LETTERS TO THE EDITOR Letters are selected for their expected interest for our readers. Some letters are sent to reviewers for advice; some are accepted or declined by the editor without review. Letters must be brief and may be edited, subject to the author's approval of significant changes. Although some comments 011 published articles and notes may be appropriate as letters, most such comments are reviewed according to a special procedure and appear, if accepted, in the Notes and Discussions section. (See the "Statement of Editorial Policy" at http://www.kzoo.edu/ajp/docs/edpolicy.htnl.) Running controversies among letter writers will not be published.

COMMENT ON MERMIN'S REVIEW OF QUANTUM ENIGMA BY BRUCE ROSENBLUM AND FRED KUTTNER

I liked Rosenblum and Kuttner's (R&K) book Quanturn Enigrna and Mermin's review of it [Am. J. Phys. 75(3), 287-288 (2007)], but I disagree with both in fundainental ways.

R&K's main contention, that con- scious observation is required for a complete quantum measurement, is a groundless and unnecessary extrava- gance. For example, a photon making a permanent mark on a photographic plate is surely a quantum measure- ment, even if nobody is around to look at it. Once the mark is made, an ob- server can read it years later, or never, and the mark is still there in any case. To question the rcality of such a mark is like questioning the reality of any other macroscopic object, such as the moon. It's an unnecessary extrava- gance to assume that consciousness is required.

The authors' answer seems to be that a human brain is needed because, when the photon makes its mark, the plate merely becomes entangled with the photon and this plate-plus-photon sys- tem must then be collapsed, and we get a "von Neumann chain" of such en- tangled but uncollapsed systems until, eventually, we reach a human brain which, according to R&K, collapses the entire series. But, brains are made of atonis too. Surely the series gets en- tangled with the brain, and so we have no solution to the problem. Further- more, if brains are required to collapse quantum states. then I'd like to know if a low-IQ brain would do. How about a chimpanzee's brain? A worm's brain? Do wave packets not get collapsed on uninhabited planets?

869 Am. J. Phys. 75 (lo), October 2007

Merrnin rightly criticizes R&K's in- sistence on the centrality of conscious- ness, calling for a more balanced pre- sentation. But, then he presents his own unnecessary extravagance, namely that quantum states arc states of knowledge and not objective fea- tures of the systems they describe. This is surely a minority view.

Are we to assume that the states of a photon, or a hydrogen atom, exist only in our minds? What about states of a C60 molecule? A DNA molecule? A vi- rus? Certainly quantum field theorists assume that field quanta such as pho- tons and electrons and C60 molecules exist in the real world. Steven Wein- berg states, for example, "In its mature form, the idea of quantum field theory is that quantum fields arc the basic in- gredients of the universe.. .."' 1 find it odd that neither R&K nor Mermin re- fer to our most basic theory of the rni- croworld. quantum field theory, as they attempt to sort out the meaning of quantum physics.'

The essential ingredient in anv reso-

ing the entangled state into an incoher- ent state describable by a density op- erator in which only the probabilities of the preferred "pointer values" (ei- genvalues) of the environment have predictive power. Thesc probabilities are then classical and are no more mys- terious than is the statement that there is an 0.5 probability of heads in a single coin toss. This situation was analyzed during the 1960s by several theorists, including Niels Bohr's long- time collaborator Leon Rosenfeld, who claimed that these conclusions are in- tuitively obvious and that Bohr had looked at quantum measurements in this manner.2

Nonrealistic and extiavagant propos- als. such as "consciousness collapses the wave packet" and "quantum states are states of knowledge," are no longer needed to resolve the measurement problem. It has been resolved within the realm of normal, realistic physics.

'Alt Hobson, "Teaching quantum physics without paradoxes." The Phvsics Teacher -

lution of the measurement problem, 45(2), 96-99, and references therein.

not mentioned by Mermin and barely eon Rosenfeld, "The measuring process in quantum mechanics," Supplelnent (Com-

mentioned b~ R&K, is surely the ther- memoration Issue for the 30th Anniversilry of modynamically irreversible process the Meson Theory) to Prog. Theor. Phys. 34, that occurs between a quantum system PP. 222-231 (1965): see also the reference

therein. and any macroscopic system (such as a measuring device) that the quantum system leaves a "macroscopic mark" on. Starting from this notion, the deco- herence theory of Wojciech Zurek and others solves the von Neumann chain (or Schrodinger's cat, or classical- quantum boundary) problem. It's now known theoretically and experimen- tally that an interaction between a quantum system and its environment causes the environment to in effect monitor 'the system. very rapidly de- stroying the interference terms in the coherent entanglement between the system and the environment, and tum-

Art Hobsou Department o f Physics Un~versity of Arkansas Fayetteville, AR 72701

ahobsort@uark.edrr

REVIEWER'S RESPONSE

My review of Quantunz Enigma: Physics Encounters Consciousness mentions the idea that quantum states are states of knowledge not because I think that it currently provides all the answers, but because it was not among the many interpretations surveyed by

http:llaapt.org/ajp O 2007 American Association of Physics Teachers 869

RESOURCE LETTER Resource Letters are guides for college and university physicists, astronomen, and other scientists to literature, websites, and other teaching aids. Each Resource Letter focuses on a particular topic and is illtended to help teachers improve course content in a specific field of physics or to introduce nonspecialists to this field. The Resource Letters Editorial Board meets at the AAPT Winter Meeting to choose topics for which Resource Letters will be commissioned during the ensuing year. Items in the Resource Letter below are labeled with the letter E to indicate elementary level or material of general interest to persons seeking to become informed in the field. the letter I to indicate intermediate level or somewhat specialized material, or the letter A to indicate advanced or specialized material. No Resource Letter is meant to be exhaustive and co~nplete; in time there may be more than one Resource Letter on a given subject. A complete list by field of all Resource Letters published to date is at the website www.kzoo.edu/ajp/letters.htn~l. Suggestions for future Resource Letters, including those of high pedagogical value, are welcome and should be sent to Professor Rogcr H. Stuewer, Editor, AAPT Resource Lettcrs, School of Physics and Astronomy. University of Minnesota, 116 Church Strect SE, Minneapolis, MN 55455; e-]nail: rstuewer@physics.u~nn.edu

Resource Letter PSEn-1: Physics and society: Energy Art Iiobsona' Department of Physics, Universiry of Arkansas, Fnvetteville, Arkarrsns 72701

(Received 23 August 2006; accepted 17 November 2006)

This Resource Letter provides a guide to the physics-related literature about energy-and-society. Journal articles, books, and websites are cited for the following topics: general references, textbooks, other pedagogical resources, population growth, fossil fuels, global warming, nuclear power, side effects of nuclear power, fusion power, renewable resources (including hydroelectric, biofuels, wind, photovoltaics, direct solar, geothermal, hydrogen, and energy storage), energy efficiency, and transportation efficiency. 0 2007 American Association of Phvsrcs Teachers [DOI: 10.11 19/1.2410019]

I. INTRODUCTION

A 1996 American Physical Society National Policy State- ment said in part:

Our nation's complacency about the energy prob- lem is dangerous.. ..Such con~placency is short- sighted and risky. Low-cost oil resources outside the Persian Gulf region are rapidly being depleted, increasing the likelihood of sudden disruptions in supply. Energy-related urban air pollution has be- come a world-wide threat to human health. Atmo- spheric concentrations of COz, other greenhouse gases and aerosols are climbing; this will cause changes in temperature, precipitation, sea level, and weather patterns that lnay damage both human and natural systems.

The Council of the American Physical Society urges continued and diversified investments in en- ergy research and development, as well as policies that promote efficiency and innovation throughout the energy system. Such investments and policies are essential to ensure an adequate range of options in the decades ahead. Our national security, our environmental well-being, and our standard of liv- ing are at stake. (See http://www.aps.org/ statements/index.cfm .)

"~lectronic mail: ahobsonBuark.edu

The APS statement rings even more true today than in 1996. Because people must understand the social rarnifca- tions of energy, teachers of physics-a field that certainly includes energy-must teach it. If physicists don't teach en- ergy and society (as I will call this field), it's hard to imagine who will. Hence, this Resource Letter. It surveys books and articles that provide physics teachers and others with the re- sources needed to understand and teach the main energy-and- society topics. As E. 0. Wilson (Ref. 35) points out, it will not be easy to pull civilization through the "bottleneck" of the coming century. To pull through, it's essential that all students-scientists and nonscientists alike-understand at least some of the many physics-related social issues that con- front us. Among these issues, energy is, in the words of Chemistry Nobelist Walter Kohn (Ref. 135), "one of the make-or-break challenges of our times." As John Holdren puts it:

Energy is the most difficult part of the environment problem, and environment is the most difficult part of the energy problem. The core of the challenge of expanding and sustaining economic prosperity is the challenge of limiting, at affordable cost, the environmental impacts of an expandiilg energy supply. (Ref. 64)

You can help by becoming more aware of, and by teach- ing, this issue. One way to teach energy and society is to develop an entire course devoted to the topic. There are many such courses today, and several textbooks for such courses (Refs. 1-5).

294 Am. J. Phys. 75 (4), April 2007 http://aapt.org/ajp D 2007 American Association of Physics Teachers 294

Millikan Award Lecture, 2006: Physics For All Art ~ o b s o n ~ ) Depurrmenr qf Physics, Universig o f Arkanuus, Fuvetteville, Arkansas 72701

(Received 7 August 2006; accepted 18 August 2006)

We physics teachers must broaden our focus from physics for physicists and other scientists to physics for all. The reason, as the American Associatioll for the Advancement of Science puts it, is that "[w]ithout a scientifically literate population, the outlook for a better world is not promising." Physics for all (including the first course for scientists) should be conceptual, not technical. It should describe the universe as we understand it today, including special and general relativity, quantum physics, modem cosmology, nuclear physics, the standard model of particles and interactions, and quantum fields. Many science writers have shown that this description is possible. 11 should emphasize the scientific process and include such societal topics as global warming, nuclear weapons, and pseudoscience, because citizens necd to vote intelligently on such issues. O 2006 Americr~n Associalion of' Physics Teuchers.

[DOI: 10.1 I 1911.23538581

I. INTRODUCTION

I'm surprised, delighted, and a little overwhelmed by this award. Many thanks to the American Association of Physics Teachers. In my opinion, the AAPT is our nation's most im- portant physics organization-and I 'm not just saying that because they gave me this award! Another fine organization, the American Physical Society, is bigger and better known. But in this era of widespread uses and misuses of science and technology, science education is more important than addi- tional research. Research is important, but our biggest science-related problem today is not so much a deficit of research as it is a dcficit of public understanding and rational control of where science and technology are taking us. For that, we need education. So, more power to the AAPT!

I also thank my wife Marie Riley for her love, for being a source of much-needed stability, and for her years of encour- aging words.

In the meeting program, I gave this talk the bloated title, "Thoughts on Physics Education for the 21st Century." I'd like to re-name it "Physics For All," because that's the one thought that I want to talk about, and because our Executive Officer Bernie Khoury has used this phrasc in his excellent editorials on this topic.'

Because I've been involved for inany ycars in efforts to expand education about physics-relatedsocietal issues, I in- terpret this award as recognition of the importance of societal topics as part of a complete physics education. In this effort, I've had many collaborators, especially the many people connected with the APS Forum on Physics and Society, and more especially, many people. involved in the AAPT's infor- mal Physics and Society Education group. The key people who helped launch (at the summer 1994 AAPT meeting) and maintain that group are Al Bartlett, Jane Flood, Jane Jackson, Harvey Leff, Peter Lindenfeld, Gordon McIntosh, John Roeder, and John White.

The Physics and Society Education group helps organize meeting sessions, and has an einail discussion list. 2

"Physics for all" means physics literacy for all students, certainly all non-scientists but also all scientists. I've have four points about physics for all. (Have you ever noticed that speakers always have about four points? I mean, have you ever heard a talk with just two points?)

First and foremost, we educators must broaden our focus

from physics for scientists to physics for all. Second, physics for all should be conceptual, not technical. Third, physics for all should be about physics as we understand it today rather than as we did in the 19th century. Fourth, physics for all must be connected to its social implications.

11. BROADENING THE FOCUS

Project 2061, launched in the 1980s by the American As- sociation for the Advancement of Science. aims to improve thc nation's scientific literacy. The project's handbook, Sci- ence for All ~rnericans,~ concludes its section about "the need for scientific literacy" with these words:

"The life-enhancing potential of science and tech- nology cannot be realized unless the public in gen- eral comes to understand science, mathematics. and technology and to acquire scientific habits of mind; without n scielztifically literate population, the outlook for a better world is not [Italics added.]

Strong words from one of the world's largest scientific organizations. 'That statement is even more obviously and painfully true today than when it was writtcn in 1989. It implies that every student-evely student-needs a cultur- ally and socially relevant physics or astronomy coursc.

Why is science literacy so important? The answer is simple: industrialized de~nocracies cannot survive unless their citizens are scientifically literate. Think about it: sci- ence and technology drive every industrialized nation. And in democracies. it's the people-the taxi drivers, lawyers. teachers, journalists, politicians, mothers, and so forth-who decide about energy policy, global warming, science in the classroom, and much more. If they don't understand science, if they have negative attitudes toward science, if they are wrapped up in pseudoscjentific baloney, then the outlook for the nation is not good.

The AAAS is saying that science literacy is about survival. But, even in industrialized nations, few people are science literate. They don't know what a molecule is, or what causes the seasons. They can't or won't rcad a science-related art~clc in the newspaper. About 50% of Americans believe that hu- mans were created separately from the other aniirals and by

1048 Am. J. Phys. 74 (12). December 2006 http://aapt.org/ajp O 2006 American Association of Physics Teachers 1048

constellation in about four million years. If the anomaly is due to a con- ventional physics mechanism (such as a thermal recoil force from on-board power sources or propulsive gas leak- age from the on-board propulsion sys- tem), the spacecraft will continue to- ward the original destination with a slightly perturbed trajectory. However, if this anomaly turns out to be due to some new physics, the spacecraft's dy- namics will depend on the particular mechanism that is the origin of the anomaly. Our upcoming effort to ana- lyze the recently recovered set of Dop- pler data for the durations of the Pio- neer 10 and 11 missions should help us to establish the origin of the anomaly. The preliminary results of this analysis will be available in approximately one year.

' J . D. Anderson, P. A. Laing, E. L. Lau, A. S. Liu. M. M. Nieto, and S. G. Turyshev, "Study of the anomalous acceleration of Pioneer I 0 and 11," Phys. Rev. D 65, 08200411-50 (2002). pr-qcl0104064.

3. G. Turyshev, M. M. Nieto. and J. D. Anderson, "Study of the Pioneer Anomaly: A ProbIern Set," Am. J. Phys. 73, 1033-1044 (2005), physicsl0502123.

3 ~ . Monis, "The Pioneer Spacecraft," Am. J.

Phys. 74, 373 (2006) (preceeding letter). 4~,. Neslusan, "On the global electrostatic charge of stars," Astron. Astrophys. 372, 913-915 (2001).

Slava G. Turyshev and John D. Anderson Jet Propulsion Laboratory,

Calijonlia lnstitiite of Technolog)i, 4800 Oak Grove Drive,

Pasadena, CA 91109

Michael Martin Nieto Theoretical Divisiorz, MS-B285,

Los Alanlos National Laboratory, University of California. Los Alnmos, NM 87545

REPEATED PROBLEM SOLVING

Fiona McDonnell's editorial, "Why so few choose physics" (July 2005, pp. 583-586), carries many messages for physics educators. One of them is that "repeated problem solving (with an emphasis on reduction and simplifica- tion) through application of formulas and equations" is alienating students from our profession. Although it has been said and documented many times that problem solving is greatly over- emphasized in introductory courses for both scientists and nonscientists,'-5 many teachers still cling to traditional

math-based problems as their primary teaching tool. I hope that McDonnell's article will guide more instructors to- ward greater emphasis on qualitatively understanding the concepts of physics, in contrast to mechanically applying poorly understood equations.

