MOSES FAYNGOLD

Projects

Active Learning in Modern Physics:
A New Textbook and Active Learning Course on Special Relativity

This proposal consists of three parts:

I. The description of the recently published book on Special Relativity, upon which we are planning to build the proposed project.

II. The description of revisions and additions to this book, to make it usable as a new type of textbook for a broad range of college students.

III. The description of corresponding course and approach to teaching based on this textbook.

Part 1. The new book:

Special Relativity and Motions Faster than Light

In this part we describe the newly published book on Special Relativity [1] and some reviews on it, to show the basis to be used for a proposed textbook and corresponding course.

1A. The main features

Many of existing texts on Special Relativity can be divided into two categories: one highly

popularizing, the other highly abstract. The former, even when brilliantly written, can only convey some basic concepts, but not provide with understanding on professional level necessary for analyzing actual relativistic phenomena or solving concrete problems, let alone active working in the field. The latter is only accessible to most advanced and diligent readers with a solid mathematical background. 

On the other hand, there are many college textbooks on Modern Physics written on different levels, which fill the gap between the above two extremes; some of them are very well written (see, for instance, [2-4]). But they mostly draw upon traditional pool of technical material, and in many college curriculums this material combines Special Theory of Relativity and Quantum Physics in one course usually taught within one semester. I had taught such a course myself and my experience (shared with that of my many colleagues) shows that this is not sufficient enough to give the students solid background in either field.

This proposal can be considered as a pedagogical experiment aimed at focusing on only one of the cornerstones of Modern Physics and elucidating all its fundamental concepts and essential aspects within one semester in a way that would be both – technically detailed and emotionally enjoyable. My book [1] can be considered as the first step attempting to meet this goal. Its basic features, which have already been formulated in its Preface, are the following.

1. This book is intended to satisfy the demands of different categories of reader, such as college students on the one hand and college professors teaching Physics – on the other. To this end, many sections are written on two levels. The lower level uses an intuitive approach that will help undergraduates to grasp qualitatively, fundamental aspects of relativity theory. The higher level contains a rigorous analytical treatment of the same problems, providing graduate students and professional physicists with a good deal of novel material analyzed in depth. The readers may benefit from this approach. There are not many books having the described two-leveled structure. 

2. In addition to conventional material, the book explores a reach spectrum of phenomena, which fall outside the scope of the standard treatments. For instance, in the current book market on relativity one can spot a “hole” – an apparent lack of information about faster than light phenomena. One of the purposes of this book is to fill in the hole. The corresponding chapters (Ch. 6-8) aim to elucidate areas related to faster-than-light motions, which at first seem to contradict relativity, but upon examination reveal its consistency and depth.

3. The book gives, to my knowledge, the first systematic description of recent and very important progress in experimental fabrication of superluminal light pulses. (Similar approach has been used to dramatically slow down the light pulses, and finally, to “stop” light by encoding information it carried, into physical state of the medium.) These experiments have been described in the most prestigious magazines [5-8], and have attracted much attention in the Physics and Optics communities. The book describes the new results on the level accessible not only to students who already have some technical background, but also to educated laymen (Ch.7). It contains analysis of a simple version of this type of experiments [9-12], which can be understood by any interested person with practically no math. 

The book fills in a vast “gap” in many treatments of Special Relativity: the significant lack of

coverage of accelerated motions. This produced a widely spread misconception (even among professional Physicists!) that the theory is restricted to inertial (uniform) motions of particles. One can find even in some recently published books (see, for instance, [13]) an astounding statement that the special theory of relativity is incomplete because it cannot describe accelerated motions of any kind. This is the same as to claim that arithmetic is incomplete because it can only add the integral numbers but cannot treat fractions of any kind. How could the particle accelerators have been designed within the framework of the special theory of relativity (and work properly!), if this theory were incapable of treating the accelerated motions?

