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

Reference [12] of this article.

2 Heisenberg's tragedy (continued)

2.6 Impact of Heisenberg's research at that time

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

　At the 1958 Rochester Conference on high-energy nuclear physics held in Geneva, Heisenberg invoked the idea of a degenerate vacuum to account for internal quantum numbers, such as isospin and strangeness, that provide selection rules for elementary particle interactions (1958).*
　In an influential paper submitted in 1959,** Heisenberg and his collaborators used his concept of a degenerate vacuum in QFT [quantum field theory] to explain the breaking of isospin symmetry by electromagnetism and weak interactions. [...]
　Heisenberg's degenerate vacuum was at the time widely discussed at international conferences. It was frequently quoted, greatly influenced field theorists, and helped to clear the way for the extension of SSB [spontaneous symmetry breaking] from hydrodynamics and condensed matter theory to QFT. ([12] p. 283)

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

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

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

　Nambu's work on superconductivity led him to consider the possible application to particle physics of the idea of non-invariant solutions (especially in the vacuum state). [...]
　[...]
　[...]
　It is of interest to note the impact of Dirac and Heisenberg on Nambu's pursuing this analogy. First, Nambu took Dirac's idea of holes very seriously and viewed the vacuum not as a void but as a plenum packed with many virtual degrees of freedom. This plenum view of the vacuum made it possible for Nambu to accept Heisenberg's concept of degeneracy of the vacuum, which lay at the heart of SSB. Second, Nambu was trying to construct a composite particle model and chose Heisenberg's non-linear model, 'because the mathematical aspect of symmetry breaking could be mostly demonstrated there', although he never liked the theory or took it seriously.

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

References

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

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

On Kamefuchi's Essay about Heisenberg and Yukawa (2)

D. C. Cassidy's Uncertainty: The Life and Science of Werner Heisenberg.

2 Heisenberg's tragedy (continued)

2.3 Heisenberg's research at that time

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."

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:

February 27, 1958
I have found the following article in the Asahi Shimbun:

[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. ...

March 13, 1958
[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.]

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]:

The distribution [of the preprint on work made by Heisenberg and Pauli] was set for February 27, 1958. [...]

Three days before the preprint was to be distributed, Heisenberg announced the new formula in a lecture at the University of Göttingen physics institute. ([6] p. 542)

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"?

2.4 "The equation of the cosmos" was not a mistranslation

The description in Cassidy's book continues as follows:

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)

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.

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:

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:

([6] p. 542)

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.

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.

Polkinghorne describes Heisenberg's speech at the conference in a little more specialized style than Kamefuchi as follows:

[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)

Heisenberg's equation still had problems though he confidently showed it at the University of Göttingen.

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.

References

4. J. C. Polkinghorne, Rochester Roundabout: The Story of High Energy Physics, (W. H. Freeman, New York, 1989) p. 77.
5. T. Tabata "From Youth Diaries: University Days (5)" (2003), in the Web site IDEA and ISAAC.
6. D. C. Cassidy, Uncertainty: The Life and Science of Werner Heisenberg (W. H. Freeman, New York, 1991).
7. Max Planck: Biographical in The Nobel Prize, the Web site of the Nobel Foundation.
8. H. P. Dürr, W. Heisenberg, H. Mitter, S. Schlieder, and K. Yamazaki, "Zur Theorie der Elementarteilchen," Z. Naturf. 14a, 441 (1959).

(To be continued)
Search word: Kamefuchi-2020

On Kamefuchi's Essay about Heisenberg and Yukawa (1)

Kamefuchi's essay published in the magazine Tosho

1. Introduction

Recently, 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.

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.

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.

The author writes that he was worried about degrading the heroes, but that he recalled it essential to convey the truth.

In the present article, I describe and discuss some of the things I learned from other sources in connection with Kamefuchi's essay.

2 Heisenberg's tragedy

2.1 Description in Polkinghorne's book

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.

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)

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.

2.2 Chair Pauli's assault

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."

Polkinghorne writes these Pauli's words in more detail and once again gives his personal opinion:

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)

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.

References

1. S. Kamefuchi, Tosho No. 859, pp. 18–22 (2020).
2. W. Heisenberg, "Research on the non-linear spinor theory with indefinite metric in Hilbert space" in 1958 Annual International Conference on High Energy Physics at CERN, pp. 851–857 (CERN, Geneva, 1960).
3. Y. Katayama, "Space-time picture of elementary particles" in Proceedings of the 1967 International Conference on Particles and Fields, Ed. C. R. Hagen, G. Guralnik and V. A. Mathur (Interscience, New York, 1967) p. 157.
4. J. C. Polkinghorne, Rochester Roundabout: The Story of High Energy Physics, (W. H. Freeman, New York, 1989) p. 77.

