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Volume 66 No. 2 April - June 2010 avril à juin 2010 A PEEK INSIDE Serving the Canadian physics community since 1945 / Au service de la communauté canadienne de physique depuis 1945 THE PERIMETER INSTITUTE A L’INTÉRIEUR L’INSTITUT DE PERIMETER Canadian Association of Physicists / Association canadienne des physiciens et physiciennes www.cap.ca PHYSICS IN CANADA LA PHYSIQUE AU CANADA Canadian Association of Physicists Association canadienne des physiciens et physiciennes www.cap.ca Volume 66 No. 2 (Apr.-June 2010 / avr. à juin 2010) 67 69 71 Foreword / Préface by/par R. Myers and N. Turok 73 77 83 Why Physics Needs Quantum Foundations, by L. Hardy and R. Spekkens Editorial - “An Experiment in Theoretical Physics”, by N. Turok Éditorial - “Une expérience en physique théorique”, par N. Turok Quantum Bayesianism at the Perimeter, by C.A. Fuchs A Triple Slit Test for Quantum Mechanics, by U. Sinha, C. Couteau, F. Dowker, DE FOND ARTICLES FEATURES T. Jennewein, G. Weihs, and R. Laflamme 87 91 95 99 103 107 111 115 119 123 Spin Systems and Computational Complexity, by D. Gottesman Warped Views: Observing Black Holes, by L. Boyle and L. Lehner Analog Gravity and Black Holes, by W.G. Unruh Phenomenological Quantum Gravity, by S. Hossenfelder and L. Smolin Getting a Big Bang from String Theory, by C. Burgess Reviving Gravity’s Aether in Einstein’s Universe, by N. Afshordi Dark Forces, by B. Batell and M. Pospelov The Early LHC Era, by M. Trott The Geometry of Trees, by F. Cachazo Quark Soup: Applied Superstring Theory, by A. Buchel, R.C. Myers and A. Sinha EDUCATION AND EDUCATION CORNER ENSEIGNEMENT ET ESPACE ÉDUCATIF Cover / Couverture : Architect’s rendering of The Stephen Hawking Centre at Perimeter Institute, now under construction and expected to open in fall, 2011. Cover design by Perimeter Institute, image courtesy of Teeple Architects Inc. 127 Perimeter Scholars International, by J. Berlinsky 130 Mission: Outreach - The Why and the How of It, by J. Matlock and G. Dick 135 Perimeter Institute - Outreach - Measuring Planck’s Constant - Black Box Demonstration Advertising Rates and Specifications (effective January 2010) can be found on the PiC website (www.cap.ca - Physics in Canada). Les tarifs publicitaires et dimensions (en vigueur depuis janvier 2010) se trouvent sur le site internet de La Physique au Canada (www.cap.ca - La Physique au Canada). PHYSICS IN Croquis d’architecte du Centre Stephen Hawking à l’Institut Perimeter, maintenant sous construction et dont l’achèvement est prévu pour l’automne 2011. Couverture conçue par l’Institut Perimeter. Image courtoisie de Teeple Architects Inc. CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C i DEPARTMENTS DÉPARTEMENTS 82 Departmental, Sustaining, Corporate and Institutional Members / Membres départementaux, de soutien, corporatifs et institutionnels PHYSICS IN CANADA LA PHYSIQUE AU CANADA The Journal of the Canadian Association of Physicists 90 98 102 Congratulations / Addendum La revue de l’Association canadienne des physiciens et physiciennes News - Killam Prizes EDITORIAL BOARD / COMITÉ DE RÉDACTION 106 114 Art of Physics / L’Art de la physique 141 ISSN 0031-9147 Editor / Rédacteur en chef News - Canada Excellence Research Chairholders PiC welcomes articles / Invitation à soumettre des articles Science Policy Corner (NSERC) / Le coin de la politique scientifique (CRSNG) 142 Second Science Policy Symposium held 12-14 May 2010 in Gatineau, Quebec 144 In Memoria - H. Roy Krouse (1935-2010) - B.P. Stoicheff (1924-2010) 146 Books Received / Livres reçus 147 Book Reviews / Critiques de livres 152 Advertisement / Publicité Béla Joós, PPhys Physics Department, University of Ottawa Département de physique, Université d’Ottawa 150 Louis Pasteur Ottawa, Ontario K1N 6N5 (613) 562-5758; Fax:(613) 562-5190 e-mail: [email protected] Associate Editor / Rédactrice associée Managing / Administration Francine M. Ford c/o CAP/ACP; E-mail: [email protected] Book Review Editor / Rédacteur à la critique de livres Richard Hodgson, PPhys c/o CAP / ACP Suite.Bur. 112, Imm. McDonald Bldg., Univ. of / d’ Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5 Email: [email protected] Advertising Manager / Directeur de la publicité Greg Schinn EXFO Electro-Optical Engineering Inc. 400 av. Godin Quebec (QC) G1M 2K2 (418) 683-0913 ext. 3230 e-mail: [email protected] Board Members / Membres du comité : René Roy, phys Département de physique, de génie physique et d’optique Université Laval Cité Universitaire, Québec G1K 7P4 (418) 656-2655; Fax: (418) 656-2040 Email: [email protected] David J. Lockwood, PPhys Institute for Microstructural Sciences National Research Council (M-36) Montreal Rd., Ottawa, Ontario K1A 0R6 (613) 993-9614; Fax: (613) 993-6486 Email: [email protected] Tapash Chakraborty Canada Research Chair Professor, Dept. of Physics and Astronomy University of Manitoba, 223 Allen Building Winnipeg, Manitoba R3T 2N2 (204) 474-7041; Fax: (204) 474-7622 Email: [email protected] Canadian Association of Physicists (CAP) Association canadienne des physiciens et physiciennes (ACP) The Canadian Association of Physicists was founded in 1945 as a non-profit association representing the interests of Canadian physicists. The CAP is a broadly-based national network of physicists in working in Canadian educational, industrial, and research settings. We are a strong and effective advocacy group for support of, and excellence in, physics research and education. We represent the voice of Canadian physicists to government, granting agencies, and many international scientific societies. We are an enthusiastic sponsor of events and activities promoting Canadian physics and physicists, including the CAP’s annual congress and