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Physics Today
Another Visit with Wolfgang Pauli Karl von Meÿenn, E. L. Schücking
Published Aug 1, 2001 • 0 citations
Abstract SCHUCKING AND VON MEYENN REPLY: Yes, indeed, it was at the Solvay Conference in 1930 that Bohr reminded Einstein of his elevator. How the wrong date crept into our manuscript baffles us still.Kurt Gottfried is surprised that Pauli thought of Dirac as a formalist. Dirac was a formalist. He wrote in 1931: “The most powerful method of advance that can be suggested at present is to employ all the resources of pure mathematics in attempts to perfect and generalize the mathematical formalism that forms the existing basis of theoretical physics, and after each success in this direction, to try to interpret the new mathematical features in terms of physical entities.” 1 1. P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931) https://doi.org/10.1098/rspa.1931.0130. We disagree with Gottfried’s characterization of the Pauli equation for the electron as merely an elegant restatement of a Heisenberg–Jordan paper. Paul Ehrenfest wrote on 25 March 1931 about the Pauli equation: “This work has become very important. It has opened the way to Dirac’s ingenious work on the spin-electrons and probably also to Heisenberg’s famous work about the helium spectrum.” 2 2. W. Pauli, Scientific Correspondence, Vol. 2, K. von Meyenn, ed., Springer-Verlag, New York (1985) p. 71. Pauli introduced spinors into quantum mechanics and thus—in hindsight—made the step from two to four components not such a giant leap.We agree with Gottfried that the golden rule 3 3. K. Gottfried, Quantum Mechanics, Addison-Wesley, Redwood City, Calif. (1989), eq. 35, p. 444. is due to Dirac. When Pauli derived this equation using Dirac’s time-dependent perturbation theory, he analyzed its domain of validity using the uncertainty relation for time and energy that he had first pointed out in a letter to Heisenberg. Apparently, Pauli and Heisenberg 4 4. W. Pauli, Scientific Correspondence, Vol. 1, A. Hermann, ed., Springer-Verlag, New York (1979), p. 460. had first thought that Dirac had “gemogelt” (cheated) in its derivation.We both cherish Dirac’s beautiful physics, but his approach to theory was different from Pauli’s or Heisenberg’s. By praising Galileo, one does not demean Kepler.On Dirac’s comment about Schrödinger, we stand corrected. Luis Boya also may have a point on vacuum degeneracy. But Pauli’s crucial role in the Heisenberg theory still needs clarification. There are 144 letters from the correspondence between Pauli and Heisenberg in 1957 and 1958, up to 30 pages in length, which still await analysis.With regard to the early history of quantum field theory, we agree that much more could be said about it, and we refer Boya to Tian Yu Cao. 5 5. T. Y. Cao, Conceptual Developments of 20th Century Field Theories, Cambridge U. Press, New York (1997) https://doi.org/10.1017/CBO9780511563997. For the history of nuclear magnetism, we suggest that Boya might consult Hendrik Casimir. 6 6. H. Casimir, Haphazard Reality, Harper & Row, New York (1983); appendix B, p. 322. Boya remarks that Heisenberg “never tried using his newborn matrix mechanics to solve for the hydrogen spectrum.” On 3 November 1925 Heisenberg wrote to Pauli: “After your first letter, I had also tried at once the calculation in three dimensions and was busy just this afternoon with the evaluation of the last equations and the elimination of the many possible mistakes in calculation when the postman entered and made my work superfluous.” 7 7. See ref. 4, p. 252. The postman had brought Pauli’s three-dimensional calculation for the H-atom. We believe that Boya underrates the role Pauli played in the dialogue with Heisenberg and that a careful reading of their correspondence supports our view. Freeman Dyson, with his unique insight into physics and the ways of physicists seems to agree with our assessment.Finally, we thank Gottfried, Boya, and Dyson for their comments.REFERENCESSection:ChooseTop of pageREFERENCES <<1. P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931) https://doi.org/10.1098/rspa.1931.0130. Google ScholarCrossref, CAS2. W. Pauli, Scientific Correspondence, Vol. 2, K. von Meyenn, ed., Springer-Verlag, New York (1985) p. 71. Google Scholar3. K. Gottfried, Quantum Mechanics, Addison-Wesley, Redwood City, Calif. (1989), eq. 35, p. 444. Google Scholar4. W. Pauli, Scientific Correspondence, Vol. 1, A. Hermann, ed., Springer-Verlag, New York (1979), p. 460. Google Scholar5. T. Y. Cao, Conceptual Developments of 20th Century Field Theories, Cambridge U. Press, New York (1997) https://doi.org/10.1017/CBO9780511563997. Google ScholarCrossref6. H. Casimir, Haphazard Reality, Harper & Row, New York (1983); appendix B, p. 322. Google Scholar7. See ref. 4, p. 252. Google Scholar© 2001 American Institute of Physics.
