Wolfgang Pauli was one of the handful of theoretical physicists who formulated the quantum theory. Like Werner Heisenberg, Paul Dirac, and Pascual Jordan, Pauli was still in his twenties in the 1920's. The other great founders, Neils Bohr, Max Born, Erwin Schrödinger, and Albert Einstein, averaged twenty years older. Max Planck, who invented the quantum of action in 1900, the year Pauli was born, was forty years older. Pauli's name is on the exclusion principle which limits to two the number of fermions that can be in the same volume of phase space. With the principal quantum number n, the angular momentum quantum number l, and the magnetic quantum number m, the electron spin s (limited to values of +1/2 and -1/2) completes the four quantum numbers needed to explain the electronic structure of all the atoms. These four numbers account for the periodic table of the elements. Pauli discovered the fourth quantum number before Goudschmidt and Uhlenbeck discovered the spin itself (just as Bohr found the principal quantum number n without a physical derivation). While still a student, Pauli was encouraged by Arnold Sommerfeld to write an article on the theory of relativity for the Mathematical Encyclopedia that remains today one of the most important accounts of both special and general relativity. In his preface to a second edition shortly after Einstein's death in 1955, Pauli wrote of Einstein clinging to the dream of a unified field theory:
I do not conceal to the reader my scepticism concerning all attempts of this kind which have been made until now, and also about the future chances of success of theories with such aims. These questions are closely connected with the problem of the range of validity of the classical field concept in its application to the atomic features of Nature. The critical view, which I uttered in the last section of the original text with respect to any solution on these classical lines, has since been very much deepened by the epistemological analysis of quantum mechanics, or wave mechanics, which was formulated in 1927. On the other hand Einstein maintained the hope for a total solution on the lines of a classical field theory until the end of his life. These differences of opinion are merging into the great open problem of the relation of relativity theory to quantum theory, which will presumably occupy physicists for a long while to come. In particular, a clear connection between the general theory of relativity and quantum mechanics is not yet in sight. Just because I emphasize in the last of the notes a certain contrast between the views on problems beyond the original frame of special and general relativity held by Einstein himself on the one hand, and by most of the physicists, including myself, on the other, I wish to conclude this preface with some conciliatory remarks on the position of relativity theory in the development of physics. There is a point of view according to which relativity theory is the end-point of "classical physics", which means physics in the style of Newton-Faraday-Maxwell, governed by the "deterministic" form of causality in space and time, while afterwards the new quantum-mechanical style of the laws of Nature came into play. This point of view seems to me only partly true, and does not sufficiently do justice to the great influence of Einstein, the creator of the theory of relativity, on the general way of thinking of the physicists of today. By its epistemological analysis of the consequences of the finiteness of the velocity of light (and with it, of all signal-velocities), the theory of special relativity was the first step away from naive visualization. The concept of the state of motion of the "luminiferous aether", as the hypothetical medium was called earlier, had to be given up, not only because it turned out to be unobservable, but because it became superfluous as an element of a mathematical formalism, the group-theoretical properties of which would only be disturbed by it. By the widening of the transformation group in general relativity the idea of distinguished inertial coordinate systems could also be eliminated by Einstein as inconsistent with the group-theoretical properties of the theory. Without this general critical attitude, which abandoned naive visualizations in favour of a conceptual analysis of the correspondence between observational data and the mathematical quantities in a theoretical formalism, the establishment of the modern form of quantum theory would not have been possible. In the "complementary" quantum theory, the epistemological analysis of the finiteness of the quantum of action led to further steps away from naive visualizations. In this case it was both the classical field concept, and the concept of orbits of particles (electrons) in space and time, which had to be given up in favour of rational generalizations. Again, these concepts were rejected, not only because the orbits are unobservable, but also because they became superfluous and would disturb the symmetry inherent in the general transformation group underlying the mathematical formalism of the theory. I consider the theory of relativity to be an example showing how a fundamental scientific discovery, sometimes even against the resistance of its creator, gives birth to further fruitful developments, following its own autonomous course.In 1930, Pauli predicted the existence of another particle, electrically neutral, but carrying the needed to conserve the total spin in the beta decay of a radioactive nucleus or a neutron (n) decaying to become a proton (p). It was called the neutrino ("little neutron") by Enrico Fermi.
n0 → p+ + e− + νeThe neutrino was not discovered until a quarter-century after Pauli's prediction.
