tag:blogger.com,1999:blog-79799162024-03-08T04:22:23.733+09:00IDEA & ISAAC: Femto-EssaysIDEA and ISAAC are acronyms of private establishments. "Femto" is a combining form used in the names of units of measure that are one quadrillionth (10 to minus 15) the size of the unit denoted by the base word. Thus, the word femto-essays is used here for the name of very short essays.
(Links to book titles and the Amazon shop are made as an Amazon Associate, and I earn from qualifying purchases.) <br>Copyright © 1999-2023 by Tatsuo TabataTatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.comBlogger156125tag:blogger.com,1999:blog-7979916.post-35513168554632583552023-01-11T20:24:00.001+09:002023-01-11T20:24:53.131+09:00Mystery of the Dream and the Memory<center><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI2ktWt_TKbMZzvzrK69IEjFTxniW36fv5K-4VCN4tYE-WebCBszmCuSG-2qSnpttyFuDUS_UqlG5h9iDdy2DF8yqaJVdUVQTaHWdcT3YB563W0Rku7BMi7nM8QoV94eY6qEAspi2Lx8U6Xm66AMTfpWC9kql_zc2oyRQ374rmH_ruCIVAOA/s972/Condon-Shortley.jpeg" style="display: block; padding: 1em 0; text-align: center; "><img alt="" border="0" height="400" data-original-height="972" data-original-width="668" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI2ktWt_TKbMZzvzrK69IEjFTxniW36fv5K-4VCN4tYE-WebCBszmCuSG-2qSnpttyFuDUS_UqlG5h9iDdy2DF8yqaJVdUVQTaHWdcT3YB563W0Rku7BMi7nM8QoV94eY6qEAspi2Lx8U6Xm66AMTfpWC9kql_zc2oyRQ374rmH_ruCIVAOA/s400/Condon-Shortley.jpeg"/></a><font color="maroon" size="-1">"The Theory of Atomic Spectra" by E. U. Condon & George H. Shortley, taken from the Web site of Amazon (<a href="https://www.amazon.com/Theory-Atomic-Spectra-U-Condon/dp/0521092094/" target="_blank">https://www.amazon.com/Theory-Atomic-Spectra-U-Condon/dp/0521092094/</a>)</font></center><br><div align="justify"><font size=+2 color="teal">T</font>he 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 <font size="-1">[Note 1]</font>. 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.<br><br>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."<br><br>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.<br><br><font size="-1"><b>Notes</b><br>
<ol><li>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.'<br>(<a href="https://www.cambridge.org/jp/academic/subjects/physics/atomic-physics-molecular-physics-and-chemical-physics/theory-atomic-spectra" target="_blank">https://www.cambridge.org/jp/academic/subjects/physics/atomic-physics-molecular-physics-and-chemical-physics/theory-atomic-spectra</a>)</li></ol></font></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-39230786127116093022020-12-06T19:48:00.006+09:002023-01-11T20:26:08.610+09:00On Kamefuchi's Essay about Heisenberg and Yukawa (6)<center><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz792qHkQlTJRBKcC8Cq7P2aTseWjxpBGDr-3sTS6s8Tf0xZrDhajgeFtvoUfTlrxqI82uy33Nt15L7JstvUUTx-DutceojL-5gt8ydwGmQ_JWOPfrraWJvUIwry9BC4CprA4cFA/s800/DSCN1110.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz792qHkQlTJRBKcC8Cq7P2aTseWjxpBGDr-3sTS6s8Tf0xZrDhajgeFtvoUfTlrxqI82uy33Nt15L7JstvUUTx-DutceojL-5gt8ydwGmQ_JWOPfrraWJvUIwry9BC4CprA4cFA/s640/DSCN1110.jpg" width="400" /></a></div><font color="maroon" size="-1">References [25–28] of this article.</font></center><br><div align="justify"><font size="+0"><font size="+1" color="teal">4 Different methods of theoretical physics research</font><br><br>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.<br><br>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].<blockquote>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)</blockquote><br>Later, Nambu modified this and divided his classification into three types. [26] The explanation for each is as follows.<ul><li>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."</li><li>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.</li><li>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.</li></ul>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.<br><br>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.<br><br>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.<blockquote>[...] 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.<br>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)</blockquote><br><b>Acknowledgement</b><font size="-1"><br><br>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.</font><br><br><b>References</b><font size="-1"><ol start="25"><li>Y. Nambu, "Direction of particle physics," in <i>Proc. Kyoto Int. Symp.: The Jubilee of the Meson Theory, Kyoto, Aug. 15–17, 1985</i>, edited by M. Bando, R. Kawabe, and N. Nakanishi; Prog. Theor. Phys. Suppl. No. 85, 104 (1985).</li><li>Y. Nambu, <i>One Hundred Years of Elementary Particle Physics</i> (International Institute for Advanced Studies, Kizugawa, Kyoto Prefect., 2000) in Japanese.</li><li>M. Kaku and J. Thompson, <i>Beyond Einstein: The Cosmic Quest for the Theory of the Universe</i> (Oxford University Press, Oxford, N. Y., 1997; first edition, Bantam, 1987).</li><li>G. Holton, "What, precisely, is "thinking"? ...Einstein's answer," in <i>Einstein, History, and Other Passions</i> (AIP Press, Woodbury, 1995) p. 74. [See also "On trying to understand scientific genius," in <i>Thematic Origins of Scientific Thought: Kepler to Einstein, Revised edition</i> (Harvard University Press, Cambridge, Mass., 1988) p. 371.]</li></ol></font></font></div><div align="right"><font size="+0">(End)</font><br><font size="-1">Search word: Kamefuchi-2020</font></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-92090879300500184142020-10-22T17:21:00.006+09:002021-03-26T10:50:40.239+09:00On Kamefuchi's Essay about Heisenberg and Yukawa (5)<center><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKo4DVLM4W-3vVJo9ttdlP5005USJ3cg7u_AIWFEVlckK2naegQZLnoo69lRJlNkTsjnBBisH_2EdLmurVEOfbO2e0_STpfFoDpyiiTzUxwqjGhm07Uor4t0a9SWQmRGqfVJwpZQ/s800/DSCN1085.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="800" data-original-width="600" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKo4DVLM4W-3vVJo9ttdlP5005USJ3cg7u_AIWFEVlckK2naegQZLnoo69lRJlNkTsjnBBisH_2EdLmurVEOfbO2e0_STpfFoDpyiiTzUxwqjGhm07Uor4t0a9SWQmRGqfVJwpZQ/s640/DSCN1085.jpg" /></a></div><font color="maroon" size="-1">References [15, 18, 22] of this article</i>.</font></center><br><div align="justify"><font size="+0"><font size="+1" color="teal">3 Yukawa's tragedy</font><br><br><font color="teal">3.1 Yukawa's research at that time</font><br><br>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].<br><br>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:<blockquote>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)</blockquote><blockquote>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)</blockquote><br><font color="teal">3.2 Impact and evaluation of Yukawa's research at that time</font><br><br>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 <i>Progress of Theoretical Physics</i> 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.<br><br>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.<blockquote>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.</blockquote>Kemmer's words are a modest statement that Yukawa's second half research was barren.<br><br>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.<blockquote>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.</blockquote>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.<br><br>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.<blockquote>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)</blockquote>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.<br><br>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.<br><br><b>References</b><font size="-1"><ol start="15"><li>H. Yukawa, <i>Hideki Yukawa Self-Selected Works Vo. 2</i> (Asahi Shimbun, Tokyo, 1971) in Japanese.</li><li>Y. Katayama and H. Yukawa, "Field theory of elementary domains and particles. I," Prog. Theor. Phys. Suppl., <b>41</b>, 1 (1968).</li><li>Y. Katayama, I. Umemura, and H. Yukawa, "Field theory of elementary domains and particles. II," Prog. Theor. Phys. Suppl., <b> 41</b>, 22 (1968).</li><li>H. Yukawa, supervisor, <i>Iwanami Lectures: Basics of Modern Physics Vol. 11, Elementary Particle Theory</i> (Iwanami, Tokyo, 1974) in Japanese.</li><li>H. Yukawa, "On the interaction of elementary particles. I," Proc. Phys.–Math. Soc. Japan (3) <b>17</b>, 48 (1935).</li><li>N. Kemmer, "Hideki Yukawa. 23 January 1907–8 September 1981," Biographical Memoirs of Fellows of the Royal Society, <b>29</b>, 661 (1983). JSTOR, <a href="https://www.jstor.org/stable/769816" target="_blank">https://www.jstor.org/stable/769816</a>. Accessed July 30, 2020.</li><li>L. M. Brown, "Yukawa, Hideki," in <i>Complete Dictionary of Scientific Biography</i> (Charles Scribner's Sons, New York, 2008); online version of this article available at<br><a href="https://www.encyclopedia.com/people/science-and-technology/physics-biographies/hideki-yukawa" target="_blank">https://www.encyclopedia.com/people/science-and-technology/physics-biographies/hideki-yukawa</a>. Accessed July 31, 2020.</li><li>S. Tanaka, <i>Hideki Yukawa and Einstein</i> (Iwanami, Tokyo, 2008) in Japanese.</li><li>Y. Nambu, "Dr. Yukawa and Physics in Japan," Kagaku <b>52</b>, No. 2 (1982) in Japanese.</li><li>S. Tanaka, "From Yukawa to M-theory," in <i>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</i>, edited by S. Ishida et al. (KEK, Tsukuba, 2003) p. 3; also available as arXiv:hep-th/0306047.</li></ol></font></font></div><div align="right"><font size="+0">(To be continued)</font><br><font size="-1">Search word: Kamefuchi-2020</font><br><font size="-1">Search word: Kamefuchi-2020</font></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-6880539259772157692020-10-09T13:48:00.010+09:002021-03-26T10:49:24.685+09:00On Kamefuchi's Essay about Heisenberg and Yukawa (4)<center><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2FEJLpjSIzNq8FGT9bNAMDA-LBUm6w9MPqct6gghCCM6nAfyY5P8Mr0gaxzFLfEDpxAWcRmtySkzHhr9S0evhrakMT6W1jGri3qIlHqWLhvKcZawjZXbsE6ilTNcQELeC-3zAOw/s800/DSCN1078.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="800" data-original-width="600" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2FEJLpjSIzNq8FGT9bNAMDA-LBUm6w9MPqct6gghCCM6nAfyY5P8Mr0gaxzFLfEDpxAWcRmtySkzHhr9S0evhrakMT6W1jGri3qIlHqWLhvKcZawjZXbsE6ilTNcQELeC-3zAOw/s320/DSCN1078.jpg" /></a></div><font color="maroon" size="-1">Reference [12] of this article</i>.</font></center><br><div align="justify"><font size="+0"><font size="+1" color="teal">2 Heisenberg's tragedy (continued)</font><br><br><font color="teal">2.6 Impact of Heisenberg's research at that time</font><br><br>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.<blockquote> 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).*<br> 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. [...]<br> 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)</blockquote>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.<br><br>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.<br><br>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).<blockquote> 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). [...]<br> [...]<br> [...]<br> 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.</blockquote><br>Next time, I would like to write about a paper related to "tragedy" in the case of Yukawa.<br><br><b>References</b><font size="-1"><ol start="12"><li>T. Y. Cao, <i>Conceptual Developments of 20th Century Field Theories</i>, (Cambridge University Press, Cambridge, 1997; second edition available, 2019).</li><li>W. Heisenberg, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen, Z. Physik <b>33</b>, 879 (1925).</li><li>W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. Physik <b>43</b>, 172 (1927).</li></ol></font></font></div><div align="right"><font size="+0">(To be continued)<br>Last modified Jan 22, 2021.</font><br><font size="-1">Search word: Kamefuchi-2020</font></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-82938490309678839092020-09-17T16:26:00.011+09:002021-03-26T10:49:03.219+09:00On Kamefuchi's Essay about Heisenberg and Yukawa (3)<center><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh03SKZnzNyRqYs6U6WE-2NEOM5XcciKJhXUzem0m8b9kEy71cU7FB7DhdvXVUPaS_Lyh8qxHy6D-cUCodgh5ywMDX7aWTtiIos5MNyInMeXc457Ft6jKe1Q_gMYRfyNOpPTJJV/s800/DSCN1367.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" width="400" data-original-height="600" data-original-width="800" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh03SKZnzNyRqYs6U6WE-2NEOM5XcciKJhXUzem0m8b9kEy71cU7FB7DhdvXVUPaS_Lyh8qxHy6D-cUCodgh5ywMDX7aWTtiIos5MNyInMeXc457Ft6jKe1Q_gMYRfyNOpPTJJV/s400/DSCN1367.jpg"/></a></div><font color="maroon" size="-1">References [9, 10, 11] of this article</i></font></center><br><div align="justify"><font size="+0"><font size="+1" color="teal">2 Heisenberg's tragedy (continued)</font><br><br><font color="teal">2.5 Reasons for Pauli's Rebellion</font><br><br>Kamefuchi writes, "Pauli was a close friend of Heisenberg's since student days and coworker of this problem until three months ago. Why did he go on such outrage in a place where prominent researchers in particle physics lined up?"<br><br>Here are the words "three months ago." These probably come from the fact that Pauli had been to the United States for three months before this international conference. However, Pauli departed for the United States, according to Heisenberg's autobiography [8], a week plus a few weeks after Christmas 1957, namely around late January 1958. Thus, the duration from this time of departure to the international conference should be about five months.