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Quote by K. V. Laurikainen

“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.”

Quote by K. V. Laurikainen

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Beyond the Atom: The Philosophical Thought of Wolfgang Pauli

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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.”

“If QED [quantum electrodynamics] is merely a phenomenology, how can one account for its remarkable quantitative success? The answer is intimately related to one of its most characteristic features, renormalizability. Because of this, short distance, high energy effects in QED can be absorbed into a finite number of measurable masses and charges. For the first time in the history of physics, there exists a theory which has no obvious intrinsic limitation and enables us in principle to calculate physical phenomena to any accuracy we need in terms of a few measurable parameters such as the elementary electric charge e [fine structure constant] and the electron mass m. Thus the detailed high energy structure of the ultimate theory is irrelevant to the analysis of low energy phenomena except insofar as it determines these parameters. [Quantum Electrodynamics]”

“In the early days of atomic physics [before quantum field theory revealed the true meaning of the fine structure constant to be the strength of the coupling between the electron and photon], it was thought to have a value so close to being precisely 1/137 that numerologists started to establish cultish associations with the number 137.”

“But some numbers, called dimensionless numbers, have the same numerical value no matter what units of measurement are chosen. Probably the most famous of these is the "fine-structure constant," .... Physicists love this number not just because it is dimensionless, but also because it is a combination of three fundamental constants of nature.”

“Arnold Sommerfeld generalized Bohr's model to include elliptical orbits in three dimensions. He treated the problem relativistically (using Einstein's formula for the increase of mass with velocity), ... According to historian Max Jammer, this success of Sommerfeld's fine-structure formula "served also as an indirect confirmation of Einstein's relativistic formula for the velocity dependence of inertia mass.”

“We have one real candidate for changing the rules; this is string theory. In string theory the one-dimensional trajectory of a particle in spacetime is replaced by a two-dimensional orbit of a string. Such strings can be of any size, but under ordinary circumstances they are quite tiny, ... a value determined by comparing the predictions of the theory for Newton's constant and the fine structure constant to experimental values.”