Saturday, June 26, 2010

The Mystery of Yukawa's "New Insight" (Second Revision)

Hideki Yukawa described the climax of the development of his meson theory in his autobiography Tabibito [1]. However, this description is contradictory to the record of his academic presentation made more than a year before the date of climax. Study on this problem has revealed that two factors were responsible to this contradiction.

Yukawa's passage we treat is the following:
The crucial point came to me one night in October. The nuclear force is effective at extremely small distances, on the order of 0.02 trillionth of a centimeter. That much I knew already. My new insight was the realization that this distance and the mass of the new particle that I was seeking are inversely related to each other. Why had I not noticed that before?
"October" in this quote means that of 1934 according to the paragraph that precedes it. Note that his new insight means the realization of the inverse proportionality of the effective distance of the nuclear force (the force that binds neutrons and protons in the nuclei) to the mass of the new particle that mediates this force. Hereafter, we call this inverse proportionality distance-mass relation.

On the other hand, Yukawa made his first oral presentation at a meeting of the Physico-Mathematical Society of Japan held in Sendai in April, 1933. The title of the presentation was "A consideration about the problem of electrons within nuclei," and its abstract includes the following sentence [2]:
From the fact that the electron has the rest mass, we consider that the strength of the interaction decreases rapidly, as the distance between the neutron and the proton becomes large compared with h/(2πmc).
Here, we find that Yukawa used the distance-mass relation already in 1933. Thus, it is contradictory to call the realization in 1934 of this relation "my new insight".

We guess that the following two factors were responsible to the above contradiction.

1. Hisao Sawano of the Assahi Shimbun Company helped the publication of the Japanese version* of Tabibito by editing Yukawa's manuscript [3]. If Sawano's editing had been to such an extent as to change Yukawa's original version into more dramatic one here and there, then Sawano must have modified the passage about the climax without thinking that his change might contradict Yukawa's academic record.

2. In the work of his 1933 presentation, Yukawa treated the possibility that the electron might be the mediator of the nuclear force. This hypothesis included difficulties related to the spin and statistics of the electron. Therefore, Yukawa abandoned the hypothesis soon later. At the same time, he might also have discarded the distance-mass relation. If so, Yukawa had to rediscover it for completing the paper on the meson theory.

There are two accounts that support factor 1. One of them is Yukawa's passage in Ref. 4. He describes there that he finished writing the last section related to the discovery of the meson theory just a few hours before his trip to Europe. Perhaps, Yukawa regularly checked the changes made by Sawano in order for those not to be contradictory to facts. As for the last section, however, it is quite possible that Yukawa's trip to Europe made such a check impossible.

The other account is in the autobiographical book** [5] of Hideki Yukawa's wife, Sumi. She wrote about the days of their visit to Stockholm for Hideki's receiving Nobel Prize. On arriving at a hotel there, they found that many journalists were waiting to interview Hideki. Sumi's passage about part of the interview is as follows:
One of the questions addressed to him was this: "We hear that the Japanese people study sitting on their legs in a straw-matted room. Did you, Dr. Yukawa, write your paper sitting on your legs or sitting on a chair at the Western-style desk?" Hideki thought a little while and said, "I did in neither of those ways. I put my thoughts together at night in bed." This is true. Hideki wrote the paper that brought him Nobel Prize after he had kept thinking many nights at the age of 27 in the year of Shōwa 9 [Note by the translator: 1934]. This story seems to have wrongly come across to Japan. Thus, in Japan they believe that the idea flashed to him in the middle of a night.

This passage makes us think that the description in Ref. 1 about the sudden coming of the crucial point one night was a modification by Sawano, because it resembles the wrong information conveyed from Sweden to Japan. Further, we can consider that Sumi here denied the modified description indirectly. However, we should note Sumi's possible denial refers, in a strict sense, only to "that the idea flashed to him in the middle of a night." This is not relevant to the essential point of the contradiction, because what is contradictory is the content of the "new insight." This content is highly technical and possibly beyond Sawano's ability of rewriting. Therefore, factor 1 alone cannot be the cause of the contradiction.