DOI 10.1063/1.4796448 Related papers Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a. Scientific Correspondence with Bohr, Einstein, Heisenberg, a.o. Wolfgang Pauli. Vol. 3, 1940-1949. Karl von Meyenn, Ed. Springer-Verlag, Berlin, 1993. lxiv, 1070 pp., illus. OM 216 or OS 1,684.80 or SFr 212. Sources in the History of Mathematics and Physical Sciences, vol. 11.
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SCHUCKING AND VON MEYENN REPLY: Yes, indeed, it was at the Solvay Conference in 1930 that Bohr reminded Einstein of his elevator. How the wrong date crept into our manuscript baffles us still.Kurt Gottfried is surprised that Pauli thought of Dirac as a formalist. Dirac was a formalist. He wrote in 1931: “The most powerful method of advance that can be suggested at present is to employ all the resources of pure mathematics in attempts to perfect and generalize the mathematical formalism that forms the existing basis of theoretical physics, and after each success in this direction, to try to interpret the new mathematical features in terms of physical entities.” 1 1. P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931)
https://doi.org/10.1098/rspa.1931.0130 . We disagree with Gottfried’s characterization of the Pauli equation for the electron as merely an elegant restatement of a Heisenberg–Jordan paper. Paul Ehrenfest wrote on 25 March 1931 about the Pauli equation: “This work has become very important. It has opened the way to Dirac’s ingenious work on the spin-electrons and probably also to Heisenberg’s famous work about the helium spectrum.” 2 2. W. Pauli, Scientific Correspondence, Vol. 2, K. von Meyenn, ed., Springer-Verlag, New York (1985) p. 71. Pauli introduced spinors into quantum mechanics and thus—in hindsight—made the step from two to four components not such a giant leap.We agree with Gottfried that the golden rule 3 3. K. Gottfried, Quantum Mechanics, Addison-Wesley, Redwood City, Calif. (1989), eq. 35, p. 444. is due to Dirac. When Pauli derived this equation using Dirac’s time-dependent perturbation theory, he analyzed its domain of validity using the uncertainty relation for time and energy that he had first pointed out in a letter to Heisenberg. Apparently, Pauli and Heisenberg 4 4. W. Pauli, Scientific Correspondence, Vol. 1, A. Hermann, ed., Springer-Verlag, New York (1979), p. 460. had first thought that Dirac had “gemogelt” (cheated) in its derivation.We both cherish Dirac’s beautiful physics, but his approach to theory was different from Pauli’s or Heisenberg’s. By praising Galileo, one does not demean Kepler.On Dirac’s comment about Schrödinger, we stand corrected. Luis Boya also may have a point on vacuum degeneracy. But Pauli’s crucial role in the Heisenberg theory still needs clarification. There are 144 letters from the correspondence between Pauli and Heisenberg in 1957 and 1958, up to 30 pages in length, which still await analysis.With regard to the early history of quantum field theory, we agree that much more could be said about it, and we refer Boya to Tian Yu Cao. 5 5. T. Y. Cao, Conceptual Developments of 20th Century Field Theories, Cambridge U. Press, New York (1997)
https://doi.org/10.1017/CBO9780511563997 . For the history of nuclear magnetism, we suggest that Boya might consult Hendrik Casimir. 6 6. H. Casimir, Haphazard Reality, Harper & Row, New York (1983); appendix B, p. 322. Boya remarks that Heisenberg “never tried using his newborn matrix mechanics to solve for the hydrogen spectrum.” On 3 November 1925 Heisenberg wrote to Pauli: “After your first letter, I had also tried at once the calculation in three dimensions and was busy just this afternoon with the evaluation of the last equations and the elimination of the many possible mistakes in calculation when the postman entered and made my work superfluous.” 7 7. See ref. 4, p. 252. The postman had brought Pauli’s three-dimensional calculation for the H-atom. We believe that Boya underrates the role Pauli played in the dialogue with Heisenberg and that a careful reading of their correspondence supports our view. Freeman Dyson, with his unique insight into physics and the ways of physicists seems to agree with our assessment.Finally, we thank Gottfried, Boya, and Dyson for their comments.REFERENCESSection:ChooseTop of pageREFERENCES <<1. P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931)
