137 - Arthur I. Miller [125]
Of course 136 was not 137, but for Eddington it was close enough. He was convinced that the elusive “one” would “not be long in turning up.” As the physicist Paul Dirac put it, “[Eddington] first proved for 136 and when experiment raised to 137, he gave proof of that!” The obsessive pursuit of 137 took over Eddington’s life. American astrophysicist Henry Norris Russell remembered meeting him at a conference in Stockholm. They were in the cloakroom, about to hang up their coats. Eddington insisted on hanging his hat on peg 137.
Eddington added to the mystery by pointing out that 137 contained three of the seven fundamental constants of nature (the other four are the masses of the electron and the proton, Newton’s gravitational constant, and the cosmological constant of the general theory of relativity). Seven, of course, is a mysterious number in itself, encompassing the seven days of creation, seven orifices in the head, and seven planets in the pre-Copernican planetary system. Eddington’s speculations were a catalyst in the search for numerical relationships among the fundamental constants of nature.
In January 1929 Bohr wrote to Pauli, “What do you think of Eddington’s latest article (136)?” Pauli hardly bothered to reply, commenting only that he might soon have something to say “on Eddington (??).” The two question marks are his. “I consider Eddington’s ‘136-work’ as complete nonsense: more exactly for romantic poets and not for physicists,” he wrote to his colleague Oskar Klein a month later. He added in a letter to Sommerfeld that May, “Regarding Eddington’s = 1/136, I believe it makes no sense.” ( is the fine structure constant.)
Pauli and 137
It seemed that Pauli had not caught the 137 bug. In February 1934, however, he wrote to Heisenberg that the key problem was “fixing [1/137] and the ‘Atomistik’ of the electric charge.” At the time he was trying to find a version of quantum electrodynamics in which the mass and charge of the electron were not infinite; but no matter which way he manipulated his equations, the concept of electric charge always entered—hence the mystical “‘Atomistik’—atom plus mystic—of the electric charge.”
The problem was that quantum electrodynamics did “not take the atomic nature of the electric charge into account” when the electric charge entered the theory of quantum electrodynamics as part of the fine structure constant (that is, 1/137). “A future theory,” Pauli wrote, “must bring about a deep unification of foundations.”
As Pauli saw it, the crux of the problem was that the concept of electric charge was foreign to both prequantum and quantum physics. In both theories the charge of the electron had to be introduced into equations—it did not emerge from them. (This was similar to Heisenberg and Schrödinger’s quantum theories in which the spin of the electron had to be inserted, whereas it popped out of Dirac’s theory.)
Quantum theory exacerbated this situation in that it included the fine structure constant, 1/137 = 2e2/hc, that is, it linked the charge of the electron (e) with two other fundamental constants of nature—the miniscule Planck’s constant, h (the smallest measurement possible in the universe and the signature of quantum theory which deals with nature at the atomic level), and the vast speed of light, c (the signature of relativity theory which deals with the universe).
Pauli continued to worry about the connection between the fine structure constant and the infinities occurring in quantum theory. It was a problem that would not go away. “Everything will become beautiful when [1/137] is fixed,” he wrote to Heisenberg in April 1934. And on into June: “I have been musing over the great question, what is [1/137]?”
That year, in a lecture he gave in Zürich, he underlined the importance of eliminating the infinities that persisted in quantum electrodynamics and drew attention to the theory’s relationship to our understanding of space and time. The solution to this problem would require “an interpretation of the numerical value of the dimensionless