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January 1925: Wolfgang Pauli announces the exclusion principle

The year 1925 was an important one for quantum physics, beginning with Wolfgang Pauli’s January announcement of the exclusion principle. This well-known principle, which states that no two identical fermion particles can be in the same quantum state, provided for the first time a theoretical basis for the structure of the periodic table of the elements.

Wolfgang Pauli

Wolfgang Pauli was born in Vienna in 1900, the same year that quantum mechanics itself was born with Planck’s announcement of the idea of the energy quanta. Pauli’s father was a physician and chemistry professor at the University of Vienna, and his godfather was Ernest Mach. As a young prodigy, when he found himself bored during class, Pauli would read Einstein’s papers on relativity. By age 20 Pauli, then a student of Arnold Sommerfeld at the University of Munich, had published papers on relativity and written an encyclopedia article on relativity which greatly impressed other physicists, including Albert Einstein himself. Having learned classical mechanics and relativity, Pauli was disconcerted by quantum mechanics upon being introduced to it by Sommerfeld, and at first he found the subject rather confused.

Possibly because of his brilliance, Pauli’s professors and colleagues tolerated some of his more annoying habits, such as his custom of sleeping extremely late and rarely showing up for lectures before noon. He was also extremely critical, and famous for deriding his colleagues’ less-than-coherent work as “not even wrong.” His tendency to criticize often spurred others to clarify their ideas. Pauli also had such an amazing propensity to cause accidents that scientists began to believe that even to have him come close to one’s lab meant doom for the experiment.

After receiving his doctorate in 1921 and spending some time in Gottingen and then Copenhagen, Pauli took a position at the University of Hamburg in 1923. He gave his first lecture there on the periodic table of elements, which he found unsatisfactory because the atomic shell structure was not understood. In 1913, Bohr had proposed that electrons could occupy only certain quantized orbitals, but there seemed to be no reason why all the electrons in an atom didn’t simply crowd into the one lowest energy state. There was no convincing explanation of the structure of the periodic table. Pauli had also recently worked on trying to explain the anomalous Zeeman effect, (a consequence of electron spin) and was convinced that the two problems were somehow related.

In late 1924, Pauli made a big leap by suggesting the idea of a adding a fourth quantum number to the three that were then used to describe an electron’s quantum state. The first three quantum numbers made sense physically, since they related to the electron’s motion around the nucleus. Pauli called his new quantum property of the electron a “two-valuedness not describable classically.” Soon after making this proposal, Pauli realized that it could lead to the solution of the problem of the closed orbitals.

Then in January 1925, he announced the exclusion principle, stating that no two electrons in an atom can occupy a state with the same values for the four quantum numbers. Each electron had to be in its own unique state. Other possibilities are excluded.

Pauli’s proposed fourth quantum number puzzled physicists at the time, because no one could explain its physical significance. Pauli himself was troubled by the idea. Pauli was also bothered by the fact that he couldn’t give any logical explanation for the exclusion principle or derive it from other laws of quantum mechanics, and he remained unhappy about this problem. Nonetheless, the principle worked–it explained the structure of the periodic table and is essential for explaining other properties of matter.

Later in 1925, Samuel Goudsmit and George Uhlenbeck, inspired by Pauli’s work, interpreted the fourth quantum number as the electron’s spin. Pauli originally applied the exclusion principle to explain electrons in atoms, but later it was extended to any system of fermions, which have half integer spin, but not to bosons, which have integer spin.

In the two years after Pauli’s announcement of his exclusion principle, the new quantum mechanics took off, with Heisenberg’s formulation of matrix mechanics, and Schrödinger’s wave mechanics, which was based on de Broglie’s idea that matter can have wavelike properties.

In 1928 Pauli moved to Zurich. He spent time during World War II in the United States, and returned to Zurich after the war. In 1931, Pauli proposed the existence of a new particle, the neutrino, as a solution to the apparent lack of energy conservation in beta decay. After his many research accomplishments, he spent much of his later years thinking about the history and philosophy of science.

Pauli always insisted on having a clear and coherent explanation of a phenomenon, and always strove to find both an intuitive understanding of an experiment and a rigorous mathematical scheme. Max Born once commented that, “I knew he was a genius, comparable only to Einstein himself. But he was a completely different type of man, who in my eyes, did not attain Einstein’s greatness.” In 1945, Pauli was awarded the Nobel Prize for the discovery of the exclusion principle. He died in 1958.