<br><br>Kamefuchi then provides an answer to the above question of his own by quoting the explanation (the part in the quotation marks below) given to him later by Professor K. Broiler (at the University of Bonn) and attaching a little suspicious comment.<blockquote>"In the United States, Pauli perhaps proudly spoke about their research but got strong objections from young American geniuses to come to think that it was a difficult job. Thus, he would have wanted openly to express to the excellent people at the conference that he no longer believed in their own theory." This seems to mean that Pauli sacrificed his friend's honor for his own ...</blockquote>Broiler's explanation is a presumption, but there is a document [9] (this reference is academic, unlike Polkinghorne's book, and the following quote is in a footnote) that assertively states a similar thing as follows.<blockquote>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)</blockquote>The reference "Dürr et al., 1959" at the end of the above quote looks like the source of this entire description but is not such. It is the paper (also mentioned in the previous part of the present series as Ref. [8]) of the result of Heisenberg's continued research with young collaborators. Thus, the quote does not specify the source that Pauli received severe criticism from the U.S. physicists. However, it hints that the time of Pauli's decision to withdraw from the joint research with Heisenberg was early in the period of his visit to the United States."<br><br>By the way, there was an important person who severely criticized Pauli's lecture in the United States besides American physicists. In a collection of essays [10] by Freeman Dyson, an American theoretical physicist and mathematician born in England, we find this description:<blockquote>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)</blockquote>The statement here that Pauli "was criticized sharply by the younger generation" underscores Broiler's presumption as well as the description in Ref. [9]. Moreover, Pauli's teacher, Niels Bohr, criticized Pauli. It is a little difficult to understand that Bohr's words, "Not crazy enough," are a harsh criticism. Dyson adds the following explanation in his next paragraph (I tried to shorten it, only finding that Dyson's text was like a polished jewel and that it was impossible to do so).<blockquote>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)</blockquote>Concerning Pauli's withdrawal from the joint research with Heisenberg, the former wrote to the latter during the former's stay in the United States. This is described in Heisenberg's autobiography [11] as follows (Wolfgang in the quotation refers to Pauli):<blockquote>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)</blockquote>This story is in a chapter "The Unified Field Theory" of the autobiography, concluding by the following sentence:<blockquote>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)</blockquote>If you read the above statement only, you would feel sad. However, as Kamefuchi mentioned referring to the Japanese translation of Heisenberg's autobiography, there was the following facts. "A few weeks after the meeting, both of them were invited guests at a summer school in Varenna on Lake Como, Italy. Pauli was friendly to Heisenberg at that time." Also there, Pauli said to Heisenberg, "I think you are doing right to continue working on these problems. As for me, I have to drop out. ..." These give us a feeling of relief.<br><br>How important was Heisenberg's research at that time in the subsequent progress of theoretical physics? I would like to start the next part with such a story.<br><br><b><font size="-1">References</b><ol start="8"><li>H. P. Dürr, W. Heisenberg, H. Mitter, S. Schlieder, and K. Yamazaki, "Zur Theorie der Elementarteilchen," Z. Naturf. <b>14a</b>, 441 (1959).</li><li>J. Mehra and H. Rechenberg, <i>The Historical Development of Quantum Theory</i>, Volume 6, Part 2 (Springer, New York, 2001). [Note: I happened to have this book because I was attending the "Hideki Yukawa Study Group," once held at the Osaka Science Museum, and thought that it might be useful for discussions there.]</li><li>F. Dyson, <i>From Eros to Gaia</i> (Penguin, London, 1993; first published by Pantheon, New York, 1992). [Note: When I was still working, I recommended this book to my colleague Naoki Toyoda (currently Professor Emeritus of Tohoku University). This time I emailed him about the topics related to the present article. Then, he taught me back the presence in this book of the part quoted in the text.]</li><li>W. Heisenberg, <i>Physics and Beyond: Encounters and Conversations</i>, translated from German by A. J. Pomerans (Harper & Row, New York, 1972); original German edition, <i>Der Teil und das Ganze: Gespräche im Umkreis der Atomphysik</i> (R. Piper, Munich, 1969); Japanese version, <i>Bubun to Zentai</i>, translated by K. Yamazaki (Misuzu-Shobo, Tokyo, 1974; new edition 1999).</li></ol></font></font></div><div align="right"><font size="+0">(To be continued)</font><br><font size="-1">Search word: Kamefuchi-2020</font></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-40195267743567694952020-09-06T16:02:00.012+09:002021-03-26T10:48:35.504+09:00On Kamefuchi's Essay about Heisenberg and Yukawa (2)<center><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGwrrFcJ9MFeoOeVDV0AkUbymMtGXasp1JSi1-6mSkefFQAZbOpyynSM87HJS8Wb0x-SD8E_yB7KmUXLbeXtylpbmRWnfS-J4Mc4pqKWKjv6k2A5GbJ5SL7D9AQUNu053s_JwBBg/s800/DSCN1061.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGwrrFcJ9MFeoOeVDV0AkUbymMtGXasp1JSi1-6mSkefFQAZbOpyynSM87HJS8Wb0x-SD8E_yB7KmUXLbeXtylpbmRWnfS-J4Mc4pqKWKjv6k2A5GbJ5SL7D9AQUNu053s_JwBBg/s400/DSCN1061.jpg" width="400" /></a>
</div><font color="maroon" size="-1">D. C. Cassidy's <i>Uncertainty: The Life and Science of Werner Heisenberg</i>.</font></center><br><div align="justify"><font size="+0"><font size="+1" color="teal">2 Heisenberg's tragedy (continued)</font><br><br><font color="teal">2.3 Heisenberg's research at that time</font><br><br>Kamefuchi calls Heisenberg's research at that time "monistic field theory of elementary particles" and explains it as a big idea to derive all elementary particles starting from a single field (or equation). Then, Kamefuchi stated as follows: "I first learned of this in a newspaper, so he probably made a press conference and announced it. At that time, he might have used the adjective 'universal' for the basic equation, and it was erroneously freported as "the equation of the cosmos" in Japan."<br><br>I also saw the newspaper article about this research of Heisenberg and wrote it down in the diary at that time. It was just before my graduation from university. The diary reads:<blockquote>February 27, 1958<br>I have found the following article in the Asahi Shimbun:<blockquote>[Göttingen (West Germany) 25th UP=Kyodo] At the University of Göttingen on the 25th, Professor Heisenberg, Nobel Prize winner in physics of West Germany, gave a lecture entitled "Advancement of Elementary-Particle Theory." He announced that the research group led by him made research on "unified field theory" and found a basic equation that could explain all laws of physics without exception. The theory was the one that Dr. Einstein also thought about. ...</blockquote><br>March 13, 1958<br>[Here is the clipping of the Asahi Shimbun article entitled "This is the equation of the cosmos." It showed the basic formula of elementary particles found by Heisenberg and his coauthors.]</blockquote>I posted the copy of the diary on a page [5] of my website and destroyed the original diary. So, I do not have the clipping of "This is the equation of the cosmos" but will show the formula copied from another source later. According to the first newspaper article, Heisenberg did not hold a press conference as Kamefuchi supposed, but newspaper reporters listened to his lecture at the University of Göttingen and wrote about it. This is also clear from the following description in the biography of Heisenberg written by Cassidy [6]:<blockquote>The distribution [of the preprint on work made by Heisenberg and Pauli] was set for February 27, 1958. [...]<br><br>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)</blockquote>According to the above description, the day of the lecture was 24th local time, which is different from the date of 25th in the Asahi Shimbun. Is this difference because Asahi Shimbun did not correct the time difference for the news distributed by "UP = Kyodo"?<br><br><font color="teal">2.4 "The equation of the cosmos" was not a mistranslation</font><br><br>The description in Cassidy's book continues as follows:<blockquote>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)</blockquote>This reveals that overseas newspapers also used the term "basic equation of the cosmos," and the expression in the Asahi Shimbun was not a mistranslation.<br><br>The Asahi Shimbun separately reported the equation later than the news of the lecture at Göttingen University. Sentences that follow in Cassidy's book explain this to some extent:<blockquote>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:<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8_ccmHSlkBH3owMoFndIpBkV5nttYYdLQp522H7PV3yMQJDGJ07Ytzqteqe__wtdBmsG98_PzeLhXiHSPRMryO5EcRt55TD_zyqf2BWvuGeFG23Z77DJYCNVxLXW5hN6bdXTCKQ/s400/Heisenberg%2527s+UFT+eq.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="69" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8_ccmHSlkBH3owMoFndIpBkV5nttYYdLQp522H7PV3yMQJDGJ07Ytzqteqe__wtdBmsG98_PzeLhXiHSPRMryO5EcRt55TD_zyqf2BWvuGeFG23Z77DJYCNVxLXW5hN6bdXTCKQ/s280/Heisenberg%2527s+UFT+eq.jpg" width="280" /></a></div> ([6] p. 542)</blockquote>Heisenberg did not reveal the formula in his lecture at the University of Göttingen in February but only its name. He wrote the equation in another occasion mentioned in the above quote. However, the fact that the second lecture was two months later than the first is not consistent with the time when the Asahi Shimbun reported the equation. The second lecture was to celebrate the 100th anniversary of Planck's birth. So, I looked up his birthday and found that it was April 23. [7] This is consistent with the words, "Two months later," in the above quote. However, it is impossible for the Asahi Shimbun dated March 13 to report the lecture contents of April 23. The lecture celebrating 100 years of Planck's birth might have been made about 40 days earlier than his birthday. Despite this, Cassidy might have imagined that the second lecture celebrating Planck's birth should have been around his birthday.<br><br>The basic equation of the cosmos quoted here is the same as that in Cassidy's book but copied from a paper co-authored by Heisenberg and young researchers [7]. I will describe later how I learned of this paper.<br><br>Polkinghorne describes Heisenberg's speech at the conference in a little more specialized style than Kamefuchi as follows:<blockquote>[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)</blockquote>Heisenberg's equation still had problems though he confidently showed it at the University of Göttingen.<br><br>Pauli was a collaborator in Heisenberg's research at that time, as mentioned in the first two quotes from Cassidy's book. Why did he take a rebellious attitude at the international conference? I would like to see this point next.<br><br><font size="-1"><b>References</b><ol start="4"><li>J. C. Polkinghorne, <i>Rochester Roundabout: The Story of High Energy Physics</i>, (W. H. Freeman, New York, 1989) p. 77.</li><li>T. Tabata <a href="http://ideaisaac.web.fc2.com/diaries/diary2e.html" target="_blank">"From Youth Diaries: University Days (5)"</a> (2003), in the Web site <i>IDEA and ISAAC</i>.</li><li>D. C. Cassidy, <i>Uncertainty: The Life and Science of Werner Heisenberg</i> (W. H. Freeman, New York, 1991).</li><li><a href="https://www.nobelprize.org/prizes/physics/1918/planck/biographical/" target="_blank"><i>Max Planck: Biographical</i></a> in <i>The Nobel Prize</i>, the Web site of the Nobel Foundation.</li><li>H. P. Dürr, W. Heisenberg, H. Mitter, S. Schlieder, and K. Yamazaki, "Zur Theorie der Elementarteilchen," Z. Naturf. <b>14a</b>, 441 (1959).</li></ol></font></font></div><div align="right"><font size="+0">(To be continued)</font><br><font size="-1">Search word: Kamefuchi-2020</font></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-73399701944466493692020-08-20T20:20:00.008+09:002021-03-26T10:45:44.311+09:00On Kamefuchi's Essay about Heisenberg and Yukawa (1)<center><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiK9HVllNisPP5f6jGNdM1OQgMUhf3mzicMD0NS7BWBGOLTwyfkZeMrVO8rc2smCx9sTlxRmvYeBuZk5TomySMQjczA9XpkMeAb3thOSDGz0zeGSWeewgakeHOqX9xoLK-MROYpqg/s800/DSCN1026.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiK9HVllNisPP5f6jGNdM1OQgMUhf3mzicMD0NS7BWBGOLTwyfkZeMrVO8rc2smCx9sTlxRmvYeBuZk5TomySMQjczA9XpkMeAb3thOSDGz0zeGSWeewgakeHOqX9xoLK-MROYpqg/s400/DSCN1026.jpg" width="400" /></a></div><font color="maroon" size="-1">Kamefuchi's essay published in the magazine <i>Tosho</i></font></center><br /><div align="justify"><font size="+0"><font color="teal" size="+1">1. Introduction</font><br><br><font size="+2" color="teal">R</font>ecently, I read the essay "The life of heroes" [1] by theoretical physicist and Professor Emeritus of the University of Tsukuba, Susumu Kamefuchi. The heroes mean here two giants in his field, Werner Heisenberg and Hideki Yukawa. What the author writes is "witness testimony" of the heroes' tragedies in their later years.