(To be continued)
Serch word: Kamefuchi-2020

From Fujioka's Fluid Drop Model of Atoms to Einstein–Arakatsu Relationship

I 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.

---

Bill: Was Prof. Yoshio Fujioka's "fluid drop" model of the atom known as ekiteki?
And if so, why?

Tatsuo: 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).

Bill: Prof. Ayao Kuwaki was a Japanese scientist and a friend of Albert Einstein. When did he die, exactly?

Tatsuo: According to the information page of him in "Wikipedia" (Japanese edition), Ayao Kuwaki was born on September 9, 1878, and died on May 16, 1945.

Bill: 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.

Tatsuo: Sure, the student should not have been Kuwaki.

Bill: 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.

Tatsuo: I have no idea about that person.

Bill: If you provide a number of possibilities, I'll check each one. Did Hideki Yukawa study under Einstein?

Tatsuo: 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.

Bill: 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.

Tatsuo: The Japanese physicist Jun (Atsushi) Ishiwara seems to have studied under Einstein in Germany (石原純 - Wikipedia). Ishiwara worked as an interpreter when Einstein visited Japan in 1922.

Bill: 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.

Tatsuo: I don't think that Einstein had other Japanese students or followers in Germany.

Bill: I know of another.

Tatsuo: You Know? Who is he?

Bill: Dr. Bunsaku Arakatsu.

Tatsuo: Oh, Bunsaku Arakatsu was a teacher of my teacher and an experimental physicist. So, I didn't think he had studied under Einstein. Wikipedia page for him (Japanese edition) 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.

Bill: Can you find any photos of Einstein and Arakatsu together? If you can, please send them to photografr7@yahoo.com.
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.
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 A Letter from Korea.

Tatsuo: I don't have any photo of Arakatsu.
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.
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.

Bill: I am familiar with Kimura. I am also aware that Konan, Japan is different than Konan, Korea.

Tatsuo: 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.

Bill: Yes, that would be fantastic. And if anyone has any questions or comments, they can contact me directly at bill.streifer@gmail.com.

Tatsuo: Thanks a lot for your permission.

Bill: Stay in touch.

—A few days later we had additional exchange as given below.—

Bill: You can add this: According to page 15 of the book Uranium Matters: Central European Uranium in International Politics, 1900–1960 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."

Bill: 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.

Tatsuo: 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.

(Last modified on July 29, 2015)

The Couple Talks about the Volume of the Truncated Cone

On June 7, my wife and I joined a bus trip to Exhibition of Paintings from State Pushkin Museum 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).

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.

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.

To see the formula and the derivation of it, visit here. 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 Pappus-Guldin theorem (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.

Boy of Age 16 Asks Me about Relativity, etc. 21. Does Time Really Exist? What Is Time?

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. (GFDL or CC-BY-SA-3.0), via Wikimedia Commons.

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.

Aaron: Do we control in time? Or does it control in us?

Ted: 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?

Aaron: 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?

Ted: 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.

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.

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.

References

1. "Time," Wikipedia: The Free Encyclopedia (February 19, 2013, at 06:41).
2. Graeme Stemp-Morlock, Melting Spacetime, Web site FQXi Community (April 30, 2012).

(Originally written on October 14, 2011)

Boy of Age 16 Asks Me about Relativity, etc. 20. Have You Heard about Naruto?

Cover of the first Japanese Naruto manga volume.

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.

Aaron: I just wanted to ask you if you have heard about Naruto.

Ted: 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 Wikipedia 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 Akamaru Jump."

Aaron: Yes, it's one of the best Japanese anime series. Ninjas can travel near the speed of light.

Ted: Oh, Naruto has then a relationship to relativity. Ha-ha!

Reference

1. Naruto, Wikipedia: The Free Encyclopedia (January 24, 2013 at 19:01).

(Originally written on October 7, 2011)

Boy of Age 16 Asks Me about Relativity, etc. 19. Do All the Forces in Nature Travel at the Same Speed as That of Light?

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⁻ 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 Wikimedia Commons.

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.

Aaron: Do all the forces in nature travel at the same speed as that of light?

Ted: 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 10⁻¹⁷–10⁻¹⁶; Ref. 1), so that we can regard that the weak force is transmitted almost instantaneously for it actually to work.