'One of the earliest and best demonstrations is David Hestenes, Malcolm Wells, and Gregg Swackhamer, "Force concept inventory." Phys. Teach. 30, 141-166 (1992).

' ~ a u l C. Hewitt. "Directly to stage three-and you're out!," J. Coll. Sci. Teach. 24, 6-7 (1994).

3 ~ o h n Roeder, "Hewitt champions relevancy of physics," report on a talk by Paul Hewitt, Teachers Clearinghouse for Science and Soci- ety Edocarion, Spring 2004, p. 19. Copies are avaiIable from John Roeder, 194 Washington Road, Princeton, NJ 08540-6447, (JLRoederOaol.com).

4Art Hobson, "Designing science literacy courses," J. Coll. Sci. 'reach. 30, 136-137 (2000).

' ~ a r b a r a Whitten, Suzanne Foster, and Marga- ret Dancombe, "What works for women in undergraduate physics?," Phys. Today 56(9), 46-51 (2003).

Art Hobson Professor Emeritus of Physics

Universiv of Arkansas Fayetteville, AR 72701

ahobson @ uark. edu

MAKE YOUR ONLINE MANUSCRIPTS COME ALIVE

A picture is worth a thousand words. Film or animation can be worth much more. If you submit a manuscript which includes an experiment or computer simulation, why not make a film clip of the experiment or an animation of the simulation, and place ~t on EPAPS (Electronic Physics Auxiliary Publication Service). Your online nianuscript will have a direct link to your EPAPS webpage.

See http://www.kzoo.edu/ajpEPAPS.html for more information.

371 Am. 1. Phys., Vol. 74, No. 5, May 2006 I ~ t t e r a to the Editor 374

Electrons as field quanta: A better way to teach quantum physics in introductory general physics courses

Art ~ o b s o n ~ ) Department of Physics, Universiiy of Arkansas, Fayetle\~ille, Arknnsos 72701

(Received 18 August 2004; accepted 4 March 2005)

I propose a conceptual change in the way we teach nonrelativistic quantum physics in introductory survey courses and general modem physics courses. Traditional instruction treats radiation as a quantized electromagnetic wave that, because it is quantized, is observable only as discrete field quanta, while treating matter as particles that are accompanied by a wave function. In other words, traditional instruction views radiation as fundamentally a field phenomenon, and matter as fundamentally a particle phenomenon. But quantum field theory has a more unified view, according to which both radiation and matter are continuous fields while both photons and material particles are quanta of these fields. The quantum ficld theory view of radiation and matter clarifies particle identity issues, dispels students' Newtonian misconceptions about matter, arguably resolves the wave-particle paradox, is the accepted view of contemporary physics, and might be the simplest and most effective teaching approach for all students. I propose that we make this field-theory viewpoint thc conceptual basis for teaching non-relativistic quantum physics. O 2005 American Associotior~ qf

Phy~ics Teachers.

[DOI: 10.1 119/1.1900097]

I. INTRODUCTION

I proposc a conceptual change in the way we teach non- relativistic quantum mechanics in introductory courses, in- cluding nonmathematical courses for nonscientists, math- based physics survey courses for scientists, and general modern physics courses. Traditional instruction treats radia- tion as a quantized electromagnetic wave and hence observ- able only as discrete field quanta, while treating matter as particles that are accompanied by a wave function. I11 other words, traditional instniction views radiation as fundamen- tally a field phenomenon and matter as funda~nentally a par- ticle phenomenon. But quantum field theory has a more uni- fied view, according to which both radiation and matter are continuous fields with both photons and material particles quanta of these ficlds. As Wcinberg has put it: "Material particles can be understood as the quanta of various fields, in just the same way as the photon is the quantum of the clec- tromagnetic field." ' And, "In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and the particles are just bundles of energy and momentum of the ficlds." 2.3 The quantum field theory view of radiation and matter clarifies particle identity issucs, dispels students' Ncwtonian misconceptions about matter, arguably resolves the wave-particle paradox, is thc acccpted view of contemporary physics,'J and niight be the simplest and most effective teaching approach for all students. I propose that we make this field-theory viewpoint the conceptual basis for teaching nonrelativistic quantum mechanics.

So that there not be misunderstandings, I do not propose any change of the present mathematical formalism for teach- ing nonrelativistic quantum mechanics, and do not propose teaching quantum field theory to introductory students. I pro- pose only that we incorporate the qualitative notion of mate- rial particles as field quanta into introductory pedagogy.

This paper is organized around four experiments that high- light the fundamental symmetry between radiation and mat- ter: the double-slit experiment for both radiation and matter,

showing that both are waves in a field, and a time-resolved or "time-lapse" look at both experiments, showing that the interference fringes are formed by particlelike field quanta.

11. ELECTRONS AS FIELD QUANTA

Consider the experimental results shown in Figs. 1-4. These experiments highlight not only the dual wave-particle nature of radiation and matter that is central to quantum physics, but also the symmetry between radiation and matter that is central to quantum field theory.

Young's experiment (Fig. 1) is evidence for the wave na- ture of light, confilming that light is a wave in a field-an extended entity that comes through both slits and interferes with itself. Figure 2 is evidence that this wave is quantized, that is, it appears as localized bundles or quanta having en- ergy h v. Because these field quanta are localized and carry energy and momentunl, they qualify as particles, although of a very non-Newtonian sort because they are really excita- tions of a continuous ficld, and it is the entirefield that is excited rather than some particular point within the field. A closer look shows that the field-scrcen interactions occur ran- domly on the screen (see Fig. 2), but their statistical distri- bution is described by the intensity of the interference pattern (see Fig. 1). Thus a predetermined wave pattern, quantum indeterminacy, particles (photons), and the probabilistic in- terpretation are all implicit in Figs. 1 and 2. Other experi- ments such as the photoelectric effect can highlight the same essentials, but the double-slit results are pedagogically more direct and compelling, and have direct analogs in experi- ments with matter (see Figs. 3 and 4). In any case, evidence for light quanta has been used for decades to introduce stu- dents to quantum physics.

Figures 3 and 4 are the obvious analogs for matter of Figs. 1 and 2 for radiation. Here we enter new pedagogical terri- tory. Traditional instruction is inconsistent with the analogy between the two pairs of figures. According to traditional instniction, matter is fundamentally made of particles, par- ticles that, as far as students can know, are Newtonian and

610 Am. J. Phys. 73 (71, July 2005 http;//attpt.ordajp 8 2005 Amcncan Association of Physics Teaehcrs 630

LETTERS TO THE EDITOR Letters are selected for their expected interest for our readers. Some letters are sent to reviewers for advice; somc arc acccptcd or declined by thc cditor without revicw. Lctters must be brief and may bc edited, subject to the author's approval of significant changes. Although some comments on published articles and notes may be appropriate as letters, most such commcnts are revicwcd according to a special procedure and appear, if accepted, in thc Notes and Discussions section. (See thc "Statement of Editorial Policy" in the January issue.) Running controversies among letter writers will not be published.

THE WAVE FUNCTION AND REALITY

Thc quotation "Confusing thc wavc function with rcality" attributcd to Morton Tavcl [Am. J. Phys. 72,651 (2004)l is pos- sibly misleading. Tavcl statcs that "Onc of the things that I find most disturbing is thc degree to which the wavc function has be- come a surrogate for the system itself. .. One would think that intelligent people would not mistake the description for the object."

But according to our most fundamental physical thcory, "quantum fields arc the ba- sic ingredients of the univcrsc," ' and "ma- terial particles can bc understood as thc quanta of various fields, in just thc same way as the photon is the quantum of the electromagnetic ficld." The Schrhdingcr wave function is not logically the same thing as a quantum field, but it is closely related. Thus so~netl~ing very much likc the wave function is "the system itself." Let me explain, using the double-slit cxperi- ment as an examplc.

Thc double-slit expcrimcnt with an clcc- tron bean1 was first pcrfonncd by Jonsson in 1974.~ The outcome is a double-slit in- tcrfcrcncc pattern, just as in the analogous Young's experiment with light. According to quantum field theory, the interfercnce fringcs are thosc of a quantum field, namely, thc "clcctron field." This electron ficld (or "matter field," or in the careful tenninologv of T. Y Cao. "fermion .,<

ficld" 4, is physically real, just as thc clcc- tromagnctic field is physically real.' The field goes through both slits, even if only a single clcctron appcars on thc scrccn.

In Jonsson's nonrelativistic nonintcract- ing electron experiment, the electron ficld is mathcn~atically identical to the Schro- dingcr wave function for a singlc elcctron. However, the field and tllc wave function are logically distinct. The wave function is a nonphysical probability distribution that exists in 3N dimensions for an N-body sys- tem. In Jonsson's experiment the one-body wave function and the electron field are mathematically identical, but logically dis- tinct. The wave function is nonphysical, but the interference pattern is direct evidence

197 Am. 1. Phyr. 73 (3), March 2005

of a real, physical, and continuous electron ficld that goes through both slits.

Individual electrons arisc from the fact that the clcctron field is quantizcd, just as photons arise from the fact that the electro- magnetic ficld IS quantizcd. In othcr words, thc electron field can absorb or emit energy only in d~screte packages and must thcrc- fore appear as individual point-likc interac- tions with the vicwing scrccn. The quanti- zation of the electron field is especially clear in the 1989 double-slit experiment of Tonomura er 0 1 . ~

Strictly speaking, Tavel is con-ect in say- ing that thc wave function is not physically real. But the electron field, which 1s math- ematically idcnt~cal to the Schrodingcr wave function in the case of the double slit cxpcrimcnt. is physically rcal. As Stcvcn Weinberg puts it, it is a "basic ingredient of the univcrse." '

'Steven Weinberg, "What is quantum field thcory and what did we think it was?," in C ~ I I - ceptual Foundations of Quanttrm Field Theory, cdited by Tian Yu Cao (Cambridge U.P., Cam- bridge, UK, 1999), p. 242.

'steven Weinberg, quoted in Heinz Pagels, The Cosmic Code (Bantam Books, New York, 1983). p. 239.

laus us Jonsson, "Electron dimaction at mul- tiple slits," Am. J. Phys. 42, 4-11 (1974). 4 . T~an Yu Cao (private communication). 'AS Wcinberg puts it, "fields arc conditions of space itself, considered apart from any matter that may be in it." See Steven Weinberg, Fac- ing Up: Scielice and Its Culturrrl ~dveisaries (I-iaward U.P., Cambridge. MA, 2001), p. 167. Similarly, Einstein insisted that fields arc real. In Albat Einstein and Leopold h~fcld, The Eiolurio~r of' Pl~ysics (Simon and Schuster, Ncw York, 1938), pp. 148-156, they writc "The electromagnetic field is, in Maxwell's theory, something real. The elecwic ficld is pro- duced by a changing magnetic field. quite in- dependently, whctlier or not there is a wirc to tcst its cxistence."

6 ~ . Tonomura. J. Endo, T. Matsuda, T. Ka- wasaki, and H. Exawa, "Demonstration of single-electron buildup of an interference pat- tcm."Am. J. Phys. 57, 117 (1989). The expcri- nient, including thc photographic results, is re- viewed in Gcorge Grecnstcin and Arthur G. Zajonc, The Quantum Challenge (Joncs and Bartlett, Sudbury, Massachusetts, 1997), pp. 1-7.

Alt Hobson Emeritus Professor of Plysics

Universip ofArkansas Fayetteville, Arknnsa.~ 72701

Emtril: ahobson@uark.edz~

ON AN ELLIPTICAL PROPERTY OF PARABOLIC TRAJECTORIES

A recent article in this journal1 showcd the cxistcncc of an elliptical property re- lated to the parabolic trajectories of projec- tile motion. The same result can be found in an older trcatisc on pal-ticlc dynamics by ~ a c ~ i l l a n . ~ MacMillan further showed that in addition to this elliptical property, two circular properties and another para- bolic property could bc found within the parabolic trajectories. Thus, properties of three members of the conic sections havc been found. It would be interesting to see if the remaining mcmbcr of the family (the hyperbola) exists in this interesting problem.

'1. L. Fcmandcz-Chapou, A. L. Salas-Brito, and C. A. Vargas, "An elliptic propcrty of parabolic trajectories." Am. J. Phys. 72, 1109 (2004).

'w. D. MacMillan, Theoretical ~fechai~ics: Statics and the Dynamics of a Particle (Dover. New York, 1958), pp. 249-254.

Arjun Tan Deportment of Pliysics

Alohun~o A & M Universip Normal, AIaholna 35762

E-mail: urjun.lan@emoil.uamu.edz~

WORK AND ENERGY

In the September issue1 of AJP, Clifford Swartz writes, "To find out who is doing the work, ask who is gctting paid" (or pcr- haps better, to keep focused on immediate cncrgy transfers: "ask who is paying"). While it is correct to define work as an en- ergy transfer bctween an agent and a rccipi- ent, this is not always the best starting point in an i~itroductory coursc. For example, suppose I drop a ball. If the system is cho- sen to be the ball alone, work is done on it as it falls. We immediately recognize this simply because a net gravitational force is acting on the ball while it moves, and tiof

http://aapt.orp/ajp @ 2005 Amcrncan Association of Phys~cs Tcachcrs 197

P a ~ e Marshall BR 2 1 1 21 6 2 0 0 4 0 8 41 U h r ~ e l t g t l - t)

Phys. perspect. 6 (2004) XXX-YYY 1422-6944104103OXXX-Z DO1 10.1007ls00016-004-211-? I physics in Perspective

Book Reviews Stephanie Pace Marshall, Judith A. Scheppler, and Michael J. Palmisano, ed., Science Literacy for the Twenty-First Century. Amherst and New York: Prometheus Books, 2003,321 pages. $29.00 (cloth).

This collection of thirty-one essays by eminent scientists and science educators commemorates the eightieth birthday of Leon Lederman, who has the unusual distinction of being at once a Nobel laure- ate and one of the nation's foremost science educators. Like most collections of essays by different authors, this collection is a mixed bag ranging from thought-provoking to pedestrian, and over a vari- ety of topics. The editors have arranged the essays into six broad categories: Inv~tations to Scientific Study. Reframing Science Learning, Reframing Science Teaching, Scientific Stewardship, Demystifying Science for Public Policy, and The Lederman Legacy for Education.

Nearly all of the essays are about some aspect of science literacy for non-scientists.At least five gen- eral themes emerge: America's science-education system is failing badly and in many ways both as regards science literacy and also as regards education for future scientists. Second, the nation desper- ately needs a scientificalIy literate populace, as suggested for example by the American Association for the Advancement of Science's report, Science for All Americarrs; but the scientific community is far from answering this need and in fact many scientists see science literacy as a low priority that they pre- fer to ignore.Third, "inquiry" or "active-engagement" pedagogical methods really work and are a key to improving science education. Fourth, it is at least as important to teach how science works as it is to teach the facts and theories of science. Fifth, there is a difference between doing science, which requires technical proficiency including mathematics, and understanding science, which requires hard but non- technical thinking.

