactory which expresses the relation between the value of [the fine structure constant] and charge conservation in the same complementary was as that between the space-time description and energy-momentum conservation.Charles P. Enz
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For [Wolfgang] Pauli the central problem of electrodynamics was the field concept and the existence of an elementary charge which is expressible by the fine-structure constant ... 1/137. This fundamental pure number had greatly fascinated Pauli, .... For Pauli the explanation of the number 137 was the test of a successful field theory, a test which no theory has passed up to now.Charles P. Enz