Saturday, December 29, 2012

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)

Wednesday, December 26, 2012

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)

Monday, December 24, 2012

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)

Saturday, December 15, 2012

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)

Monday, December 10, 2012

Leo Tolstoy and Mathematics

Leo Tolstoy. By Scan by User: Gabor [Public domain], via Wikimedia Commons.

These days I am reading Leo Tolstoy's autobiographical novels Childhood, Boyhood and Youth by Japanese translations in Shinchō World Literature Volume 16 (1972). In the first half of Youth, there is an episode that the hero, "I", passes the entrance examination to the mathematics department of a university.

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.

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.

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 nth power of a binomial x + y, where n 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).

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?

References
  1. "Leo Tolstoy," Wikipedia: The Free Encyclopedia (December 8, 2012 at 19:10).
  2. "Binomial theorem," Wikipedia: The Free Encyclopedia (November 25, 2012 at 04:39).

Thursday, December 06, 2012

Classifications of Theoretical Physicists, Especially of Yukawa and Tomonaga

The 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:
Passage from knowing to understanding and to feeling and vice versa from feeling to understanding and to knowing —Antonio Gramsci, "Prison Notebooks" [2]

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.

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.

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.

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.

Kamefuchi's essay concludes as follows:
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.

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]:
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.

As for the modes to which Yukawa and Tomonaga belongs, Nambu writes as follows [3]:
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.

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.

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.

References
  1. S. Kamefuchi, Tosho No. 766, p. 2 (December, 2012) in Japanese.
  2. English translation has been obtained from: Antonio Gramsci, Selections from the Prison Notebooks, edited and translated by Q. Hoare and G. N. Smith, p. 767 (ElecBook, London, 1999).
  3. Y. Nambu, The Legacies of Yukawa and Tomonaga, AAPPS Bulletin Vol. 18, No. 6, p. 7 (2008)