Reference

1. J. Christman. The Weak Interaction, Physnet (Michigan State University, 2001) p. 2.

(Originally written on October 1, 2011)

Boy of Age 16 Asks Me about Relativity, etc.18. Why Is the Speed of Light Constant?

Albert Einstein in 1931 by Doris Ulmann [Public domain], via Wikimedia Commons.

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.

Aaron: Why doesn't the speed of light change?

Ted: 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.

By the way, I have learned, on Twitter this morning, the Reuters news 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.

Aaron: 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?

Ted: 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.

(Originally written on September 23 and 24, 2011, except for "Note" below)

Note about "faster-than-light neutrino" measurements:

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).

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 Physical Review (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 here.) 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).

References

1. E. S. Reich, "Embattled neutrino project leaders step down," Nature (April 2012).
2. The OPERA Collaboration, "Measurement of the neutrino velocity with the OPERA detector in the CNGS beam using the 2012 dedicated data," arXiv:1212.1276 [hep-ex] (December 2012).
3. "Faster-than-light neutrino anomaly," Wikipedia, The Free Encyclopedia (15 December 2012 at 14:07).

(Originally written on September 23 and 24, 2011)

Boy of Age 16 Asks Me about Relativity, etc.17. What Is Golden Physics?

Carl Sagan's The Demon-Haunted World explains methods to help distinguish between ideas that are considered valid science, and ideas that can be considered pseudoscience. — "The Demon-Haunted World," Wikipedia: The Free Encyclopedia (November 12, 2012 at 02:36).

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.

Aaron: I just wanted to ask you about golden physics. What is it?

Ted: 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.

Aaron: Have you heard about the physicist Mohamed El Naschie? It is his theory.

Ted: 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 RationalWiki gives useful information. The essence is given below:

—Mohamed El Naschie is an Egyptian mathematician, physicist and engineer. He served as editor-in-chief of the journal Chaos, Solitons & Fractals. 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.—

The page mentioned has the link to the El Naschie Watch 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.

(See also Ref. 4, which probably appeared after my original reply had been written.)

References

1. "Mohamed El Naschie," RationalWiki (August 21, 2012, at 16:56).
2. El Naschie Watch, Blog site.
3. "Introduction to Mohamed El Naschie," El Naschie Watch (May 6, 2010).
4. "Mohamed El Naschie," Wikipedia: The Free Encyclopedia (December 13, 2012 at 12:58).

(Originally written on September 16 and 17, 2011)

Boy of Age 16 Asks Me about Relativity, etc.16. What Is the Paradox about Time Travel?

Hand colored etching Mr. Fezziwig’s Ball by John Leech from A Christmas Carol by Charles Dickens. [Public domain], via Wikimedia Commons.
A Christmas Carol 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.

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.

Aaron: I think they say that there is a paradox about time travel. What is it?

Ted: 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.

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.

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.

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.

Aaron: 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?

Ted: 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.

[Next day, Ted again wrote to Aaron, writing as follows:]

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.

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.

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.

References

1. Time travel, Wikipedia, The Free Encyclopedia (December14, 2012 at 23:29).
2. Grandfather paradox, Wikipedia, The Free Encyclopedia (December17, 2012 at 08:09).
3. Novikov self-consistency principle, Wikipedia, The Free Encyclopedia (November 26, 2012 at 03:04).

(Originally written from July 29 to 31, 2011)

Boy of Age 16 Asks Me about Relativity, etc.15. What is String Theory?

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 (CC-BY-3.0), via Wikimedia Commons.]

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.

Aaron: 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?

Ted: "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.

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.

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.

Reference

1. Alberto Güijosa, What is String Theory?

(Originally written on July 18, 2011)

Boy of Age 16 Asks Me about Relativity, etc.14. Relations among the Expansion of the Universe, Gravity, Relativity Theory and Dark Energy

George Gamow's book My World Line, in which Einstein's words "the biggest blunder
I had ever made in my life" were first written.

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.

Aaron: 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?

Ted: 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).

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."

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).

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.

Note: Earlier, Aaron asked what would happen to the relativity theory if dark energy were true (see here). 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.

References

1. Physics Nobel Explainer: Why Is Expanding Universe Accelerating? National Geographic, Daily News (October 2011).
2. George Gamow, My World Line: An Informal Autobiography (Viking, New York, 1970) p. 44.
3. Dark energy, Wikipedia, the free encyclopedia (November7, 2012 at 00:22).
4. 3 Alternative Ideas, ibid.

