On Kamefuchi's Essay about Heisenberg and Yukawa (5)

References [15, 18, 22] of this article.

3 Yukawa's tragedy

3.1 Yukawa's research at that time

Kamefuchi writes, "The lectures progressed, and Yukawa called up K's name for the presentation of his paper co-authored with collaborator K, "Space-time picture of elementary particles." K is Yasuhisa Katayama (1926–1978), familiar to those who know about Yukawa's later studies (as for the bibliographic information of the paper published in the proceedings, see Ref. [3] given in the first part of this article). This research belongs to the work of elementary domain theory that Yukawa worked on with coworkers in his later years. About this work, Yukawa writes in the "Preface" of Ref. [15], "I was able to formulate a theory in 1967 with the great efforts of Mr. Yasuhisa Katayama." Yukawa continued somewhat proudly, "The following year, I was able to publish a paper co-authored with Katayama and a paper with the additional coworker, Umemura." These papers are Refs. [16] and [17].

Three years later, Yukawa wrote Preface and "Part V Unified Theory of Elementary Particles" as the supervisor of Ref. [18]. In them, he frankly writes the reaction of academia to the theory of elementary domains and his own thought as follows:

In Part V, we decided to follow a path towards a unified theory. It will not be the only way, nor is it guaranteed to reach its goal. On the contrary, it is the path that many researchers consider to be the largest deviation from the legitimate one. ([18], Preface, p. vii)

If we proceed in this direction, we may, in the end, have to run into the problem of the quantization of space-time itself in some sense. The concept of the elementary domain itself may still be incomplete in that it assumes the Minkowski space behind it as a four-dimensional continuum. However, all the elucidation remains in the future. ([18] Part V, p. 608–609)

3.2 Impact and evaluation of Yukawa's research at that time

Looking up the number of citations of papers [16] and [17] by Yukawa and his coworkers on Google Scholar, we find the number 46 only for [17]. I have noticed from the number of citations of my own papers that Google Scholar's statistics are inaccurate. For example, if there are similar titles, they are sometimes wrongly regarded as the same paper. Therefore, for [16] and [17], I would like to use, instead of Google Scholar's, the numbers in the journal Progress of Theoretical Physics and at the Crossref site linked to it. Using the sum of the number of citations from these two sources (no duplication of citing papers between the two), it is 39 for [16] and 28 for [17]. Compared to Yukawa's Nobel Prize-winning paper [19], which has more than 2,400 citations (according to Google Scholar), the former numbers are small. However, there might be a possibility that Yukawa's work on the elementary domain will make new contributions to the development of particle theory in the future. I would like to quote an experts' view on this point.

Nicholas Kemmer (1911–1998), who was a Russian-born nuclear physicist working in Britain, described Yukawa's research after the 1940s in reference [20] as follows.

Yukawa devoted the greater part of his subsequent life as a research worker to the quest for a better, deeper fundamental theory. He published over twenty papers spanning a period of twenty years developing various approaches to this goal. Central to his thinking was the belief that the association of any elementary particle with a single geometrical point in space was in some deep sense mistaken; the key concept in many of his publications is the 'non-local field'. [...] We cannot see into the future and say with confidence that all the ideas presented in these papers are lacking in any grains of deeper truth that we do not yet perceive. And we cannot measure the stimulation that readers of his papers on the way to developing ideas of their own may have received. Even so it is a fact that in present day work one would be hard put to find reference to or influence of his later publications.

Kemmer's words are a modest statement that Yukawa's second half research was barren.

Professor Emeritus Laurie Brown, who is an American theoretical physicist and historian on quantum field theory and particle physics, stated in Ref. [21] as follows.

The idea of nonlocal fields (which is to be distinguished from the idea of local fields having nonlocal interaction) gradually became a theory of elementary particles with internal structure. By the late 1960’s it was superseded by Yukawa’s concept of "elementary domain", based upon the quantization of the classical continuously deformable body. These fundamental ideas do not play a major role in current theoretical physics but may well be vindicated in a future physics.

Here, the last words after "but" give Yukawa fans (I am one of them) hopes for the future. However, Brown, similarly to Kemmer, seems to have added these words in honor of Yukawa, who had established meson theory and the method of particle physics at a young age.

Sho Tanaka (1928–2019), a particle physicist and emeritus professor at Kyoto University, introduces Japanese-born researchers' evaluation of Yukawa's postwar research together with his own views [22]. Here, I would like to quote Yoichiro Nambu's words about "Dr. Yukawa's postwar research activities," which seem to be the outspoken and sharpest criticism.

Unfortunately, [Yukawa's postwar research] was not very fruitful. Aside from the relentless efforts he made to understand elementary particles as things with a geometric spread, the content and method seem to have been too naive. With the development of the gauge field theory, the geometrical view has become very important, and there is a possibility that the internal quantum numbers may be reduced to geometry. However, it cannot be said that his idea was a seed of these developments. The influence he had on younger Japanese scholars since the theory of mesons was more indirect. (Quoted from [23]; [22] p. 311)

Tanaka himself points out in Ref. [24] that the D0 brane of string theory is close to the idea of ​​Yukawa's elementary domain. However, this may be one of the developments that Nambu considers as independent of Yukawa's idea.

