No Regrets for Unfulfilled Ambitions

This post is the translation of my contribution, originally published in Japanese in the alumni magazine of my alma mater, Kanazawa Kindai Senior High School (presently Kanazawa Commercial High School), Kinsho–Kindai Press, No. 64, pages 26–27 (2024). The English of the translation has been improved with the aid of ChatGPT.

---

The photograph captures a moment from 1998 when I was invited to Kharkiv University in Ukraine. Now, I find myself concerned about the fate of those who warmly welcomed me then, amidst Russia's ongoing military incursion.
Seventy years have elapsed since I finished high school, and I am honored to commemorate this milestone with a written piece. Reflecting on my contributions to this magazine, I recall writing about my travel to a summer academic conference in Southeast Canada in the 20th issue (1980), which celebrated the school's 80th anniversary. Subsequently, in the 47th issue (2007), I penned an article on the newspaper club alumni association titled "Ten Gatherings." Furthermore, my essay "Guash Painting as a Hobby," initially published in a booklet by the Kansai branch, was reprinted in the 63rd issue (2023). From these writings, readers might deduce my involvement in the newspaper club during my school days, my subsequent engagement in research with international conference participation, either in the realm of sciences or humanities, and my leisure pursuit of watercolor painting, but no more.

Allow me to supplement the above information with that of my school years. An excerpt from the Kinsho–Kindai Centennial History (2000) sheds light on my involvement with the student council magazine Shinju:

In the initial issues, a strong literary trend prevailed. However, from the fourth issue, scholarly articles emerged, [including] Tatsuo Tabata's "The Use of 'with' in Alice's Adventures in Wonderland.''

The fourth issue referred to above coincided with my second year at school. The actual title of my contribution was simply "Alice's Adventures in Wonderland," and its content was not an article but a personal essay. The essay appreciated the opening sections of Lewis Carroll's Alice's Adventures in Wonderland, a text I encountered in Principal Akiyama's English class, evoking analytic reflections on Carroll's prose. Consequently, it may have been perceived as a research paper. In the subsequent fifth issue of Shinju, at the behest of my homeroom teacher, Mr. Sakai, who also taught me English, I authored a partial Japanese translation of the English literary work The Private Papers of Henry Ryecroft. Concurrently, inspired by Mr. Kuwayama, who had assigned us Japanese language homework the previous summer, I submitted a piece of fiction titled "A Star Shining in the Summer Sky," which I had written for said homework. Initially hesitant to submit what I deemed an immature work, I eventually acquiesced to Mr. Kuwayama's advice, who assured me, "It will serve as a cherished memento." The primary focus of my classmates' intrigue was identifying the inspiration behind the female protagonist.

This additional information may portray me solely as a humanities enthusiast. However, I pursued scientific endeavors, receiving the Takamine Prize (See "Note added to the reprint edition") and enrolling in the Faculty of Science at Kyoto University. My decision to join Kyoto University was chiefly motivated by my aspiration to study theoretical particle physics under the tutelage of Dr. Hideki Yukawa, Japan's inaugural Nobel laureate, and emulate his groundbreaking achievements. Following my receipt of the Takamine Prize, close friends even jested, "You're destined for the Nobel Prize next!" However, during my final year of university, I opted to specialize in experimental nuclear physics, a decision influenced by various factors. Subsequently, upon completing my master's degree, I joined the Radiation Center of Osaka Prefecture, established by Professor Kiichi Kimura, my mentor in the specialty. I earned my Ph.D. in science through an electron backscattering experiment. In 1990, following the center's amalgamation into Osaka Prefecture University (now Osaka Metropolitan University), my designation transitioned from senior researcher to professor. I retired in 1999, honored with the title of Professor Emeritus. Since then, I have continued my modest research work at my fictitious private institutes, the names of which are given on my website.

Although my ambitions did not materialize precisely as envisioned, I enjoyed a fulfilling research career, contributing a few papers that continue to be cited even after five decades. Consequently, I harbor no regrets regarding my erstwhile aspirations. My enduring reverence for Dr. Yukawa allowed me to delve into his Nobel Prize-winning work alongside fellow physics enthusiasts as an advisor for the "Citizens' Association for Research on Hideki Yukawa," active at the Osaka Science Museum for the centenary of his birth in 2007. Furthermore, I fondly recall delivering a lecture titled "The Influence of the Chinese Classics on Yukawa's Work" at a Kyoto University alumni local gathering in Himeji in 2010. I urge current students of our alma mater and young alumni to have ambitions, for they will foster a meaningful and fulfilling life.