All authors appear to have a common understanding of the meaning of science literacy. As James Trefil puts it: A scientifically literate person can deal with scientific matters arising in public life with the same ease that an educated person would exhibit in dealing with political, legal, or economic mat- ters. Most essayists agree with Trefil that "this kind of literacy isn't a luxury - it's a necessity. Without it, our democratic system would degenerate into one in which decisions are made either hy an intellec- tual elite or by demagogue-driven mobs."

This is in many ways a hopeful collection, because it recounts many science-literacy successes: Fer- milab's involvement in K-12 science education (Marjorie Bardeen); the Illinois Teachers Academy for Mathematics and Science, a center for retraining K-6 teachers (Lourdes Monteagudo); the Illinois Math and Science Academy for scientifically talented high school students (Stephanie Pace Marshall); MIT's "open-courseware" experiment to make its course materials available, free of charge, anywhere on Earth (Charles Vest); Rice University's Model Laboratory program to involve middle-school teachers in science education by year-long residency in an urban Houston middle school (Elnora Harcombe and Neal Lane); the fascinating story of "miracle worker" Annie Sulliven's interactive and inquiry-based teaching methods in the "impossible" educationa1 triumph of guiding the deaf and blind Helen Keller toward an astonishing command of idiomatic English, and of Alexander Graham Bell's involvement in that triumph (Dudley Herschbach); people's innate interest in topics like black holes, warp drive, and time travel, and the implications for education (Lawrence Krauss); the ingrained but sadly unrecog- nized, love of nature and science demonstrated in people's enthusiasms for fishing, horticulture, eco- tourism, hunting, automobile repair. dinosaurs, and gambling probabilities (Stephen Jay Gould); Led- erman's efforts to reexamine the high-school science curriculum and to encourage a more logical sequence putting physics first,chemistry second, and biology third (the editors' "Brief Biography").

But these essays also have their dark side. Ironically, this is most vividly illustrated by Leon Leder- man,instigator of many of the hopeful programs recounted in these essays.Lederman begins the book's Epilogue with characteristic wit: "The wisdom contained in this book is awesome, the praise is fulsome, and my response task is gruesome. There is a common theme, the many failures of our education sys-

SPECIAL FEATURE: ENERGY AND THE ENVIRONMENT

Physics literacy, energy and the environment Art Hobson

Univcrsity of Arkansas, Fayetteville, AR 72701, lJSA

E-mail: ahobson@uark.edu

Abstract Socially aware science literacy courses are sorely needed in every nation that is industrialized and democratic. This article puts societal topics into the more general context of science literacy, suggests that socially significant topics can fit comfortably into a physics literacy course, looks at energy and environment issues, and discusses how one might teach three such issues: energy use in transportation, global ozone depletion and global warming.

Physics literacy for all citizens According to the American Association for the Advancement of Science's (AAAS) project Science for All Americuns (Rutherford and Ahlgren 1990), "The life-enhancing potential of science and technology cannot be realized ui~less the public in general coines to understand science, mathematics. and technology and to acquire scientific habits of mind; without a scientifically literate population, the outlook for a better world is not promising."

Indeed, industrialized deinocracies will not survive unless their citizens are scientifically literate. This is true for the very simple reasons that, in industrial nations, many of the most crucial decisions concern science and technology, and in democracies, citizens decide. Citizens really do need to know about energy, the environment and a host of other science-related topics.

But today's industrialized democracies are far from scientifically literate. For example, physicist and educator David Goodstein observcs that "our [American] educational system is bad enough to constitute a threat to the ideal of Jeffersonian democracy . . . Approximately 95 percent of the American public is illiterate in science by any rational definition of science literacy" (Goodstein 1992).

Jon Miller, Director of the International Center for the Advancement of Scientific Literacy and Professor of Journalism at Northwestern University, is a leader in the measurement and analysis of the public understanding of science. He defines 'civic scientific literacy' as (1) an understanding of basic scientific concepts such as the molecule and the structure of the solar system, (2) an understanding of the nature of scientific inquiry, and (3) a pattern of regular information consumption, such as rcdding and understanding popular science books. By this measure, Miller reports that approximately 10% of American adults qualified as civic scicntifically literate in the 1980s and early 1990s. but that this proportion increased to I 7% by 1999. He goes on to report that, rather surprisingly, the proportion of scientific literacy is even lower than this in Canada, Japan and the EU. Miller comments that these levels may be too low for the requirements of a strong democratic society in a new century of accelerating scientific development (Miller 2002 and references therein).

All of this points to anecd for scicnce literacy courscs at evcry cducational level. But few if any nations offer anything that comes close to fulfilling this requirement, especially in physics. Certainly this is true in the USA, where the great

003 1-9120/03/020109+06$30.00 0 2003 10P Publishing Ltd PHYSICS EDI:CATION 38(2) 109

American Journal of Physics, v 71, Issue 4, p 295295,2003.

SOLAR BLACKBODY SPECTRUM AND THE EYE'S SENSITIVITY

Virginia Trimble's wonderful article on cosmology (December 2002, pp. 11 75.- 1183) states that "any blackbody source at a temperature near that of the sun ... is bound to look white. This is not a coincidence, but a product of evolution; our eyes are most sensitive at the peak of the solar spectrum." I had believed this for years, until I read Bernard Soffer and David Lynch's article in AJP, November 1999, pp. 946~- 953. They show that the quoted statement is mislead- ing and erroneous, because the spectral ra- diance versus wavelength graph is a density distribution function whose peak position changes when plotted in terms of a differ- ent variable such as frequency, while the eye's sensitivity is an ordinary function. Furthermore, "the eye does not appear to be optimized for detection of the available sunlight. ... It is likely that we are viewing the world with a souvenir of the human evolutionary voyage."

Art Hobson UniversiT), qf Arkansas

Fayetteville, Arkansas 72 701 Electronic mail: ahobson@uark.edu

the broad remark is that there are good rea- sons that we do not have eyes that are pri- marily sensitive to far IR, UV, mm. radio, or x-ray emission. Although astronomers sometimes speak of the sun as belonging to a category of "yellow" stars, people who measure color for a living (for example, my father was a chemist specializi~~g in color- forming materials) define "white" as the appearance of things like clean paper in full, clear sunlight.

Virginia Trimble Department of Physics and Astwnomy

U17iversiV of California Irvine, California 92697

GATEWAYS INTO ELECTRONICS

In the review of my book, Gatewa,vs into ~lectronics,' that appeared in the May 2001 issue of AJP: the reviewer ponders at length about its suitability for his students at UC, Berkeley and decides that Guteways is not for them. This choice is of course his prerogative. He does, however, make a statement to which I would like to respond, namely, that Gatewqjs is not suitable for an introductory course.

As I wrote in the Preface, the chapters in

pinning for the elementary chapters or deal with complementary topics such as trans- mission lines and signal recovery. For cx- ample, Chapter I discusses simple linear systems to the extent required in subse- quent elementary chapters and involves only complex numbers and linear differen- tial equations, whereas Chapter 2 is a full- blown exposition of generalized functions and integral transfom~s that leads to the convolution theorem for linear systems and Shannon's sampling theorem. Chapter 2 is intended for those who might eventually find it of interest, but in a first reading, or if only an introductory treatment is desired, it can be skipped or postponed with no loss of continuity.

Gatewavs has its origins in an introduc- tory course for students straight out of high school, so that although it is true that the text has become more mathematical and now has juniors in physics preferably in mind, its thrust has not changed and the elementary chapters remain, as they were at the outset, quite accessible to beginners.

'Pcter C. Dunn. Gatewqs into Electronics (Wiley, New York, 2000). A brief description and a table of contents are available at (www.atnazo~l.com).

'~oel Fajans, review of Ref. 1 , Am. J. Phys. 69, .. .. ~ ~ .

Merits of Advanced Placement Reexamined

J erry Gollub and Robin Spital's rec- ommendations for improving the

Advanced Placement physics pro- gram (PHYSICS TODAY, May 2002, page 48) are excellent, as far they go. But they omit the fact that AP physics makes sense only if i t is pre- ceded by a broad conceptual physics course. The College Board states that "the strongly recommended format for both [AP] Physics B and Physics C courses is a second-year course following the usual introduc- tory physics course" that "better pre- pares [students] for more analytical approaches taken in AP co~rses ."~ Unfortunately, most AP students have had no previous course that emphasizes concepts over calcula- tions (see PHYSICS TODAY, October 1999, page 68).

For a t least three reasons, a broad and conceptual first course is an essential prerequisite to any more technical course. First, as the College Board and lots of physics education research have shown, a grounding in the concepts of physics is an essential prerequisite to a meaningful math-based treatment.

Second, for many practical rea- sons, math-based high-school courses must concentrate on Newtonian mechanics. So-called modern physics, our current view of the physical universe, is hardly men- tioned. Many future biology, medi- cine, engineering, and other stu- dents, then, will never take a course that presents such central concepts as quantum uncertainty and the relativity of time.

And third, traditional math-based courses give no time to such societal topics as energy resources, global warming, pseudoscience, and scien- tific methodology. Yet it is fairly obvi- ous that industrialized democracies cannot survive unless their citizens are literate in such topics. The

Letters and opinions are encouraged and should be sent to Letters, PHYSICS TODAY, American Center for Physics, One Physics Ellipse, College Park, MD 20740-3842 or by e-mail to ptletter@aip.org (using your surname as "Subjectn). Please include your affil- iation, mailing address, and daytime phone number. We reserve the right to ed~t letters.

American Association for the Advancement of Science puts this fairly strongly: "Without a scientifi- cally literate population, the outlook for a better world is not promi~ing."~

Students who skip a broad con- ceptual course to enter AP physics are harmed more than helped; they would opt for the broader course were the AP choice not available. Although AP physics is better than no physics at all, a conceptual course plus AP is far better still.

References 1. Advanced Placement Program Course

Description: Physics, College Board, New York (May 2001).

2. F. J. Rutherford, A. Ahlgren, Science for All Americans, Oxford U . Press, New York (1990), p. vi.

ART HOBSON (ahobson@uark.edu)

University of Arkansas Fayetteville

I applaud PHYSICS TODAY for featur- ing an article on advanced physics

education in American high schools. Jerry Gollub and Robin Spital offer good suggestions for what high- school physics students need. I am greatly disappointed, though, that so much attention was given to the Advanced Placement program. I took AP courses in Latin, Spanish, Calcu- lus BC, and Physics (mechanics only), and I believe the AP program is more of an obstacle than an aid to provid- ing quality advanced education. Stu- dents use AP exams only to boost their resumks. And from the reaction of faculty, I concluded that AP scores did tremendous things for the reputa- tions of high schools. So much for knowledge for knowledge's sake.

The article did not mention the economics of the AP program. Cur- rently, the cost for taking the AP examinations is $85 each. Why should a student or his or her par- ents have to pay such a hefty sum, especially when the high cost of col- lege tuition is looming? How much of that fee goes toward paying graders of the exam and how much toward promoting the AP program and lob- bying high-school administrators? Although students are informed of the many benefits of taking AP exams, very few are told that most universities and colleges offer place-

ment tests for free. The most dis- paraging effect of the high cost is on students with lower socioeconomic status. As the authors stated, those students "do not fare as well on the examinations (on average)," which makes the exam an even larger waste of their money.

The loss to the student is not only monetary. This year, the AP examina- tions were administered during the first week in May, which gave AP stu- dents limited time to learn advanced, complex topics. Given the limited time and a very structured syllabus, laboratory experience falls by the wayside. The statistics I would like to see are the numbers of AP teachers who offer experimental work to their students. I would expect very few, because the pressure is mounting to achieve high test scores. The irony is that, as scientists and teachers of sci- ence, we preach to students that theo- ry and experiment work hand-in- hand to advance our understanding of the universe.

I am also disappointed in the authors' suggestion that "formal cal- culus should not be required." With- out calculus, physics reduces to a set of equations that the authors do not want students to memorize. Stu- dents should be given the elegant mathematical tools to broaden their understanding of physics.

I suggest we abandon the AP pro- gram altogether. The University of Chicago does not accept AP scores, and that stance has not hurt its repu- tation. Let's break the constraints of the standardized system and allow schools to develop their own advanced curriculum. Of course, local cunicu- lum development on an as-needed basis will require qualified, confident, and experienced physics teachers. College professors are expected to develop their own courses; why not high-school teachers?

MICHAEL H . WOOD (mikewood@jlab.org)

Thomas Jefferson National Accelerator Facility

Newport News, Virginia

0 ne of Jerry Gollub and Robin Spital's principal recommen-

dations for improvements to the Advanced Placement physics program is to develop a high-school physics

dccaying atom tr~ggcrs a spray of catnip irathcl- tllan cyanidc) into the box occupied by our car. If the spray is activated, the cat will relax Into a blissful q~~anturn state. Othcnvise the cat, annoyed to be cooped up in a dark box, will become excited to a per- turbetl state. Then-if you believe the C'ope~~llagcn interpretation of q~~anturn r~~eclianics-~111til r l~c box is opened, tlie cat's stilte will be described by the super- [,osltlorl

\I/= Slll tu'l' , + cos ff'P.( .

"\\'ill1 I I I C assistuncc of Sarah SRIIC Blindcr R I I ~

Amy Rcbccca Bl~~l~lcr, Burns Park Elcmcnt;~l-y 'Icliool. A n n Arbor. M I .

T H E LANGUAGE OF PHYSlCS

My reply to Robert I-I. ~ o m e r , ' who asks ~f anyone else out tl~crc agrees with his no- tion that hcat is not a noun, is: count nic in!

Words ant1 syntax (thc arrangement of

words) are important, and should he serious rnatters for physica educators. Indecd, we al-e careful about our dcfinitiona of such words as hcat, force, and accclcration. But we arc insutEciently critical of the physics profession's standard choices of words and syntax, which are often inaccurate and mis- leading. The problem 1s that these inaccu- rate for~ns are ingrained by generations of use, and ncarly irnl,ossiblc to changc. Phys- ics educators should study the standard us- age, and ask whether other word choices would better promote student learning. For example, do students understand thermody- namics better when the instructor strictly avoids tlie word "heat," and, if so. then what alternative word choice works best? As a textbook author, I would be delighted to incorporate more accurate but unconven- tional l ang~~agc if I had the prior support of a group of physics educators who had re- searched that language.

The editorial suggests that, instead of "heat," we might LISC "Q." This is a bad idea, for two reasons. First, it would further alienate nonscientists who already view physics as mcanir~glcssly abstract. Second, like "heat," Q fails to get across the proper concept.

The proper concept, and tlie point of the editorial, is that heat is an action, not a thing. In other wosds it is a vcrb. "to heat," not a noun. We should use it only as a vcrb. Wc heat things, we do not "add heat." An appropriate "nounized" form of thih \erb would be "heating." as in tlic plin~sc "heating is done by tlic flame on the soul,," which is eclui~alent to "the flame heats the soup."

Taking Romer's editorial a step further: Physicists tend to represent major concepts by nouns, even when those concepts repre-

sent actions rather than things. It's a sig- nificant inaccuracy. because the universe is really about action, not things. AFtcr all, the most basic "stutr ' is energy, the capac~ty to do work.

Altl~ough the verb "to heat" is the most obvious example. "forcc" is a morc sig- nificant example of this inaccuracy. "Force" represents the action of pushing or pulling, so its syntax sliould be the same as that of "push." It is a verb, "to force." not a noun. Instead of "A exerts a forcc on H" [or worse yet "A imparts a force to B"), the simple "A forces R" is morc ac- curate. The latter usage might sound un- ~iatural today. but tlie dit'ference between the two usages is tlie same as tlie difference between "A cxcrts ;I push on B" and the morc n a t ~ ~ r a l "A p u s h e B." When we use "Force" as a noun, we uggcst that Force I S

an object. something you can pick up dnd carry around. As all carefill physics tcacli- ers know. this cl.catcs cnornlous miscon- ceptions. By choosing accurate ternis and syntax, we call reinfol-cc correct concep- tions and discourage niisconccptions.