<br><br>Heisenberg's tragedy occurred at the International Conference on High Energy Physics held at CERN in July 1958. The chairperson Pauli began to attack violently against his lecture, denying his study [2] altogether.<br><br>Yukawa's tragic incident happened at the International Conference on Particles and Fields held at the University of Rochester in August 1967. He was chairing a session, and his collaborator K was going to give a talk on the paper [3] co-authored with the former. Then, most of the audience stood up from their seats and left the room.<br><br>The author writes that he was worried about degrading the heroes, but that he recalled it essential to convey the truth.<br><br>In the present article, I describe and discuss some of the things I learned from other sources in connection with Kamefuchi's essay.<br><br><font color="teal" size="+1">2 Heisenberg's tragedy</font><br><br><font color="teal">2.1 Description in Polkinghorne's book</font><br><br>Kamefuchi begins to write the stories saying, "these seem not much talked about." However, I recently read the same story about Heisenberg in a book [4]. The author of the book is a British theoretical physicist, theologian, and Anglican priest, Polkinghorne. He describes twenty international conferences on high energy physics from 1950 to 1980 to make this book a unique history book of this field of research. In the book, Polkinghorne writes in a slightly more detailed manner than in Kamefuchi's essay by citing, from the proceedings, Pauli's words of the attack on Heisenberg's speech. The book also has a photo of Pauli at that time, with the caption including his remark, "No credits for the future," on Heisenberg's speech. The story ends with the following words, which are sympathetic to Heisenberg.<blockquote><font size="-1">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)</font></blockquote>Readers of this article may wonder that the book on the history of physics contains emotional words, so I would like to add some explanations about the character of this book. This is not a textbook with an objective description or a non-emotional scholarly book, but a book for the general public. (The general public here might be limited to those who are mainly interested in science. I read this book as a person who thinks high energy physics as one of his hobbies.) Thus, the descriptions in this book are rather light-hearted and make fun reading materials that convey the atmosphere of the conference and the characteristics of famous scholars. We can also infer the nature of this book from the fact that the title and subtitle include the words "roundabout" and "story," respectively.<br><br><font color="teal">2.2 Chair Pauli's assault</font><br><br>Kamefuchi describes the chair Pauli's behavior as follows [1]: "He stood up, spoke in place of the speaker, behaved increasingly violent, and got so abusive as I have never heard in a physics conference." Some may wonder: Why did no participants protest the chair's behavior? The answer can be imagined from the following. Before the above description, Kamefuchi writes as follows: At the beginning, the chair Pauli, who was well known for his harshness, expressed the following introductory words, "I don't think there are any new ideas, but I'll open the session anyway."<br><br>Polkinghorne writes these Pauli's words in more detail and once again gives his personal opinion:<blockquote><font size="-1">It would be of no use waving your hands in front of him and expressing the hope that it would all work out right in the end. ([4] p. 77)</font></blockquote>At this point, Pauli already brought the entire audience to his knees, and no one could dare to advise him, who was famous for his effective spiciness.<br><br><font size="-1"><b>References</b><ol><li>S. Kamefuchi, <i>Tosho</i> No. 859, pp. 18–22 (2020).</li><li>W. Heisenberg, "Research on the non-linear spinor theory with indefinite metric in Hilbert space" in <i>1958 Annual International Conference on High Energy Physics at CERN</i>, pp. 851–857 (CERN, Geneva, 1960).</li><li>Y. Katayama, "Space-time picture of elementary particles" in <i>Proceedings of the 1967 International Conference on Particles and Fields</i>, Ed. C. R. Hagen, G. Guralnik and V. A. Mathur (Interscience, New York, 1967) p. 157.</li><li>J. C. Polkinghorne, <i>Rochester Roundabout: The Story of High Energy Physics</i>, (W. H. Freeman, New York, 1989) p. 77.</li></ol></font></font></div><div align="right"><font size="+0">(To be continued)</font><br><font size="-1">Serch word: Kamefuchi-2020</font></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-39644899392301353562019-05-23T20:36:00.001+09:002020-12-23T17:29:25.871+09:00My Thought on Goro Shimura<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdCiwv80YZ3DZmjtNKUxDchhBLIdjF1wUWA-HI60hkWyBZKRVz8ffxIfKWfeRXycBpNNR2SB9Y3jeEo_iTk8IKkVq4vMq4Wic_K5pRCLCXeuoCG2gLYRImjLJrRaXZShZ1DmO4/s1600/Shimura%2527s+autobiography.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdCiwv80YZ3DZmjtNKUxDchhBLIdjF1wUWA-HI60hkWyBZKRVz8ffxIfKWfeRXycBpNNR2SB9Y3jeEo_iTk8IKkVq4vMq4Wic_K5pRCLCXeuoCG2gLYRImjLJrRaXZShZ1DmO4/s400/Shimura%2527s+autobiography.jpg" width="281" height="400" data-original-width="562" data-original-height="800" /></a><br />
<font size="-1" color="teal">Shimura's autobiography written in Japanese.</font></div><br />
<font size=+2 color="teal">G</font>oro Shimura, Princeton’s Michael Henry Strater University Professor of Mathematics, Emeritus, died on Friday, May 3, in Princeton, New Jersey, at the age of 89 (Ref. 1). I found a blog (Ref. 2) intended to honor Shimura’s life and legacy and wrote my thought on him there. My contribution (the second entry in Ref. 2) is quoted below.<br />
<br />
<blockquote>It is quite sad to hear about the passing of Professor Shimura, but his legacy will continue forever through his achievements.<br />
A little relationship between Professor Shimura and me is as follows: Haruko Iwasaki, who is one of my classmates in elementary school and was a professor of Japanese language at Princeton University in her thirties, was once invited to Professor Shimura’s home because of their common native country. After moving to the University of California, Haruko got a copy of Professor Shimura’s autobiographical book, “The Map of My Life” (Springer, 2008), from a person who came from an overseas country. This happened because the latter heard that the former had been an acquaintance with Professor Shimura at Princeton University. After that, Haruko became Professor Emerita, came back to Japan, and gave me the book, saying “You’re the only scientific person I know in Japan.” I enjoyed the book very much and wrote a review of it (<a href="https://ideaisaac.blogspot.com/2011/10/mathematicians-unique-autobiography.html" target="_blank">https://ideaisaac.blogspot.com/2011/10/mathematicians-unique-autobiography.html</a>) with the bottom line, “Most books I read in the afternoons this summer and early autumn made me sleepy, but Shimura’s autobiography was a complete exception.”</blockquote><br />
<b>References</b><br />
<ol><li>Liz Fuller-Wright, “Professor Emeritus Goro Shimura 1930–2019,” <a href="https://www.math.princeton.edu/news/professor-emeritus-goro-shimura-1930-2019" target="_blank">https://www.math.princeton.edu/news/professor-emeritus-goro-shimura-1930-2019</a>.</li>
<li>In Memoriam • Princeton University Employees, <a href="https://blogs.princeton.edu/memorial/2019/05/goro-shimura/" target="_blank">https://blogs.princeton.edu/memorial/2019/05/goro-shimura/</a>.</li>
</ol>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-38409387386088199482019-01-14T11:49:00.000+09:002019-01-14T11:49:58.675+09:00A Minuscule Relationship between Leon Lederman and Me<center><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtDjyEBZsIdOgHeUF5AHd-Qu9R5VZ971MQkDH6tyetERaMKCmZQv7x-a_s_Prt9eShMdfH-JU2Ss26JHg1OK0NGDm6-6ZhApTo_uCTx4qPt94TOZn9md-c8spsksOP1iklMjgN/s1600/IMG_20181005_0001.jpg" imageanchor="1" ><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtDjyEBZsIdOgHeUF5AHd-Qu9R5VZ971MQkDH6tyetERaMKCmZQv7x-a_s_Prt9eShMdfH-JU2Ss26JHg1OK0NGDm6-6ZhApTo_uCTx4qPt94TOZn9md-c8spsksOP1iklMjgN/s400/IMG_20181005_0001.jpg" width="294" height="400" data-original-width="1176" data-original-height="1600" /></a></center><font size=+2 color="teal">O</font>n October 5, 2018, I read the following sad news on <a href="https://physicsworld.com/a/nobel-laureate-leon-lederman-dies-aged-96/" target="_blank">a Web page of physicsworld</a>:<blockquote><font size="-1">Leon Lederman, the US particle physicist who shared the 1988 Nobel Prize for Physics with Melvin Schwartz and Jack Steinberger, died on 3 October aged 96.</font></blockquote><br />
I happened to receive a letter type-written by Leon Lederman's secretary and signed by Lederman because I wished in 1979 to visit Fermilab, where he was the director at that time. I submitted his letter along with other overseas travel documents to the administrative department of the Radiation Center of Osaka Prefecture. So, I now have its Xerox copy only (see the photo).Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-4907933224427743282015-11-14T16:30:00.000+09:002015-11-14T16:30:10.816+09:00Accidental Similarity between Abstract Painting and Physical Data<center><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAP3x8HrHgqYi3wBLUNP3T2DPcIE6IX5Al_W2_Fgi0X-De8aW0dx_XbYBOBO7qBAJDmNPMt2-U-53I0OE_FzmaKRP87p7j0F5FleJwItfnVsFO2FeT3sG5-E0JXFqil5vJngk_/s1600/Saiko%2527s+work.jpg" imageanchor="1" ><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAP3x8HrHgqYi3wBLUNP3T2DPcIE6IX5Al_W2_Fgi0X-De8aW0dx_XbYBOBO7qBAJDmNPMt2-U-53I0OE_FzmaKRP87p7j0F5FleJwItfnVsFO2FeT3sG5-E0JXFqil5vJngk_/s400/Saiko%2527s+work.jpg" /></a><br><font size="-1" color="teal">Fig. 1. Saiko Yoshihara's painting on the post card to tell about her solo exhibition.</font></center><br />
<font size=+2 color="teal">A</font> friend of mine, Saiko Yoshihara, is a painter joining Shinsho Fine Art Association. She is going to hold a solo exhibition in Hanamaki, Iwate, from December 3 to 20, 2015. The other day I got a postcard from her. The card was to tell about the exhibition and carried one of her abstract paintings shown in Fig. 1. In this painting she used drip technique as used by Jackson Pollock. The black dots suggest something like remains of disaster (she lives in Soma, Tohoku region, where big earthquake occurred in 2011), but there are also images of a brain and a new life, which are going to overcome the disaster. The light and tender tone of colors in the overall work seems to emanate hopes for the future. Thus, I liked this painting very much.<br />
<br />
One thing in this painting surprised me. It was a series of black dots starting from lower left and going to the upper right. It is quite similar to experimental data plotted in figures of my physics papers. First, I was reminded of a figure in Ref. 1, which showed the range–energy relation of electrons in aluminum and copper in logarithmic scales. I draw the figure (see Note) by cutting the whole region of the vertical and horizontal scales into two and juxtaposing the different regions into one graph by the use of different scales for bottom and top as well as right and left. This made it difficult for laypersons to grasp the whole trend at a glance. Therefore, similarity appeared only in my brain.<br />
<br />
<center><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtEgxDyy7GDTxODVy41_o6m78z36vl66HjGDfHhG24j-bi2Kkh98aiGSHK-9Y-ajpMS01LtrE1yrBj-CinPOK6y1bxpQ8P6ckDFAYXUUCRJB6NrqncLsajmVjAj_fw0DqKxAK2/s1600/%25E9%25A3%259B%25E7%25A8%258B%25E3%2583%25BB%25E3%2582%25A8%25E3%2583%258D%25E3%2583%25AB%25E3%2582%25AD%25E3%2582%2599%25E3%2583%25BC%25E6%259B%25B2%25E7%25B7%259A.png" imageanchor="1" ><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtEgxDyy7GDTxODVy41_o6m78z36vl66HjGDfHhG24j-bi2Kkh98aiGSHK-9Y-ajpMS01LtrE1yrBj-CinPOK6y1bxpQ8P6ckDFAYXUUCRJB6NrqncLsajmVjAj_fw0DqKxAK2/s400/%25E9%25A3%259B%25E7%25A8%258B%25E3%2583%25BB%25E3%2582%25A8%25E3%2583%258D%25E3%2583%25AB%25E3%2582%25AD%25E3%2582%2599%25E3%2583%25BC%25E6%259B%25B2%25E7%25B7%259A.png" /></a><br><font size="-1" color="teal">Fig. 2. Range–energy relation of electrons in aluminum and copper in logarithmic scales.</font></center><br />
To make similarity visible to Saiko and other persons, I have made a new graph by combining two copies of the original figure. In the new graph shown as Fig. 2 above, each of the vertical and horizontal scales extends naturally over the whole region considered. The size of Fig. 2 is made equal to that of Fig. 1. Similarity is now seen between the series of dots in Saiko’s work and the long, two adjacent curves at the middle of the new graph.<br />
<br />
