137 - Arthur I. Miller [55]
But Pauli and his colleagues were dissatisfied. Among other problems, Dirac’s equation for the electron predicted that objects with negative energy should actually exist. Physicists believed particles of negative energy to be like negative time: they simply could not exist. Heisenberg commented to Pauli that Dirac’s equation was the “saddest chapter in modern physics.” Furthermore, it did nothing to elucidate Pauli’s exclusion principle.
Pauli’s anti-Dirac equation
In 1934 Pauli set out to find an equation to supplant Dirac’s. His colleague in this was his assistant Victor Weisskopf. Weisskopf had been a student of Born’s and Bohr’s. Like Pauli, he was Viennese. The two shared a deep appreciation for literature and music, in particular Mozart’s operas. Weisskopf was also a concert-level pianist. Well over six feet tall, athletically built, and with a cultured air, he stands out in group photographs.
Viki, as Weisskopf became known to his friends, loved to tell the story of his first meeting with Pauli in the fall of 1933:
The first time I came to see him, I knocked at the door—no answer. He was in a very bad mood at that time, the whole period was a difficult one for him for personal reasons. When he didn’t answer, after a few minutes I opened the door. ‘You are Weisskopf; yes, you will be my assistant. I will tell you that I wanted to take [Hans] Bethe but he works on solid state [physics]. I don’t like this kind of physics although I started it.’ He gave me some problem…and after a few weeks I showed him what I had done; he was very dissatisfied with it and he said, ‘I should have taken Bethe.’
This was Pauli’s idea of humor, but it also shows what a difficult, sharp-tongued man he could be. Many people could not handle his sardonic sense of humor and this led, no doubt, to some physicists thinking twice before taking on the job of his assistant. But despite the inauspicious start Pauli’s collaboration with Weisskopf was to be both fruitful and memorable.
The two came up with an equation that had many of the same properties as Dirac’s and agreed with relativity theory. But while Dirac’s was for any particle with half a unit of spin, theirs was for particles with no spin. None had been detected at the time. However, when they included spin in their equation it no longer agreed with relativity.
But why? As he was fiddling about with his equations Pauli realized something entirely new: that particles with no spin differ fundamentally from particles with half a unit of spin. Particles with half a unit of spin—1/2, 3/2 and so on (known as Fermions after the Italian physicist Enrico Fermi)—obeyed Fermi-Dirac statistics (discovered by Fermi and Dirac in 1926), meaning that the overall wave function (that is, the solution of the Schrödinger equation) for a collection of Fermions exhibited antisymmetry.*
The only known such particles at the time were the electron, neutron, neutrino, and proton. Particles with whole-number spin—zero, one, and so on (called Bosons after the Indian physicist Satyendra Nath Bose)—obey Bose-Einstein statistics (discovered by Bose and Einstein in 1924), meaning that they have an overall wave function that remained the same when their positions and spins are exchanged; it was symmetrical. In other words, the two sets of particles have different symmetry properties. From this Pauli deduced that the exclusion principle applies to particles with half a unit of spin and not to particles with a whole unit of spin.
There was no obvious reason for this. The only conclusion was that nature had spoken. Something more than mathematics was involved in wave equations. Physicists now began investigating the properties of wave equations for particles of any sort of spin. The difficult mathematics involved was very much to Pauli’s taste.
Six years later, in 1940, he summarized and extended this work. Instead of using any particular wave equation