https://doi.org/10.1098/rspa.1931.0130 . Google ScholarCrossref, CAS2. W. Pauli, Scientific Correspondence, Vol. 2, K. von Meyenn, ed., Springer-Verlag, New York (1985) p. 71. Google Scholar3. K. Gottfried, Quantum Mechanics, Addison-Wesley, Redwood City, Calif. (1989), eq. 35, p. 444. Google Scholar4. W. Pauli, Scientific Correspondence, Vol. 1, A. Hermann, ed., Springer-Verlag, New York (1979), p. 460. Google Scholar5. T. Y. Cao, Conceptual Developments of 20th Century Field Theories, Cambridge U. Press, New York (1997)
https://doi.org/10.1017/CBO9780511563997 . Google ScholarCrossref6. H. Casimir, Haphazard Reality, Harper & Row, New York (1983); appendix B, p. 322. Google Scholar7. See ref. 4, p. 252. Google Scholar© 2001 American Institute of Physics.
Meanwhile, on 18 September 1931, Heisenberg wrote to Bohr that ‘my work seems to be somewhat gray on gray’ (Pauli, 1985). By 1931 the bright future for quantum physics that seemed just over the horizon in the fall of 1927 paled with the formulation of relativistic quantum mechanics. Besides the as yet uninterpreted negative energy states, there was the electron's divergent self-energy and the continuous energy spectrum of β-particles in the supposedly two-body final state of nuclear β-decay, which implied that energy was not conserved in nuclear reactions (Bohr, 1932) and that perhaps quantum mechanics was not valid within the nucleus (to be discussed in Chapter 5). Measurement problems in a quantum theory of the electromagnetic field At the 20–25 October 1930 Solvay Conference, Bohr, Dirac, Heisenberg and Pauli concurred that fundamental difficulties in quantum electrodynamics might be clarified by investigating measurability of electromagnetic field quantities. Upon his return to Copenhagen from Brussels, Bohr continued discussing field measurements with Lev Landau, who happened to be visiting at Bohr's institute. In December 1930 Landau went on to Zürich, where he interested Pauli's assistant Rudolf Peierls in field measurements. Their deliberations led to a joint 1931 publication entitled ‘Extension of the uncertainty principle to relativistic quantum theory’ (Landau and Peierls, 1931). Measurement of an electric field can be accomplished through measuring the change in momentum of a charged test body placed in the field.
How is it that physicists can invent equations, so rich in structure, so detailed in consequences, and so closely in agreement with experience? What does it mean when we create equations that agree with experiment to ten decimal places? Do these equations have a reality of their own? This essay is based on a lecture originally presented at the Trieste conference in honor of Paul Dirac in 1972 . It is more than fifty years since Paul Dirac gave us one of the most beautiful inventions of the twentieth century: H = c a · p + β mc 2 I once asked Professor Dirac how he came upon his masterpiece. If my memory serves (I hope he will correct me if it does not), he said that in the late 1920s most physicists, trying to calculate with relativistic quantum mechanics, were content to use the Klein–Gordon equation modified with ad-hoc corrections. In his attempt, Dirac did not try to put in the electron spin but rather to treat in a consistent manner the simplest possible problem: that of a spinless, relativistic electron. The critical moment came when he realized that 4 × 4 matrices were required. “How long did it take you from that point?” “About two weeks”. I couldn't refrain: “why so long?” He was a bit taken aback; then, his attention focused perhaps on those two glorious past weeks, he nodded as though to agree in silence why so long?