<center><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKW4h2W16r5BiREAq35Vi7Dhfi-ejIcsVZWdcThqyrbpmJZI_ktLQeD27ibQJUO240IeU9SCAbRdFVvhkGXPUo06Zn2p_DL0cHeE3m-57PbT3cQo1VZX86y3qHCqWinMKHma-2/s1600/%25E5%25BE%258C%25E6%2596%25B9%25E6%2595%25A3%25E4%25B9%25B1%25E4%25BF%2582%25E6%2595%25B0.png" imageanchor="1" ><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKW4h2W16r5BiREAq35Vi7Dhfi-ejIcsVZWdcThqyrbpmJZI_ktLQeD27ibQJUO240IeU9SCAbRdFVvhkGXPUo06Zn2p_DL0cHeE3m-57PbT3cQo1VZX86y3qHCqWinMKHma-2/s400/%25E5%25BE%258C%25E6%2596%25B9%25E6%2595%25A3%25E4%25B9%25B1%25E4%25BF%2582%25E6%2595%25B0.png" /></a><br><font size="-1" color="teal">Fig. 3. Backscattering coefficient as a function of atomic number divided by the energy of the incident electrons.</font></center><br />
Saiko’s painting has other series of dots that deviate further from the uppermost one as they go further to right. This trend is also seen in the range–energy relations of electrons for higher atomic numbers, but the deviations are not so large as in the painting. Thinking about this, I was reminded of another figure in the other paper of mine, Ref. 2. This figure, reproduced in Fig. 3 with modification to make the size equal to that of Fig. 1 again, shows the backscattering coefficient as a function of atomic number divided by the energy of the incident electrons. Data for different materials lie on slightly different curves, similarly to Saiko’s plural number of series of dots.<br />
<br />
Why did Saiko, who has never seen the figures in my paper, draw dots arranged like those physical data? The curves represented by Saiko’s dots and experimental data in my papers are of the type called "S-shaped curve" or "logistic curve." Such a curve often appears in natural phenomena. It also represents one of natural paths of the movement of the right hand going from far lower left to far upper right on a large canvas of F100 size (162×130 cm). Considering these, it is not so strange to see such a similarity.<br />
<br />
<b>Note</b><br />
<br />
It was the days when personal computers were not yet available, and I draw the figure by hand on a B4-size sheet of tracing paper.<br />
<br />
<b>Reference</b><br />
<br />
1. T. Tabata, R. Ito and S. Okabe, "Generalized semiempirical equations for the extrapolated range of electrons," Nucl. Instrum. Methods <b>103</b>, 85 (1972) (<a href="http://dx.doi.org/10.1016/0029-554X(72)90463-6" target="_blank">DOI:10.1016/0029-554X(72)90463-6</a>, <a href="https://www.researchgate.net/publication/229237594_Generalized_semiempirical_equations_for_the_extrapolated_range_of_electrons" target="_blank">post-print available</a>). This is the most cited paper in my publications (see <a href="https://scholar.google.com/citations?user=GdJiR-wAAAAJ" target="_blank">here</a>).<br />
2. T. Tabata, "Backscattering of electrons from 3.2 to 14 MeV," Phys. Rev. <b>162</b>, 336 (1967) (<a href="http://dx.doi.org/10.1103/PhysRev.162.336" target="_blank">DOI:10.1103/PhysRev.162.336e</a>, <a href="https://www.researchgate.net/publication/239043092_Backscattering_of_Electrons_from_3.2_to_14_MeV" target="_blank">post-print available</a>). This is my thesis paper.<br />
Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-58771017285715709892015-07-13T11:41:00.000+09:002015-07-29T11:58:49.935+09:00From Fujioka's Fluid Drop Model of Atoms to Einstein–Arakatsu Relationship<div align="justify"><font size=+2 color="teal">I</font> have made a lot of exchanges with Bill Streifer (a researcher and freelance journalist on Intelligence, nuclear work and North Korea) at the Quora site from July 9 to 13, 2015. Most part of our exchanges is reproduced here by Bill's permission.<br />
<br />
<hr size="1" width="35%"><br />
<b>Bill:</b> Was Prof. Yoshio Fujioka's "fluid drop" model of the atom known as ekiteki?<br />
And if so, why?<br />
<br />
<b>Tatsuo:</b> I haven't learned about Yoshio Fujioka's "fluid drop" model of the atom but guess that if he proposed such a model, it should have been called "ekiteki" model. "Ekiteki" is the Japanese word for "fluid drop" (eki=fluid, teki=drop).<br />
<br />
<b>Bill:</b> Prof. Ayao Kuwaki was a Japanese scientist and a friend of Albert Einstein. When did he die, exactly?<br />
<br />
<b>Tatsuo:</b> According to <a href="https://ja.wikipedia.org/wiki/桑木彧雄" target="_blank">the information page of him in "Wikipedia" (Japanese edition)</a>, Ayao Kuwaki was born on September 9, 1878, and died on May 16, 1945.<br />
<br />
<b>Bill:</b> At the end of the war, an American airman met a man who claimed to be a student of Einstein in Germany. When I learned of Kuwaki, I suspected it might have been him. But now I see that's not possible since Kuwaki died in May 1945 and the "meeting" took place in September 1945.<br />
<br />
<b>Tatsuo:</b> Sure, the student should not have been Kuwaki.<br />
<br />
<b>Bill:</b> He might not have been a graduate student of Einstein, but he may have attended Einstein's lectures in Germany. Can you guess who he might have been? [And he lived in northern Korea in 1945!] An Einstein scholar is not willing to guess.<br />
<br />
<b>Tatsuo:</b> I have no idea about that person.<br />
<br />
<b>Bill:</b> If you provide a number of possibilities, I'll check each one. Did Hideki Yukawa study under Einstein?<br />
<br />
<b>Tatsuo:</b> No, Yukawa didn't study under Einstein, but they met each other for the first time in Princeton on the former's return trip from Europe in 1939.<br />
<br />
<b>Bill:</b> Einstein wasn't in Germany very long. I wonder if any Japanese or Korean scientists studied under Einstein when he taught there, or even attended his lectures.<br />
<br />
<b>Tatsuo:</b> The Japanese physicist Jun (Atsushi) Ishiwara seems to have studied under Einstein in Germany (<a href="https://ja.wikipedia.org/wiki/石原純" target="_blank">石原純 - Wikipedia</a>). Ishiwara worked as an interpreter when Einstein visited Japan in 1922.<br />
<br />
<b>Bill:</b> Thanks. Did Einstein have other Japanese students or followers in Germany? Kuwaki appears to be a little too old. I'm looking for a Japanese scientist who lived until 1946 at least.<br />
<br />
<b>Tatsuo:</b> I don't think that Einstein had other Japanese students or followers in Germany.<br />
<br />
<b>Bill:</b> I know of another.<br />
<br />
<b>Tatsuo:</b> You Know? Who is he?<br />
<br />
<b>Bill:</b> Dr. Bunsaku Arakatsu.<br />
<br />
<b>Tatsuo:</b> Oh, Bunsaku Arakatsu was a teacher of my teacher and an experimental physicist. So, I didn't think he had studied under Einstein. <a href="https://ja.wikipedia.org/wiki/荒勝文策" target="_blank">Wikipedia page for him (Japanese edition)</a> writes that he studied in Europe (Berlin, Zurich and Cambridge) for two years from 1926. It must have been a short time during this period that he studied under Einstein. By the way, his look is similar to Einstein's in some photos of him.<br />
<br />
<b>Bill:</b> Can you find any photos of Einstein and Arakatsu together? If you can, please send them to <a href="mailto:photografr7@yahoo.com">photografr7@yahoo.com</a>.<br />
Is your teacher still alive? If so, could you ask him if Arakatsu or Yukawa visited Konan (Hungnam), Korea during the war? By the way, Konan and Hungnam are the same place, Konan is the Japanese pronunciation and Hungnam the Korean pronunciation.<br />
You might also be interested in knowing that my article about an Austrian chemist who worked at Konan for more than two years (1935-1937 & 1940), will appear in a book being published by the University of Vienna Korean Dept. later this summer. The name of my article is <i>A Letter from Korea</i>.<br />
<br />
<b>Tatsuo:</b> I don't have any photo of Arakatsu.<br />
My teacher Kiichi Kimura at Physics Department, Kyoto University died in 1992. I haven't heard of Arakatsu's or Yukawa's visit to Hungnam (Konan), Korea. However, Arakatsu was associated with another Konan. Namely, he was the president of Konan University in Kobe, Japan, after his retirement from Kyoto University. Konan of Korea and Konan of the university in Kobe are different from each other when written in Chinese characters. The former Konan is written as 興南, and the latter, 甲南.<br />
I have not so much interest in the history of science in Korea. However, if you write about some history of physics in Japan, I would like to read it very much.<br />
<br />
<b>Bill:</b> I am familiar with Kimura. I am also aware that Konan, Japan is different than Konan, Korea.<br />
<br />
<b>Tatsuo:</b> May I quote our exchanges made here these days in one of my blog sites written in English? Some friends of mine might be much interested in our exchanges.<br />
<br />
<b>Bill:</b> Yes, that would be fantastic. And if anyone has any questions or comments, they can contact me directly at <a href="mailto:bill.streifer@gmail.com">bill.streifer@gmail.com</a>.<br />
<br />
<b>Tatsuo:</b> Thanks a lot for your permission.<br />
<br />
<b>Bill:</b> Stay in touch.<br />
<br />
—A few days later we had additional exchange as given below.—<br />
<br />
<b>Bill:</b> You can add this: According to page 15 of the book <a href="https://books.google.co.jp/books?id=q2IhoDujFBsC&printsec=frontcover&dq=Uranium+Matters:+Central+European+Uranium+in+International+Politics,+1900–1960&hl=en&sa=X&redir_esc=y#v=onepage&q=Uranium%20Matters%3A%20Central%20European%20Uranium%20in%20International%20Politics%2C%201900–1960&f=false" target="_blank"><i>Uranium Matters: Central European Uranium in International Politics, 1900–1960</i></a> by Zbyněk A. B. Zeman and Rainer Karlsch, the Japanese physicist, Dr. Bunsaku Arakatsu "studied at Berlin University ... under Einstein, becoming a member of Einstein's close circle of friends."<br />
<br />
<b>Bill:</b> I returned to the original document, and I am now convinced that the American airman met a Korean scientist, not a Japanese scientist in Korea in September 1945. But it's still interesting that Arakatsu was a close friend of Einstein, so all of this work wasn't for nothing.<br />
<br />
<b>Tatsuo:</b> I've been on a trip to my hometown since Tuesday and am writing a belated reply. Thanks a lot for your additional information. We surely have gotten a good fruit.<br />
<br />
(Last modified on July 29, 2015)</div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com1tag:blogger.com,1999:blog-7979916.post-80513682351969884872014-08-09T10:14:00.000+09:002015-11-13T17:41:29.446+09:00Obituary: Shigeru Okabe (1923–2013)<center><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhiMKfnYCrZK29AbWSM1m5dCrdWIzxtxh02RfbOptkOgYtLZqK9Ma5p6Hk1mLn97bA0AJ45m1Caz-xbeJ75MpIVo3hLuxd5441pIrzXDVUQ9uK0vh7bSiQJ4M1kY66BEJytdlM/s1600/Okabe+1961.jpg" imageanchor="1" ><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhiMKfnYCrZK29AbWSM1m5dCrdWIzxtxh02RfbOptkOgYtLZqK9Ma5p6Hk1mLn97bA0AJ45m1Caz-xbeJ75MpIVo3hLuxd5441pIrzXDVUQ9uK0vh7bSiQJ4M1kY66BEJytdlM/s320/Okabe+1961.jpg" /></a><br />
<font color="teal">Shigeru Okabe in 1961.</font></center><br />
<div align="justify"><font size=+2 color="teal">S</font>higeru Okabe was born in Kagoshima and studied at the seventh high school of Japan's old education system. Then, he entered the Faculty of Science, Kyoto University. He majored in experimental nuclear physics under Professor Bunsaku Arakatsu at the Department of Physics in a handicapped environment immediately after World War II and graduated from Kyoto University in 1946. In 1949, he became an assistant professor at Tottori University. There Okabe made use of the geographical advantage that Misasa hot spring with high radon content was close there to study natural radioactivity. His study of earthquake prediction by change in the atmospheric radon concentration (Ref. 1) is internationally known as the earliest of similar studies.<br />
<br />
In 1949, he became the Chief of Radiation Source Division, Physics Department, at the Radiation Center of Osaka Prefecture (RCOP), which was just established. There he was engaged in the construction of irradiation rooms and installation and maintenance of an electron linear accelerator with the maximum energy of 18 MeV. He also pushed forward varieties of researches such as monitoring methods of electron beams, the passage of electrons through matter, photo-nuclear reactions and characteristics of solvated electrons by the use of this accelerator. During that time, he obtained Research Grant for Peaceful Use of Nuclear Technology for six years in a row, showing his high capability of planning and advancing researches. In promoting research and maintenance work, he put the right man in the right post and also took care of the division members for getting doctor's degree or an academic position at another institution.<br />
<br />
In 1973, Okabe was promoted to the Head of Physics Department, RCOP. Shortly thereafter, significant changes in the organization of research institutes were made by the Government of Osaka Prefecture to abolish the division system and to adopt the research group system. This made it necessary at RCOP to have the system of working groups in parallel with research groups for the maintenance and operation of facilities and equipment. In such an upheaval, Okabe exhibited his prowess in research management. At the same time, he contributed a lot of review papers to journals in the fields of applied physics and nuclear energy, and also showed much influence on the development of Radiation Division, Japan Society of Applied Physics.<br />
<br />