With regard to factor 2, we find a strong support for this in Ref. 6, where Kawabe and Konuma write as follows:
In the manuscript of the presentation of April 1933, Yukawa corrected his idea in the abstract to read "the actual calculation does not yield this result." Further, in the draft "Bose electron theory" written almost at the same time as the above manuscript (it had been preserved in the file "Manuscripts of seminars and colloquia, 1934–1935"), he wrote, ". . . the term including the Compton wavelength of the electron appears as a kind of phase factor, . . . and, as a consequence, we cannot say the force decreases rapidly with increasing distance."
The above quote clearly shows that Yukawa once fully discarded the distance-mass relation and that the rediscovery of it was necessary.

The words "My new insight" in the quote from Ref. 1 is not the literal translation of the original words. The literal translation of the relevant passage would be as follows:
One night in early October, a thought flashed through my mind. The nuclear force has only an extremely short effective range. It is on the order of 0.02 trillionth of a centimeter. This has been known since earlier time. What I noticed is that this effective range and the mass of the new particle that accompanies the nuclear force would be inversely proportional to each other. Why did I not notice such a thing until then?
If we omit the last sentence in the above passage,*** the thought that flashed Yukawa's mind does not necessarily mean to be new; it can be the revival or the rediscovery of an earlier thought. Thus, the first and the last sentences in the Yukawa's original manuscript, before Sawano's modification, might have been:
In early October, a thought came to my mind. . . . Why did I not examine this again until then?
Then, the passage is a less dramatic depiction of the development of the meson theory but does not contradict to his earlier use of the distance-mass relation. Hideki Yukawa's own autobiography was translated into English, French and German. Therefore, the wrong version of the story modified by Sawano has become famous world over. This is unfortunate. Sumi Yukawa's account quoted above should be informed widely.

(This article owes much to the discussion we have had at Osaka Science Museum among the members of "Citizens' Study Group on Hideki Yukawa.")


* The Japanese version of Tabibito first appeared as a series of 112 stories in Asahi Shimbun from March to July, 1958.

** The title Kuraku-no-Sono was taken from the street name in Nishinomiya City, where Hideki and Sumi Yukawa lived in the years shortly after their marriage. It has the meaning of "the garden (sono) of joys and sorrows (kuraku)."

*** See also the same passage in the German version [7]: Eines Abends Anfang Oktober hatte ich mit einem Mal die richitige Idee. Die Kernkraft hat eine äußerst kurze Reichweite: nur 2/10-billionstel Zentimeter. Das wußte ich schon vorher. Was ich nun bemerkte, war vielmehr, daß die Reichweite und die Masse der zur Kernkraft gehörenden neuen Teilchen zueinander in umgekehrter Proportion stehen müßen. Warum war ich nicht schon eher darauf gekommen!

  1. H. Yukawa, Tabibito (The Traveler), translated by L. Brown and R. Yoshida (World Scientific, 1982) p. 202.
  2. H. Yukawa, Sūbutu-gakkaisi, Vol. 7, No. 2 (1933) quoted in Nihon-no Buturigaku-shi (History of Physics in Japan) (Tokai University Press, 1978) p. 319 (in Japanese; English translation of the quoted passage by the present author).
  3. H. Yukawa, Atogaki (Afterwords) in Tabibito, (Kadokawa, 1960) (in Japanese).
  4. H. Yukawa, Hon-no Naka-no Sekai (The World in Books) (Iwanami, 1963) p. 182 (in Japanese).
  5. S. Yukawa, Kuraku-no-Sono (Kōdansha, Tokyo, 1976) pp. 349–350 (in Japanese; English translation of the quoted passage by the present author).
  6. M. Kawabe and M. Konuma, Butsuri Vol. 37, p. 265 (1982) (in Japanese).
  7. Hideki Yukawa: Tabibito - Ein Wanderer, Grosse Naturforscher Band 48, ed. Erwin Müller-Hartmann, transl. Claus M. Fischer, p. 175 (Wissenschaftliche Verlagsgesellschaft, Stuttgart, 1985).