Anatoly Svidzinsky, Marlan Scully, and Dudley Herschbach have illustrated well how the molecular theory might have looked had quantum mechanics not been invented. It’s worth noting that Niels Bohr was not alone in his attempts to extend semiclassical mechanics to systems more complex than the hydrogen atom. From 1913 to 1925, many semiclassical models of two-electron systems were proposed.As we see from the authors’ figure 3a, Bohr assumed that electrons in hydrogen molecules move around the molecular axis out of phase. It is a remarkable fact that Werner Heisenberg put forward in 1922 a two-electron atomic model that had electrons moving similarly out of phase and that ascribed a fractional quantum number (½) to the bending mode of the configuration.11. G. Tanner, K. Richter, J.-M. Rost, Rev. Mod. Phys. 72, 497 (2000). https://doi.org/10.1103/RevModPhys.72.497 Although Heisenberg’s model predicted the ground-state helium level, which was in excellent agreement with the spectroscopic data, Bohr opposed the model, since a noninteger quantum number was considered sacrilege. For the same reason, Bohr never published his own results. However, the asynchronous two-electron atomic model turned out to be the fertile one, though the corresponding classical configurations can have very complex structure.22. P. Grujic, N. Simonovic, J. Phys. B 28, 1159 (1995). https://doi.org/10.1088/0953-4075/28/7/011REFERENCESSection:ChooseTop of pageREFERENCES <<1. G. Tanner, K. Richter, J.-M. Rost, Rev. Mod. Phys. 72, 497 (2000). https://doi.org/10.1103/RevModPhys.72.497, Google ScholarCrossref, ISI2. P. Grujic, N. Simonovic, J. Phys. B 28, 1159 (1995). https://doi.org/10.1088/0953-4075/28/7/011, Google ScholarCrossref, ISI© 2014 American Institute of Physics.
Some time ago, John Bell and I wrote a tongue-in-cheek article on the interpretation of quantum mechanics;11. J. S. Bell, M. Nauenberg, in Preludes in Theoretical Physics, A. de Shalit, H. Feshbach, L. van Hove, eds., North Holland, Amsterdam (1966), p. 270;reprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge U. Press, New York (1987), p. 24. in it we remarked that only a minority of physicists had any interest in the topic and that the typical physicist thought he would understand it “if ever he can spare twenty minutes to think about it.” According to David Mermin, however, that situation has changed dramatically, and “new interpretations [of quantum mechanics] appear every year.”Actually, most textbooks on the subject continue to be based on the well-established Born interpretation of quantum mechanics, which postulates that the absolute square of the Schrödinger wavefunction, projected onto a particular quantum state, gives the probability for the occurrence of that state after an appropriate measurement has been made. Mermin indicated that the problem with the Born interpretation involves a confusion, “prevalent among physicists,” regarding the nature of probability. He presented his preference for a “personalist Bayesian view,” which leads separate “agents,” like Eugene Wigner and his friend, to make different probability assignments based on their beliefs. But as Richard Feynman remarked, “Nature does not know what you are looking at, and she behaves the way she is going to behave whether you bother to take down the data or not.”22. R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, vol. 3, Addison-Wesley, Redwood City, CA (1989), p. 3–7.Indeed, as applied to experiments, probability simply corresponds to the relative frequency for the occurrence of a given final state after identical states are prepared initially and measurements are made by appropriate detectors—devices that, through an irreversible macroscopic