Okabe retired from the Head of Physics Department, RCOP, in 1981 and became professor at the Faculty of Engineering, Fukui University. While being engaged in education, he returned to the study of natural radioactivity. Making use of geographical advantage again, he studied radon concentrations in snow. He also played an active part in research committees, made outside the university, of exo-electron and radon.<br />
<br />
In 1989, Okabe retired from Fukui University and established Radon Science Laboratory at his home, continuing his study intensively. In 1993, he published a fine art book entitled entitled <i>Collection of Occasional Sketches</i>. It contains about sixty watercolors and drawings made as a hobby from his school days. He was also known as a gourmet and often enjoyed going to good restaurants in Osaka and Kyoto.<br />
<br />
Leaving the great achievements as described above, Okabe passed away on June 30, 2013, at the age of 89.<br />
<br />
<b>Note</b><br />
<br />
The author of this article, Tatsuo Tabata, is much indebted to Dr. Okabe for his kind supervision and enjoyable collaboration in the earlier years of the former's professional career.<br />
<br />
(Minor modifications made November 13, 2015)<br />
<br />
<b>Reference</b><br />
<ol><li>S. Okabe, Time variation of the atmospheric radon-content near the ground surface with relation to some geophysical phenomena. Memoirs of the College of Science, University of Kyoto, Series A, Vol. XXVIII, No. 2, Article 1, pp. 99–115 (1956). (According to Google Scholar, this paper has been cited by 39 articles as of August 9, 2014.)</li>
</ol></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-18152778368377007272013-06-19T17:52:00.000+09:002013-06-20T10:21:03.313+09:00The Couple Talks about the Volume of the Truncated Cone<center><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKLPuMDzn1gYIZfwNqLfaOg5GdB4xDjZgB4m0UEIwdHBKJtIaof0KmpRKPpla1TdJL2AqBn6kq-eI-F-T9N5Z_a7O3l_ehCwA_H1AlvmBoJK9RhVcltC_6q61nGgWSwQxIrG8ooQ/s1600/D130607627.jpg" imageanchor="1" ><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKLPuMDzn1gYIZfwNqLfaOg5GdB4xDjZgB4m0UEIwdHBKJtIaof0KmpRKPpla1TdJL2AqBn6kq-eI-F-T9N5Z_a7O3l_ehCwA_H1AlvmBoJK9RhVcltC_6q61nGgWSwQxIrG8ooQ/s320/D130607627.jpg" /></a></center><div align="justify"><font size=+2 color="teal">O</font>n June 7, my wife and I joined a bus trip to <i>Exhibition of Paintings from State Pushkin Museum</i> and Flower Festival Commemorative Park. We had lunch at a French restaurant, whose building was a nationally designated Important Cultural Property. At the lunch table, a couple younger than my wife and I took the seats in front of us. Let's call them Mr. and Ms. N. A glass containing water from the well of the restaurant and some ice cubes was prepared for each person from the beginning of the lunch course (see the photo above).<br />
<br />
At some stage of the lunch course, Mr. N took the glass and asked Ms. N if she could guess how to calculate the volume of the solid of such a form. She said, "Add a small cone to make it a large cone. Calculate the volume of the large cone and subtract the volume of the small cone from it." Mr. N replied that it would be very cumbersome. Then, he said that the volume can be obtained as the mean of volumes of three cylinders having the same height as the solid. His voice was so low that I was unable to hear the radii of the three solids, but from the movement of his hands, I supposed that he referred to the radii of the top and bottom circles of the truncated cone and a certain mean of the two. He additionally stated that we could obtain the formula by integration of the circular area.<br />
<br />
I had never heard of the formula for the volume of the truncated cone, and thought it wonderful that Mr. N learned it and remembered it for some reason. However, I also wondered why he who spoke of a more complex method of integration said that his wife's simpler method was cumbersome. After returning home, I calculated the volume by Ms. N's method and easily found that the third radius mentioned by Mr. N was the geometric mean of the radii of the top and bottom circles.<br />
<br />
To see the formula and the derivation of it, visit <a href="http://ja.wikipedia.org/wiki/円錐台" target="_blank">here</a>. The explanation is in Japanese, but readers might easily follow equations by looking at a diagram included. The third method mentioned there by the use of <a href="http://en.wikipedia.org/wiki/Pappus%27s_centroid_theorem" target="_blank">Pappus-Guldin theorem</a> (also known as Pappus' centroid theorem; the second theorem is relevant here), however, might be a little difficult to understand, if you have never heard of that theorem.</div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-71147439191559004272013-05-09T16:07:00.000+09:002013-05-09T16:07:04.591+09:00Yukawa's Utushi-e<div align="justify"><font size=+2 color="teal">W</font>hen I read the English translation, by L. Brown and R. Yoshida, of Yukawa's autobiographical book <i>Tabibito</i>, I found many errors and sent a list of corrections to Brown. The list included <i>shadow pictures</i> as the translation of "うつしえ (<i>utsushi-e</i>)." Yukawa mentioned it together with ground-cherries and Kintaro wheat-gluten bars, etc. as things sold at street-stalls at a fair in his childhood. <i>Utsushi-e</i> meant both shadow pictures (写し絵) and transfer pictures (移し絵), but shadow pictures are played rather than sold. So, I thought the correct translation of utsushi-e should be transfer pictures but was not confident about this. In my childhood transfer pictures were surely popular among children. In the days when Yukawa was a child, however, sheets for shadow pictures (the equivalent to slides of the present days) might have been sold, and they might have enjoyed a picture show by passing lamplight through them. (This story was given in Part I, Chapter 1, of my book <a href="http://tttabata.yolasite.com/passage-through-spacetime.php" target="_blank"><i>Passage through Spacetime</i></a>.)<br><br>Recently I read Soseki's autobiographical novel <i>Michikusa</i> and found the following passage:<br><blockquote>Of course, he was able to get whatever toys he wanted. Tools for <i>utsushi-e</i> (写し絵) were also included in it.</blockquote>In Notes section at the end of <i>Michikusa</i>, the following description is given about <i>utsushi-e</i>:<br><blockquote>The thing that reflects pictures drawn on glass onto a screen made of cloth or paper, in the dark; a magic lantern.</blockquote>These indicate that the shadow picture was one of popular toys in Meiji period, to which childhood days of both Soseki and Yukawa belonged. Soseki was born in 1867; Yukawa, in 1907; and I in 1935. As for the year of birth, therefore, Yukawa and I are closer than Soseki and Yukawa. However, there was a big change of cultural environments when electric lights spread through the country [an almost full spread in Tokyo was achieved in 1912 (Ref. 1)]. In my childhood, I saw a projector of 8-mm film in a nearby home already being used instead of a magic lantern. Thus, Soseki and Yukawa had much in common in their childhood, and I have to admit that the translation, "shadow pictures," by Brown and Yoshida was quite right.<br><br><b>Reference</b><ol><li><a href="http://www.fepc.or.jp/enterprise/rekishi/taishou/index.html" target="_blank">Chronology of electricity from Taisho to Showa</a>, A Web page of the Federation of Electric Power Companies of Japan.</li></ol></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-52177556733288569062013-02-19T21:57:00.000+09:002018-11-02T10:31:47.552+09:00Boy of Age 16 Asks Me about Relativity, etc. 21. Does Time Really Exist? What Is Time?<center><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivZogoYUz4kbkJHNqVyjN3V4OyGEnf3YwW27MFnx525uwOQ-68KIPNctTlohjk970yXq71etIBNSBEJUoFnFWlHc9g56rAgNI37GOhQyFYRskvpmAwoqHJhE68JZCMArCy2HPw/s1600/Relativity_of_Simultaneity.jpg" imageanchor="1" ><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivZogoYUz4kbkJHNqVyjN3V4OyGEnf3YwW27MFnx525uwOQ-68KIPNctTlohjk970yXq71etIBNSBEJUoFnFWlHc9g56rAgNI37GOhQyFYRskvpmAwoqHJhE68JZCMArCy2HPw/s320/Relativity_of_Simultaneity.jpg"></a></center><blockquote><center><font size=-1 color="maroon">Relativity of simultaneity: Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and occurs later in the red frame (Ref. 1). The original PNG file of the figure was created by Army1987; Acdx converted it to SVG. (<a href="http://www.gnu.org/copyleft/fdl.html" target="_blank">GFDL</a> or <a href="http://creativecommons.org/licenses/by-sa/3.0" target="_blank">CC-BY-SA-3.0</a>), via <a href="http://commons.wikimedia.org/wiki/File%3ARelativity_of_Simultaneity.svg" target="_blank">Wikimedia Commons</a>.</font></center><br />
<div align="justify"><font size=-1>A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.</font></div></blockquote><div align="justify"><b>Aaron:</b> Do we control in time? Or does it control in us?<br />
<br />
<b>Ted:</b> I do not understand what you exactly mean by the words "control in" in your question. The question sounds like a philosophical one rather than that of physics. But I can say this: Time is one of physical dimensions connected to the Universe or Nature. Therefore, human being can do nothing to affect it. However, "psychological time" (duration of time one feels about a definite length of physical time under different situations) can be controlled by the adjustment of one's mind. Am I talking in the wrong direction than you expected?<br />
<br />
<b>Aaron:</b> Sorry, I want to know if time really exists. In relativity, time also seems to be relative, right? A body that travels at a speed close to that of light can slow time, right? So, what is time?<br />
<br />
<b>Ted:</b> I see, Aaron. Time is one of dimensions of the physical framework of the Universe, "spacetime," and is the measure of durations of events and the intervals between them. It has a definite meaning when we consider the movement of something. If there were nothing moving around in the Universe, time would be meaningless and could be said that it does not exist. However, the real Universe includes a lot of moving things. So, time is a meaningful and useful concept. Duration of events and simultaneity depend on the coordinate system (reference frame) on which it is measured (see the figure above), but this does not deny the reality of time.<br />
<br />
By the way, the slowing-down of the passage of time (time dilation) occurs for the fast-moving body, as you mentioned, but this occurs for the moving system as a whole, i.e., your biological activity and ability also slow down. So, you cannot do much more thing during the high-speed flight in a rocket compared with what you can do on the earth in the same duration of time. You cannot be the master of time but remain to be its slave.<br />
<br />
It would be another problem to ask if time is a fundamental concept. There is a growing movement to create a theory that shows spacetime is emergent, i.e., not fundamental (see for example Ref. 1). In this respect, time is one of things still mysterious.<br />
<br />
<b>References</b><br />
<ol><li><a href="http://en.wikipedia.org/wiki/Time" target="_blank">"Time,"</a> <i>Wikipedia: The Free Encyclopedia</i> (February 19, 2013, at 06:41).</li>
<li>Graeme Stemp-Morlock, <a href="http://www.fqxi.org/community/articles/display/167" target="_blank">Melting Spacetime</a>, Web site <i>FQXi Community</i> (April 30, 2012).</li>
</ol>(Originally written on October 14, 2011)</div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-10084946911033226212013-02-15T10:06:00.000+09:002013-02-15T10:18:03.022+09:00Boy of Age 16 Asks Me about Relativity, etc. 20. Have You Heard about Naruto?<center><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxNWPOADuCB_eolfVLdF0R8Q3T9kE0HOdfAlwtfWTzVl3FNBkj5gKI1zkL8pkImUDyTJtRuxcMUD5fqYyf48zADPGF5t4PhHRd-TGCfcE1CPXrywgU9Kv5bHb4T0cDOIMzl-6V/s1600/NarutoCoverTankobon1.jpg" imageanchor="1" ><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxNWPOADuCB_eolfVLdF0R8Q3T9kE0HOdfAlwtfWTzVl3FNBkj5gKI1zkL8pkImUDyTJtRuxcMUD5fqYyf48zADPGF5t4PhHRd-TGCfcE1CPXrywgU9Kv5bHb4T0cDOIMzl-6V/s320/NarutoCoverTankobon1.jpg" /></a></center><blockquote><center><font size=-1 color="maroon">Cover of the first Japanese Naruto manga volume.</font></center><br />
<div align="justify"><font size=-1>A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.</font></div></blockquote><div align="justify"><b>Aaron:</b> I just wanted to ask you if you have heard about Naruto.<br />
<br />
<b>Ted:</b> What I think of from the word "Naruto" is tidal whirlpools in the Naruto Strait, Japan. However, this is probably not what you mean. Perhaps, you mean this (though it is not related to the physics of relativity): Naruto (ナルト), an ongoing Japanese manga series written and illustrated by Masashi Kishimoto. I don't know about it. So, I quote a passage from a <i>Wikipedia</i> page (Ref.1): "The plot tells the story of Naruto Uzumaki (note by Ted: Uzumaki means tidal whirlpools), an adolescent ninja who constantly searches for recognition and dreams to become the Hokage, the ninja in his village who is acknowledged as the leader and the strongest of all. The series is based on a one-shot comic by Kishimoto that was published in the August 1997 issue of <i>Akamaru Jump</i>."<br />
<br />
<b>Aaron:</b> Yes, it's one of the best Japanese anime series. Ninjas can travel near the speed of light.<br />