(Originally written on June 27 and July 5; modified to a large extent.)

Boy of Age 16 Asks Me about Relativity, etc. 13. Mass and Weight

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
from the ratio G1 to G2 of gravitational forces depending on graviattional masses, the rod
would rotate. The mirror is used to monitor the rotation. Subsequent experiments used
a different setup for improved accuracy. For details, see the "Eötvös experiment"
page of Wikipedia. Image by Petteri Aimonen (Own work)
[Public domain], via Wikimedia Commons.

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.

Aaron: 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?

Ted: 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.

Aaron: Thank you so much for your answer. By the way, Have you heard about Dr. Who?

Ted: No, I have not. I am not so much interested in science fiction stories except for old ones. However, I have learned from Wikipedia the followings about it: Doctor Who 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 Wikipedia page) Thanks for your mentioning of Dr. Who.

Further reading

1. "Mass versus weight," in Wikipedia, the free encyclopedia.
2. "Mass," ibid.
3. "Gravitation," ibid.
4. "Equivalence principle," ibid.

(Originally written on June 9 and 20, 2011.)

Small Relationship between the Late Physicist Tonomura and Me

On Wednesday, May 2, mass media reported the following news:

Physicist Tonomura dies at 70
A fellow at electronics giant Hitachi Ltd. tipped as a future Nobel Prize winner for years, Akira Tonomura died of pancreatic cancer early on May 2, 2012, at a hospital in Saitama Prefecture. He was 70. Tonomura was known for developing electron holography for observing microscopic structures in matter using the wave nature of electrons and confirming the so-called Aharonov-Bohm effect, the existence of which had long been disputed among physicists. (Kyodo)

An obituary of Tonomura also appeared at the Web site of European Superconductivity News Forum. Besides his achievements described in the above report, the experiment in which Tonomura and his coworkers showed the quantum interference of single electrons is famous because Robert Crease mentioned it in his book "The Prism and the Pendulum: The Ten Most Beautiful Experiments in Science" (Random House, 2003; paperback, 2004). We can see the movie of this experiment in the video of Tonomura's lecture delivered at the Royal Institution in 1994. It is quite a pity that the possibility of Tonomura's receiving Nobel Prize was lost by his passing.

I exchanged email messages with him once. Within one and a half hours, he replied to my pointing out of a minor error in his review paper written in Japanese, showing his sincere personality. In order to make him learn, if he wanted to do so, what a person I am, I appended the URL of my homepage at the end of my message. So, he browsed the homepage and, unexpectedly, wrote words to praise it (regrettably, I am not updating the homepage these years). I would like to express my condolence by quoting our email messages below:

From: Tatsuo Tabata
To: Akira Tonomura
Date: Date: Thu, 6 Jan 2005 08:01
Subject: Some words about "Quantum mechanics: Japanese contributions to its fundamentals"

Dear Dr. Tonomura,

I read your article published in Butsuri Vol. 60, No. 1, p. 3 and learned much from it. I am only afraid that the expression, "S. Weinberg who made the final theory and got Nobel Prize," in line 8 of the second paragraph, Chapter 1, is not correct. Surely, Weinberg published a book entitled, "Dreams of a Final Theory" (1992; paperback 1994). However, such a theory is yet dreams of physicists, just as the whole title of his book indicates. What is made by Weinberg and Abdus Salam independently and extended by Sheldon Glashow is the unification of electromagnetism and the weak interaction, and it is part of what is called the Standard Model.

We hear that the purpose of the series of papers "Physics in Japan: The Past 100 Years and the Prospect," of which yours is one, is "to tell the public about the deep interest and charm of physics." Then, it would extremely be important to describe correctly even about minute points. I would like to recommend you to publish a correction in the next issue.

Sincerely,
Tatsuo Tabata
Home page, http://www3.ocn.ne.jp/~tttabata/

(Originally written in Japanese)

From: Akira Tonomura
To: Tatsuo Tabata
Date: Thu, 6 Jan 2005 09:28
Subject: Re: Some words about "Quantum mechanics: Japanese contributions to its fundamentals"

Dear Professor Tabata,

Thank you for your email message in which you pointed out an error in my paper. Surely, the expression, 'S. Weinberg who "made" the final theory and got Nobel Prize,' is incorrect. Passages of the paper have been much modified by the instruction of the editorial committee that senior high school students should be able to understand them. Therefore, I would like to consult a member of the committee to publish a correction.