Such misconceptions reflect the flaws in the programs of Modern Physics taught in many colleges. They also show that traditional dynamics of a point mass treated in many textbooks is not enough to sufficiently alert the students to real potential power of the special theory of relativity. One of the goals of this book (and the offered course) is to dispel the myth that accelerated motions cannot be treated in the framework of the Special Relativity. The students will find a standard treatment of accelerated motion in Ch. 4, which is devoted to the relativistic dynamics of a point mass. In addition to this material, however, we describe in Ch. 5 subtle phenomena associated with accelerated motion of extended bodies (Sec. 5.4, 5.5), and motions in rotating reference frames, including famous experiments with the atomic clocks flown around the Earth (Sec. 5.7, 5.8). In Ch. 6 the students will find the relativistic description of the rotational motion of a rod and motion of charged particles in a magnetic field, and in Ch. 8 we consider accelerated superluminal motions (Sec. 8.10, 8.12).

A couple of decades ago there had been a great controversy in scientific literature about hypothetical superluminal particles – tachyons. After extensive discussion it was decided by the overwhelming majority of physicists that tachyons cannot exist since their existence would bring about violations in causality. Yet the readers will find in the book a description of real tachyon-like objects that can be “manufactured” in the laboratory. Such an object possesses a kind of duality, which allows one to represent it as either superluminal, or subliminal object, depending on what physical quantities are chosen for its description. Some readers may be surprised to learn that such “dual” supeluminal objects can routinely propagate with the light pulses in a specially designed communication line, while the information encoded in them propagates slower than light. This may provide them with a deeper understanding of the nature of signal transfer.

Many of these topics can be found only in professional journals. Yet they represent recent progress in our understanding of the world, and their inclusion in a corresponding Physics course would definitely make it more modern. I hope that the students would benefit from such a course.

As already mentioned above, the book tends to satisfy also the demands of the readers with minimal background in math. They will find in many sections an easy part showing the inner core of a phenomenon, its physical picture. These readers can stop at this – they have grasped the main idea.

For the better prepared, after they have been made capable of seeing rather complicated features involved, does there follow a quantitative description with the equations and other details. Many examples discussed are quite unusual and thought provoking, they often start as unsolvable paradoxes, to be, after a few unexpected turns, finally resolved. One can find an example of such approach in Ch. 5, Sec. 5.4.

Another example of this approach can be found in the discussion of phase and group velocities (Chapter 6, Sec. 6.12). They are discussed on three different levels. The first one – intuitive – gives a pictorial representation of the phenomenon using a simple model. This will help the beginner with no math at all grasp the relationship between the two velocities. Then the same relationship is obtained graphically. Finally, it is obtained by analyzing the superposition of two wave functions. The two last levels are appropriate for everybody familiar with college math. The first one may be good for two extreme categories of reader: the least prepared at the one pole, and the most sophisticated (e.g. college professors) – at the other one. The former may find it good to learn, while the latter may find it good to teach. 

In summary, the book can be used as a complimentary reading for college students taking courses in Physics. High school and college teachers can use it as a pool of examples for class discussion. And, because it contains much new material beyond standard college programs, it may be of interest for all those curious about workings of Nature.

1B. The response

This part contains the reviews on the described book.

"Dr. Moses Fayngold has written an extremely interesting book on special relativity and what happens in theory when objects travel at speeds faster-than-light. Undergraduates and graduate students will find his vivid detailed examples very helpful in learning relativity, and in working out many fascinating paradoxes of relativity -- including both the familiar "twin paradox" and less-familiar apparent contradictions of relativistic puzzles.

I recommend this book highly to scientists in all fields, to physics teachers, to their students, and to seriously curious laymen."

Dr. Stephen Rosen, Chairman
Science & Technology Advisory Board

Director, Scientific Career Transitions
1776 Broadway, Suite 1806
New York, NY 10019
212-397-1021
srosenc@verizon.net
www.careerchangeability.com/scientists

…………………………….

Everybody knows that motion with the speed faster than light is impossible.

Dr. Moses Fayngold wrote a 309-page book about superluminal motion. Not a science fiction work, not a fantasy, but a book on special relativity written by a theoretical physicist, an expert in this field. It is as serious and accurate, as a scientific journal publication, and as absorbing and entertaining as a good scientific popularization. Among hundreds books on relativity this one is special. It covers a variety of topics, including the most recent ones that could not always be found in the classical publications. I read it with increasing interest, gave it to my colleagues, and would recommend it to both professionals and students.

Many will be surprised to find in the book something they had not even thought about. I am sure that the book will have more editions.