<br />
<b>Ted:</b> Oh, Naruto has then a relationship to relativity. Ha-ha!<br />
<br />
<b>Reference</b><br />
<ol><li><a href="http://en.wikipedia.org/wiki/Naruto" target="_blank"><i>Naruto</i></a>, <i>Wikipedia: The Free Encyclopedia</i> (January 24, 2013 at 19:01).</li>
</ol>(Originally written on October 7, 2011)</div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-21985701445582909452013-02-13T10:39:00.000+09:002018-11-02T10:33:38.488+09:00Boy of Age 16 Asks Me about Relativity, etc. 19. Do All the Forces in Nature Travel at the Same Speed as That of Light?<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimU_nBQYUVT9L1_m2aNySKHeeCjXhkxBFy9v18aAS7lAXEpyfN8g2MXdaN4H7xZVNPZpo7KHmo2VPcw8rrkd9lHHyU3gGgsf1cYYSzcBAtcDks14hLxn0Fc1QFzC7PckKmlbHx/s1600/256px-Beta_Negative_Decay.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="256" width="256" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimU_nBQYUVT9L1_m2aNySKHeeCjXhkxBFy9v18aAS7lAXEpyfN8g2MXdaN4H7xZVNPZpo7KHmo2VPcw8rrkd9lHHyU3gGgsf1cYYSzcBAtcDks14hLxn0Fc1QFzC7PckKmlbHx/s400/256px-Beta_Negative_Decay.jpg"></a></div><blockquote><center><font size=-1 color="maroon">The Feynman diagram for the beta-minus decay of a neutron (n) into a proton (p) , due to the weak force, i.e., via an intermediate heavy W<sup><font size=-2>−</font></sup> boson. One of down quarks (d) in the neutron decays into an up quark (u) to make a proton, emitting an electron and an electron anti-neutrino. By Joel Holdsworth (Joelholdsworth) [Public domain], via <a href="http://commons.wikimedia.org/wiki/File%3ABeta_Negative_Decay.svg" target="_blank">Wikimedia Commons</a>.</font></center><br />
<div align="justify"><font size=-1>A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.</font></div></blockquote><div align="justify"><b>Aaron:</b> Do all the forces in nature travel at the same speed as that of light?<br />
<br />
<b>Ted:</b> There are four known fundamental interactions in nature to cause fundamental forces in the universe: gravitational, electromagnetic, strong nuclear, and weak nuclear interactions. Among these interactions, the mediators of three interactions, i.e., the gluon for the strong interaction, the photon for electromagnetic interaction and the graviton for the gravitational interaction, have (or assumed to have) zero mass. Therefore, the forces based on these interactions are transmitted by the speed of light. The remaining one interaction, weak interaction, is mediated by the heavy W and Z bosons and cannot be transmitted by the speed of light. However, the effective range of the weak force is quite short (around 10<sup><font size=-2>−17</font></sup>–10<sup><font size=-2>−16</font></sup>; Ref. 1), so that we can regard that the weak force is transmitted almost instantaneously for it actually to work.<br />
<br />
<b>Reference</b><br />
<ol><li>J. Christman. <a href="http://physnet2.pa.msu.edu/home/modules/pdf_modules/m281.pdf" target="_blank"><i>The Weak Interaction</i></a>, Physnet (Michigan State University, 2001) p. 2.</li>
</ol>(Originally written on October 1, 2011)</div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-86706358894064015782012-12-29T16:41:00.000+09:002018-11-02T10:34:51.566+09:00Boy of Age 16 Asks Me about Relativity, etc.18. Why Is the Speed of Light Constant?<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeKAdXRMveGrQRwXaj6P2R-cxto3P-J-o0jyfqlz5CG6TVz2DItihYLJ2_Eh2NCDp24A4GYqPcdJ-L5YNWjbs3K7lb4DlSVV32USqZ7dczLs_rcMrv-tQRKNuQIHYt_CFJoUR-/s1600/Einstein_by_Doris_Ulmann.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="400" width="299" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeKAdXRMveGrQRwXaj6P2R-cxto3P-J-o0jyfqlz5CG6TVz2DItihYLJ2_Eh2NCDp24A4GYqPcdJ-L5YNWjbs3K7lb4DlSVV32USqZ7dczLs_rcMrv-tQRKNuQIHYt_CFJoUR-/s400/Einstein_by_Doris_Ulmann.jpg"></a></div><blockquote><center><font size=-1 color="maroon">Albert Einstein in 1931 by Doris Ulmann [Public domain], via <a href="http://commons.wikimedia.org/wiki/File%3AAlbert_Einstein%2C_by_Doris_Ulmann.jpg" target="_blank">Wikimedia Commons</a>.</font></center><br />
<div align="justify"><font size=-1>A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.</font></div></blockquote><br />
<div align="justify"><b>Aaron:</b> Why doesn't the speed of light change?<br />
<br />
<b>Ted:</b> It is gratifying that you think so deeply as to want to know the reason for the constancy of the speed of light in vacuum. However, no one knows the reason. It was initially Albert Einstein's assumption in developing the special theory of relativity. Then, many experiments have confirmed the correctness of the theory, and the assumption has been accepted as one of true facts. So, presently there is no reason or cause to which physicists attribute the constancy of the speed of light.<br />
<br />
By the way, I have learned, on Twitter this morning, <a href="http://www.reuters.com/article/2011/09/22/science-light-idUSL5E7KM4CW20110922" target="_blank">the Reuters news</a> that neutrinos were found to break the speed of light by a group of physicists working on an experiment dubbed OPERA, which was run jointly by the CERN particle research center and the Gran Sasso Laboratory in Italy. If this experiment be confirmed to be correct, it will make an immense challenge to theoretical physicists.<br />
<br />
<b>Aaron:</b> The news is extremely serious. The title of the report says, "Finding could overturn laws of physics." But it would not invalidate the theory of relativity, right?<br />
<br />
<b>Ted:</b> Yes, it would do so, to some extent. Namely, if the neutrino experiment were correct, it would require a correction of the theory of relativity. However, many experiments and observations have been consistent with that theory. Further, neutrinos produced by the explosion of the 1987 supernova arrived at the earth not earlier than light from the same source. So, I highly doubt the correctness of the experiment just reported.<br />
<br />
(Originally written on September 23 and 24, 2011, except for "Note" below)<br />
<br />
<b>Note about "faster-than-light neutrino" measurements:</b><br />
<br />
In March 2012, the OPERA team confirmed that the measurements first announced in September 2011 were skewed by a combination of a faulty cable and flawed timing in the experiment’s master clock (Ref. 1). The group repeated its measurement and have reported the final results that are consistent with the special theory of relativity (Ref. 2; see also Ref. 3 for the whole story about the measurement of the neutrino speed).<br />
<br />
I was not surprised at reading the news of possibly wrong measurements because I had once encountered a paper that reported the results of erroneous measurements in the prestigious journal <i>Physical Review</i> (the author's name was Dressel). The results were inconsistent not only with many previous authors' but also with my own that had just been obtained. Thus, I was able timely to publish my results in the same journal, pointing out possible causes of errors in Dressel's measurements. (You can see the abstract of my paper <a href="http://prola.aps.org/abstract/PR/v162/i2/p336_1" target="_blank">here</a>.) Later, Dressel found the real cause of errors by himself. Some or many scientists believe "it is right to release an 'uncomfortable' result for scrutiny and then seek an instrumental or methodological effect that might explain it," as the OPERA spokesman Antonio Ereditato is reported to have said (Ref. 1).<br />
<br />
<b>References</b><br />
<ol><li>E. S. Reich, <a href="http://www.nature.com/news/embattled-neutrino-project-leaders-step-down-1.10371" target="_blank">"Embattled neutrino project leaders step down,"</a> <i>Nature</i> (April 2012).</li>
<li>The OPERA Collaboration, <a href="http://arxiv.org/abs/1212.1276" target="_blank">"Measurement of the neutrino velocity with the OPERA detector in the CNGS beam using the 2012 dedicated data,"</a> arXiv:1212.1276 [hep-ex] (December 2012).</li>
<li><a href="http://en.wikipedia.org/wiki/Faster-than-light_neutrino_anomaly" target="_blank">"Faster-than-light neutrino anomaly,"</a> <i>Wikipedia, The Free Encyclopedia</i> (15 December 2012 at 14:07).</li>
</ol>(Originally written on September 23 and 24, 2011)</div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-45887154360065488232012-12-26T10:25:00.000+09:002013-01-14T16:14:02.593+09:00Boy of Age 16 Asks Me about Relativity, etc.17. What Is Golden Physics?<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNq3Uc0JNo-bwUYz7j8EEWxlkb4slLfZzuzpBilsTCA_ZNR2_WpDPWQ86RSCcRgHGgHGl199ZN_4aDnNJC5sSoP4af9_VUOKGawxQt6WqELBfjsqzBMrWQU5cHcsGtOJx34KAY/s1600/D121226787.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="400" width="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNq3Uc0JNo-bwUYz7j8EEWxlkb4slLfZzuzpBilsTCA_ZNR2_WpDPWQ86RSCcRgHGgHGl199ZN_4aDnNJC5sSoP4af9_VUOKGawxQt6WqELBfjsqzBMrWQU5cHcsGtOJx34KAY/s400/D121226787.jpg" /></a></div><center><font size=-1 color="maroon"><br />
<a href="http://www.amazon.com/exec/obidos/ASIN/0345409469/institutfordat07" target="_blank">Carl Sagan's <i>The Demon-Haunted World</i></a> explains methods to help distinguish between ideas that are considered valid science, and ideas that can be considered pseudoscience. — "<a href="http://en.wikipedia.org/wiki/The_Demon-Haunted_World" target="_blank"><i>The Demon-Haunted World</i></a>," <i>Wikipedia: The Free Encyclopedia</i> (November 12, 2012 at 02:36).</font></center><blockquote><div align="justify"><font size=-1>A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.</font></div></blockquote><br />
<div align="justify"><b>Aaron:</b> I just wanted to ask you about golden physics. What is it?<br />
<br />
<b>Ted:</b> I have never heard of the phrase "golden physics" and would like to confirm if you mean "golden age of physics." If you mean any other thing, please let me know where, or in relation to what, you got the phrase.<br />
<br />
<b>Aaron:</b> Have you heard about the physicist Mohamed El Naschie? It is his theory.<br />
<br />
<b>Ted:</b> I have heard the name Mohamed El Naschie for the first time and made a search on the Internet. The "Mohamed El Naschie" page (Ref. 1) of <i>RationalWiki</i> gives useful information. The essence is given below:<br />
<br />
—Mohamed El Naschie is an Egyptian mathematician, physicist and engineer. He served as editor-in-chief of the journal <i>Chaos, Solitons & Fractals</i>. His research centers on a theory of everything called "E-infinity theory", a "fractal cosmology model" which he developed in 1994. El Naschie characterizes his theory as follows: "This models a harmonic production of quarks and elementary particles through a golden section [Note by Ted: Here "golden" appears] centered Cantorian fractal spacetime." El Naschie's theories are regarded as not even wrong by almost all physicists and mathematicians.—<br />
<br />
The page mentioned has the link to the <i>El Naschie Watch</i> Web site (Ref. 2). This is the blog site that describes critically about this man in detail and includes the words, 'Dr. Mohamed El Naschie is pseudoscientist crackpot who makes grandiose claims about being a "paradigm-shifting" high-energy physicist' (Ref. 3). From the descriptions of his work on Ref. 1, I believe that the words "pseudoscientist crackpot" is quite true and do not recommend you to learn about his physics.<br />
<br />
(See also Ref. 4, which probably appeared after my original reply had been written.)<br />
<br />
<b>References</b><br />
<ol><li>"<a href="http://rationalwiki.org/wiki/Mohamed_El_Naschie" target="_blank">Mohamed El Naschie</a>," <i>RationalWiki</i> (August 21, 2012, at 16:56).</li>
<li><a href="http://elnaschiewatch.blogspot.jp/" target="_blank"><i>El Naschie Watch</a>,</i> Blog site.</li>
<li>"<a href="http://elnaschiewatch.blogspot.jp/2010/05/concise-introduction-to-mohamed-el.html" target="_blank">Introduction to Mohamed El Naschie</a>," <i>El Naschie Watch</i> (May 6, 2010).</li>
<li>"<a href="http://en.wikipedia.org/wiki/Mohamed_El_Naschie" target="_blank">Mohamed El Naschie</a>," <i>Wikipedia: The Free Encyclopedia</i> (December 13, 2012 at 12:58).</li>
</ol>(Originally written on September 16 and 17, 2011)</div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-34627331642813720262012-12-24T10:43:00.000+09:002013-01-14T16:11:51.438+09:00Boy of Age 16 Asks Me about Relativity, etc.16. What Is the Paradox about Time Travel?<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8IDBDBJhpSNEqkouz7S11eq93oghvwF7ZdgaxjHUVCbOA5P9nGUXoM6SFfO7cMCYB2B8-ct090FxWAdb7uBrGjfRtSbuJoCUNlPXVHaHxfeBle6jF4ep6Lk3T2zbcVNp0-Ncl/s1600/A_Christmas_Carol.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="400" width="306" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8IDBDBJhpSNEqkouz7S11eq93oghvwF7ZdgaxjHUVCbOA5P9nGUXoM6SFfO7cMCYB2B8-ct090FxWAdb7uBrGjfRtSbuJoCUNlPXVHaHxfeBle6jF4ep6Lk3T2zbcVNp0-Ncl/s400/A_Christmas_Carol.jpg" /></a></div><center><font size=-1 color="maroon"><br />
Hand colored etching <i>Mr. Fezziwig’s Ball</i> by John Leech from <i>A Christmas Carol</i> by Charles Dickens. [Public domain], via <a href="http://commons.wikimedia.org/wiki/File%3AA_Christmas_Carol_-_Mr._Fezziwig's_Ball.jpg" target="_blank">Wikimedia Commons</a>.<br />
