At the 1958 Rochester Conference on high-energy nuclear physics held in Geneva, Heisenberg invoked the idea of a degenerate vacuum to account for internal quantum numbers, such as isospin and strangeness, that provide selection rules for elementary particle interactions (1958).* In an influential paper submitted in 1959,** Heisenberg and his collaborators used his concept of a degenerate vacuum in QFT [quantum field theory] to explain the breaking of isospin symmetry by electromagnetism and weak interactions. [...] Heisenberg's degenerate vacuum was at the time widely discussed at international conferences. It was frequently quoted, greatly influenced field theorists, and helped to clear the way for the extension of SSB [spontaneous symmetry breaking] from hydrodynamics and condensed matter theory to QFT. ([12] p. 283)
Nambu's work on superconductivity led him to consider the possible application to particle physics of the idea of non-invariant solutions (especially in the vacuum state). [...] [...] [...] It is of interest to note the impact of Dirac and Heisenberg on Nambu's pursuing this analogy. First, Nambu took Dirac's idea of holes very seriously and viewed the vacuum not as a void but as a plenum packed with many virtual degrees of freedom. This plenum view of the vacuum made it possible for Nambu to accept Heisenberg's concept of degeneracy of the vacuum, which lay at the heart of SSB. Second, Nambu was trying to construct a composite particle model and chose Heisenberg's non-linear model, 'because the mathematical aspect of symmetry breaking could be mostly demonstrated there', although he never liked the theory or took it seriously.
次回は湯川の場合の「悲劇」に関連する論文について述べたい。
文献
T. Y. Cao, Conceptual Developments of 20th Century Field Theories, (Cambridge University Press, Cambridge, 1997; second edition available, 2019)
W. Heisenberg, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen, Z. Physik 33, 879 (1925).
W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. Physik 43, 172 (1927).
と疑問を呈している。ここに「三カ月前」とあるが、パウリがこの国際会議より前に三カ月間の訪米をしていたことからの「三カ月」であろう。しかし、パウリがアメリカへ出発したのは、ハイゼンベルクの自伝 [8] によれば、1957 年のクリスマス前から a week プラス a few weeks あと、つまり 1958 年 1 月下旬頃で、その時から数えれば、国際会議までの期間は五カ月ほどになる。
Although Pauli drafted the first preprint, entitled 'On the Isospin Group in the Theory of the Elementary Particles,' he withdrew from further collaboration in January 1958, after he encountered severe criticism and opposition to the theory from the U.S. physicists at the American Physical society meeting in New York; thus Heisenberg was left to work out the details of the theory with younger collaborators (Dürr et al., 1959). ([9] p. 1120, footnote)
上記の引用末にある "Dürr et al., 1959" という文献は、この記述全体の典拠のようにも見えるが、そうではなく、これはハイゼンベルクが若手共同研究者たちと研究を続けた結果として発表した論文（前回も記した [8]）である。したがって、パウリがアメリカ物理学会の席上でアメリカの物理学者たちから厳しい批判を受けたということの典拠を明記してはないのだが、パウリがハイゼンベルクとの共同研究から手を引く決心をしたのは、渡米早々のことだったようである。
Pauli happened to be passing through New York, and was prevailed upon to give a lecture explaining the new idea [of Heisenberg and Pauli] to an audience that included Niels Bohr, who had been mentor to both Heisenberg and Pauli [...]. Pauli spoke for an hour, and then there was a general discussion during which he was criticized sharply by the younger generation. Finally, Bohr was called on to make a speech summing up the argument. "We are all agreed," he said, "that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough." ([10] pp. 105-106)
When the great innovation appears, it will almost certainly be in a muddled, incomplete, and confusing form. To the discoverer himself it will be only half-understood. To every body else it will be a mystery. For any speculation that does not at first glance look crazy, there is no hope. ([10] p. 106)
なお、パウリがハイゼンベルクとの共同研究から手を引くということは、前者がアメリカ滞在中に後者へ手紙で書き送っていたのである。このことはハイゼンベルクの自伝 [11] に次のように記されている（引用文中 Wolfgang とはパウリを指す）。
Then we were divided by the Atlantic, and Wolfgang's letters came at greater and greater intervals. [...] Then, quite suddenly, he wrote me a somewhat brusque letter in which he informed me of his decision to withdraw from both the work and the publication [of our common project]. ([11] p. 235)
自伝中にこの話が記されているのは、"The Unified Field Theory" と題する章であり、その章は次の文で結ばれている。
Toward the end of 1958 I received the sad news that he [Wolfgang] had died after a sudden operation. I cannot doubt but that the beginning of his illness coincided with those unhappy days in which he lost hope in the speedy completion of our theory of elementary particles. I do not, of course, resume to judge which was the cause and which the effect. ([11] p. 236)
H. P. Dürr, W. Heisenberg, H. Mitter, S. Schlieder, and K. Yamazaki, "Zur Theorie der Elementarteilchen," Z. Naturf. 14a, 441 (1959).