process, provide a permanent record of the outcome. Hence, the results of an experiment are independent of any observers, whose only role is to set up appropriate measurement devices, calculate the probabilities from quantum theory, and then write papers based on the recorded results.As Max Born also emphasized, in classical mechanics the situation is analogous, when one takes into account that in practice initial conditions in an experiment are known only imprecisely.33. M. Born, Dan. Mat. Fys. Medd. 30 (2), 1 (1955). Hence the observed evolution of the system is also determined by a probability function that satisfies the Liouville equation. But in that case, after a measurement is performed, no one talks about the “collapse” of this classical function, whereas in quantum mechanics it is common to use that controversial expression for the Schrödinger wavefunction.Mermin discussed a “shifty split” between the classical and the quantum domain, a split that supposedly “haunts quantum mechanics.” He claimed that “regardless of what is split from what, all versions of the shifty split are vague and ambiguous.” However, that is not always the case, as a simple example shows. Consider an initial quantum wavepacket for a particle under an attractive central force that varies inversely with the square of the radial distance—the classic problem of planetary motion from the viewpoint of quantum mechanics, for example, or an excited electron in a Rydberg atom. For a finite time, the wavepacket will follow a classical Keplerian elliptic orbit, but like the Liouville distribution for the analogous classical problem, from the outset it will disperse due to the spread in initial position and momentum.For the classical distribution to be in close correspondence with the quantum wavepacket, its initial spread is assumed to satisfy the uncertainty relation. Eventually, however, the head of the wavepacket, like in the classical distribution, will catch up with its tail. Afterwards, further spreading of the wavepacket leads to interference effects between the two components, and the classical–quantum correspondence ceases to be valid. The time when such interference effects first appear is of order nτ/3, where n is the mean principal quantum number of the wavepacket and τ is the Kepler period.44. M. Nauenberg, Phys. Rev. A 40, 1133 (1989). https://doi.org/10.1103/PhysRevA.40.1133 Experimentally, that transition has been observed to agree with theory in Rydberg atoms55. M. Nauenberg, C. Stroud, J. Yeazell, Sci. Am., June 1994, p. 44. https://doi.org/10.1038/scientificamerican0694-44 for n = 100, τ = 152 picoseconds, and nothing shifty about this classical–quantum correspondence is found. For planetary orbits, however, n is of order 1070, and therefore the answer to Albert Einstein’s often repeated remark “Is the moon there when nobody looks?” (see David Mermin, Physics Today, April 1985, page 38) is yes.REFERENCESSection:ChooseTop of pageREFERENCES <<1. J. S. Bell, M. Nauenberg, in Preludes in Theoretical Physics, A. de Shalit, H. Feshbach, L. van Hove, eds., North Holland, Amsterdam (1966), p. 270; Google Scholarreprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge U. Press, New York (1987), p. 24. Google Scholar2. R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, vol. 3, Addison-Wesley, Redwood City, CA (1989), p. 3–7. Google Scholar3. M. Born, Dan. Mat. Fys. Medd. 30 (2), 1 (1955). Google Scholar4. M. Nauenberg, Phys. Rev. A 40, 1133 (1989). https://doi.org/10.1103/PhysRevA.40.1133, Google ScholarCrossref, CAS5. M. Nauenberg, C. Stroud, J. Yeazell, Sci. Am., June 1994, p. 44. https://doi.org/10.1038/scientificamerican0694-44, Google ScholarCrossref© 2012 American Institute of Physics.
