, Wolfgang Pauli and
Rudolf Peierls, Pauli made many important contributions as a physicist, primarily in the field of
quantum mechanics. He seldom published papers, preferring lengthy correspondences with colleagues such as
Niels Bohr from the
University of Copenhagen in Denmark and
Werner Heisenberg, with whom he had close friendships. Many of his ideas and results were never published and appeared only in his letters, which were often copied and circulated by their recipients. In 1921 Pauli worked with Bohr to create the
Aufbau Principle, which described building up electrons in shells based on the German word for building up, as Bohr was also fluent in German. Pauli proposed in 1924 a new quantum degree of freedom (or
quantum number) with two possible values, to resolve inconsistencies between observed molecular spectra and the developing theory of quantum mechanics. He formulated the Pauli exclusion principle, perhaps his most important work, which stated that no two electrons could exist in the same quantum state, identified by four quantum numbers including his new two-valued degree of freedom. The idea of spin originated with
Ralph Kronig. A year later,
George Uhlenbeck and
Samuel Goudsmit identified Pauli's new degree of freedom as
electron spin, in which Pauli for a very long time wrongly refused to believe. In 1926, shortly after Heisenberg published the
matrix theory of modern
quantum mechanics, Pauli used it to derive the observed
spectrum of the
hydrogen atom. This result was important in securing credibility for Heisenberg's theory. Pauli introduced the 2×2
Pauli matrices as a basis of spin operators, thus solving the nonrelativistic theory of spin. This work, including the
Pauli equation, is sometimes said to have influenced
Paul Dirac in his creation of the
Dirac equation for the
relativistic electron, though Dirac said that he invented these same matrices himself independently at the time. Dirac invented similar but larger (4x4) spin matrices for use in his relativistic treatment of
fermionic spin. In 1930, Pauli considered the problem of
beta decay. In a letter of 4 December to
Lise Meitner et al., beginning, "
Dear radioactive ladies and gentlemen", he proposed the existence of a hitherto unobserved neutral particle with a small mass, no greater than 1% the mass of a proton, to explain the continuous spectrum of beta decay. In 1934,
Enrico Fermi incorporated the particle, which he called a
neutrino, "little neutral one" in Fermi's native Italian, into his theory of beta decay. The neutrino was first confirmed experimentally in 1956 by
Frederick Reines and
Clyde Cowan, two and a half years before Pauli's death. On receiving the news, he replied by telegram: "Thanks for message. Everything comes to him who knows how to wait. Pauli." In 1940, Pauli re-derived the
spin-statistics theorem, a critical result of quantum field theory that states that particles with half-integer spin are
fermions, while particles with integer spin are
bosons. In 1949, he published a paper on
Pauli–Villars regularization: regularization is the term for techniques that modify infinite mathematical integrals to make them finite during calculations, so that one can identify whether the intrinsically infinite quantities in the theory (mass, charge, wavefunction) form a finite and hence calculable set that can be redefined in terms of their experimental values, which criterion is termed
renormalization, and which removes infinities from
quantum field theories, but also importantly allows the calculation of higher-order corrections in perturbation theory. Pauli made repeated criticisms of the
modern synthesis of
evolutionary biology, and his contemporary admirers point to modes of
epigenetic inheritance as supporting his arguments.
Paul Drude in 1900 proposed the first theoretical model for a
classical electron moving through a metallic solid. Drude's classical model was also augmented by Pauli and other physicists. Pauli realized that the free electrons in metal must obey the
Fermi–Dirac statistics. Using this idea, he developed the theory of
paramagnetism in 1926. Pauli said, "Festkörperphysik ist eine Schmutzphysik"—solid-state physics is the physics of dirt. ==Personality and friendships==