Pauli on MeasurementsPauli distinguished two kinds of measurements. The first is when we measure a system in a known state ψ. (It has been prepared in that state by a prior measurement.) If we again use a measurement apparatus with eigenvalues whose states include the known state, the result is that we again find the system in the known state ψ. No new information is created, since we knew what the state of the system was before the measurement. This Pauli called a measurement of the first kind. In the second case, the eigenstates of the system plus apparatus do not include the state of the prepared system. Dirac's transformation theory tells us to use a basis set of eigenstates appropriate to the new measurement, say the set φn. In this case, the original wave function ψ can be expanded as a linear superposition of states φn with coefficients cn,
ψ = ∑n cnφn,where cn2 = | < ψ | φn > |2 is the probability that the measurement will find the system in state φn. Pauli calls this a measurement of the second kind. It corresponds to von Neumann's Process 1, interpreted as a "collapse" or "reduction" of the wave function. In this measurement, all the unrealized possibilities are eliminated, and the one possibility that is actualized produces new information (following Claude Shannon's mathematical theory of the communication of information). We do not know in advance which of the possible states becomes actual. That is a matter of ontological chance. If we did know, there would be no new information. There is a fundamental and deeply philosophical connection between multiple possibilities and information. When one possibility is actualized, where do all the other possibilities go? For Hugh Everett, III, they go into other universes.
Pauli and the Compton EffectWhen, in 1923, the discovery of the Compton effect provided evidence for Albert Einstein's "light-quantum hypothesis, Pauli objected to the explanation that a free electron had scattered the photon (a high energy x-ray). An isolated "free" electron cannot scatter a photon, he maintained. Pauli was one of the few scientists to take Einstein's light-quantum hypothesis of 1905 seriously. Einstein's 1917 paper on the emission and absorption of radiation by matter had not convinced many physicists of the reality of light quanta before Compton's experimental evidence. No one was prepared to renounce the wave theory of light, with its well-established interference properties. Moreover, there was almost universal unhappiness with the irreducible and ontological chance that Einstein found in the direction and timing of emitted radiation. Pauli's biographer, Charles Enz, described the work
Shortly after Pauli's paper , Einstein and Ehrenfest published a different interpretation of Eq. (4.22) . By writing F = bρν (a1 + b1ρν1) scattering may be understood as a composite process consisting of the absorption of a quantum ν followed by the emission of a quantum ν1. Pauli has given a beautiful account of this entire subject in Section. 5 of his 'Quantentheorie' . There he concludes: "In order to maintain the connection between emission and absorption on the one hand and scattering on the other hand also in quantum theory it seems therefore natural in quantum theory to assume always scattering processes as consisting of two partial processes. . . . Although in the case of free electrons there is no case of emission and absorption we will have to hold on to the decomposition of the scattering processes into two partial processes" (translated from Ref. , p. 28).
Pauli and Kepler
THE INFLUENCE OF ARCHETYPAL IDEAS
WorksÜber das thermische Gleichgewicht zwischen Strahlung und freien Electronen,"
Zeitschrift für Physik, 18, 227, 1923 (PDF) "Zur Quantentheorie des Strahlungsgleichgewichts (Einstein and Ehrenfest on Pauli),
Zeitschrift für Physik, 19, 301, 1923 (PDF) "Das Wärmegleichgewicht bei Streuprozessen," Section 5, "Quantentheorie," in H. Geiger and K. Scheel (eds.), Handbuch der Physik, vol.23, 226, pp.22-29, 1926 (PDF)
For ScholarsJagdish Mehra's 1958 quotation from Pauli (Mehra and Rechenberg v. 1-1, p.xxiv)
'Als ich jung war, glaubte ich der beste "Formalist" meiner Zeit zu sein. Ich glaubte, ich wäre ein Revolutionär. Wenn die grossen Probleme kämen, würde ich sie lösen und darüber schreiben. Die grossen Probleme kamen und gingen vorüber, andere lösten sie und schrieben darüber. Ich war doch ein Klassiker und kein Revolutionär..' ('When I was young I thought I was the best formalist of the day. I thought I was a revolutionary. When the great problems would come I shall be the one to solve them and to write about them. The great problems came and went. Others solved them and wrote upon them. I was of course a classicist rather than a revolutionary.') And then, as an afterthought, he added: 'Ich war so dumm als ich jung war.' ('I was so stupid when I was young.') Well, he was not to be taken literally.