It would be interesting to include in the second edition the dramatic story of Oliver Heaviside, who was the first to predict what much later was discovered as Cerenkov radiation - the electromagnetic waves emitted by an electron moving faster than light.

Prof. Edward Parilis

California Institute of Technology,

Pasadena, CA ,90125

e-mail : <parilis@caltech.edu> 

……………………..

…This book is a rare example of the treatment that is profoundly instructive and enjoyable to read. In it the features of a reading book for educated laymen blend successfully with rigorousness and depth of a monograph for professional scientists. Intriguing and thought provoking, it can be used by students to learn basic principles of the theory of relativity, and by physics teachers to illustrate these principles and analyze their implications before any student audience.

In many discussions of the theory of relativity there is only a brief mentioning about motions faster than light. This produced a spectrum of speculations, including a widespread and totally misleading opinion among many that such motions are impossible in principle. 

Moses Fayngold gives a brilliant discussion of superluminal motions and shows how they relate to the theory. Some of the problems discussed by him are unique and cannot be found in any other book.

I would recommend “Relativity and Motions Faster than Light” to anyone who wants to get a deep understanding of one of the cornerstones of Modern Physics. 

Vladimir Tsifrinovich

Polytechnic University

vtsifrin@duke.poly.edu

……………..

… I find the book to be highly worthwhile. It covers material which is usually only found scattered around various journals, not gathered together in one coherent way, as it is here.

If I were browsing in the science section of a book-store or library, the table of contents would immediately attract me as intriguing. These non-standard topics serve as complementary backup to the usual treatment of relativity. By emphasizing the effects involving faster than light phenomena that do not violate the physical principles, they deepen my own understanding of this subject. I think many physicists would find in the quirky phenomena discussed, grounds for new thought on an established subject. It is precisely by examining the places where it looks most like you can violate relativity’s axioms, that you find out how subtle the theory really is, and why the axioms are still intact. This book details in a way that is usually not dwelled upon in ordinary texts, how certain phenomena can happen at greater than light speed, while none of them transmit matter, energy, or information at greater than light speed. 

The book does, I think, fill a need for supplementary reading material, to the standard texts.

It expands on the concepts without getting hyper-specialized. The level is appropriate for graduate students, and for physics major under grads with the requisite mathematical background, who want to deepen their knowledge, but the book has also appeal just for the curious, because it is written in such a way that the kernel of most of the explanations could be understood even by those without extensive mathematical background. 

David Green

greend@newschool.edu

…………………………

… I have read the book with great interest and quickly have become a captive audience.

Dr. Fayngold knows how to tell a story.

… The assertion of Special Relativity that speed of light in a vacuum is the greatest possible speed for information transfer led many to attempt to disprove this aspect of the theory. Thus, from time to time, we hear in media reports that a speed greater than the speed of light was finally discovered. In his book, Dr. Fayngold explains these claims and shows that none violates the relativity postulates. His explanations are beautifully written. A joy to read for both scientists familiar with the subject and laymen who would like to attain some understanding of Special Relativity. The author employs an array of characters – people he met and fictional figures from well-known fairy-tales or from his vivid imagination – to present the various aspects of Special Relativity. Some sections are just marvels: the chapter on the super-fast train kept me in such suspense and wonderment that I did not want it to end. I laughed, I learned, and I wanted to know what was next. The author often uses conversational style of writing, which makes reading very easy. He avoids jargon and blank statements such as “it can be shown” or “after some algebra it is obvious that.” Despite his non-technical writing style, which might imply a “watering down” of the subject, the author treats the technical aspects of the theory with rigor and clarity. Nowhere in the text does he compromise the physics.

“Relativity and Motions Faster than Light” will be an important contribution to a library of books on Special Relativity. In his book, Dr. Fayngold discusses topics often omitted by other authors. His is a rare book that uses water in a swimming pool to explain relativity of space and time. His is the only book I know of that discusses relativity of a gravitational force (Section 2.10) and that treats the issue of speeds faster than light with so much depth.

Dr. Fayngold clearly understands the intricacies of Special Relativity and is able to convey them to a reader. The book is informative and authoritative, but at the same time it is humorous and entertaining.