J. Mehra and H. Rechenberg, The Historical Development of Quantum Theory, Volume 6, Part 2 (Springer, New York, 2001).［注：私がこの本をたまたま持っていたのは、かつて大阪科学館で持たれていた「湯川秀樹を研究する会」に参加していて、その会で討論の参考になりそうなことが書いてあると知ったからである。］
F. Dyson, From Eros to Gaia (Penguin, London, 1993; first published by Pantheon, New York, 1992).［注：私がまだ勤務していた頃、この本を当時の同僚だった豊田直樹氏（現・東北大名誉教授）に勧めたようだが、今回は本記事に関わる話題を彼にメールで告げたところ、本文に引用した箇所がこの本にあることを逆に彼から教えられた次第である。］
W. Heisenberg, Physics and Beyond: Encounters and Conversations, translated from German by A. J. Pomerans (Harper & Row, New York, 1972); original German edition, Der Teil und das Ganze: Gespräche im Umkreis der Atomphysik (R. Piper, Munich, 1969); Japanese version, 部分と全体, translated by K. Yamazaki (Misuzu-Shobo, Tokyo, 1974; new edition 1999).
The distribution [of the preprint on work made by Heisenberg and Pauli] was set for February 27, 1958. [...] Three days before the preprint was to be distributed, Heisenberg announced the new formula in a lecture at the University of Göttingen physics institute. ([6] p. 542)
An eager reporter in the audience relayed word of a sensational new "world formula" around the world. One enthused press agent proclaimed, "Professor Heisenberg and his assistant, W. Pauli, have discovered the basic equation of the cosmos! ([6] p. 542)
Two months later, more than 1800 listeners turned out to hear Heisenberg reveal the secret of the cosmos in the same auditorium on the occasion of Max Planck's one-hundredth birthday. During his highly technical talk, Heisenberg carefully wrote his new equation on the overhead projector in the darkened room:
[Heisenberg] had conjectured a 'non-linear spinor equation', whose solutions he thought would correspond to the structure of matter as it was then known. Not only was his equation hard to work with, but in the course of the attempt use was made of the dangerous concept of an infinite metric, something which could result in the appearance of unphysical ghosts. ([4] p. 77)
その本はイギリスの理論物理学者、神学者、英国国教会司祭であるポーキングホーンが、1950 年から 1980 年までの 20 回に及ぶ国際会議を記述することによって綴った、高エネルギー物理学の異色の歴史書である。その本の中でポーキングホーンは、パウリがハイゼンベルクの講演中にその内容を攻撃した言葉を会議録から引用して、亀淵氏のエッセイにあるよりもやや詳しく述べている。また、その記述の前のページには、ハイゼンベルクの講演に対するパウリの発言の一つ "No credits for the future" を添えて、その時のパウリの写真も載っている。そして、その話は、ハイゼンベルクに同情的な感想を含む次の言葉で締めくくられている。
It was a scene at once farcical and sad. Justification lay with the sceptical Pauli but Heisenberg was one of the greatest physicists of the twentieth century who should have been able to enjoy a more dignified close to his career. ([4] p. 77)
W. Heisenberg, "Research on the non-linear spinor theory with indefinite metric in Hilbert space" in 1958 Annual International Conference on High Energy Physics at CERN(CERN, Geneva, 1960) p. 851.
Y. Katayama, "Space-time picture of elementary particles" in Proceedings of the 1967 International Conference on Particles and Fields, Ed. C. R. Hagen, G. Guralnik and V. A. Mathur (Interscience, New York, 1967) p. 157.
J. C. Polkinghorne, Rochester Roundabout: The Story of High Energy Physics, (W. H. Freeman, New York, 1989).
