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Michael Arbib
Bernard Baars
Gregory Bateson
John S. Bell
Charles Bennett
Ludwig von Bertalanffy
Susan Blackmore
Margaret Boden
David Bohm
Niels Bohr
Ludwig Boltzmann
Emile Borel
Max Born
Satyendra Nath Bose
Walther Bothe
Hans Briegel
Leon Brillouin
Stephen Brush
Henry Thomas Buckle
S. H. Burbury
Donald Campbell
Anthony Cashmore
Eric Chaisson
Jean-Pierre Changeux
Arthur Holly Compton
John Conway
John Cramer
E. P. Culverwell
Charles Darwin
Terrence Deacon
Lüder Deecke
Louis de Broglie
Max Delbrück
Abraham de Moivre
Paul Dirac
Hans Driesch
John Eccles
Arthur Stanley Eddington
Paul Ehrenfest
Albert Einstein
Hugh Everett, III
Franz Exner
Richard Feynman
R. A. Fisher
Joseph Fourier
Lila Gatlin
Michael Gazzaniga
GianCarlo Ghirardi
J. Willard Gibbs
Nicolas Gisin
Paul Glimcher
Thomas Gold
Brian Goodwin
Joshua Greene
Jacques Hadamard
Patrick Haggard
Stuart Hameroff
Augustin Hamon
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Hyman Hartman
John-Dylan Haynes
Donald Hebb
Martin Heisenberg
Werner Heisenberg
John Herschel
Jesper Hoffmeyer
E. T. Jaynes
William Stanley Jevons
Roman Jakobson
Pascual Jordan
Ruth E. Kastner
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Stephen Kosslyn
Ladislav Kovàč
Rolf Landauer
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Pierre-Simon Laplace
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Ulrich Mohrhoff
Jacques Monod
Emmy Noether
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Howard Pattee
Wolfgang Pauli
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Colin Pittendrigh
Max Planck
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John von Neumann
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Daniel Wegner
Steven Weinberg
Paul A. Weiss
John Wheeler
Wilhelm Wien
Norbert Wiener
Eugene Wigner
E. O. Wilson
H. Dieter Zeh
Ernst Zermelo
Wojciech Zurek


Free Will
Mental Causation
James Symposium
Wolfgang Pauli

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.

n0p+ + e + νe

The neutrino was not discovered until a quarter-century after Pauli's prediction.

Pauli on Measurements
Pauli 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 von shannon's mathematical theory of the communication of information. We do not know 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 Effect
When, 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 [1], Einstein and Ehrenfest published a different interpretation of Eq. (4.22) [2]. 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' [3].

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. [3], p. 28).

Pauli and Kepler


Although the subject of this study is an historical one, its purpose is not merely to enumerate facts concerning scientific history or even primarily to present an appraisal of a great scientist, but rather to illustrate particular views on the origin and development of concepts and theories of natural science in the light of one historic example. In so doing we shall also have occasion to discuss the significance for modern science of the problems which arose in the period under consideration, the seventeenth century. In contrast to the purely empirical conception according to which natural laws can with virtual certainty, be derived from the material of experience alone, many physicists have recently emphasized anew the fact that intuition and the direction of attention play a considerable role in the development of the concepts and ideas, generally far transcending mere experience, that are necessary for the erection of a system of natural laws (that is, a scientific theory). From the standpoint of this not purely empiristic conception, which we also accept, there arises the question, What is the nature of the bridge between the sense perceptions and the concepts? All logical thinkers have arrived at the conclusion that pure logic is fundamentally incapable of constructing such a link. It seems most satisfactory to introduce at this point the postulate of a cosmic order independent of our choice and distinct from the world of phenomena. Whether one speaks of the "participation of natural things in ideas" or of a "behaviour of metaphysical things — those, that is, which are in themselves real," the relation between sense perception and idea remains predicated upon the fact that both the soul of the perceiver and that which is recognized by perception are subject to an order thought to be objective.

Every partial recognition of this order in nature leads to the formulation of statements that, on the one hand, concern the world of phenomena and, on the other, transcend it by employing, "idealizingly," general logical concepts. The process of understanding nature as well as the happiness that man feels in understanding, that is, in the conscious realization of new knowledge, seems thus to be based on a correspondence, a "matching" of inner images pre-existent in the human psyche with external objects and their behaviour. This interpretation of scientific knowledge, of course, goes back to Plato and is, as we shall see, very clearly advocated by Kepler. He speaks in fact of ideas that are pre-existent in the mind of God and were implanted in the soul, the image of God, at the time of creation. These primary images which the soul can perceive with the aid of an innate "instinct" are called by Kepler archetypal ("archetypalis"). Their agreement with the "primordial images" or archetypes introduced into modern psychology by C. G. Jung and functioning as "instincts of imagination" is very extensive. When modern psychology brings proof to show that all understanding is a long-drawn-out process initiated by processes in the unconscious long before the content of consciousness can be rationally formulated, it has directed attention again to the preconscious, archaic level of cognition. On this level the place of clear concepts is taken by images with strong emotional content, not thought out but beheld, as it were, while being painted. Inasmuch as these images are an "expression of a dimly suspected but still unknown state of affairs" they can also be termed symbolical, in accordance with the definition of the symbol proposed by C. G. Jung. As ordering operators and image-formers in this world of symbolical images, the archetypes thus function as the sought-for bridge between the sense perceptions and the ideas and are, accordingly, a necessary presupposition even for evolving a scientific theory of nature. However, one must guard against transferring this a priori of knowledge into the conscious mind and relating it to definite ideas capable of rational formulation.