Note added to the reprint version: The Takamine Prize is one of the programs run by the Dr. Takamine Jokichi Memorial Association, which was established in the spring of 1945 to honor the achievements of Dr. Takamine Jokichi, a great scientist and international figure born in Kanazawa, and to promote science education. The first Takamine Prize was awarded in 1951. On those days, 10 students (5 each for the main and secondary prizes) outstanding in science and chemistry were selected from junior and senior high school students in Ishikawa Prefecture, respectively. At the 21st award in 1971, a school prize was established in addition to the individual prize, and high school students were instead excluded from the nominees. (Reference was made to the Kanazawa City website.)

Mystery of the Dream and the Memory

"The Theory of Atomic Spectra" by E. U. Condon & George H. Shortley, taken from the Web site of Amazon (https://www.amazon.com/Theory-Atomic-Spectra-U-Condon/dp/0521092094/)

The memory about the book I hadn't remembered for decades suddenly appeared in my dream the night before last as the names of two co-authors, "Condon–Shortley." Even after waking up, I couldn't remember its title but thought it was probably a book about condensed matter physics. Searching the authors' names on the Internet, I found it to be a masterpiece, "The Theory of Atomic Spectra," published in 1935 [Note 1]. We can divide physics into two subfields: physics on condensed matter and that on particles and nuclei. Physics on atomic spectra belongs to the former. So, my thought was correct.

My university student days were soon after World War II and in a period of confusion, and many pirated editions of masterpieces about various topics in physics appeared in Japan. An upper-year student with a part-time job related to pirated edition publishers would often come to our classroom to advertise those editions. Once, he might have said about the bootleg version of this book, "Condon–Shortley is coming out. It's a classic book on the theory of atomic spectra." During a lecture on atomic spectra, the teacher might have said, "You can learn more about this in Condon–Shortley book." Further, I may have heard one of my classmates say, "I'm not sure if I should buy Condon–Shortley."

I majored in "atomic nuclei" and had no interest in "atomic spectra." So, I have neither wanted to read that book nor remembered it for more than 65 years after graduation. Nonetheless, I recalled the authors' names in a dream. Such is an extremely curious and mysterious phenomenon.

Notes

1. On the publisher's website, it reads: When first published, a reviewer in Nature said that 'Its power and thoroughness leave the general impression of a work of the first rank, which successfully unifies the existing state of our knowledge, and will prove for many years a starting point for further researches and an inspiration to those who may undertake them.'
   (https://www.cambridge.org/jp/academic/subjects/physics/atomic-physics-molecular-physics-and-chemical-physics/theory-atomic-spectra)

On Kamefuchi's Essay about Heisenberg and Yukawa (6)

References [25–28] of this article.

4 Different methods of theoretical physics research

Kamefuchi divides the methods of theoretical physics research into the "ascending type" and the "descending type" to explain why Heisenberg's and Yukawa's later studies were unfinished. In the "ascending type," the researcher "builds up the theory from the basic points." In the "descending type," he or she "sets a hypothetical principle at a high level far beyond the existing theoretical system and descends from there to try to deduce all the laws of physics. Kamefuchi adds, "In the latter method, one has to rely on intuition or analogy. Neither of these has objectivity or inevitability. So, mostly one goes astray." He then infers: Both Heisenberg and Yukawa achieved results by the former method in the first half of their career. However, they turned to the latter type in the second half, failing to complete the research.

Yoichiro Nambu also described a similar classification of research methods [25, 26]. Kamefuchi thinks that the research method can change between the first and the second half for one researcher. On the other hand, Nambu names them by the proper name of famous physicists as if a researcher uses a single method throughout his or her life. However, we should understand each of them to be the one related to the representative, successful research done by the physicist used for the naming. Nambu calls his categories "Yukawa mode" and "Dirac mode" in [25]. As an explanation, I will introduce a concise one in the book by Michio Kaku and Jennifer Thompson [27].