There arc Inany more examples of mis- leading usagc in physics. Rccausc physi- cists resist change even more strongly tlial~ do educators in other fields, it is difficult to changc tradilional language. Howcvcr, our tudents anci our protkssion would bellelit by a critical cxamir~ation of our own ~vords. '~ohcr l tI. Romcr. ..I leal I i rlor :I noull." ,4111. J . P I I ~ 69 (21, I07 IOtj (2001 1.

Art Hohson Dr , /~a~- r~ r~ r~ t t / c ~ f ' P/ IJ .YI~, \ L' t i ivc~r.~i/ j : ( ? ~ ' , ~ I . ~ ~ I I I . Y O Y

Fc~vc~//evi l le, .'It-kc~n.~us 72 70 1 E lec ,~ ro~ i i c nlciil: u /?o /~sor?~~r r r~k .ed~~

I Fol lr-~rt~n. 2001

QUAKER MEETING

I t was clcar, then, w h o among scientists judged tlic valuc o f scientific results: cvery rncmber o f

the group. a s in a Quaker rnccting. "The authority o f scientific opinion remains esse17fiull): mtrtuol:

it is estahlislied hc.n.vec~n scie~itists, not above them." There were leading scientists, scientists who worked with ~~nusua l fertility at the growing points of their fields; but science had no ultiniate leaders. Consensus ruled.

f<~cliard Rhodcs, TIIc, .h*fukin,v ol'11zc -Ifomic. Bo,rih (Simon & Schuster, New York, 19861, 11. 34.

634 Am. J. Phys., Vol. 69, No. 6, June 2001 Letters to the Editor 634

figure 2 as it appears today in the classical mechanics and electromag- museum, no evidence of the explo- netism with at most a superficial sion exists. The museum is open to introduction to special relativity and the public. See http://www.haiger- "old" (pre-1925) quantum physics. We loch.de/keller/EKELLER.htm. seldom hmt that Newton's laws are

MICHAEL THORWART only low-energy approximations to the EGIDIUS FECHTER quantum-relativistic principles that Atomkeller Museum seem to describe the universe, that

I I Haigerloch, Germany

I I Born Coined the Term

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(email: sales@amptek.com www.amptek.com I Circle number 45 on Reader Service Card

I n the article by Gerald Holton (PHYSICS TODAY, July 20001, the

photograph caption on page 39, stating that Werner Heisenberg

named the new physics "quantum mechanics," is misleading.

The expression "quantum mechanics" was first used in the sci- entific literature by Max Born in a 1924 article in which he discussed "the formal passage from classical mechanics to a quantum mechanics."'

When Heisenberg wrote his famous paper2 that laid the founda- tions of the new theory, he used Born's expression; the term was com- mon in aiticles by Born, Pascual Jor-

I dan, Heisenberg, Wolfgang Pauli, and Paul Dirac that appeared imme- diately afterward. In particular, Born and Jordan's paper that introduces the subject of matrix mechanics bears the title "On Quantum mechanic^."^

These statements are based on Bar- tel Leendert van der Waerden's well- known book on the history of quantum mechanics," which includes English translation of the principal works.

References 1. M. Born, Zeitschrift fur Phys. 26, 379

(1924). 2. W. Heisenberg, Zeitschrift fur Phys.

33, 879 (1925). 3. M. Born, P. Jordan, Zeitschrift fur

Phys. 34, 858 (1925). 4. B. L. van der Waerden, Sources of

Quantum Mechanics, Dover Publica- tions, New York (1967).

CARLOS D. GALLES (cgalles@satlink.com)

National Uniuersity of Rosario Argentina

Education Must Capture Student Enthusiasm 'p'he success of the play Copen- i hagen demonstrates once again

the public's potential enthusiasm for physics and related societal topics.

Now cut to pliysics education, where introductory courses dwell on

Newtonian mechanics is not valid for most phenomena, and that an enor- mous conceptual gulf exists between a Newtonian clockwork mechanism and contemporary physics.

Do physics students experience the depth and excitement elicited by Copenhagen? I think not. Do they sense the wonder of the uncertainty principle, or do they, a t best, merely run through yet another formulaic calculation involving symbols called delta-x and delta-p? Do they ever hear anything about, say, quantum entanglement, a phenomenon that has perplexed physicists since the 1930s, that is comparable in signifi- cance to quantum uncertainty, and about which significant new results have appeared regularly since the 1960s? Even in courses for nonscien- tists, in which there is no constraint to cover the encyclopedic minutia of Newtonian mechanics, we fill our students' brains with watered-down versions of the "real" physics courses that are based on the manipulation of classical formulas.

We are living in what should be the golden age of physics education. Physics has never been so exciting. We've been given the Big Bang, dark matter, quantum entanglement, and much more. A smash Broadway hit is even based on the subtleties of physics, and of its social implica- tions. We are not required to throw this excitement away when we enter the classroom. Small enrollments, student antipathy to anything titled "physics," and lukewarm public sup- port need not be our fate. By replac- ing formulaic manipulation with con- ceptual understanding, and above all by focusing on modern concepts and societal connections, teachers can capture the latent enthusiasm for ideas that is so evident in the success of Copenhagen.

ART HOBSON (ahobson@mail.uark.edu)

Uniuersity of Arkansas Fayetteuille

1' antazis Mouroulis (PHYSICS TODAY, November 2000, page 78)

writes that teaching "the Big Bang to college sophomores is a bad idea." He goes on to say "Real science courses should be taught only when students have the background to appreciate

LETTERS TO THE EDITOR Letters are selected for their expected interest for our readers. Some letters are sent to reviewers for advice; some are accepted or declined by the editor without review. Letters must be brief and may be edited, subject to the author's approval of significant changes. Although some comments on published ar~icles and notes may be appropriate as letters, most such comments are reviewed according to a special procedure and appear, if accepted, in the Notes and Discussions section. (See the "Statement of Editorial Policy" in the January issue.) Running controversies among letter writers will not be published.

SCIENCE LITERACY AND department: Faculty research comes first, roadblock is present research-oriented hir-

DEPARTMENTAL PRIORITIES followed by Ph.D. students, then Masters ing and tenure practices. New faculty mem-

Kudos to von ~ a e ~ e r ' for pointing with alarm to the widening gulf between the sci- entific elite and our scientifically illiterate general population. Scientific illiteracy is a fundamental problem of our times, for a so- ciety that is industrialized and democratic cannot survive unless its people are scien- tifically literate. To solve the problem, we scientists will have to emerge from our laboratories and talk with nonscientists, and begin considering and teaching the connec- tions between science and society. We have not really begun to do this.

For example, how many physics depart- ments would be willing to devote the equivalent of 1 faculty member in 20 to nurturing the scientific understanding of the nonuniversity public, a remedy suggested by von Baeyer? In my experience, depart- ments are unwilling to devote this much ef- fort to the education of nonscientists even within the university, let alone devoting this much effort outside the university. Just consider the priorities of any large physics

students, upper-level undergraduate majors and courses, introductory courses for ma- jors, introductory courses for other scien- tists and engineers, and finally, lowest of the low and often entirely absent, physics for nonscientists. With these priorities, what hope can there be of serious university-supported attention to nonstu- dents? And what hope can there be of bridging the science literacy gap?

We can bridge the gap, and, as a corol- lary, rescue our profession from its self- destructive tendencies, only by turning this list of priorities nearly on its head. For ex- ample, every department should assign top priority to seeing that a large proportion, say 50%-75%, of all the nonscience under- graduates on their own campus take a science-literacy physics course oriented to- ward topics such as scientific methodology and the connections between physics and society .2

But traditiona1 attitudes and structural roadblocks stand in the way. An important

bers are selected for their research exper- tise, never primarily for their teaching ability. New faculty understand quite clearly the reasons for their employment. They understand that if they are to obtain tenure-i.e.. if they are to keep their j o b - then teaching along with everything else must be subordinated to the goal of an out- standing research performance.

We physicists will have to stretch in un- accustomed ways if we are to bridge the gulf

' ~ a n s Christian von Baeyer, "Guest comment: Science under siege," Am. J. Phys. 66, 943- 944 (1998). he AAAS report Science for All Americans (Oxford U.P., New York. 1990) describes the general approach that is needed.

Art Hobson Department of' Physics University of' Arkansas

Fayetleville, Arkansas 72 701 ahobson@conzp.uark.edu

6 November 1998

r UNDERSTANDING YOUR OWN TALK I also demanded that the speaker understood what h e w a s saying. It w a s surprising h o w often

formulae would occur where the speaker did not really know the meaning of the symbols h e w a s using, o r diagrams where the speaker could not explain what w a s plotted. Unfortunately, I had a tendency t o fall asleep, especially when I d i d not understand. A t a slightly higher level I tried t o elicit a n explanation of the various "It is easily shown"s that adorn the scientific literature. A l l told, I hope the courses gave not only specific information o n technical points, but also a n education in scientific attitude.

Emilio Segr;, A Mind Always in Motion-The Arrtobiography of Emilio Segri (University of California Press, Ber- keley, L993), p. 231.

177 Am. J. Phys. 67 (3). March 1999 8 1999 American Association of Physics Teachers

Physics in Perspective, v 4, n 4, p 494-495,2002.

494 Book Reviews Phys. perspect.

George Gamow and Russell Stannard, The NEW World of'Mr Tompkins. Cambridge, United Kingdom: Cambridge University Press, 1999, ix + 258 pages. $24.95 (cloth), $16.95 (paper).

This is a revised and updated version of Gamow's 1965 classic Mr Tompkins in Paperback, which is in turn a revised and updated version of Gamow's even more classic Mr Tompkins in Wonderlan~l (1940) and Mr Tompkins explores the Atom (1945). Science popularizer Russell Stannard revised 14 of the 15 chapters in Gamow's original and added four entirely new chapters.

George Gamow (1904-1968) was an influential physicist and cosmologist, a founder of the big bang theory and popular with the general public as a science writer and lecturer. The two earliest Mr Tompkins books were widely read by non-scientists and scientists as an entertaining and authoritative introduction to the remarkable ideas of recent physics, for example c as the universal speed limit, relativistic length contraction, curved space, the second law of thermodynamics and Maxwell's demon, the expanding universe, quantum uncertainty, atomic structure, and nuclear structure.

The Mr Totnpkins books, including Stannard's version, are neither science fiction nor straightforward science popularization, but instead a mix of fantasy and science. Mr C. G. H. (the initials are purposeful, as we will see) Tompkins is a mild-mannered bank clerk with a short attention span and a vivid imagination. Having extra hours on his hands, he attends a public lecture on Einstein's theory of relativity. During the lecture by "the professor" (Gamow's stand-in), and frequently throughout the book, Tompkins nods off into a dreamworld where the marvels of physics are commonplace experiences. In these other worlds, the speed of light ( c ) is so slow, or the gravitational constant (G) is so large, or Planck's constant jh) is so large, that special relativistic, general relativistic, and quantum effects manifest themselves directly.

Stannard updates Gamow's physics. The 14 revised chapters are slightly updated, for instance by the brief introduction of dark matter and the theory of cosmic inflation into a chapter on spatial curvature. Gamow's explanations are slightly improved upon but largely unchanged. The four new chapters are devoted entirely to new results since 1965: Stellar and galactic black holes, the cosmic background radiation, the strangeness quantum number, SU(3) symmetry, the latest in particle accelerators, quarks, gluons, the standard model of particle physics, supersymmetry, string theory, and cosmic inflation, all in the spirit and style of Gamow's original. The entire revision was done with the approval of the Gamow family.

Stannard also updates Gamow's book linguistically and socially. "By Jove!" becomes "Ah!," "The Gay Tribe of Electrons" becomes "The Merry Tribe of Electrons," and so forth. Happily, the professor's daughter Maud is radically transformed. For Gamow, she is a "painting" student who seldom speaks up for herself when her "Daddy" is around. In a typical exchange in the 1965 edition, Maud pouts and says, "Daddy, if you are talking physics again. I think 1 will go and d o some work." The professor replies, "All right, girlie, you run along." In Stannard's revision, Maud is a prominent professional artist who is deeply conversant with the entire range of modern physics, assertive, and frequently remonstrative with her "Dad" for being overly academic and out of touch with non-scientists such as Tompkins.

Notwithstanding the historical importance of the originals, and the faithfulness of Stannard's revision, 1 cannot recommend this book either for the general reader or for scientists. The problem lies not in Stannard's revision but in the original works, as viewed today. In the 1940s, the Mr Tompkins books were a welcome breakthrough in rendering modern physics interesting and understandable to the general public. But today they do not measure up to recent non-technical science writing, and they are stylistically dated. Stannard's revision is too close to the original to change this assessment.

Mr Tompkitw alternates largely between the professor's lectures, and Tompkins' dreams. Thus, Tompkins falls asleep during the professor's lecture about special relativity, and dreams of a city in which the speed of light is 20 miles per hour. Special relativistic length contraction, time dilation, aging, and so forth, are described in an entertaining fashion, but without any discussion of the theory because it's Tompkins' dream, not the professor's. This is a neat idea, and it works fairly well.

The professor, in the lecture through which Tompkins snoozed, then explains the physics behind the dream. But many explanations are too compressed and technical for most non-scientists. For a typical example,

Guest Comment: The ozone parable

Was it Joan Baez who sang, during the days of nuclear weapons testing in the atmosphere, "What have they done to the rain?" Today we need a new song, "What have we done to the ozone?" It is a song we can all sing because all of us, especially we in the "advanced" countries, made it happen. It must be sung softly, to ourselves, for it is a song of self-reproach rather than protest. "They" did not blow a hole in the ozone, it was us, us taking a million daily thoughtless actions around the globe, us living in air- conditioned, spray-canned, styrofoamed convenience.

A brief history: Chlorofluorocarbons (CFCs) were syn- thesized in 1930. These wonderfully inert chemicals cre- ated the air-conditioning revolution that facilitated Amer- ica's great shopping cathedrals and summer automobiling odysseys. CFCs caused little fuss until 1973-1974 when academic chemists discovered that free chlorine has a ter- rific appetite for laboratory ozone, and asked where all these harmless CFCs might be drifting. During the previ- ous 40 years of profit taking, nobody had thought of this question.

The new theory was that CFCs could find their way to the stratosphere where they could destroy the dilute band of ozone that makes life, chemists, and spray cans possible. This created the great spray can debate, a classic stand-off between environmentalists and business that resulted in a classic compromise: In the U.S. CFC-powered spray cans were taken off the market, but the big problems, coolants and foams, remained. It was the first time that a substance suspected of causing global harm had been regulated before the effects had been fully demonstrated, so it was a victory of sorts for theoretical science.

That was in 1978. Then everybody forgot CFCs for sev- eral years.

Fortunately, a few scientists had kept an eye on the Antarctic since 1950, a lonely service unrelated to the CFC wars. They observed a curious trend, beginning in 1977 and strengthening each year until 1985 when they finally reported it. A temporary hole opened in the ozone every spring. A few scientists were sufficiently impressed by these findings that ozone expeditions were mounted beginning in 1986, the ozone hole was confirmed, and the subtle strato- spheric chemistry of the Antarctic was sorted out.