David Mermin cautions against taking our “most successful abstractions to be real properties of our world.” I think he has set up a straw man. To me, the tenable realist position is not that our concepts are real but rather that they have a correspondence to reality: There can be many such correspondences, each with its utility, none capturing reality—whatever that is.I am not surprised he uses that argument to bolster the position “that quantum states are calculational devices.” In the vein of the disagreement about reality he cites, between Bishop Berkeley and Samuel Johnson, I recall a similar disagreement, between Mermin and John Bell, concerning the foundations of quantum theory. It took place at a meeting in Erice, Italy, in August 1989. Bell had finished his now famous talk “Against ‘Measurement,’ “ in which he argued that there is something wrong with quantum theory, that its rules of application are ill-defined. 1 1. J. Bell, Sixty-Two Years of Uncertainty, A. Miller, ed., Plenum, New York (1990), p. 17, https://doi.org/10.1007/978-1-4684-8771-8_3 reproduced in Phys. World 3, 33 (August 1990). He introduced the acronym FAPP, meaning that quantum theory is good “for all practical purposes” but insufficient for a truly fundamental theory. In the question-and-answer session, Mermin gave an argument not unlike the one in his Reference Frame. When he was done, Bell replied, “FAPPtrap,” and that was that.Mermin says that if one takes his view, it “can diminish the motivation for theoretical or experimental searches for a ‘mechanism’ underlying … the ‘collapse of the wavefunction’—searches that make life harder than it needs to be.” But why would one want to diminish such motivation? Might not the deficiencies of quantum theory elucidated by Bell be a clue to some deeper theory? And is that not good for physics? Certainly, in this generation, in which we did not predict the acceleration of the universe nor know the nature of dark energy or dark matter, we should have the humility to think that perhaps we do not yet have the “final” quantum theory. For example, in standard quantum theory, how or why an event occurs is a complete mystery. Nature determines an outcome, but we are told it is impossible for us to understand that in terms of anything deeper. Things happen for no reason at all. Why should we follow Mermin’s advice and not try to do better?In my own work and that of Gian-Carlo Ghirardi, Alberto Rimini, and Tullio Weber, we have developed what is called a dynamical theory of wave-function collapse (continuous spontaneous localization, or CSL). 2 2. Two reviews are P. Pearle in Open Systems and Measurement in Relativistic Quantum Field Theory, H. P. Breuer, F. Petruccionne, eds., Springer, Berlin (1999), p. 195 and A. Bassi, G. C. Ghirardi, Phys. Rep. 379, 257 (2003). https://doi.org/10.1016/S0370-1573(03)00103-0 To Schrödinger’s equation, a term is added that describes the interaction of matter with a randomly fluctuating field, so that a state vector in a superposition of macroscopically different states rapidly evolves to one of them. The final state describes the world as we see it. Therefore, the state vector can be said to correspond to reality and not be merely a computational device. Bell regarded CSL as an example of a well-defined theory, which overcomes his objections to standard quantum theory. Moreover, it provides a mechanism, a description, for the occurrence of events. And it makes some predictions that differ from those of standard quantum theory, so it is experimentally testable. Experiments so far have shown that the coupling of random field to matter must be mass proportional, but otherwise they have neither confirmed CSL nor denied it. This is a good thing, and that such attempts should not be discouraged, as Mermin’s article does, was underlined by Richard Feynman, who said in 1964,We have to find a new view of the world that has to agree with everything that is known, but disagree in its predictions somewhere, otherwise it is not interesting. And in that disagreement it must agree with nature. If you can find any other view of the world which agrees over the entire range where things have already been observed, but disagrees somewhere else, you have made a great discovery. It is very nearly impossible, but not quite, to find any theory which agrees with experiments over the entire range in which all theories have been checked, and yet gives different consequences in some other range, even a theory whose different consequences do not turn out to agree with nature. 3 3. R. Feynman, in The Character of Physical Law, MIT Press, Cambridge, MA (1970), p. 171. REFERENCESSection:ChooseTop of pageREFERENCES <<1. J. Bell, Sixty-Two Years of Uncertainty, A. Miller, ed., Plenum, New York (1990), p. 17, https://doi.org/10.1007/978-1-4684-8771-8_3 , Google ScholarCrossrefreproduced in Phys. World 3, 33 (August 1990). , Google Scholar2. Two reviews are P. Pearle in Open Systems and Measurement in Relativistic Quantum Field Theory, H. P. Breuer, F. Petruccionne, eds., Springer, Berlin (1999), p. 195 and , Google ScholarCrossref A. Bassi, G. C. Ghirardi, Phys. Rep. 379, 257 (2003). https://doi.org/10.1016/S0370-1573(03)00103-0 , , Google ScholarCrossref, ISI3. R. Feynman, in The Character of Physical Law, MIT Press, Cambridge, MA (1970), p. 171. Google Scholar© 2009 American Institute of Physics.