Next time, I would like to think about different research styles of theoretical physics in connection with Kamefuchi's thought about the common reason why the research of Heisenberg and Yukawa around the time of the "tragedy" ended unfinished.

References

15. H. Yukawa, Hideki Yukawa Self-Selected Works Vo. 2 (Asahi Shimbun, Tokyo, 1971) in Japanese.
16. Y. Katayama and H. Yukawa, "Field theory of elementary domains and particles. I," Prog. Theor. Phys. Suppl., 41, 1 (1968).
17. Y. Katayama, I. Umemura, and H. Yukawa, "Field theory of elementary domains and particles. II," Prog. Theor. Phys. Suppl., 41, 22 (1968).
18. H. Yukawa, supervisor, Iwanami Lectures: Basics of Modern Physics Vol. 11, Elementary Particle Theory (Iwanami, Tokyo, 1974) in Japanese.
19. H. Yukawa, "On the interaction of elementary particles. I," Proc. Phys.–Math. Soc. Japan (3) 17, 48 (1935).
20. N. Kemmer, "Hideki Yukawa. 23 January 1907–8 September 1981," Biographical Memoirs of Fellows of the Royal Society, 29, 661 (1983). JSTOR, https://www.jstor.org/stable/769816. Accessed July 30, 2020.
21. L. M. Brown, "Yukawa, Hideki," in Complete Dictionary of Scientific Biography (Charles Scribner's Sons, New York, 2008); online version of this article available at
    https://www.encyclopedia.com/people/science-and-technology/physics-biographies/hideki-yukawa. Accessed July 31, 2020.
22. S. Tanaka, Hideki Yukawa and Einstein (Iwanami, Tokyo, 2008) in Japanese.
23. Y. Nambu, "Dr. Yukawa and Physics in Japan," Kagaku 52, No. 2 (1982) in Japanese.
24. S. Tanaka, "From Yukawa to M-theory," in Proc. Int. Symposium on Hadron Spectroscopy, Chiral Symmetry and Relativistic Description of Bound Systems, Nihon Daigaku Kaikan, Feb. 24-26, 2003; KEK Proceedings 2003-7, edited by S. Ishida et al. (KEK, Tsukuba, 2003) p. 3; also available as arXiv:hep-th/0306047.

(To be continued)
Search word: Kamefuchi-2020
Search word: Kamefuchi-2020

On Kamefuchi's Essay about Heisenberg and Yukawa (4)

Reference [12] of this article.

2 Heisenberg's tragedy (continued)

2.6 Impact of Heisenberg's research at that time

About the research of Heisenberg and Yukawa at the time of the event mentioned in the essay, Kamefuchi wrote, "Unfortunately, both the studies were unfinished." I'll write later about what he wrote as a common reason for the incompleteness of them. Even though Heisenberg's research at that time was incomplete in itself, the concepts used in it seems to have had a considerable positive effect on other researchers. Concerning this, I would like to quote the description by Professor Cao of Boston University, who specializes in the history of science.

　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)

The word "degenerate vacuum" that appears many times in the above quote is closely related to the SSB (spontaneous symmetry breaking) in the last sentence. The reference cited at the place of the symbol * is the reference [2] in Part 1 of the present article, and the paper cited at ** is the reference [8] in Part 2. The former is the lecture of "Tragedy" published in the proceedings, and the latter is the paper published later in collaboration with young researchers.

By the way, if you look up the number of citations of these papers on Google Scholar, it is 16 for the former and 226 for the latter. Cao uses the words "frequently quoted" for Heisenberg's work at the time. However, the above citation numbers are much smaller than those of Heisenberg's famous papers. Namely, the citation number for the Nobel Prize-winning paper on the formulation of quantum mechanics based on matrices [13] is 1709, and that for the work on the uncertainty principle [14] is 4697. (All the citation numbers are as of July 27, 2020.) The reason for the small citation numbers for the research during the period of "tragedy" seems that it did not succeed as the whole concept.

Speaking of the application of SSB to particle physics, I remember that the reason for receiving the Nobel Prize by Yoichiro Nambu was "discovery of the mechanism of SSB in particle physics." So, I have thought that it was almost Nambu's originality. However, in fact, Heisenberg's research had an impact on Nambu. About this, I make here a bit long quote from Cao's book (numbers representing Nambu's papers cited are omitted).

　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.

Next time, I would like to write about a paper related to "tragedy" in the case of Yukawa.

References

12. T. Y. Cao, Conceptual Developments of 20th Century Field Theories, (Cambridge University Press, Cambridge, 1997; second edition available, 2019).
13. W. Heisenberg, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen, Z. Physik 33, 879 (1925).
14. W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. Physik 43, 172 (1927).

(To be continued)
Last modified Jan 22, 2021.
Search word: Kamefuchi-2020