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)

Hans Svensson (1935–2011)

On January 23, 2012, I received an email message with an attachment from my former coworker Pedro Andreo in Stockholm. The attachment was a PDF file of the latest issue of European Medical Physics News [1], in which the report of interview with him [2] and a page in memory of Hans Svensson [3] were contained. Pedro is one of two authors who wrote about memories of the Swedish radiation physicist Svensson on that page.

Searching on the Internet, I found the report "Hans Svensson — In memoriam" [4] written in Swedish. According to the report, Svensson died on December 7, 2011, after a short illness. He was born on March 18, 1935, and began his academic career as a student in Lund in 1956. In 1963, he came to Umeå as a medical physicist and received his doctorate there in 1970 in the subject of radiation physics. In 1982, he became full-time professor of radiation physics associated with the mission of an operation manager, a position he held until his retirement in 2000. During his career, he had significant international commitments and received a number of prestigious awards. He has been active professor emeritus at Umeå University since 2000.

Pedro praises Svensson's work done as the Chairman of Report Committee for ICRU Report 35 [5] by the words "probably his greatest single achievement" [3]. I learned Svenssons's name well before the publication of this report, probably by ICRU Report 21 [6], which was the earlier version of ICRU Report 35 with an essentially same title as that and contained seven papers of Svensson's group in its list of references.* I talked with Svensson twice, once on a day of the International Conference on Radiation Research held in Tokyo in 1979 and next in his office at IAEA in May 1989 (the above photo was taken on the latter occasion). Both our meetings were of a short time, but I vividly remember his kindness. Indeed, it was he who gave me helpful advice to cooperate with Pedro.** I sincerely pray for Hans Svensson to sleep peacefully in heaven.

References

1. European Medical Physics News, Winter 2011/12 (2012).
2. "Pedro Andreo — the road to and through Medical Physics," ibid. p. 6.
3. "Hans Svensson — one of the Pioneers in our field," ibid. p. 23.
4. M. Karlsson, "Hans Svensson — In memoriam," Web page of Radiofysik.org (2012).
5. Radiation Dosimetry: Electrons with Initial Energies Between 1 and 50 MeV, ICRU Report 21 (International Commission on Radiation Units and Measurements, 1972).
6. Radiation Dosimetry: Electron Beams with Energies Between 1 and 50 MeV, ICRU Report 35 (International Commission on Radiation Units and Measurements, 1984).

Notes

* By the way, the list of references in ICRU Report 21 also contained six of our papers on the work done at Radiation Center of Osaka Prefecture; and a similar list in ICRU Report 35, five later papers on our work.
** The collaboration produced 11 papers published in refereed journals in the period 1991–1998.

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)

Boy of Age 16 Asks Me about Relativity, etc.7. Would Einstein Have Liked Harry Potter or High School Musical?

Albert Einstein in 1893 (age 14).
By Kenosis at en.wikipedia [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: Would Einstein have liked Harry Potter or High School Musical, if he were alive now? What do you think about these fiction stories?

Ted: Oh, these are not questions about physics but fascinating ones. I have never been well acquainted with those. However, I believe that I would have liked to read the book of Harry Potter and to watch High School Musical on TV, if I were now at your age. This is because I hear that these stories contain some flavor of science fiction and because, at the age of fifteen, I enjoyed reading Mark Twain's The Adventures of Tom Sawyer (in Japanese translation) and a science fiction series about space travel in a magazine for children.

As for Einstein, it is extremely difficult to assess whether he would have liked Harry Potter or High School Musical. In his childhood, Einstein is said to have read and discussed many books with Max Talmey, a medical student from Poland. Those books are reported to have included a series of popular science books (Ref. 1). Einstein's mother was a talented pianist and ensured the children's musical education (Ref. 2). From these facts, it would not be totally wrong to think Einstein would have liked Harry Potter and High School Musical, if he were now at your age.

Additional message written by Ted: Last evening, I was reading the book on the theory of time written, without using equations, by Sean Carroll (Ref. 3) and found that he, a theoretical cosmologist at the California Institute of Technology, mentions Voldemort and Professor Trelawney from the Harry Potter books. So, this famous scientist seems to have liked Harry Potter as you do. Isn't this a happy report to you?

References

1. Banesh Hoffmann, Albert Einstein (New american Library, New York, 1972). p. 24.
2. "Albert Einstein," in Wikipedia, The Free Encyclopedia (2 January 2012 at 19:05) footnote 1.
3. S. Carroll, From Eternity to Here: The Quest for the Ultimate Theory of Time (Plume, London, 2010) p. 184.

(Originally written on March 2 and 9, 2011)

Boy of Age 16 Asks Me about Relativity, etc.6. What Is Dark Matter?

Strong gravitational lensing as observed by the Hubble Space Telescope in Abell 1689 indicates the presence of dark matter (Ref. 1). Image by NASA, N. Benitez (JHU), T. Broadhurst (Racah Institute of Physics/The Hebrew University), H. Ford (JHU), M. Clampin (STScI), G. Hartig (STScI), G. Illingworth (UCO/Lick Observatory), the ACS Science Team and ESA [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: What is dark matter? How did they know about it?

Ted: It is difficult for me to give my own, accurate description of dark matter. So, here I write a summary of the excellent Web page written by Professor Martin White at Lawrence Berkeley National Laboratory (Ref. 2).

Dark matter is "stuff" which cannot be seen directly. Its existence is inferred indirectly from observations of motions of astronomical objects, specifically, stellar, galactic, and galaxy cluster/supercluster observations. The basic principle of these observations is that if we measure velocities in some region, then there has to be enough mass there for gravity to stop all the objects flying apart. Such measurements done on large scales indicate that the amount of inferred mass is much more than can be explained by the luminous stuff. Hence, we infer that there is dark matter in the Universe.

Dark matter candidates are usually divided into two broad categories, with the second group being sub-divided:

• Baryonic*
• Non-Baryonic
• Hot dark matter and
• Cold dark matter.

For more details, see Ref. 2 and links there.

* Baryonic matter is matter composed mostly (with regard to mass) of baryons, which in turn are composite particles made up of three quarks, and includes atoms of any sort.

References

1. "Dark Matter," Wikipedia, The Free Encyclopedia (2 January 2012 at 17:44).
2. Martin White, Dark Matter.

(Originally written on March 2, 2011)