137 - Arthur I. Miller [126]
So what had happened? Why did Pauli suddenly begin to discuss his thoughts on 137? Perhaps it was the effect of Jung’s analysis opening his mind to mystical speculations.
In 1935, the senior scientist Max Born, Pauli’s mentor at Göttingen who was then at Cambridge, published an article entitled, “The Mysterious Number 137.” He looked into the reasons why 137 should have such mystical power for scientists. The main reason was that it seemed to be a way in which one could achieve the Holy Grail of scientific studies—linking relativity (the study of the very large—the universe) with quantum theory (the study of the very small—the atom).
In his article he looks at some of the qualities that make the number “mystical,” prime among them being that even though it is made up of fundamental constants that possess dimensions, it is itself dimensionless. It is also enormously important in the development of the universe as we know it. He writes: “If [the fine structure constant] were bigger than it really is, we should not be able to distinguish matter from ether [the vacuum, nothingness], and our task to disentangle the natural laws would be hopelessly difficult. The fact however that has just its value 1/137 is certainly no chance but itself a law of nature. It is clear that the explanation of this number must be the central problem of natural philosophy.”
In 1955, at the hundredth anniversary of the ETH, Pauli addressed a huge audience in the main lecture hall of the physics department at Gloriastrasse on the subject “Problems of Today’s Physics.” Contrary to his usual style Pauli spoke from a prepared manuscript. He obviously found this difficult. With a flourish he threw the paper aside and spoke off the cuff with great passion and verve. The crux of his argument was the vital importance of the fine structure constant and also what an impenetrable problem it was. It did not merely designate how two electrons interact with each other, it was not merely a constant to be measured; what scientists had to do was “to accept it as one of the actual main problems of theoretical physics.” There was thunderous applause.
Realizing its fundamental importance in understanding spectral lines in atomic physics and in the theory of how light and electrons interact, quantum electrodynamics, Pauli and Heisenberg were determined to derive it from quantum theory rather than introducing it from the start. They believed that if they could find a version of quantum electrodynamics capable of producing the fine structure constant, it would not contain the infinities that marred their theories. But nothing worked. The deeper problems that beset physics—not only how to derive the fine structure constant but how to find an explanation for the masses of elementary particles—remain unsolved to this day.
In 1985 the brash, straight-talking, American physicist Richard Feynman, who had studied Eddington’s philosophical and scientific papers on 137, wrote in his inimitable manner:
It [1/137] has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. Immediately you would like to know where this number comes from…. Nobody knows. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man.
The magic number 137
So where did this magic number come from? How did Sommerfeld, who discovered it, alight on it? To get a glimpse of his thought processes, we need to take a short mathematical journey.
Mulling over the problem of the structure of spectral lines, Sommerfeld took another look at the key equation in Bohr’s theory of the atom as a miniscule solar system. It is
This is an equation for the energy level of the lone electron in an atom’s outermost shell, such as the electron in a hydrogen atom or in alkali atoms—hydrogen-like in structure, in that they have one electron free for chemical reactions, while all the rest are in closed shells (Pauli studied them in his work on the