I am convinced that the physics community will enthusiastically receive this book and that it will be widely adopted by physics and engineering teachers as a complementary textbook. Therefore, I urge you again to publish this book.

In what follows, I briefly comment on the specific sections and chapters assigned to me for review:

Section 2.10. What is Horizontal?

This section deals with geometrical aspects of Special Relativity. A plane horizontal in one reference frame may not appear to be horizontal in another reference frame. Dr. Fayngold uses water level in a swimming pool! Everybody can relate to water surface. Using clear arguments, the author is able to demonstrate that water surface in a swimming pool from which water is drained is not horizontal for all observers. He shows that this is due to relativity of time. From emptying swimming pools, he makes the leap to stars and shows that aberration of stellar light has the same root cause as non-parallelism of water surface.

Section 5.4. Predicaments of Relativistic Train

This is truly a great section. I have never read anything as entertaining and informative related to Special Relativity. In this section, Dr. Fayngold clearly demonstrates his artistry in writing a good story. This section also brings new and original elements into expositions of Special Relativity: relativity of gravity and real constraints on terrestrial travel at speeds almost equal to the speed of light.

Section 5.6. The Twin Paradox

The so-called twin paradox is probably the most well known consequence of Special Relativity. Dr. Fayngold offers a solid presentation of this topic. The strength of this section lies in his use of space-time diagrams, a powerful tool in studying consequences of Special Relativity. This chapter will be of great use to both students and laymen. Students will benefit from a clear and non-obtrusive mathematical presentation, and laymen will develop an intuitive understanding of this paradox. Dr. Fayngold wrote this chapter and other chapters in such a way that the reader skipping equations would still be able to understand the main point. A brief description of what an equation means and what it implies follows almost every important equation.

Section 6.11. Weird Dry Spots, Superluminal Shadow, and Exploding Quasars

This section is another marvel. I was intrigued by what Dr. Fayngold can create from steadily falling rain and a moving umbrella. I will never forget that sometimes to stay dry, one would have to run with a speed greater than light, but as Dr. Fayngold reminds us, this is impossible. Having an umbrella – a moving umbrella – is not always enough to stay dry in rain. Then, as if in a surreal theatre (rain becomes light, umbrella becomes a quasar…), the author applies the results from a moving umbrella to superluminal speeds discovered in gas flows near quasars. He shows that this is purely a geometrical effect and that no object actually moves with a speed greater than light.

Section. 6.12. Phase and Group Velocities

This is a section that many students of physics and engineering will find very useful in clarifying the concepts of phase and group velocities. There is always some confusion regarding these velocities in plasma. Since the phase velocity of light can be greater than the speed of light in a vacuum, some students think that this violates Special Relativity. Dr. Fayngold pedagogically explains this apparent paradox both using mathematical formalism and analogies.

Chapter 7. Slow Light and Fast Light

I remember that about one year ago the media reported on an experiment in which a pulse of light can outrun itself, i.e., it emerged from a chamber before it actually entered one. This was big news. My students asked me if this experiment shows that speeds faster than light are possible and that Special Relativity is not correct. If my students read Dr. Fayngold’s book, it would be very clear to them that these experiments in no way imply superluminal signaling. In this chapter, the author combines tales about Alice’s adventures with modern age experiments in physics to explain the phenomena of fast and slow light. This is a great chapter.

Slawomir S. Piatek,

Research Professor

Department of Physics

New Jersey Institute of Technology

Part II. Description of the intended changes

and expansion of the previous book.

In this project, we propose to revise the existing book, which has already received many positive responses, by enhancing its educational and instructive features. We are planning to use this book as a basis for a textbook on Special Relativity as a separate course. The goal is to improve the existing text in the few ways.

1. Eliminating the errors and misprints of the first edition.

2. Expanding the references to include most essentially relevant books, reviews, and articles.

3. Adding a new chapter on Electrodynamics in the spirits of John Bell famous article “How to teach Special Relativity” [1]. 

4. Adding new sections that would shed more light on various aspects of Special Relativity.

5. Adding problems, which would be a crucial step to make the existing text useful not only as a general interest book, but also usable as a college textbook. The problems will also be provided with solutions, but the latter will come as a separate complementary volume - the Instructor’s Solutions Manual, which would be distributed only among the instructors, together with the instructor desk copies.