<i>A Christmas Carol</i> is considered to be one of the first depictions of time travel in both directions, as the main character, Ebenezer Scrooge, is transported to Christmases past, present and yet to come.</font></center><br />
<blockquote><div align="justify"><font size=-1>A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.</font></div></blockquote><br />
<div align="justify"><b>Aaron:</b> I think they say that there is a paradox about time travel. What is it?<br />
<br />
<b>Ted:</b> Any theory that would allow time travel would require that problems of causality (the relationship between the cause and effect that the former should come before the latter) be resolved. From this viewpoint, the concept of time travel seems to give contradictions, examples of which are stated as paradoxes. One of the best examples is the grandfather paradox.<br />
<br />
The grandfather paradox is a hypothetical situation in which a time traveler goes back in time and attempts to kill his grandfather at a time before his grandfather met his grandmother. If he did so, then his mother or father never would have been born, and neither would the time traveler himself. In that case, the time traveler never would have gone back in time to kill his grandfather. This is in contradiction to the assumption at the start.<br />
<br />
This paradox has been used to argue that backwards time travel must be impossible. A number of hypotheses have been postulated to avoid the paradox, such as the idea that the past is unchangeable. However, any of those hypotheses has not become an accepted theory because the theoretical possibility of time travel itself is unknown.<br />
<br />
To write the above explanations, I referenced the Wikipedia pages of "Time travel" (Ref. 1) and "Grandfather paradox" (Ref. 2). So, if you want to learn in more details, you can consult those pages.<br />
<br />
<b>Aaron:</b> It's amazing. Now, I have an idea about how to go backwards in time. Time is like a line and flows in one direction, like a river, and we can go in both directions, in a river. This means that we can also control ourselves in time. If we can go back in time, we can kill Hitler and make the future without stupid World War II. But, I have to find how this is possible in a theoretical way. What do you think? Is it funny?<br />
<br />
<b>Ted:</b> Your idea is appealing. However, it does not seem to be a physical idea about how to go backwards in time, but I'm afraid that it is an idea about what you would like to do if you could go backwards in time. Further, only killing Adolf Hitler would not prevent the World War II totally. You may need to kill also Benito Mussolini in Italy and Hirohito in Japan and to change all the factors related to nationalism or imperialism and international tensions of those days.<br />
<br />
[Next day, Ted again wrote to Aaron, writing as follows:]<br />
<br />
However, your idea also included a good point. If you go backwards in time not to kill your grandfather but to kill Hitler, you can escape the paradox of your not being born. Thus, your idea is a good step toward the solution of the paradox.<br />
<br />
I compared your idea with Novikov self-consistency principle. This principle was proposed by a Russian (and former Soviet) theoretical astrophysicist and cosmologist, Igor Dmitriyevich Novikov, in the mid-1980s and have been regarded as an important contribution to the theory of time travel (Ref. 3). I have just learned it from Wikipedia.<br />
<br />
According to this hypothetical principle, the only possible time lines are those entirely self-consistent. So, anything a time traveler does in the past must have been "part of history all along." Your idea is partly similar to this principle, in the successful removal of the inconsistency about the time traveler's birth, though killing Hitler is inconsistent with the real history. You can have confidence in your ability of thinking about physics.<br />
<br />
<b>References</b><br />
<ol><li><a href="http://en.wikipedia.org/wiki/Time_travel" target="_blank">Time travel</a>, <i>Wikipedia, The Free Encyclopedia</i> (December14, 2012 at 23:29).</li>
<li><a href="http://en.wikipedia.org/wiki/Grandfather_paradox" target="_blank">Grandfather paradox</a>, <i>Wikipedia, The Free Encyclopedia</i> (December17, 2012 at 08:09).</li>
<li><a href="Novikov self-consistency principle" target="_blank">Novikov self-consistency principle</a>, <i>Wikipedia, The Free Encyclopedia</i> (November 26, 2012 at 03:04).</li>
</ol>(Originally written from July 29 to 31, 2011)</div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-85148836705182776412012-12-15T20:41:00.000+09:002012-12-15T20:57:22.007+09:00Boy of Age 16 Asks Me about Relativity, etc.15. What is String Theory?<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVd0JgzeoMHelPDA-lt4zDymCc1uw29quNHLpQesuEEUToQCZPWJMeOCkaNTxChtRdKCwX5J_vPORIElSsvokQVkzMAGeqZVDWp4BipcEU1fonuqhVGygW0ZH1BB8Ysn_CcJxb/s1600/string+theory.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="400" width="191" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVd0JgzeoMHelPDA-lt4zDymCc1uw29quNHLpQesuEEUToQCZPWJMeOCkaNTxChtRdKCwX5J_vPORIElSsvokQVkzMAGeqZVDWp4BipcEU1fonuqhVGygW0ZH1BB8Ysn_CcJxb/s400/string+theory.jpg" /></a></div><div align="justify"><blockquote><center><font size=-2 color="maroon">Different levels of magnification of matter, ending with the string level: 1. Macroscopic level – Matter. 2. Molecular level. 3. Atomic level – Protons, neutrons, and electrons. 4. Subatomic level – Electron. 5. Subatomic level – Quarks. 6. String level. [By MissMJ (<a href="http://creativecommons.org/licenses/by/3.0" target="_blank">CC-BY-3.0</a>), via Wikimedia Commons.]<br />
<br />
</font></center></blockquote><blockquote><font size=-2>A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.</font></blockquote><br />
<b>Aaron:</b> What is string theory? I have read a little about it. It seems to be the theory of everything that Einstein was working on. Dr. Michio Kaku is probably working on how to find it. However, there are many equations in this theory. How can I understand it?<br />
<br />
<b>Ted:</b> "What is string theory?" is a difficult question for me. In my student days, this theory was not yet born. So, some years ago I wanted to learn a little bit of it and bought a graduate level text book on this theory written by the physicist you just mentioned, i.e., Michio Kaku. However, it was pretty difficult for me to learn it by myself, and I have not read the book yet.<br />
<br />
The essential idea of string theory is that all of the different "fundamental" particles are different manifestations of one basic object, a string (see the figure above). I hear that the equations of this theory gives a lot of solutions, and presently it is difficult to determine which of those solutions reflect the laws of physics in the real world. In this situation, there is the supposition that there may be many worlds, in each of which one of many solutions is applicable. (However, it is a vexing problem how we can verify the applicability of solutions in other worlds). A number of gifted physicists are studying this theory, but some famous physicists do not think that this is the right direction to advance the study of theoretical physics. Further, it is said that we humans don't yet have enough mathematical methods fully to explore this theory.<br />
<br />
String theory is such a complex and difficult thing. You had better learn it after enough mastering of quantum mechanics and relativity. Taking such a step is indispensable also considering the fact that string theory aims at the unification of quantum mechanics and general relativity. However, there are a number of Web pages explaining string theory for non-scientists. See, for example, Ref. 1 and links given in it.<br />
<br />
<b>Reference</b><br />
<ol><li>Alberto Güijosa, <a href="http://www.nucleares.unam.mx/~alberto/physics/string.html" target="_blank">What is String Theory?</a></li>
</ol>(Originally written on July 18, 2011)</div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-74826187011164856762012-12-10T16:20:00.000+09:002012-12-10T16:20:11.754+09:00Leo Tolstoy and Mathematics<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgo4cQ2nbESmqkoIu-yPd2cFnEJq2846cDV-Svk3aBIByNnQRDxKYv0APbydluwCnozRsRzU4tFZ6AMg3qZLQ9YkjW5tLaX3trw_9JDjRrEmDOI1CbatbtylBzKAaBSxTU864o5/s1600/Lew_Tolstoi.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="400" width="288" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgo4cQ2nbESmqkoIu-yPd2cFnEJq2846cDV-Svk3aBIByNnQRDxKYv0APbydluwCnozRsRzU4tFZ6AMg3qZLQ9YkjW5tLaX3trw_9JDjRrEmDOI1CbatbtylBzKAaBSxTU864o5/s400/Lew_Tolstoi.jpg" /></a></div><center><font color="maroon" size=-1>Leo Tolstoy. By Scan by User: Gabor [Public domain], via Wikimedia Commons.</font></center><br><div align="justify"><font size=+2 color="teal">T</font>hese days I am reading Leo Tolstoy's autobiographical novels <i>Childhood</i>, <i>Boyhood</i> and <i>Youth</i> by Japanese translations in <i>Shinchō World Literature</i> Volume 16 (1972). In the first half of <i>Youth</i>, there is an episode that the hero, "I", passes the entrance examination to the mathematics department of a university.<br><br>The examination is made in the following manner: Each applicant takes a piece from the problem cards held by a professor and answers to the problem chosen, in front of the professor. In the mathematics examination, there were two professors. The hero was called at the same time as another applicant, and they secretly exchanged the cards they chose. The card the hero initially took was of the problem about "combinatorics," which he thought difficult. However, the question he got by exchanging the cards was about "Newton's binomial theorem," which he had tried to solve just before the examination. Thus, the hero was able to answer it perfectly.<br><br>Reading this, you may wonder if Tolstoy studied in the mathematics department. In fact, Tolstoy began studying law and oriental languages at Kazan University and left university in the middle of his studies (Ref. 1). Therefore, the story of the entrance to the mathematics department is fictional.<br><br>I learned "combinatorics" and "the binomial theorem" in senior high school. However, the latter was not Newton's but the basic one. The basic "binomial theorem" describes a formula for the algebraic expansion of <i>n</i>th power of a binomial <i>x</i> + <i>y</i>, where <i>n</i> is a positive integer. Isaac Newton generalized the formula to allow real exponents, and the formula can be generalized further, to complex exponents (Ref. 2).<br><br>It was probably at university that I learned about generalized binomial theorem. Therefore, Newton's binomial theorem seems to be too difficult for the entrance examination of university. It is also strange that the hero thought Newton's binomial theorem easier than combinatorics. This is because we learn combinatorics as preparation for studying the basic binomial theorem. Thus, I guess that problems of mathematics were also invented by Tolstoy on the basis of his superficial knowledge of these terms of mathematics. What do you think?<br><br><b>References</b><ol><li><a href="http://en.wikipedia.org/wiki/Leo_Tolstoy" target="_blank">"Leo Tolstoy,"</a> <i>Wikipedia: The Free Encyclopedia</i> (December 8, 2012 at 19:10).</li><li><a href="http://en.wikipedia.org/wiki/Binomial_theorem" target="_blank">"Binomial theorem,"</a> <i>Wikipedia: The Free Encyclopedia</i> (November 25, 2012 at 04:39).</li></ol></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com2tag:blogger.com,1999:blog-7979916.post-65619861934843386542012-12-06T09:15:00.000+09:002012-12-06T09:15:49.579+09:00Classifications of Theoretical Physicists, Especially of Yukawa and Tomonaga<div align="justify"><font size=+2 color="teal">T</font>he theoretical physicist Susumu Kamefuchi published an essay entitled "Gramsci's words, Yukawa, Tomonaga, and Sakata" [1]. At the beginning of the essay, Kamefuchi quotes the following words:<blockquote>Passage from knowing to understanding and to feeling and vice versa from feeling to understanding and to knowing —Antonio Gramsci, "Prison Notebooks" [2]</blockquote><br>Kamefuchi likens the three elements in the above quotes, i.e., feeling, understanding and knowing to three stages of research in theoretical physics, i.e., (I) practitioner's stage, (II) theorist's stage and (III) natural philosopher's stage. Then, he thinks about the question in which stage each of Hideki Yukawa, Sin-Itiro Tomonaga, and Shoichi Sakata was good at working or liked to work, in order to classify them into corresponding three types, I, II and III, of physicists.<br><br>Sakata was called a person of methods and his successful studies, i.e., the two-meson theory and the Sakata model of elementary particles were phenomenological. From these facts, Kamefuchi classifies Sakata into type I.<br><br>Tomonaga had an excellent mastery of mathematics and expertise in constructing theories based on different physical requirements, producing the super‐many‐time theory, which lead him to the finding of the renormalization method and to the winning of Nobel Prize. Thus, Kamefuchi classifies him into type II.