I have browsed your home page and been much impressed to learn that it contains newest information not only about science but also other wide fields. I hope that your activity proceeds further.

Thanking you again for your message,

Sincerely,
Akira Tonomura

(Translated from Japanese by T. T.)

Boy of Age 16 Asks Me about Relativity, etc. 12. If Dark Energy Is Real, What Will Happen to the Relativity Theory?

Estimated distribution of dark matter making up 22% of the mass of the universe and dark energy making up 74%, with 'normal' matter making up only 0.4% of the mass of the universe. By PeteSF at en.wikipedia [Public domain], via Wikimedia Commons.

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.

Aaron: If dark energy* is true, what will happen to the relativity theory?

* In 1998, observations of Type Ia supernovae by the High-z Supernova Search Team followed in 1999 by the Supernova Cosmology Project suggested that the expansion of the universe is accelerating. (This work was awarded by the Nobel Prize in Physics in 2011.) Dark energy is a hypothetical form of energy that permeates all of space and causes this accelerating expansion of the universe. The exact physics behind dark energy is yet unknown. (Adapted from Ref. 1.)

Ted: It is a difficult question for me, so that I have consulted Ref. 1. We see the following explanation there:

"Some theorists think that dark energy and cosmic acceleration are a failure of general relativity on very large scales, larger than superclusters. However, most attempts at modifying general relativity have turned out to be either equivalent to theories of quintessence, or inconsistent with observations."

Thus, we can assume that, at the worst, general relativity might be necessary to be supplemented by a new theory for extremely large distances beyond the size of superclusters. Even in that case, however, it would not mean that general relativity was wrong but that it was a highly accurate approximation to the true theory of gravitational phenomena.

References

1. "Dark energy," Wikipedia: The Free Encyclopedia (11 February 2012 at 02:02).

(Originally written on June 9, 2011)

Boy of Age 16 Asks Me about Relativity, etc. 11. How Do We Prove a=F/m?

Newton's first and second laws, in Latin, from the original 1687 Principia Mathematica. Source: http://www.loc.gov/exhibits/world/images/s123.jpg
[Public domain], via Wikimedia Commons.

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.

Aaron: How do we prove a=F/m?

Ted: Your question is considered to be equivalent to this: Can we derive Newton's second law of motion F=ma from a more fundamental principle? (Here, F is the net external force acting on a body, m is the mass of the body and a is the acceleration the body obtains.) We cannot derive this equation from any other principle. Newton assumed it and presented it as a law. The validity of the equation can experimentally be confirmed. For example, we measure accelerations of the bodies of different masses by applying the same force to find that the result is inversely proportional to the known masses. Another confirmation comes from the application of the law to planetary motion. The law combined with Newton's law of universal gravitation neatly explains Kepler's laws of planetary motion empirically found. Thus, the equation is certainly a law. This law can be considered equivalently as a fundamental postulate in the (classical) mechanics of a particle* or as a definition of force and mass [1].

* The mechanics of a particle treats the motion of bodies (objects) which are considered or idealized as a particle, in the sense that the extent of the body is neglected in the evaluation of its motion, i.e., the object is small compared to the distances involved in the analysis, or the deformation and rotation of the body is of no importance in the analysis [2].

By the way, April 18 was the anniversary of Albert Einstein's death, so that I made a short blog post about it. Please enjoy the article here.

References

1. H. Goldstein, Classical Mechanics (Addison-Wesley,1950) p. 1.
2. "Newton's laws of motion," Wikipedia: The Free Encyclopedia (19 February 2012 at 09:36).

(Originally written on April 20 and 22, 2011)

Boy of Age 16 Asks Me about Relativity, etc.10. Body's Mass Increases with Increasing Speed. Then, Why Is Light Mass Zero?

The diagram of Ole Roemer's method, used in 1676, to determine the speed of light by observing the eclipse (D) and reappearance (C) of (B) Jupiter's moon Io from different locations (E, F, G, H, L, K) in Earth orbit around the Sun (A). By Roemer.jpg: Ole Roemer derivative work: Gregors (Roemer.jpg) [Public domain], via Wikimedia Commons. (This diagram is not directly related to the present question, but is put here by the reminiscence from the speed of light.")

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.

Aaron's question of this time is closely related to the question made in the fifth story of this series, "The object's mass is zero when it is traveling at the speed of light, right? Where does its mass go?" Ted's answer to that question seems to have been insufficient for his understanding.

Aaron: According to Einstein's relativity, the mass of a body will increase when its speed approaches the speed of light, right? Then, how does it come that light has zero mass?