In one of humankind's most graceful moves, CFCs are being phased out and banished by international treaty. In- spired mainly by a scientific theory and calling nevertheless for actual cuts and then a ban on a popular and profitable industry, the 1987 Ozone Treaty was a re'al first. The treaty was not influenced greatly by the ozone hole. It was signed mainly because scientists thought that gradual, world- wide, long-term damage to the stratosphere was theoreti- cally probable. Negotiations began in 1982, long before anybody suspected that there was an ozone hole. It is one of history's great success stories, and is recounted well b U.S. negotiator Richard Benedick's in Ozone Diplomacy. Y

But the patient is dying. While we were all enjoying the air conditioning at the mall, CFCs were slipping into the stratosphere. They won't go away anytime soon. Despite the ban, chlorine levels will rise for another 3 years, level off for 10 years, then go into a slow decline that will return it to present levels by the year 2020, and to a hopefully "safe" level (the 1975 level) in 2075. To the next century, we have bequeathed a sickness in the stratosphere.

971 Am. J. Phys. 60 (11 ), November 1992

Ozone erosion is now above 4% per decade, and accel- erating. We know little of how bad it will get. Erosion is now year-round and world-wide, exposing crops and peo- ple in the summer when they are most vulnerable. Ozone is 5% thinner over the Northern Hemisphere than it was a decade ago. In the U.S. where skin cancer has already doubled since 1980, reduced ozone is expected to cause an extra 12 million skin cancer cases and 200 000 deaths over the next 50 years. The ozone hole hit record levels again in 1991. In Australia, which already has the world's highest skin cancer rate, ozone depletion occasionally pushes ul- traviolet levels 20% above normal, and television airs daily UV readings and warnings. F. Sherwood Rowland, One of the chemists who discovered the problem in 1974, says "What's happening is close to the worst fears."

Ozone is a parable for our times. It calls us to attend less to shopping and more to Earth. Will we learn anything from the parable?

In my neighborhood, some people want to build a new jetport. It will be good for business. Yet jet airplanes al- ready strain the fragtle chemistry of the stratosphere. Earth will not support a further expansion of jet travel, yet sel- dom is this factored into future travel plans.

The nation is saddened by layoffs at General Motors, due to foreign competition and a declining economy. And yet few note that this is only the tip of a larger iceberg, that we are at the end of the age of the fossil-fueled automobile because global warming will not support it.

World population growth has been faster than exponen- tial for the past 2000 years, with another inevitable dou- bling coming soon. Few seem to notice that Earth cannot sustain so many of our species.

This is a small sampling of the lessons of the ozone parable. The lessons are fundamental, going beyond style, convenience, politics, and economics, to nature herself.

And who makes it their business to deal with the fun- damental questions of the natural world? Could we phys- icists have some responsibility in these matters? Did we help mind the store during those 40 years while the down- side of CFCs went unnoticed? Did we teach this significant and fascinating scientific topic to the public and to our students once the dangers were discovered? Or did we keep, instead, to our ivory research towers, and to the safe ground of teaching physics as we learned it, with few con- nections to the world?

To paraphrase Einstein, the unleashed power of science and technology have changed everything save our modes of thinking. Physicists, central to this power, can be instru- mental in changing those modes of thinking, but only if we are willing to change our own modes of thinking. We could, for example, devote more of our professional lives to physics-related cultural and social concerns. The APS Fo- rum on Physics and Society is one avenue for such activity. Or we could, for another example, devote real effort to educating the nonscientific majority about the physics that is relevant to their lives and our planet.

Art Hobson Department of Physics. University of Arkansas.

Fayetteville, Arkansas 72701

'R. Benedick, (hone Diplomacy (Harvard University Press, Cambridge, MA, 1991).

Q 1992 American Association of Physics Teachers 97 1

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WHAT MAKES

A CURVE BALL

CURVE'?

The Physics of Sports

optical activity. In fact, many of the t amino acids are dextrorotatary.

Drup K. KQNDEPVDI Wok Areal Uaiwrisity

8/91 Winston-hlem, North Carofina

A V ~ E O V , GOLDANSK~~ AND KUZ'MIN REPLY: D Dilip K. Kondepudi asks why, if the choice of the '$igni' of handedness in the course of prebiotic mirror-symme- try breaking was accidental, this sign turns out to be the same all over the f i r th .

In Fact, for the obtaining of opposite signs of handedness in different do- mainsoit-heEarthYs biosphere it is not sufficient to admit the possibility of initial formation of bath "left"' and "right" are- in the mume of prebiotic evolution. It je also nese~ary that the time between the apwaranee of two such areas of o p p i t e sign be much shorter than the time required for the "takeover" of the entire biosphere by the very first domain of life with some definita sign of handedness.

Our estimates indicate that this latter condition is: not satisfied.' I> Kondepudi and his colleaaues have

ihat the sign of the handed- ness of the Earth's biosphere was prekferrnimd by a very small global advantage factor (g- 10-"%-name- ly, by weak neutraf currenb thraugh "a process similar to Ggnal averaging that happens in the neighborhoed of the critical paint." See, for example, references 2 and 3 [references 23. and 22 of our P E C Y S ~ ~ ~ WDAY mti~le). Xn fact, this standpoint of Konde-

pudi" can by tro means be canaid- ered generdiy acwpted, Since the abavmentioned publications, at least four papers fcry different re search wi%h mnclusions in contradiction to t h w of Kondepudi and his colleague$ have appeared, Hawever, as far as we know, Konde- put% has never presented any a r p - men* against the essence of the objections expressed in those papers and, moreover, has never mentianed elsewhere the existence of references 67.

We would like to emphariir~ that the main contradtdictjon between the conclusions of references 2 and 3 and references 4-7 concerns the problem of whether weak n@atral currents played a decigiue role in the choice of the haded~ess ~f&rth's fiimphere.

Aspiring to maximum impa&iali.ty, we refiected in our Pnrsrcsr TQ~DAV article the standpoints of both 8$dc?s and supplied readers with corre- sponding references, We join with Kondepudi in urging interested readers to read the cited references

and nut to take any rmarka a t face hms of pseudoscience becam &ey value' have grea.tar social support. It is

inwnsi&nt to criticize occult beliefs Ref errtrtte~ while ignorhg Fundamentalist Chr48- 1. t. 1,. Maramv, V. V. Kuz'mjn, V. 1, G ~ I - tian bdiefs. Critiques that confront

detnlii, DoW. Biophys, (Proc. Acad. Sei, only the occult will fail, for the larger USSR) 274, frfi 119841; 215, 71 (19841. irrationality will continue to floudh See also ref. 189 in V. I. Goldanskii, and believers in the occult will be V. V. Kuz'min, Soy. Phys. Uap. 32, 1 unconvinc& because they will a t (1989). least sense the inconsistency,

8. D, K, Kondepudi, G. W. Nelson, Phye, This matter must be Rev. Lett. 50, 1023 (1983k Nature 314, directly, exp~,c+tiy but tactfully in 438 t 1985). cl-s and in texhooh. But atu-

3. F, k s , D. KodeFudi, P. den& mu& not feel &at their beliefs Phpica 21D, 296 fX986i. are being attacked, for then they will,

4. Yn, 8. Zel'dovich, A. S. Mikhailov, smith out. t:hinung. Rhlm. Fiz. 6,582 (1986) ISov, J. C%em. T~~ sgprosch real)y the one Phys. 5, 2985 (199011, thaG is most in accord with scientific

5% V. A. Avetisav, V, V, Kuz1mEn, S. A. An- methotfolop;y: IJMnt the ikin, Chem. Phys. 112, 179 (19871. have an open elm dkmsion d t h dl

6. X,V. ALkandrov, Khirn. Fiz. 6, 1011 views e.neaurwi, and let studeats (1987) XSov. J- C h m . Ph~e. 6, 1975 make up, or not their own (1990,J' minds. We must be respectful of

7. S.Orossmm,A.S. Wkhailw.2. Phys. retidon in $enera, dl ;nbove &Condfmsd Matter 78, Y 119901, vtrnr~ A. A~~~~ bumbie. We should be aware %at

vrTAU, 1. GOtOANSKIl wien~e is limited, that e;cienceFs pad- vLADIMm V, K U z f i ~ j ~ uck (such * nuclear weapo~m4 are N. ,yemcnov ftmlihrte often tragically in need of the kind of

of~hemica l p h ~ l s i ~ guidance that religion saa provide, I f / 9 I Moscow, Russia and that the Bible contains profound

truths that are sometimes expressed in literary and symbolic Porn&

The question of religion's impact on Getting Religion and the understanding of s f iena is prob-

Science to "Talk ably America" sost serious science literacy matter. Quoting Alftd

Teny Smith's letter on religious bar- North Whitehead B can't. ~OC$W the riers to scimtifi~ underghnding precise ref@reace-can say reader (June 1991, page 145) s%r.t.uck a famil- help me% "When we consider wha% iar chord, This problem arises in my religion is for mankind and what liberdarts physics class, usudliy in science is, it is no exaggeration to say connection with Big Bang cosmotagy that the future 6aur8e of hitory and with the rarlioaclivedatingof the depends upon the decision af Earth, generation ns to the relations between

The problem is woat in biology, thm. ' 'Th i s is still true for our where 83% of ow high school pradu- generation. atas and 48% af oar college graduates reject one of the field% guiding princb Reference ples, namely evolution.' Such stati* 1. J, D. MiIler, "The Seientificduy IIfiter- tics are indicative of America's parve- ate," Public Opinion Lab,, h'arthern II- sive scientific illiteracy. As most of linois U.. b h l b 119851, C. Norman, your invited ph@cs literacy panel Science 809 (1990). pointed out (November 1990, page 6Q), &T EOBSON %he main solution L science educa- Uniwversity ofArkansas tion. But most physicists don't seri- 7'g1 Fu.vetteuille, Arkansas ously concern themselves with educa- tion, and certainly not with the kinds In his June 1991 letter, '&my Smitb of touchy questiom raised by Smikh's suggests &at reitgious beliefs wnkrib letter. And so, at our peril, we have ute to scientific illitaracy. There is largely ignored these problems. certainly a good deal of trukh in that.

This problem of religious belief Some beliefs about God" relaGon&tp needs to bt? seen in the larger contexk with the world m&e-&~nce e m a of pseuddence, Most &=tifie db- khreat, and s c i ~ ~ ~ c id- may ire cumions of pseudc~$cienee include disto- or truncated ta, make them only soalled occult hliefs such ah3 coaf~rmt~t;ogomereli@oww~~Iiivi~w~. aetmlogy and ext~aensary pewep But 'the ~omtruetive iixggehltiqn for tian, Certainly, these togia need % dealing with this problem h t Wt;h k discussed, But belids in the "lit- mseeks i$ no$ that;brE->Q tSi~d, &fen- ewl' (EsEodeal md eci@ntBc} t k t h ti@ I o u l d ' b PJiUihg b engage & of the Bible are far more harmful . ilidiogue with religious be&fs* dis-

them of their obligation to respect the rights of others.

Professor Fang Lizhi has expressed particular concern about several of these scientists and students. Among them are: Wang Juntao, a graduate in physics, prominent academic, and prodemocracy activist at the Research Institute for Economic, Technologi- cal, and Social Development; Liu Gang, a graduate $tudent in physics at Beijing Universi y, on the govern- ment's top wante 4 list of students; and Shao Jiang, a qathematics student and leader of th& Autonomous Stu- dents' Union in :~leij in~.

I ask your readps to join me in call- ing for their release and for the imme- diate release of all those scientists and students of scienck accused of nonvio- lent "counter-r/evolutionary" of- fenses. Please con act me through the Robert F. Kenne y Memorial Center for Human Rig ts, 12 East 33rd Street, New York, I NY 10016to obtain an appeal writteq to the Chinese A- cademy of Sciencjes. The appeal also asks that the namds of all such persons arrested and imprisoned since June, 1989 be ~ublishe d .

I ask you to joiqi me in agreeing not to participate in aby international sci- entific conferenc+ held in China, at least until the edd of 1990, and to make this commitment public by ob- taining and signidg the appeal. While we should maintbin individual con- tacts with our C inese counterparts, by boycotting th 1 se conferences we will be sending a clear signal to the Chinese authoritihs of our determina- tion.

The reaction ofthe Chinese Acade- my to the earlier appeal on behalf of

president of the ahadern; commented on the boycott in t/he official press and emphasized his d ire to "develop and promote scienti f? c exchanges with other countries."

Yuri Orlov Senior Scientist

Cornell University Ithaca, NY 14853 4 September 1990

INTRODUCTORY PHYSICS: TRIMMING THE BLOATED ELEPHANT

In introductory courses for non- scientists, the elephant is easy to trim. Unlike courses for scientists, there is no imperative here to "cover every- thing," although unfortunately many liberal arts physics courses appear to ape the content and style of the alge- bra- and calculus-based courses, only at a "lower" level.

Our Physics and Human Affairs (PHA) course (one semester, 500 studentdyear) covers most of the great ideas of physics, devotes 50% to modern topics (relativity, quantum, atomic, nuclear), and maintains rel- evance to nonscientists by emphasiz- ing the methodological, historical, philosophical, and societal contexts. We do this by omitting math (except for numbers, proportionalities, graphs), quantitative problems, rota- tional motion, momentum, angular momentum, fluids, electromagnetism (except what is needed for electro- magnetic waves), and the Bohr atom (the quantum atom is more appropri- ate for physics literacy).

~ ibe ra l arts physics needs to be viewed as a different course, not a wa- tered down version of the technical courses. In many ways, PHA is more sophisticated than the more math- ematical courses, because it is interdis- ciplinary. Appropriate applications are ozone depletion, nuclear weapons effects, energy options, and evaluating pseudoscience, instead of such tech- nique-oriented applications as blocks on inclines and electric circuits.

Those 80% of our students who are nonscientists don't need encyclope- dias of physics techniques, they need an understanding of the universe around them and its relation to their lives and the life of the planet.

Art Hobson Physics Department

University ofArkansas Fayetteville. A R 72701

16 March 1990

WHAT ABOUT ESP? It was interesting to learn [Law-

rence S. Lerner, "Feynman on ESP," Am. J. Phys. 58, 424-425 (1990)] that Feynman, a theoretical physicist, responded to a question about ESP with a comment about experimental difficulties-namely, that ESP results were not reproducible. Certainly that is a feature of pseudoscience generally. But there is a deeper, theoretical ob- jection to ESP and to much of pseudo- science generally, and that is that it is not falsifiable.

Typically, pseudoscience claims are so stated as to defy definitive test. You can drain Loch Ness through a fine filter without proving that the Mon- ster was never there. To establish that ESP was involved in a particular series of observations, one would have to shoulder the burden of proving that ( 1 ) all conceivable "natural" explana- tions were ruled out; and (2) there was an "unnatural" explanation.

Even if you could shoulder the first burden, which is usually as impracti- cal as draining Loch Ness, how do you shoulder the second, when "unnatu- ral" or "extrasensory" is undefined? You are not merely looking for a nee- dle in a haystack, but you really don't know what you are looking for at all. The analogous situation in the legal process calls for summary dismissal of a pleading because it poses no legally adjudicable issue.

If students are taught "The Theory of Theories,"' they can apply it to learn to distinguish between scientific theories and nonscientific ones, and not waste energy in trying to verify a theory that does not qualify for evalu- ation in the first place.2

Lawrence Cranberg 1205 Constant Springs Drive

Austin, TX 78746 6 May 1990

'Gerald Holton and Duane H. D. Roller, Foun- dations of Modern Physical Science (Addison- Wesley, Reading, MA, 1958), Chap. 8.