6. Preparing computer animations for visual illustrations of various relativistic effects and their 

manifestations in different conditions and different reference frames.

Part III. The description of the proposed course.

The tentative title of the course:

Special Relativity and High Energy / Particle Physics

Course outline

Part 1

Special Relativity

Lecture 1. Introduction. Review of the basic concepts of space, time, and motion.

Lecture 2. Electromagnetic phenomena. Propagation of electromagnetic waves. Speed of light - 

relative to what? Weirdness of light.

Lecture 3. The Michelson experiment. The speed of light and principle of relativity.

Lecture 4. "Obvious" does not always mean "true"! Light determines simultaneity. Light, times, 

and distances.

Lecture 5. The Lorentz transformations. The relativity of simultaneity. A proper length and a 

proper time. Decay of “atmospheric” μ-mesons.

Lecture 6. Minkowski’s world. The space-time diagrams.

Lecture 7. Problems and discussions. What is horizontal? The aberration of light.

Lecture 8. The addition of collinear velocities. Arbitrary velocities. The velocities' play.

Lecture 9. Relativistic mechanics of a point mass. Relativistic kinematics. Mass and energy.

Lecture 10. Relativistic dynamics. Two aspects of mass.

Lecture 11. Imaginary paradoxes. The three clocks paradox. The "dialogue" of two atoms.

The longitudinal Doppler effect.

Lecture 12. Imaginary paradoxes (continued). Predicaments of relativistic train.

Lecture 13. Imaginary paradoxes (continued). The twin paradox. Time travels.

Lecture 14. Accelerated motion of extended objects. The dynamics of length contraction.

Lecture 15. Motion in rotating reference frames. Circumnavigations with the atomic clocks.

Hafele and Keating experiment.

Lecture 16. Photons’ races in a centrifuge. Optical accelerometers and laser gyroscopes.

Lecture 17. Superluminal motions within special relativity. Velocity, information, signal. The 

“scissors" effect. Relativistic rotation of a rod. “Waltz” in a magnetic field.

Lecture 18. Spiraling ray. Star war games and neutron stars. Surprises of the surf

Lecture 19. Cerenkov radiation from superluminal sources. What do we see in a mirror?

Lecture 20. The apparent superluminal motions in Astrophysics.

Lecture 21. Phase and group velocities. Slow light and fast light.

Lecture 22. Superluminal motions and causality. Tachyons and tachyon-like objects. 

Part 2

Applied Relativity, High-Energy and Particle Physics

Lecture 23. High-energy collisions. How do accelerators work? Relativistic engineering.

Lecture 24. Compton effect. Reverse Compton effect in Astrophysics.

Lecture 25. Particles and anti-particles. Basics of the Particle Physics.

Lecture 26. Neutrino, its discovery, properties, and interactions. Neutrino and the Universe. 

Lecture 27. Quarks. 

REFERENCES

1. Jon Marangos, Nature, 20 July 2000, 406, 243-244;

2. L. G. Wang, A. Kuzmich, and A. Dogarin, Ibid., 277-279 

3. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature, 2001, 409, 490-493

4. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, Phys. Rev. Let. (In press)

5. R. E. Slusher, Self-induced transparency,

In Progress in Optics (Ed. E. Wolf), Bd. XII, Amsterdam, 1974

6. I. Poluektov, Yu. Popov, and V. S. Roitberg, Sov. Phys., Uspekhi, 1974, 114 (2), p. 97

7. P. G. Kroukov and V. S. Letokhov, Sov. Phys., Uspekhi, 1969, 99 (2), 169-227 

8. R. W. Chiao, Phys. Rev. A, 1993, 48, 34-37

9. P. Coles, Cosmology, Oxford Univ. Press, New York, 2001, p. 16

10. P. Tipler, Elementary Modern Physics, Worth Publishers, New York, 1992

11. K. Krane, Modern Physics.

12. J. S. Bell, How to teach Special Relativity, in “Speakable and Unspeakable in Quantum 

Mechanics,” (Cambridge Univ. Press, Cambridge, 1987), pp. 67-80