It is obviously out of the question for modern man to revert to the archaistic point of view that paid the price of its unity and completeness by a naive ignorance of nature. His strong desire for a greater unification of his world view, however, impels him to recognize the significance of the pre-scientific stage of knowledge for the development of scientific ideas — a significance of which mention has already been made at the beginning of this essay —by supplementing the investigation of this knowledge, directed inward. The former process is devoted to adjusting our knowledge to external objects; the latter should bring to light the archetypal images used in the creation of our scientific concepts. Only by combining both these directions of research may complete understanding be obtained.

Among scientists in particular, the universal desire for a greater unification of our world view is greatly intensified by the fact that, though we now have natural sciences, we no longer have a total scientific picture of the world.

The Planck-Einstein quantum of action h has added an irreducible mysterious element to our understanding of the world, the wave-particle duality
Since the discovery of the quantum of action, physics has gradually been forced to relinquish its proud claim to be able to understand, in principle, the whole world. This very circumstance, however, as a correction of earlier one-sidedness, could contain the germ of progress toward a unified conception of the entire cosmos of which the natural sciences are only a part.

I shall try to demonstrate this by reference to the still unsolved problem of the relationship between occurrences in the physical world and those in the soul, a problem that had already engaged Kepler's attention. After he had shown that the optical images on the retina are inverted in relation to the original objects he baffled the scientific world for a while by asking why then people did not see objects upside down instead of upright. It was of course easy to recognize this question as only an illusory problem, since man is in fact never able to compare images with real objects but only registers the sensory impressions that result from the stimulation of certain areas of the retina. The general problem of the relation between psyche and physis, between the inner and the outer, can, however, hardly be said to have been solved by the concept of "psychophysical parallelism" which was advanced in the last century. Yet modern science may have brought us closer to a more satisfying conception of this relationship by setting up, within the field of physics, the concept of complementarity. It would be most satisfactory of all if physis and psyche could be seen as complementary aspects of the same reality. We do not yet know, however, whether or not we are here confronted — as surmised by Bohr and other scientists — with a true complementary relation, involving mutual exclusion, in the sense that an exact observation of the physiological processes would result in such an interference with the psychical processes that the latter would become downright inaccessible to observation. It is, however, certain that modern physics has generalized the old confrontation of the apprehending subject with the apprehended object into the idea of a cleavage or division that exists between the observer or the means of observation, on the one hand, and the system observed, on the other. While the existence of such a division is a necessary condition of human cognition, modern physics holds that its placement is, to a certain extent, arbitrary and results from a choice co-determined by considerations of expediency and hence partially free.

The solution to the problem of measurement is to see that immaterial information must be created on the physical side (and compensating entropy transferred away) before an "observer" on the psychical side can make an observation, which moves part of that physical information into the psychical mind.
Furthermore, whereas older philosophical systems have located the psychical on the subjective side of the division, that is, on the side of the apprehending subject, and the material on the other side — the side of that which is objectively observed — the modern point of view is more liberal in this respect: microphysics shows that the means of observation can also consist of apparatuses that register automatically; modern psychology proves that there is on the side of that which is observed introspectively an unconscious psyche of considerable objective reality. Thereby the presumed objective order of nature is, on the one hand, relativized with respect to the no less indispensable means of observation outside the observed system; and, on the other, placed beyond the distinction of "physical" and "psychical."

Now, there is a basic difference between the observers, or instruments of observation, which must be taken into consideration by modern microphysics, and the detached observer of classical physics. By the latter I mean one who is not necessarily without effect on the system observed but whose influence can always be eliminated by determinable corrections.

And also paid for with an increase in disorder somewhere in the universe
In microphysics, however, the natural laws are of such a kind that every bit of knowledge gained from a measurement must be paid for by the loss of other, complementary items of knowledge. Every observation, therefore, interferes on an indeterminable scale both with the instruments of observation and with the system observed and interrupts the causal connection of the phenomena preceding it with those following it. This uncontrollable interaction between observer and system observed, taking place in every process of measurement, invalidates the deterministic conception of the phenomena assumed in classical physics: the series of events taking place according to pre-determined rules is interrupted, after a free choice has been made by the beholder between mutually exclusive experimental arrangements, by the selective observation which, as an essentially non-automatic occurrence, may be compared to a creation in the microcosm or even to a transmutation the results of which are, however, unpredictable and beyond human control.55
In this way the role of the observer in modern physics is satisfactorily accounted for. The reaction of the knowledge gained on the gainer of that knowledge gives rise, however, to a situation transcending natural science, since it is necessary for the sake of the completeness of the experience connected therewith that it should have an obligatory force for the researcher. We have seen how not only alchemy but the heliocentric idea furnishes an instructive example of the problem as to how the process of knowing is connected with the religious experience of transmutation undergone by him who acquires knowledge. This connection can only be comprehended through symbols which both imaginatively express the emotional aspect of the experience and stand in vital relationship to the sum total of contemporary knowledge and the actual process of cognition. Just because in our times the possibility of such symbolism has become an alien idea, it may be considered especially interesting to examine another age to which the concepts of what is now called classical scientific mechanics were foreign but which permits us to prove the existence of a symbol that had, simultaneously, a religious and a scientific function.
Über 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 Teachers
For Scholars
Jagdish 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.

Chapter 1.5 - The Philosophers Chapter 2.1 - The Problem of Knowledge
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