'This may be a flaw which the Committee for Scientific Investigation of Claims of the Paran- ormal (CSICOP) apparently does not recog- nize, since it encourages experimental investi- gation without reference to the theory of theories (P. Kurtz. private communication, 6 March 1989).

104 Am. J. Phys., Vol. 59, No. 2, February 1991 Letters to the Editor 104

Should Physicists Lay Down 'Law'?

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References

Rehabilitating Romania's Research

wrr l r : I n the. p;isl ylLnr., t . l l r Scc.ul.il?; i.c.nsc~rshir) ht!c:~n~r s<r cHc0t.l i\,c: t h :~ t :111 our. corr ra~~or~t lc~r~cc ' \\.as st.t-~ppc(l. tiIc>:~sc> 11i> 50 k IIII~ :IS t I) scbnd 11s inl 'orm;~tion about 1:) s~~cc i l i t . conl'orc.r~c,cl ;III~ an), (it (1- el. conl'er.c.ncc!s \v hich ; ~ r c bc i r~g hclcl i n i11(1 nest y ra r (II' so. IVc hcllictvr. t h ~ r t we wi l l I>(, ;~h lc to ;~ t t cnd i n the I'uture.

We ;]I.(. c.nr.r*ring IIOH' thra most t l i l l i c i~ l t p;1rt nl' ~LII. r~rvolut ion: t>uililing. 'L'l~is is \vhy l . . r(,-

.J 1ur:Ito- cluest: I f yo~r know ;In! I* t ries wI>ich havc sonlr r( l t r i l~rnrnt I hey wistr to KC-t r ~ d US, l]le;~se ask t hc.r~~ to r:onl:lct rnt,: 111.. V . I.~I)wI. Ins(.ituti. ~ I I . ~\ ron~ic ' Physics, l io- ~n;~ni:un h(.adcnly of S c i r ~ ~ c ~ s . 7ti!IOO r3~l~: t l~ l l -e !sL. -~ l~ lg l l l~ (~ l~~. KO- rrlania

Wc-a~.(> i r ~ nrc~cl oi:lIrnust e v r u - thing: ceiuil)rnenr Ihr. lascnrs, dv- t c ~ t ior~ ;1r1d signal procrssing. cwmputrrs, clscillosc*opes, spnc- tre,rrleters 2nd so on, even t.yl~ing or. c o l l s i r ~ ~ rnach i r~~z . Imoks : r r ~ c l ; ~ l l l l ~ l l~ l l s . I suspect that tiley :Ire not i n :I

~)osit . i~)r~ to drl'l.:ly shil jping cus1.s: nev- r~r l l lc l~ss. i t sccrr~s tu me t ha1 our c o n ~ n ~ u r ~ i t y has an c)ppor~tur~iL?; 10 111;ikc :i I>LIIII;III~L:~~~~~II gesture by an- s \ve r~ r~g I l l is itppeal, 1:vc.n i r r some mrnor. way. Their needs arc I-r:il. :tncl t i r r ~ c - has ctlrzlt. to r ~ i n l e y r a r c our l i on~ ; l l~ inn collc;~puos into the Krc!:lrer scicsntilic cc~n ln~~rn i l y . I assurnr i h : ~ t t 111s also t llc cnst. wi th 01 l l e r E;tstcsrn I3loc n:lti11115. l'i(::~sc k c l t'r.cc. to con- rnct me 1 1 you have :In? ce)~nrnc.r)ts. slrggc.st ions or' rlucst.ior~s.

WII.I.I,IM 11, )'EN lkym~-/n~<.nt 01 /'/I?SI<..~ i ~ n l l rls/r.r~rit,rr~~

1 1111, vr.,v1:v 4,/'f;<~,,l:~l,l L' : ) ( I !I //l,~ll.<, (;:I : j / / / i ( l : '

Contributions of a Nobelist's Colleagues I vcry r r ~ u c t ~ apy1rt.c-iat,c.d tht* (%x(-eI- Ic2r11 r~ .v i rw 01' I hr work of t ht. t hr.vc: I!)#!, physics Not~el la11l.e:itcs !l)c:- ct.rnhvr.. pagv 171. c~spc.ciali\i l)i~ca~~se: nl,v thesis rescitrch ;it (:olurnhi;~ III n ~ o l e i u l ; ~ r 1)~;rrns t ~ r o t ~ g h t me inre, I:OII~:IC~ wit 1 1 Xr~rrn i t r~ !~;IIII~~:~'S and Wolfr;~ng fJ;~ul's cont.rit~r~rionb ;in11 I)ec;~usc. In? l v r ~ g asst~c,i;~t~c.,r~ rvil.11 tlic. I!nivf:r.si~- of \?';~shingtor~ has ~~>:rt l r- III(* ;I \ri[rress to the rt.rrlar-kal)lt. d l - I I I ~ I I I I I I ~ c a r l l - rii11ues 1,y Il i ins I ) t?h~r~e l t . I n ;)I1 but orlt: rn.sL;~nc.c I believe pr.opt.r ;I<- knorvlt.elgrr~cr~l wits g i v ~ ~ n to I ie l l -

~nrl t'e c:olleagues \vl1o t-b;ivc. 11:irtici-

~ ) ; i l r , c l wit11 h im i n this clc~vi!lapn~ent, 'I'11c. c~sc-cbption is rc.l;~ted to Lhc ide:,

01' l)c~hrr~r.lt.'s rv1.111erl the "c4~an t .u~~ ju r~>p" i r ~ t tic. HIJ~;II Swedish Acade. n ~ y ' s press rclcb:~sc~ o r t l lc "shelved optical ~ ~ l c c I . l ' o ~ ~ :~rnplit it-r" i n the, I ~ I ~ Y S I ~ , ~ .I,OIIAY 11(~\vs story. :I~I c-c,ntr;ll 10 realizing. 111 3 pri~ctical \\.:ry. t h ( 8 i n i rc~dih lc ~ ~ r c c i s i o n inherent i n thc n ~ v ~ ~ s ~ ~ r c ~ r n u n r of' an opt,icaI l ' r -c~c luc~n~~ nl' :I st,orrel Icm. l u ni l hrs ~. rcenl ielri work :IS well :IS ill the iirst obser\.a~ion 1.1f'a qu:rnlum j u ~ n p ~ f ' l ~ ~ . r r . c ~ l h'rr.tr.rc* I,cjltc7rx 5ti. 2797. l!lr(6! I>r l~rni . l~ 11;!s t )~~r~ef i l .ed t'rom a colla I~or,:rl ion \\fit.h 11 is COII~:I~UC Warren S ~ ~ ~ I \ I I . I I ~ ~ ~ . 111 t11t' q u a n t u n ~ jun~p work t.itc.il 11r :ilso ilntf the assi~tanccs of'.J011 S;~r~dI)c~r~g. t hc:n :t I!rli~ersit,y O( N1:~shir~Kion ~111(le~r~gi~:11lui~tr. A his. tory 111' ion-~rapl~in:: drvrlol)rnr.ri~ w e ~ ~ ~ l t l r ~ o t I)e ctlrnplele w101c1ut tllwc. t wt] rl:lrrltts

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DF:~I~IEI;~ I~I.:PI.IES: Given i r l t(.~to, the citar ion i n r r ~ y culleag~re &lark hlcl)er- tnoit's I c t t ~ ~ woultl read. "Warren Nugournt-y. JOII Sar1dh~t.g. Hans Deh- 111c4t. 'Shc,lvrcl (-)l)tic:~l Electron :IIII- plit'i~tr.: (!l,?;vrvut ion o f Qu:~nt,un~ JUIII~S,' I1l~~.~~i~(~I reti^ ti^ Lct/[!rs 56. 2797 ! 1:)Sf;i:' :inti I l'ully :1gree rvitI1 ~111. ct)nl.vrlt,s of' 1.h~ 1ctti.1..

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Why Few Take Physics: Educated Guesses r r ~ ~ ( s A I I ~ - A ~ \ I ~ I - t l i g ~ ~ sc~loo~ l ) h ~ s i ~ ~ t,r:arl~r.r 3cirvey ri\ugust IIIHY. page :I01 j,ointz u p thr! id~.~c:~t ie)n problrms of I r o s i ~ r . 'I'ht. rr.sults shoultl no1 surprlsr. us, 1'01. I l ~ r y arc. 3 conscA- iltirnr,t: n)f thr. ~n' ior i t les o l nt-arl! ~:vcry I Jh [ j -g r :~n t , in~ r~hysics depart- me111 i n I l ~ e cotlnr I.?. r.r,sf~arch ar t l ~ r

t,op, lb l lowrd I,: doctoral (lissc-rta- tio11s. y~~ t~ lu ; t t ,e critrrscs :tnd u n t f t ~ - #r;~duntc. ~)hjdsic,\ 1n;rjor coursr:. A t t h t 1)ortorn ;i~.(, t hc. int,roduc.toq courst!s l i ~ r scic*nce ;\nd r n g i n ~ e r ~ n g st,urienti; ant1 pc.rh:~~rs, if' t he dr.l)ari. ment 1s <-!spc.c.~:~lly bre):td-minded. :I c1)11rst* lt11, the ren):~ininc SO(;> 111. t l ~ stud(-.r~t ~ ~ ~ ~ l ~ t r l a l r o n .

r 7 1 l lc c~trursc~ l'r.~r nrinsc.ior~ t ists. i f ' 01'- 1'1-rrtl nt all. I:. not t:~ug-t~r by (,IIo?;I? ~)llysic:s I;~c.trll\i rn r rn l~ r rs w11r1 aspire t,o j~ t r I .~ l~r ta t i~rnr ;lnd Ipn~~rc:. 'I'his i s I hc "wurrrcad do\\~rl" physics course; generally :I Iboring 1rrl:igr (11' "rr;tl" ~)hysics-tJ~;~t is. 01' t t 1 ( ~ 5 ~ourses tl1:tl h:~vr lots of ~ ( ~ t r i i i i r ~ ~ ~ s and pre~l~lems

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Hertz's Bonn Voyage No Farewell to Radio 111 111s ; ~ r t 1 c . 1 ~ 1111 I l ~ ~ ~ ~ i ~ ~ i c h Herv~ ihf;11.~11 l !I$\J, ! ) L I ~ < ' 501. V J O S ~ ~ I ~ F. k f u l l igar l ,st,;rt.c,s. "IVhtcn I le l ' t z arr ived i r l L l t i l l l l ill ISS!). 1.10 1 t . l ~ t h a t he had don(; :IS ~ n u c l i \ v ~ t h radio waves 33 sccrrrt.rl ~ ~ i ~ s s i l ) l i . L L ~ th:ir Lime.'. Hertz i n 1itc.1 con>pleletJ r l>e major. por t ion of h i5 Inst ~!Icc.t~~orn:cgnetic.s exper iment . l ~ ~ ~ l ~ l ~ i l i c ~ l as " 0 1 1 t l r c Nechanical ,\CI IOII ( > I ' FICLY 1 . 1 ~ LV:tv(.s OII I V i r e ~ , " ~ :llt(?l. 1 1 1 1 ~ v i ~ > ~ t o 1 3 ~ l l l l l .

Reference

Strike 'Law' from the Physics Dooks l.,lT ( ~I<LII~~s :11,1 l<. l~ ~ '~ l~ l l (~ (..'011cc-pr of' bl:~ .-.." I.J\IIII, l!lF!J, lj:jg(, :{I ! l ~ ~ g l i l ~ g l ~ t > o u r nl'rari 10 I-I(YII> u p o u r ph!r;~c; I; ingu;~gr* 14,'~. n~.t:*d \voriiz rhar real iy I I I : I : \ t ~ r ~ l l ~ t ~ ~ . ~ . : ~ n ( i i d a l e tor I ~ ~ > ~ I I ~ ( ~ \ ~ ( ~ I ~ . I ~ ~ I I I is "I:I\v "

J\> t*v(,~.>- g,loiI ,.<.I<,I~! 1st l<nr~\vs. sci- I I I I I I I S I I U ~ E:\-rn CI~II>I?~V:II iL?ll i t 1 ~ * I I ~ ~ I - C > ~ r l i g h t IIIJ t';ilsi-

1 1 r c l \Vl!y I t l ~ n # I t ) \,:tL COI~III ILI~ ~15ir1c I l i t , : I I J ~ I ) I I I ~ 151 \vo~. i i "l:iiv"'.' ' I l i e ' Ian- <u;tg,:c 4 ,I' ~ ( I I i i -~.c.r~rttt > I J ~ I ~ > I C ~ recog- 1>17.I.3 1111~ S~ILI:,~,(III 1-p S I I C ~ L I ~ ~ I I ~ of I l~,i .-~.r l l>c.~-.~.> u n t . c - r ~ : t i ~ ~ r y p r i ~ > r : i ~ ~ l e , 111t- j ~ ~ . i ~ i ~ : i l ~ l ( , $11 ~ ~ ~ l : ~ ~ i v i t , > - ; i l i c i so (JII,

I S \ ' l . r l I l t r ~ i ~ f h II(.I v l i ~ l a t ~ o l l s or thesc II;IV+. ? t . ~ II~~I.II ~illllll~, nlll \ V I ~ + ? I ~ wr

LI 1-11 l o olr11.1- (;rn(l ol't~:tl r tx l )e~~intcr i ta l . I \ ~n~ :o r -~ . t . c r !~ pl>\s11:+, \vr. find Sew- l c ~ r i ' , . "la\vs." Iic.plcl-'s "l:r\vs" ail11 ( . \ r L l i I.11-1okt.'- ' . la\\." \v f l ic .h i~ a r u l e of' r l lu rnh :I: ibe.t I . 'This t15;igc~ is tlr:eply l ~ l l i . ~ l ~ ~ : ~ ~ l i l l ~ r4- t ,.~l.lCl~~~l>l. ;111ci (1.) 11ur1- .-<,i(*:~tist:, I.~II. i t ror~~.~~;i( l~(:t ,s IIIC, I>IIII-

l . l i J ~ t l l ~ l l l ~ ~ , op(* I I ..]I~l~ll 0 1 I ~cic~r1t i t ic n ~ c . t h o ~ j . 1i't. III.IY~ t o IGIII "la\v" 1'rt.m

our. ..cic.n[~~ir ~:o~.;ll)~rl;rr.y IL might aL lir.4 F r ~ u n d otlrl t o >pc.;lk of st-\\.. ~ o r r ' s ti~l-c,t. prirlc.lplr.;. I)ul 11 \\-ill soon v,uni l n , + l i ~ ~ ~ i l , 11 w r l l 111.3 corrccr . and I( ~ 1 1 1 PIIII~~IICP I p ~ ~ l d i c I I I I ( ~ ~ ~ > ~ ~ I I ( ~

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ICBM vulnerability: Calculations, predictions, and error bars Art Hobson Department of Physics, University of Arkansas Fayetteuille, Arkansas 72701

(Received 6 August 1987; accepted for publication 15 October 1987)

The theory of intercontinental ballistic missile (ICBM) silo vulnerability is reviewed, and the present and probable future (mid-1990s) vulnerability of US silos is analyzed. The analysis emphasizes methodology, sources of information, and uncertainties. US ICBMs might still be survivable today but they will certainly be vulnerable to ICBM attack, and perhaps even to submarine-launched ballistic missile attack, by the mid- 19909. These calculations are presented not only for their immediate importance but also to introduce other physicists to some of the quantitative methods that can be used to analyze international security topics.