The Yukawa mode is deeply rooted in experimental data. Yukawa was led to his seminal idea of the meson as the carrier of the nuclear force by closely analyzing the data available to him. The Dirac mode, however, is the wild, speculative leap in mathematical logic that led to astonishing discoveries, such as Dirac's theory of antimatter or his theory of the monopole [...]. Einstein's theory of general relativity would fit into the Dirac mode. ([27] p. 85)

Later, Nambu modified this and divided his classification into three types. [26] The explanation for each is as follows.

• Einstein mode (top-down): To create a theory by assuming that "nature should follow this principle." Example: Einstein's theory of gravity (general theory of relativity), made under the assumption that "in general, space may be curved."
• Yukawa mode (bottom-up): To start from the working assumption that "behind the new phenomenon, there is some new field or particle, apart from deep reasons." Examples: Yukawa's meson theory and Pauli's neutrino hypothesis.
• Dirac mode (from heaven): To assume that a mathematically beautiful theory should be true. Examples: Dirac's monopole theory, supersymmetry theory, and string theory, currently being explored.

Einstein's general theory of relativity, which was an example of the Dirac type at the stage of literature [25], was promoted to the independent one. As a result, the Einstein type (top-down) and the Yukawa type (bottom-up) have become equivalent to Kamefuchi's "descending type" and "ascending type," respectively. Nambu states about the examples of Dirac-type as follows. 'The existence of the monopole is now the natural consequence of the quantum field theory, but we still need to confirm it by observation. Studies of supersymmetry and string theories are currently in full swing, so we can say that it is "the heyday of Dirac mode" nowadays.' However, the success or failure of these theories is still unclear, and it is interesting to keep an eye on what a future comes for the high energy physics theory.

By the way, I wonder if Einstein's general theory of relativity is entirely top-down. This is because it is known that there was a thought experiment at the starting point for him to come up with this theory as quoted by Holton ([28], p. 78): "For him, at least in the vicinity, there is no gravitational field during the fall, for example, given an observer who falls freely from the roof." Kamefuchi does not state that Einstein's mode of thinking had been top-down since the time of the general theory of relativity. Instead, he writes that Einstein also turned to the use of the top-down method in the 30 years of his later life for trying unsuccessfully to unify the gravitational and electromagnetic fields.

Here I would like to add the story in Kaku and Thompson's book [27] that Nambu's friends named a type that combines the first two classifications by Nambu "Nambu Mode." They made this naming in commemoration of Nambu's 65th birthday (1985). I quote the related part below.

[...] This mode combines the best features of both modes of thinking and tries carefully to interprete the experimental data by proposing imaginative, brilliant, and even wild mathematics. The superstring theory owes much of its origin to the Nambu mode of thinking.
Perhaps some of Nambu's style can be traced to the clash of Eastern and Western influences represented by his grandfather and father. [...] ([27] p. 85)

Acknowledgement

I heartily thank Naoki Toyota, Professor Emeritus, Tohoku University, for his telling me that there is a story in Ref. [10] that Bohr criticized Pauli's lecture as well as for his other useful suggestions provided by email exchanges on the topic of this article.

References

25. Y. Nambu, "Direction of particle physics," in Proc. Kyoto Int. Symp.: The Jubilee of the Meson Theory, Kyoto, Aug. 15–17, 1985, edited by M. Bando, R. Kawabe, and N. Nakanishi; Prog. Theor. Phys. Suppl. No. 85, 104 (1985).
26. Y. Nambu, One Hundred Years of Elementary Particle Physics (International Institute for Advanced Studies, Kizugawa, Kyoto Prefect., 2000) in Japanese.
27. M. Kaku and J. Thompson, Beyond Einstein: The Cosmic Quest for the Theory of the Universe (Oxford University Press, Oxford, N. Y., 1997; first edition, Bantam, 1987).
28. G. Holton, "What, precisely, is "thinking"? ...Einstein's answer," in Einstein, History, and Other Passions (AIP Press, Woodbury, 1995) p. 74. [See also "On trying to understand scientific genius," in Thematic Origins of Scientific Thought: Kepler to Einstein, Revised edition (Harvard University Press, Cambridge, Mass., 1988) p. 371.]

(End)
Search word: Kamefuchi-2020

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