<br><br>Yukawa's work to create a comprehensive theory of particles starting from "nonlocal fields" or "elementary domains" corresponded to the process of going from knowing to understanding and to feeling, but was not completed. However, Yukawa said in his later year, "Such a fundamental theory was my ultimate purpose, and the meson theory was a byproduct on my way." Yukawa often presented his opinion about various cultural problems (creativity, genius, learning, peace, etc.), displaying his characteristic of being an excellent thinker in culture as well as in physics. From these facts, Kamefuchi classifies Yukawa into type III.<br><br>Kamefuchi's essay concludes as follows:<blockquote>The fact that Yukawa, Tomonaga and Sakata belonged to the three different types was rather lucky to the development of particle theory in Japan. The three leaders played the role of antithesis against each other so that the study of particle physics in our country made a balanced progress. […] I believe that this was the basis of the Nobel-prize winning studies by the physicists of the next generation, Yoichiro Nambu, Masatoshi Koshiba, Toshihide Maskawa and Makoto Kobayashi.</blockquote><br>Kamefuchi's classification scheme of physicists reminds me of a similar classification proposed by Yoichiro Nambu. His classification as summarized by himself is as follows [3]:<blockquote>Once I classified theoretical physicists into three types according to their different styles of approach, and called them Heisenberg (H), Einstein (E) and Dirac (D) modes, referring to their most characteristic contributions respectively, i.e., quantum mechanics, theory of gravitation and the Dirac equation. Heisenberg’s is heuristic, bottom-up and inductive. Einstein’s is axiomatic, top-down and deductive. Dirac’s is abstract, revolutionary and esthetic.</blockquote><br>As for the modes to which Yukawa and Tomonaga belongs, Nambu writes as follows [3]:<blockquote>It would be safe to say that Yukawa belonged to H when he proposed the meson. He failed in E when he tried his hand at nonlocal theory. I have a bit of difficulty applying this to Tomonaga, but I will assign him to E. Most theorists belong to H or E. But, when it comes to contrasting Yukawa and Tomonaga, it may be appropriate to use the analogy to designer vs. craftsman.</blockquote><br>Kamefuchi's type II and type III seem to correspond to Nambu's H mode and E mode, respectively. However, when we consider the corresponding categories identical, it causes inconsistency between Kamefuchi's and Nambu's classification of Yukawa and Tomonaga. The inconsistency comes from the difference in the viewpoint between Kamefuchi and Nambu. Namely, Kamefuchi attach importance on the physicist's preference of a method, especially for the classification of Yukawa, and Nambu, on the physicist's successful work.<br><br>On the other hand, Kamefuchi's type II and type III seem to correspond to Nambu's category of craftsman and that of designer, respectively. In this case, we can regard the corresponding categories as nearly equal without causing inconsistency between Kamefuchi's and Nambu's classification of the two physicists. The consistency in this case arises because Nambu's classification here is based on methodology of the physicists, similarly to Kamefuchi's.<br><br><b>References</b><ol><li>S. Kamefuchi, Tosho No. 766, p. 2 (December, 2012) in Japanese.</li><li>English translation has been obtained from: Antonio Gramsci, <a href="http://www.walkingbutterfly.com/wp-content/uploads/2010/12/gramsci-prison-notebooks-vol1.pdf" target="_blank"><i>Selections from the Prison Notebooks</i></a>, edited and translated by Q. Hoare and G. N. Smith, p. 767 (ElecBook, London, 1999).</li><li>Y. Nambu, The Legacies of Yukawa and Tomonaga, AAPPS Bulletin Vol. 18, No. 6, p. 7 (2008)</li></ol></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com2tag:blogger.com,1999:blog-7979916.post-90799269489468292372012-11-07T20:23:00.000+09:002012-12-21T17:40:59.289+09:00Boy of Age 16 Asks Me about Relativity, etc.14. Relations among the Expansion of the Universe, Gravity, Relativity Theory and Dark Energy<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5WolyBl8icgPFyjeas5Dd-b5THkjA6NeknjuMLLIy755BuvgfEb_HvEUqndG2SPJ6ukT2gU4aO89MVTIPy6MtRou624gMM2xzGhmMDRF85CIrQCFmZxftpkWhDVUy8wHKEP20/s1600/Gamow.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="400" width="277" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5WolyBl8icgPFyjeas5Dd-b5THkjA6NeknjuMLLIy755BuvgfEb_HvEUqndG2SPJ6ukT2gU4aO89MVTIPy6MtRou624gMM2xzGhmMDRF85CIrQCFmZxftpkWhDVUy8wHKEP20/s400/Gamow.jpg" /></a></div><div align="justify"><blockquote><center><font size=-2 color="maroon">George Gamow's book <i>My World Line</i>, in which Einstein's words "the biggest blunder<br />
I had ever made in my life" were first written.<br />
<br />
</font></center></blockquote><blockquote><font size=-2>A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.</font></blockquote><br />
<b>Aaron:</b> Why is the universe expanding? Where is gravity? What about Einstein's relativity? Some scientists say that the universe is expanding because of dark energy, don't they?<br />
<br />
<b>Ted:</b> The expansion of the universe is considered possibly due to the initial condition of the Big Bang, with which our universe started. In 1998, two teams of astronomers suggested on the basis of their observations of Type Ia supernovae that the expansion of the universe had been accelerating. (Saul Perlmutter and Adam Riess of the U.S. and Brian Schmidt of Australia contributed to this finding and won Nobel Prize in Physics in 2011.) Until this discovery, physicists were convinced that gravity should be causing the expansion rate of the universe to slow. To explain the accelerated expansion, dark energy, which produces the mysterious force to repel gravity, was proposed and has been constituting the most accepted theory. Scientists are still trying to find what dark energy exactly is (Ref. 1).<br />
<br />
As explained above, dark energy is the notion that appeared after the discovery of the accelerated expansion. With regard to the relation between the expansion of the universe found earlier and the relativity theory, there is a fascinating history. After formulating the equation of general relativity, Einstein tried to find the distribution of masses that would lead to a stable universe unchangeable with time (a static universe was the prevailing hypothesis those days). He found that the equation was incorrect to produce such a universe. Therefore, he added a term to the equation, which became known as the "cosmological term" or the "cosmological constant."<br />
<br />
The Russian mathematician Alexander Friedmann found that Einstein's treatment had been wrong and that the original equation of general relativity was correct to predict time-dependent universes as well including an expanding one, which became the observational fact by Edwin Hubble's work, in the late 1920s, of measuring the redshifts of light from galaxies. Thus, changing the original equation was a mistake, and Einstein once told Gamow that the introduction of the cosmological term was the biggest blunder he had ever made in his life (Ref. 2).<br />
<br />
One possible source of dark energy, supposed to explain the accelerated expansion, is the "cosmological constant," a constant energy density filling space homogeneously, and the other is scalar fields (Ref. 3). Therefore, Einstein's biggest blunder has become a central concept of the present cosmology.<br />
<br />
<b>Note:</b> Earlier, Aaron asked what would happen to the relativity theory if dark energy were true (see <a href="http://ideaisaac.blogspot.jp/2012/02/boy-of-age-16-asks-me-about-relativity_23.html" target="_blank">here</a>). I took this as the question about a possible failure of general relativity under the presence of the accelerated expansion. So, I quoted from Ref. 4 the description of some theorists' thought that a failure might happen on scales larger than superclusters. However, the equation of the general relativity with the cosmological constant might prove to be an excellent theory except for such an extreme case.<br />
<br />
<b>References</b><br />
<ol><li><a href="http://news.nationalgeographic.com/news/2011/10/111004-nobel-prize-physics-universe-expansion-what-is-dark-energy-science/" target="_blank">Physics Nobel Explainer: Why Is Expanding Universe Accelerating?</a> National Geographic, Daily News (October 2011).</li>
<li>George Gamow, <i>My World Line: An Informal Autobiography</i> (Viking, New York, 1970) p. 44.</li>
<li><a href="http://en.wikipedia.org/wiki/Dark_energy" target="_blank">Dark energy</a>, Wikipedia, the free encyclopedia (November7, 2012 at 00:22).</li>
<li><a href="http://en.wikipedia.org/wiki/Dark_energy#Alternative_ideas" target="_blank">3 Alternative Ideas</a>, ibid.</li>
</ol>(Originally written on June 27 and July 5; modified to a large extent.)</div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0tag:blogger.com,1999:blog-7979916.post-2911656491205948522012-10-31T10:21:00.000+09:002012-10-31T10:50:20.491+09:00Boy of Age 16 Asks Me about Relativity, etc. 13. Mass and Weight<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvBXzgXTnmV49pdOU_diUE2Fy_cG-bmHruOTDhdrPK4jubFXBrFwIGL0egg2ot976iI8nFp3KcrZC14RxUkovDlJfOMeRcVXvRiq9QrEM4BJWcXjStV_xqPTTBGYv7xVbhJ8Gc/s1600/Original_Eotvos_experiment.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="400" width="337" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvBXzgXTnmV49pdOU_diUE2Fy_cG-bmHruOTDhdrPK4jubFXBrFwIGL0egg2ot976iI8nFp3KcrZC14RxUkovDlJfOMeRcVXvRiq9QrEM4BJWcXjStV_xqPTTBGYv7xVbhJ8Gc/s400/Original_Eotvos_experiment.jpg" /></a></div><div align="justify"><blockquote><center><font size=-2 color="maroon">Illustration of the first experiment performed by Eötvös to determine whether the inertial mass equals the gravitational mass. If the ratio F1 to F2 of centrifugal forces depending on inertial masses would differ<br />
from the ratio G1 to G2 of gravitational forces depending on graviattional masses, the rod<br />
would rotate. The mirror is used to monitor the rotation. Subsequent experiments used<br />
a different setup for improved accuracy. For details, see the <a href="http://en.wikipedia.org/wiki/Eötvös_experiment" target="_blank">"Eötvös experiment"</a><br />
page of <i>Wikipedia</i>. Image by Petteri Aimonen (Own work)<br />
[Public domain], via Wikimedia Commons.<br />
<br />
</font></center></blockquote><blockquote><font size=-2>A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.</font></blockquote><br />
<b>Aaron:</b> When a body travels at the speed of light, it's mass will be much bigger than at rest. But what about its gravity or weight? It will also be much bigger than at rest. Is this correct?<br />
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<b>Ted:</b> It is an excellent question, but I have to correct the expression of your question a little bit before answering it. The body of non-zero mass cannot travel with just the speed of light but can only approach that speed. So, you should say, "When a body travels near the speed of light, …" You're right to expect that when a body's mass becomes larger with increasing speed, the body's weight or the gravitational force acting on the body also becomes larger compared with its weight when it was at rest in the same gravitational field. This is the result of "the equivalence principle" of general relativity, i.e., the law of the equality of the inertial and gravitational mass. Since the 17th century, repeated experiments demonstrated that inertial and gravitational mass are equivalent. One of the methods of such experiments is shown above. In 1915, Einstein included this observation a priori in the equivalence principle of general relativity.<br />
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<b>Aaron:</b> Thank you so much for your answer. By the way, Have you heard about Dr. Who?<br />
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<b>Ted:</b> No, I have not. I am not so much interested in science fiction stories except for old ones. However, I have learned from <i>Wikipedia</i> the followings about it: <a href="http://en.wikipedia.org/wiki/Doctor_Who" target="_blank"><i>Doctor Who</i></a> is a science fiction television program produced by the BBC and originally broadcast from 1963 to 1989. The program depicts the adventures of a mysterious, time-traveling humanoid alien who is known only as the Doctor and explores time and space in the "TARDIS," a sentient machine for four-dimensional traveling. (There is further information about its history, episodes, characters, etc. in the <i>Wikipedia</i> page) Thanks for your mentioning of Dr. Who.<br />
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<b>Further reading</b><br />
<ol><li><a href="http://en.wikipedia.org/wiki/Mass_versus_weight" target="_blank">"Mass versus weight,"</a> in <i>Wikipedia, the free encyclopedia</i>.</li>
<li><a href="http://en.wikipedia.org/wiki/Mass" target="_blank">"Mass,"</a> ibid.</li>
<li><a href="http://en.wikipedia.org/wiki/Gravitation" target="_blank">"Gravitation,"</a> ibid.</li>
<li><a href="http://en.wikipedia.org/wiki/Equivalence_principle" target="_blank">"Equivalence principle,"</a> ibid.</li>
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<p class="text">(Originally written on June 9 and 20, 2011.)</p></div>Tatsuo Tabatahttp://www.blogger.com/profile/14506724657678911790noreply@blogger.com0