Ted: The relativistic increase of mass is caused, so to speak, as a result of "prohibiting" the acceleration of a body with a finite rest mass to a speed equal to or larger than the speed of light in vacuum. The light quantum, or the photon, has zero mass and always has the maximum constant speed without getting acceleration, so that no "prohibition" works on light. Light is a distinct entity in the Universe.

The above explanation is quite metaphorical. Physicists' understanding is just that the photon always has zero mass and light speed without suffering any change, even independently of relative velocity of the observer to the photon, because this hypothesis proposed by Einstein is consistent with every observation.

(Originally written on April 8 and 9, 2011)

Boy of Age 16 Asks Me about Relativity, etc.9. Recommended Books on and by Einstein for Young People

Books recommended.

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.

This time, Aaron does not pose a question, but write about Einstein as follows by appending many photos of Einstein to his email message:

Aaron: Oh my God! That smile of Einstein! I'm gonna die. I want a hug from him! He's cute, isn't he?

Ted: You have a sizeable collection of photos of Einstein and talk about him like a lover. Now there are a lot of biographies of him for people from young to adult ages (a search of paperbound books by the key words "biography Einstein" at Amazon.com gives a list of about 500 titles). Have you read any of those for adults?

I liked a book written in a relatively early year (first published in 1972). It is entitled "Albert Einstein, Creator and Rebel." The author is Einstein's close collaborator Banesh Hoffmann. Another book about Einstein I recommend to young people is "Einstein: A Centenary Volume" edited by A. P. French (published by Heinemann for the International Commission on Physics Education, 1979). You may find copies of these books at a library or an old-book shop.

As for books by Einstein, "The Evolution of Physics" written together with one of his co-workers Leopold Infeld (Touchstone, 1967, still available; first edition 1938; my copy, Cambridge University Press, 1978) is one of the most excellent books for young people to learn about the development of ideas in physics from early concepts to relativity and quanta.

By the way, it is Einstein's birthday and is also π day, today. The reason for the latter is that it is March (the 3rd month) 14th. So, his birthday is especially convenient to remember. Do you have any party for this day at your home?

(Originally written on March 11 and 14, 2011)

Boy of Age 16 Asks Me about Relativity, etc.8. "I Can't Get Gauss's Flux Theorem"

Gauss's portrait published in Astronomische Nachrichten 1828.
By Siegfried Detlev Bendixen [Public domain],
from Wikimedia Commons.

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.

Aaron: I have a problem with Maxwell's equations. We don't learn them at school, and there're a lot of math. I'm not ready for that level of math. So, I can't get Gauss's flux theorem. But I want to understand it.

Ted: You are quite ahead of school lessons. Gauss's flux theorem was formulated by Carl Friedrich Gauss in 1835 and is also known as Gauss's law. I learned it only at university.

Concepts of physics can be learned to some extent without the use of math. For example, Gauss's law is stated by words as follows: The electric flux through any closed surface is proportional to the enclosed electric charge (quoted in Ref. 1 from Ref. 2).

However, true understanding of working and beauty of physics and practical application of physical laws require mathematics. Especially, if you want to become a physicist, early study of essential mathematics together with physics would be useful. Gauss's law can be expressed either by the equation of the integral form or by the equation of the differential form. The equivalence of the two equations can be shown by the use of the divergence theorem in vector calculus. Doesn't this sound interesting? (See, for example, Ref. 1.)

In The Feynman Lectures on Physics (Ref. 3), Gauss's law appears in Chapter 4 of Volume II after necessary mathematical preparation of "Vector Integral Calculus" in Chapter 3. Why don't you learn by the use of that fine textbook of Feynman? If you want to understand Maxwell's equations before studying Feynman's hefty books, however, Daniel Fleisch's A Student's Guide to Maxwell's Equations (Ref. 4) might be useful. Fleisch also explains the equations after giving the preparation of necessary mathematics.

References

1. "Gauss's law," Wikipedia: The Free Encyclopedia (5 January 2012 at 13:53).
2. Raymond A. Serway, Physics for Scientists and Engineers with Modern Physics, 4th edition (1996).
3. Richard P. Feynman, edited by Robert B. Leighton and Matthew Sands, The Feynman Lectures on Physics, Boxed set: The New Millennium Edition (Basic Books, 2011).
4. Daniel A. Fleisch, A Student's Guide to Maxwell's Equations (Cambridge University Press, 2008).

(Originally written on March 5–12, 2011)