137 - Arthur I. Miller [34]
Pauli’s paper on the exclusion principle contained none of the mathematical fireworks for which he had become famous. Rather, it was the fruit of his patient examination of data. By searching out patterns among numbers, he came up with what scientists call a restrictive or prohibitive principle. Another example is the principle of relativity, which asserts that the laws of physics must be the same in every laboratory, regardless of its motion. There is no reason for this to be so. Yet it must be, to formulate a systematic theory of how objects from the size of basketballs to planets move. It also enables scientists to predict numerous phenomena, such as the bending of starlight by massive objects, a prediction of relativity theory that was later proved to be true in real life. There is no way of deriving the principle of relativity mathematically. It is simply an axiom.
But what about the exclusion principle? Could it be derived? Pauli was not sure, nor was anyone else.
Hard though it was to understand its deeper meaning, scientists quickly realized the exclusion principle’s importance in explaining the periodic table of chemical elements and thus, also, atomic structure. It also helped clarify why metals are hard and what the fate of stars might be. Pauli had made a discovery that would shape the path of physics in the future and change our understanding of the cosmos.
The search for the meaning of the exclusion principle
Pauli immediately notified Bohr and Heisenberg of his discovery and sent them the draft manuscript of his paper. It was, he wrote them firmly, at the very least “not a bigger nonsense” than the schemes other scientists proposed for understanding the structure of the atom. At least Pauli had avoided hypotheses with no basis such as Bohr’s force of unknown origin, which distorted a core in two different ways. He suspected that his exclusion principle could not be derived from Bohr’s theory of the atom. Understanding it lay rather, he suggested, in the as-yet-unknown properties of “motion and force in quantum theory.” Remembering his many attempts to support Bohr’s theory—the hydrogen-molecule ion, the helium atom, and the core models of atomic structure—all of which ended in failure, he wrote that he would prefer to interpret the exclusion principle free of any model of the atom, especially a model containing the concept of electron orbits. He was sure that the key factors in describing the characteristics of an electron had to be its energy and momentum. Those were real because they were measurable; electron orbits and shells were not. In this Pauli was true to his godfather Ernst Mach’s philosophy—to avoid any unmeasurable concepts in a theory of physics, for those were purely metaphysical.
Heisenberg and Bohr were amused by Pauli’s exclusion principle. Here was proof, Heisenberg wrote to Pauli, that Pauli was entering the “land of the formalist philistines,” practicing a style of physics “of which you had insulted me. [In fact, you] had broken all hitherto existing records [in rising] to an unimagined, giddy height (by introducing individual electrons with 4 degrees of freedom).” Everyone knew that electrons had to move in three-dimensional space like everything else in the universe, and therefore three quantum numbers should surely suffice. Pauli had frequently accused Bohr and Heisenberg of coming up with “swindles.