I. INTRODUCTION wide range of knowledgeable opinion about present and

For better or for worse, physics and war have been inter- twined since at least the time of the early Greeks, when Archimedes devised machines to defend Syracuse against land and sea assault by the Romans.'pz In these days of the strategic defense initiative, "third generation" nuclear weapons, technical questions about arms control, and in- tense public debate about such topics, the connection is tighter than ever. It behooves physicists to be involved, as physicists and as human beings, in this debate, for whether we like it or not, as long as there is war the fruits of our craft will surely find application in the invention of the engines of destruction.

Since the advent of nuclear weapons, an important and recurrent physics-related question for both superpowers has been: How much is enough to deter the other super- power from using its nuclear weapons, and to prevent it from gaining an advantage through the threat of such use? Since the early 1970s, when the MX missile program be- gan, the US focus on this question has been mainly on the actual or perceived vulnerability of US intercontinental ballistic missiles (ICBMs) to attack by Soviet ICBMs. The problem is that more vulnerable weapons are less likely to deter because they are subject to destruction by a first strike from the other side. An equally important point may be that more vulnerable weapons are more dangerous because they are implausible for use in a retaliatory strike and hence the other side fears their use in a first strike, and also be- cause vulnerable weapons pressure the side possessing them toward risky "hair-trigger" rules of engagement de- signed to ensure the use ofsuch weapons before they can be destroyed.

This article studies only the US side of the vulnerability equation, focusing on the ICBM problem. The bomber "leg" ofthe US strategic triad (ICBMs, SLBMs, bombers) has always been about 70% vulnerable to short-warning attack by sea-launched ballistic missiles (SLBMs) ." The US submarine leg, on the other hand, is widely acknowl- edged to be invulnerable throughout the remainder of the century.69 Much more controversy surrounds the present and future degrees of vulnerability of the ICBMs, and the significance of that vulnerability. Around 1980, the ICBMs on both sides began to be vulnerable to attacks on missile silos by increasingly accurate ICBMs of the other side. As we will see in more detail below, there is Way a

future US ICBM vulnerability. This article brings physical and mathematical methods

to bear on the problems of calculating US ICBM vulnerabi- lity today and predicting it in themid-19909. These calcula- tions are presented not only for their immediate impor- tance but also to introduce other physicists to some of the quantitative methods that can be used to analyze interna- tional security topics. Motivated by the belief that a broad spectrum of scientists can and should contribute to the study of such topics, we emphasize methodology and sources of information. Hopefully, others will be encour- aged to check and build upon this work, and to use similar methods to analyze a variety of science-related wadpeace topics.

Obviously there will be some uncertainty in our conclu- sions, not only regarding the future but even regarding present vulnerability. As we will see, the uncertainties arise not From the theory, which is generally accepted by most analysts, but from the parameters that are put into the the- ory when making specific calculations. Unfortunately, the uncertainties are not always acknowledged in the litera- ture. In this article, we include the complete range of plau- sible values of all parameters, and hence calculate a range of plausible values of such quantities as silo vulnerability.

Webegin our analysis by presenting the standard theory of silo destr~ction.'*'~ We then study the present situation and find that, depending on which end of the "vulnerability error bars" one believes, US ICBMs might still be surviva- ble today. But we find, on the basis of reasonable technolo- gical predictions about the future, that this will no longer be true in the mid-1990s. We then discuss briefly the signifi- cance of these findings, especially the international security implications of the uncertainties inherent in every analysis of strategic vulnerability.

11. THE THEORY OF SILO DEmRUCTION

We begin by reviewing the standard theory of silo de- ~truction.'~-'~ Most analysts agree that the theory gives reasonably accurate predictions and that any improve- ments on the assumptions of the theory [for instance, using an elliptically symmetric distribution in place of the circu- larly symmetric distribution, Eq. ( 1 ) below, or using a wn- tinuous probability distribution to replace the "cookie cut- ter" assumption] would alter the predictions by only a

829 Am. J. Php . 56 (9). September 1988 @ 1988 Aqerican Association of Physics Teachers 829

APPLIED PHYSICS COMMUNICATIONS, 6(4), 253-277 ( 1 9 8 6 - 8 7 )

MISSILE VULNERABILITY: THEORY, PRACTICE, AND ARMS CONTROL IHPLICATIONS

Art Hobson Department of Physics University ~f Arkansas Fayet tevi l le , AR 72701

ABSTRACT

We review t h e theory of ICBM a i l o v u l n e r a b i l i t y , and analyze the v u l n e r a b i l i t y of three recently-proposed bas ing modes f o r t h e new Midgetman ICBM. These modes a r e superhard s i l o basing, and two mobile basing modes. The r e s u l t s a r e used t o c a l c u l a t e the v u l n e r a b i l i t y of the f u l l U.S. ICBM fo rce i n t h e 19908, as a func t ion of Midgetman baeing and of Sov ie t fo rce l e v e l s (uncon- s t r a i n e d , SALT-constrained, SALT plua 50% cu te , and f i n i t e o r minimum de te r rence ) . These calcula t ions a r e preaented b o t h f o r t h e i r immediate importance and a l s o t o in t roduce o t h e r p h y s i c i s t s t o some of t h e q u a n t i t a t i v e methods t h a t can be used t o analyze i n t e r n a t i o n a l s e c u r i t y topice.

INTRODUCTION

The s t r a t e g i c forces of both superpowers are pe rce ived by

some t o b e inc reas ing ly vulnerable. The bomber "legs" o f the

s t r a t e g i c t r i a d s have always been about 70% vulnerable t o ahot t -

warning a t t a c k by sea-launched ballistic miaei les (SLBM~) . Around

1980, t h e land-based intercont inenta l b a l l i s t i c m i s e i l e s (ICBMs)

on both a ides began t o be wlne rab le t o high-accuracy ICBM a t t a c h

on m i s s i l e s i l o s . However, the di f ference between ICBM and SLBM

f l i g h t t i n e s (30 minutes vereue 15 minutes) makes i t d i f f i c u l t t o

success fu l ly des t roy both ICBMs and bombers because i f t h e e n t i r e

a t t a c k is launched simulteneously then t h e SLBMa w i l l explode

Copyrlght0 1987 by Marcel Dskkcr, Inc.

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References

1 1) ( ; I > t ~ r v ~ ~ , h l ~ ~ n , % 1 , ~ ! C r p t 1.1~1 t'r\qr 40, 7:Kf 1 l!t77,

:! Y Bou l~~and . "1.itluld ('ryb1.11~ 111 UIIII'$EI- val S y ? t ~ n ~ s ' ' In Sit1111 SI~IP l't~v>ic.>, SIII~- pl+~r111~1>1 1.1. 2.W 8 l ! C K t

FI~~: I )~,~I I . .J I < . \ H s t f< ,~ t . / , , / ! t'w A-urvf /,,II'P, -~,rt,tr :,..,

,- %2 / ~ < 1 1 , , :\ iff8 1 ~#;ll;~:~~~ll,;

Physicisls and nuclear war I tviis very ~11east.tl 111 set: !our. .JLIII~. c t l ~ f a . ~ r ~ a l (page 1121 urgrng i lh,~i~d.~.<ta to

get ~ n v o l v e d i r ~ 1ecichi1lL: t h r ~echlidiltrgy uf' nuelc2ar- cvitr ( { I studcr~r. ancl tht. gerreral p t ~ t > l ~ c : i r ~ c l c a l l ~ n ~ trrl I t ~ r n ~ t t ~ rucha r~y t ' r t h l r v r ~ r ~ t ~ i b ; ~ ~ h l n ~ ~ 1 1 ~ t V ~ ~ : l l h

v i . ~ t hv Nuc.lt?ill- \Vnr I.:duc~n~~t)~r 1'rojc.c.t (11 [Ill: F ' rd~br i~r la r~ 01' .~~ILJTI~. ; I I~ Sc~,.n- li.;b I . l r ~ u , r v ~ r . 1 hi.litr\t. t l ia t rli;ln\ unl\.t,:.srtlr.* i t r ~ d ,.1.illrg1.2 \v i l l f ind 11

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I ~ I K ~ iil' rni>dt.rri d e s r r . \ ~ ~ t it.ln Su\.h ;I

c.uur>ta. I!, I),. \ *~ah le . nlust b i ~ t ~ .u l y ~ r ~ t e r d ~ s c ~ p l ~ r ~ d r ! . . o f f e r~ng c3cv\nornlc.;. I l ~ s t v r y . ~ r u i ~ l t c a l >c~r~ncr. , s t r c u ~ l u ~ y . i l nd st! on, and 15 t~r,-t ~ ; r~ iL :hr by ~ n t r r d i s r r - 1)lirr;iry I;lculr?; rc.,trrls Sur I? rc;lrrla c . s - 1st 1)otcntr;rlly or\ III;I~I~ C~III~ILI,~!~. h u ~ 11 IS ~1iIl i t .olt t4> dr:i\v thtvn cogi:tllc~r ant1 SU~IJI? :~[>propr l :~tc. t C : i c l ~ ~ r r ~ ~ I ~ ~ ~ I ~ I , I ; I I ~ r\ "hrldgc." hc~\vr-:n ~ c l r r r c r ~ : ~ n t l not!. sic.nct. tac.ulry c~,ncl.l.l~c-d WILII thc pr~.r l ) I t .~~~ ~ I I IIII,:~~;II \v;rr ,~p~w;ir . C O O

r.i.qu~~.c{l. .I.. I.. .I 1111 h t r t l \ v r c r~ -uc.lL tranrh I)II d ~ t l ~ . r c n r L.:IIIIIJII-I,.; I hr(rt lch. , jut tht. na l lon .and ~ h c \ ~ i r t ' l t l ' 1

LII thtl IICI~. 01 ~ I - c L I I ~ ~ : : s u c h trr111~t:> and IIII~?, ,J 2roo r~ 01 ' ! ; t c ~ u l l ~ ~ Iron1 ( I ~ t r c > r ~ r ~ t o r i l t t ~ r ~ t f l e . ,ICI.II~* tI1v II:I~I~III,

a l l tvhbn1 [ ) ; I~ I I~- I~ ; I I~ (~ III tI1t3 II:III~II- MAGNETS AND

\VI,IV ( ~ O I I ~ ~ I C ~ I ~ I ~ ~ ~ ~ on t t ~ c '1.t1rtb.11 of CRYOSYSTEMS Nuc.lt.;~r \\'<tr la51 r\;o\-t~n~\lt.r. h , ~ \ . t ~ $!r. <:IIIIZP~ *I I W \ ~ OI.C;IIIIZ;IIII~II " l l ~ ~ ~ l \ * c l (.':IIII~II.~~> to P ~ I : ~ ~ I I [ XLIA:I~,~II- LV;,I " We are leaders c I't'A31 i u r +1111ri. l)cl>t~C S I I I ~ ~ > 1 1 ~ 1 1 1:1.1(< t ~ ' o ~ l l , ~ l ~ : 1 , ~ l I l :\c,.lll.l#~, \v ,~ . - l~ l l l~ : t i~ l l , r)(.'2f10:i(;b (-'~~~.I..!.IIIC ,,I W . I ~ . I ~ ~ I S ~ L :III'~ I I < ~ ~ > ~ . I I : I I I I > ~ ~ \ X I , * I I ( * c-~I~I.III~.~~:I:IIIc CRYOGENIC CONSULTANTS LIMITECI \\~lll., >c~lcltt lst grt,ur:>, .uci1 .I. I'.!A 5 1.1 ( . ' S , ;i11,1 1's ti , 10 111111.111. . i r l ~ I p ~ r , - ,I uc-I. nu11er1:11. I to r t,t.tur>t:.> 8 ~ : ~ d C.;IIIII~~IS

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Ergodic properties of a particle moving elastically inside a

Arthur Hobson Department of Physics, Universiry of Arkansas, Fayetteville, A r k a m 72701 (Received 16 May 1975)

The flow of a classical particle bouncing elastically inside an arbitrary polygon is investigated. If every interior angle is a rational multiple of o, thme exists precisely one isolating integral in addition to the energy; this integral is described in detail; any possible third integral is nonisolating. If one or more interior angles is an irrational multiple of .rr, the second integral becomes everywhere nonisolating and non-lebague- measurable, i.e., the second integral disappears. The flow of two hard points bouncing elastically in a fmite one-dimensional box is equivalent to the flow of a point particle moving elastically inside a ri@t triangle having interior angle tan-' (mJm,)"2, so the preceding remarks apply to this model. Nonrigorous arguments are given in support of the notion that the polygon model is ergodic and mixing, but is not a C- system.

I. INTRODUCTION will stimulate others to prove (or disprove!) ergodicity of the polygon model. There has been a recent resurgence of interest in the

rigorous analysis of simple classical Hamiltonian sys- tems, mainly in the hope of illuminating some basic problems of statistical mechanics.'-5 F o r instance, Sinai's proof' that the N-body, hard sphere gas in a fi- nite box has the strongly "random" K-system property (and is therefore a l so mixing and ergodic) makes it ap- pear likely that realistic classical many-body systems have such "randomness" built into their mechanics.

Lebowitz has suggested3 that it would be interesting to study the ergodic properties of the unequal-mass one- dimensional hard point gas, i. e., N hard points movipg elastically inside a finite one-dimensional box. Even for the case N = 2, this problem turns out to be surprisingly complicated. Casati and ~ o r d ' have recently performed computer experiments for the case N = 2, and have con- cluded that the system appears to be ergodic and mixing when the parameter 6 defined by

tan0 = (m,/m,)' (1)

is a n irrational multiple of n, and that the system is not a C-system (and hence not a K-system). Of course, computer experiments cannot prove such results.

A s is proven in the Appendix, the two-body hard point gas may be canonically transformed into a single point moving elastically (i. e., a t constant speed, with equal- angle bounces from the walls) in two dimensions inside a right triangle with interior angle 0 given by (I). Hence the ergodic properties of this "right-triangle model" a r e identical to those of the two-body hard point gas. But a brief study of the right-triangle model reveals that no extra complication is introduced by generalizing to the "polygon model, " i. e., a single point of mass rn moving elastically in two dimensions inside a n arbi t rary (but nonintersecting) polygon with interior angles el, 02, . . , 6, (Fig. I).

This paper is mainly devoted to the statement and proof of some of the ergodic properties of the polygon model (see Sec. 11, Theorems 1,2, and 3). The primary question, i. e., ergodicity o r nonergodicity of the model, remains open, although ergodicity is strongly indicated (see Sec. 111). Hopefully, publication of these results

II. A FEW ERGODIC PROPERTIES OF THE POLYGON MODEL

The model is defined in Sec. I. It is a conservative Hamiltonian system with H(P,,p,) =@: +p:)/2m, where Pi = m dq,/dt (i = 1, 2). Definitions: "configuration space" Q is the set of a l l points (q,, q,) inside o r on the boundary of the polygon. The se t r = Q x R' is "phase space, " with points denoted (ql, q2,p1,p2). The "energy surface" r (E) means a l l (q,, qz, pl,p,) E I' which satisfy H@t,pz) = E. The "momentum phase angle" 6 means the angle which the line f rom the origin to the point (P,,p,) makes with the pl axis i n momentum space, s o that

"Reduced phase space" means the cylinder X = Q X[O, 2n) (base Q, height 2n), with points labeled x = (q,, q,, $1. Any moving phase point is confined to a single l?(E); we will henceforth restr ic t our attention to the motion on r ( E ) . This motion can be described in t e r m s of the motion of the "reduced phase point" x = (ql, q2, +) EX, since the mapping f rom r ( E ) to X is one-to-one. The flow in X will be represented by the one-parameter group of transformations T', i. e., T ' x means the reduced phase point a t t ime t corresponding to the initial (at t = 0) point x ; t may be positive o r nega- tive; If the atom hits a vertex a t time t o > 0 (1, < O), Tsx is undefined for t > to (t <to). The complete path in X passing through x a t t = 0 is denoted P(x) , i. e., P(x)

FIG. 1. The polygon model, tor the case n = 5. The dashed line i s a portion of a path.

2210 Journal of Mathematical Physics. Vol. 16, NO. 11, November 1975 Copyright O 1975 American Institute of Physics

Downloaded 13 Mar 2008 to 130.184.237.6. Redistribution subject to AIP license or copyright; see http:/ljmp.aip.orgljmplcopyright.jsp

Bulletin of the American Physical Society, v 18, Issue 4, p 724-724, 1973

t iga t ed t h e t a r g e t pa i r s : WN, W; InN In; GaN, Ge; metals. The formalism applies to photoemis sion a s well a s other surface-redated problems. Si3N4, S i ; and AlN, Al. The s toichiometr ies of the

compounds were ve r i f i ed using e l l ipsometry techniques +Research sponsored by the U.S. Air Force Office and an e l ec t ron microprobe. of Scientific Research, Air Force System Command, under AFOSR Grant No. 71-1978.

KM13 Analysis of U a ~ n e t i c Bubble Sensor U e t a l l u r u

KM 11 Calculation of Many Bodv Effects on Energy by Nuclear Backscattering. J.F. Ziegler , J.E.E. Baglin, A. Gangulee. IBU-Research, Yorktown Heights, New York

Distribution C w e s in Pkloemission. + 10598--Uagnet bubbles a r e i n j ec t ed , s t ee red , and aensed J.I. GERSTEN and N. IZOAR, City College, CUNY by a metal iza t ion of permalloy (Ni 80%. Fe 20%) and p l d --A study of the energy distribution curves of ( e l e c t r i c a l contact ) . This system has been s tudied in photoemitted electrons h m the simple metals has d e t a i l by consider ing the layered metal f i lms of Fe-Au, been made. Several mechanisms responsible for Ni-Au, and then the more complex PeNi-Au. These PrOducing photoemitted electrons a re considered. couples were s tudied a s a funct ion of hea t treatment

In additlon to the usual surface ejection mecha- (150'-350.C; 10 min-72 h r s ) . Marked in t e rd i f fus ion was observed, a t l e v e l s an order of magnitude above nism we investigate the emission produced by the so l id s o l u b i l i t i e s . Diffus ion constanta and act ivat ion

imaginary optical potential. R o c e s s e s involving energies were evaluated with reference t o Seeman- bulk and surface plasmons a re studied. The con- BoNin X-ray d i f f r a c t i o n a ~ l y s i s of t h e same samplee. tribution to the ape- of low energy secondary Indicat ions of the e lus ive Au-Ni compound phase a r e electrons arising from plasmon decay are calcu- discussed. lated. Energy distribution curves are being cal- culated involving the above mechanisms and a comparison with experiment will be made.

KM 14 Sput ter inu of Potassium Halides i n an A r

+Research sponsored by the U .S. Air Force Office of Scientific Research, Air Force System Command, under AFOSR Grant NO. 71-1978. and Ar' ion i r r a d i a t i o n . The i r r a d i a t i o n produced

v e l l defined spot pa t t e rns when t h e c r y s t a l surfaces had minimum damage. Eject ion of t h e halogen was

KM12 Inves t iga t ion of Braguts Rule using Various thought t o be due t o t h e < l l O > c o l l i s i o n sequences Nitroxen-Compound Targets . J.B.B. Baglin, J. P. a r i s i n g from t h e recombination of t h e Vk cen t r e and Ziegler , J. J. Cuomo. W.U. Uolzen, IBU-Research. an e lect ron. This l e d t o t h e accumulation of Torktovn Heights, New York 10598-Bragg's Rule ( the potassium l aye r s on t h e surface . Exposing t h e a d d i t i v i t y of s topping powers f o r ions i n compou$ds) damaged c r y s t a l s t o air l e d t o t h e oxidat ion of has been inves t iga t ed by e l a s t i c a l l y s c a t t e r i n g He potassium as seen from t h e random spec t r a of t h e ion9 a t 2 MeV from t h i n t a r g e t s (about 500 atoms thick) Rutherford backacat ter ing of 1 . 5 MeV protons Prom of pure elements and t h e i r n i t r i d e s . Comparisons w i l l a damaged KCP c r y s t a l face. be made between n i t r i d e lmyers ( fo r example InN) and corresponding pure element f i l m (In) . We have inves- +Work supported i n pa r t by NSF

THURSDAY AFTERNDON, 26 APRIL 1973 ALEXANDRIA ROOM, SHERATON PARK A T 2:00 P. M.

(J. L. LEBOWITZ presiding)

Statistical Physics and Cr i t i ca l Phenomena

KN 2 B x n d State Effects in the Kinetics of Dilute Quantum Gases. * K . E. HAWKERr and W. C . SCHIEVE,

w s . - - m e t h o d s developed Untversltv of Texas a t Austin-- It i s well known that in previouslyl are applied to the analysis of N order to obtain a kinetic equation for dilute g a s e s which classtcal one-dimensional hard points (or rods) glves the correct equilibrium equation of s tate in the bi- tn a box of length L . Exact expresstons are nary collision approximation (BCA) one must include the obtained for the motion of a l l N par t ic les , for collisional transfer corrections to the Boltzmann equation arbt trary tni t t a l phase potnts. Liouville's due to spatially non-local effects . Such calculations equatton may be solved exactly for arbi trary have been restricted to the c a s e of potentials which can- t n t t t a l probabiltty dtstr tbutions. All reduced not form bound states. We show that withln the BCA one dlstr tbutlons, expectatton values. correlat ton can obtain a kinetic equation for the singlet distribution functtons e tc . may be obtatned exactly. Thil function which does give the correct equilibrium equation work f s an extension of the work of Lebowttz of s tate including the effects of bound s ta tes in the sec- and others, whlch neglected wall effects . The ond virlai coefficient. In order to do this it i s necessary present work I s exact for f i n t t e L , and hence to retain certain non-decaying contributions from the ini- represents an exact non-tqi i iTFiun analysts of tial correlations arising from bound pairs. Physically the a system for whtch there e x i s t bto character- kinetic equation describes a dilute g a s of interacting I s t t c ttmes: a hydrodynamic t i = ~ / v , and a monomers in which a certain number of dimers, which klnetlc ttnie L/Nv. For large N , these tlmes were present initially, propagate freely. are wtdely separated.

l k t h u r Hobson and David N. Loants, Phys. Rev. *Submitted by JACK S. TURNER 173. 285 (1968). TL. Lebwltz and J . K . Percus, Phys. Rev.

t ~ e s e a r c h supported by the Robert A. Welch Foundation

724

Volume 28A, number 3 P H Y S I C S L E T T E R S 18 November 1968

the same a s the result Jeff = -0.13 eV obtained by Jones and Budnick [4] from the Al-Knight shift in GdA12 based on the uniform conduction

-8% electric spin polarization model.

% We express our thanks to Dr. J. I. Budnick for

og many helpful discussions and we are grateful to - J. H. Wernick of the Bell Telephone Laboratories for kindly supplying us with the samples.

L

Fig. 1. Temperature dependence of the thermoelectric power and electrical resistivity of GdA12.

One knows from the study of the Boltzmann equation for transport [g] that S and a (the elec- trical conductivity = l/p) a re related by

thereby giving r 2 k 2 ~ 1 Ap AS =- -- 31el P AE '

where k i s the Boltzmann constant and e the electronic charge. By substituting the values of 4P and AS at various fixed temperatures, we ob- tain the exchange interaction A E = Jeff(0) = 40.12 0.01) eV. The above value i s very much

References

1. V. Jaccarino, J. Appl. Phys. 32 (1961) 102s. 2. R. E-Gegenwarth. J. I. Budnick, S-Skalski and J. H.

Wernick, Phys. Rev. Letters 18 (1967) 9. 3. M. Peter, D.Shaltie1. J. H. Wernick, H. J. Williams,

J. B. Mock and R. D-Sherwood. Phys. Rev. 126 (1962) 1395.

4. E. D.Jones and J. I. Budnick. J. Appl. Phys. 37 (1966) 1250.

5. H. J. Williams, J. H. Wernick, E. A. Nesbitt and R. C. Sherwood. J. Phys. Soc. Japan 17 supplement B-1 (1962) 91.

6. J. Crangle and J. W.Ross, Proc. Intern. Cod. on Magnetism, Nottingham 1964 p h e Institute of Physics and the Physical Society of London. 1965) p. 240.

7. ~ . s t a l i i i sk i and S. Pokrzywnicki. Phys. Stat. Sol. 14 (l966) K157.

8. J. A. Mydosh, M. P. Kawatra and J. I. Budnick. Phys. Letters 24A (1967) 421.

9. J. M. Ziman, Principles of the theory of solids (Cambridge University Press. Cambridge, 1964) p. 202.

FURTHER COMMENTS ON IRREVERSIBILITY * t

A. HOBSON Department of Physics. University of Arkansas,

Fayetteuille. Arkansas, USA

Received 4 October 1968

Further comments a r e given concerning Balescu's views on irreversibility in statistical mechanics.

In a recent exchange of letters [I, 21, argu- letter [2] have already been dealt with in the au- merits have been given for and ag&st the point thor's previous letter [I]. In this letter, the au- Of view of the Prigogine theory 13-51 toward the thor would like to just clarify a few points and to Origin of irreversibility in statistical mechanics. rectify One S ~ ~ ~ O U S Imi~quotation contained in Most of the points contained in Balescu's recent Balescu's letter 121.

Balescu does not directly answer the ques-

* Supported in part by the National Science Foundation. tions raised in ref. [l], but instead brings up This paper concludes the discussion (Edltor). several matters (such as quantum mechanics,

NASA (1946) d i a b a t i c f l o v a l l ows one t o s t a r t from l i n e a r MCCABEE , Naval Ordnance I a b and J.A.WHITE, American U. ' Schroedinger equa t i on f o r one e l e c t r o n , t o p a s s t o c l u s t e r

of molecules , d i a b a t i c f low, t o end v i t h macroscopic non- -- We p re sen t a parametr ic equa t i on of s t a t e which is l i n e e r Blas ius-Prandt l (1908) boundary l a y e r flow. I n t e r - developed from assumed f u n c t i o n a l dependences o f AT

-. m l e c u l a r f o r c e s a c t i o n r e p l a c e s continuum s o l i d s de fo rm- . T-Tc,PP= P. ;cC, and (&p/df) on t h e pa r ame t r i c va r - t i o n syatem. Cur l d i s t u rbances superimposed dn system fur- i a b l e s "rr"and O. For t h e lpaTticul8r choices AT = n i sh r ig-zag p a t t e r n of p a t h l i n e s of molecular c l u s t e r s p e r f e c t l y analogous t o i n s t an t aneous ly f rozen turbulence r ( 1 - b e e p ) , Af' = P re, , and (ap/Jf) osci l lograms from wind-tunnel t e s t s . Applied t o v e l o c i t y where P , b, and k a r e :onstante and P and 6 T a r e t h e s tan" boundary l a y e r a l ong p l a t e , thermal boundary l aye r along dard c r y t i c a l exponents,and t h e chemical p o t e n t i a l p l a t e , c i r c u l a r c y l i n d e r , v a r i a b l e a l t i t u d e s of s tandard a t d i f f e r e n c e a s a func t i on of r and 8 i a g iven by

KK 5 Viscous D i s s i p a t i o n Models Developed from t h e t a i n r e s u l t s of a formula t ion i n which t h e A p equabion Lagrangian Form of t h e Dynnmical Equations. MARY is made t o f i t emp i r i c a l l y determined cons t an t

contours f o r C02. f unc t i ons which e x a c t l y s a t i s f y t he Lagrsngian form of t h e N a v i e r S t o k e s equa t i ons have been found. Supported i n pert by Zhe Nat ional Science Foundation. These func t i ons r ep r e sen t models f o r v i s cous d i s s i - pa t i on of k i n e t i c energy i n unbounded and semi-

KK 9 s t a t i s t i c a l Mechanics of t h e Non-Rela t iv is t ic i n f i n i t e incompress ib le f l u i d s . The d i s t o r t i o n Zachariasen Model. ROBERT G W Y and PETER 8. SHAW, experienced by a f l u i d element i n such a flow model

i s dep i c t ed . S t a t e Univ.--The s t a t i s t i c a l mechanics o f t h e non- r e l a t i v i s t i c Zachar iasen model i s s t ud i ed t o c l a r i f y t h e

%RC-NAS Res ident Research Assoc i a t e mechanism of macroscopic mat ter - -ant imat ter s epa ra t i on proposed by 0 m e s . l The model con t a in s a s elementary p a r t i c l e s a B p a r t i c l e , i ts a n t i - p a r t i c l e t h e B, p a r t i c l e

KK ~ ~ ~ l ~ i ~ ~ the M~~~~ carlo Method to Lonn-Ranned and an A p a r t i c l e . The i n t e r a c t i o n a l l ' m s f o r t h e v i r t u a l t ransformat ion between A and BB p a i r s . I n t h e l i m i t o f i n f i n i t e bare A-par t ic le r e s t energy and i n f i n i t e coupl ing

t i o n envisaged by Omnes.

*Submitted by R. L. Cibbs. 'R. m e s , Phys. Rev. L e t t . 23, 38 (1969).

'S . C. Brush. H. L. S a h l i n , and E . T e l l e r , J. Chem. Phys . KK lo Ergodic ProPerties o f a B i l l i a r d -11 in 8 Polygon. ARTHUR HOBSON, U. o f Arkansas.--The flow of a c l a s s i c s 1 p o i n t - p a r t i c l e bouncing e l a s t i c a l l y i n s ide an a r b i t r a r y polygon i s i nves t i ga t ed . I f every i n t e r i o r

KK Three-bod in a Localized Densit Gradient.* ang l e i s a r a t i o n a l mu l t i p l e o f I , t h e r e e x i s t 8 pre-

R. L. Gibbs and Ticson La. Tech ".--when'a many- c i s e l y one isolating i n t e g r a l i n a d d i t i o n t o t he energy;

body Vavefunction i s w r i t t e n y = * exp ( -u ) , t h e energy this second lntegral may be written In the form 4

f ( p l , p2) - cog ( N J ~ I ~ ) + s in4(N#/4)

second i n t e g r a l d isappears . The f l o v o f two hard rods

spacing, i . e . , we g ive t h e va lue of tsn-1(m2/ml)112, and hence t h e preceding remark. apply f t r , , \ : j ~ ~ X V ; U ~ ~ * V ~ U ; ~ ~ ~ ... di; /d s,,

By comparing previous c a l c u l a t i o n s on t h e quantum e l e c t r o n t o t h i s model.

&as1 some r a t h e r i n t e r e s t i n g q u a l i t a t i v e s ta tements can be made concerning t h e c o r r e l a t i o n s .

KK 11 An Orthoraonal Transformation t o Uncouple Omaae r ' a

%upported i n p a r t b y t h e Research Corpora t ion . Phenomenolo~ica l Equations. R.E. KENNEDY and R.J. BRUNO,

~ u . s . Becker, A . A . B roy l e s , Tucson Dunn, Phys. Rev.. Cre iphton U.--Irreversible phenomerm such a s t h e P e l t i e r

175, 1, 224 (1968). and Seebeck e f f e c t have been s u c c e s s f u l l y de sc r i bed twine t h e Onsagar p l enomsno lo~ i ca l equat ions . The Onsager s- qua t i ons can be appl ied t o t h e problem o f i o n t r a n s p o r t a-