national physics journal. We are proud to offer and continually enhance our web site as a key resource for individuals pursuing careers in physics and physics education. Details of the many activities of the Association can be found at http://www.cap.ca . Membership application forms are also available in the membership section of that website. L’Association canadienne des physiciens et physiciennes a été fondée en 1946 comme une association à but non-lucratif représentant les intérêts des physicien(ne)s canadien(ne)s. L’ACP est un vaste regroupement de physiciens oeuvrant dans les milieux canadiens de l’éducation, de l’industrie et de la recherche. Nous constituons un groupe de pression solide et efficace, ayant pour objectif le soutien de la recherche et de l’éducation en physique, et leur excellence. Nous sommes le porte-parole des physiciens canadiens face au gouvernement, aux organismes subventionnaires et à plusieurs sociétés scientifiques internationales. Nous nous faisons le promoteur enthousiaste d’événements et d’activités mettant à l’avant-scène la physique et les physiciens canadiens, en particulier le congrès annuel et la revue de l’Association. Nous sommes fiers d’offrir et de développer continuellement notre site Web pour en faire une ressource-clé pour ceux qui poursuivent leur carrière en physique et dans l’enseignement de la physique. Vous pouvez trouver les renseignements concernant les nombreuses activités de l’ACP à http://www.cap.ca. Les formulaires d’adhésion sont aussi disponibles dans la rubrique “Adhésion” sur ce site. II C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) Normand Mousseau Chaire de recherche du Canada, Département de physique Université de Montréal, C.P. 6128, Succ. centre-ville Montréal, Québec H3C 3J7 (514) 343-6614; Fax: (514) 343-2071 Email: [email protected] Michael Steinitz, PPhys Department of Physics St. Francis Xavier University, P.O. Box 5000 Antigonish, Nova Scotia B2G 2W5 (902) 867-3909; Fax: (902) 867-2414 Email: [email protected] Robert Thompson, PPhys Dept. of Physics and Astronomy University of Calgary, 2500 University Dr. NW Calgary, Alberta T2N 1N4 (403) 220-5407; Fax: (403) 289-3331 Email: [email protected] ANNUAL SUBSCRIPTION / ABONNEMENT ANNUEL : $42.00 Cdn + GST or HST (Cdn addresses), $41.00 US (US addresses); $46.00 US (other/foreign addresses) Advertising, Subscriptions, Change of Address/ Publicité, abonnement, changement d’adresse: Canadian Association of Physicists / Association canadienne des physiciens et physiciennes, Suite/Bureau 112, Imm. McDonald Bldg., Univ. of/d’ Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5 Phone/ Tél: (613) 562-5614; Fax/Téléc. : (613) 562-5615 e-mail/courriel : [email protected]; Website/Internet : www.cap.ca Canadian Publication Product Sales Agreement No. 0484202/ Numéro de convention pour les envois de publications canadiennes : 0484202 © 2010 CAP/ACP All rights reserved / Tous droits de reproduction réservés WWW.CAP.CA (select Physics in Canada / Option : La Physique au Canada) FOREWORD A PEEK INSIDE THE PERIMETER INSTITUTE “Every great advance in science has issued from a new audacity of imagination.” – John Dewey “It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with experiment, it’s wrong.” – Richard P. Feynman W e were delighted to be invited to prepare this theme issue of Physics in Canada, and we hope you will enjoy the glimpse provided here into the diverse research activities at Perimeter Institute (PI). From its inception, spacetime and quantum theory have been at the heart of PI research. While these topics might at first sight seem abstract and somewhat remote from the real world, we hope that you will see in these pages that here at PI, we still live by the maxim that nature and experiment are a theorist’s best guide. One of Perimeter’s unique features is its group working on quantum foundations. Rob Spekkens and Lucien Hardy eloquently lay out the case for their field, describing both the motivations and the impact it has had. Among these was the recent experimental confirmation of Hardy’s Paradox by groups at both the University of Toronto and Osaka University, which may in time yield practical applications. Christopher Fuchs also gives his perspective on a fresh approach to unraveling the conundrums of quantum mechanics with the help of Bayesian probability theory. Quantum information science emerged as an offshoot of quantum foundations, and now flourishes with the promise of new technologies which may transform our society. Perimeter was instrumental in launching the Institute for Quantum Computing (IQC) at the nearby University of Waterloo, both partners with which PI enjoys strong synergistic relations. In two articles here, we see the synergies between quantum information and other areas of theoretical physics. In their article, Urbasi Sinha, Raymond Laflamme and colleagues give an account of a new triple slit experiment which tests the basic tenets of quantum mechanics following a proposal by PI’s Rafael Sorkin. Then Daniel Gottesman describes how work on quantum computational complexity classes has provided unexpected insights into spin glasses. On PI’s spacetime theme, we begin with two thoroughly different accounts of black holes. Once an exotic toy in the theorists’ playground, these phenomena of ultra-strong gravity have become the workhorses of modern astrophysics. In their article, Luis Lehner and Latham Boyle describe new astrophysical observations which may teach us more about black holes through their impact on light and gases caught in their immense gravitational fields. In contrast, Bill Unruh, one of PI’s Distinguished Research Chairs, hopes to tame these dynamos in his ‘bathtub’. His article tells a remarkable story about how doing experiments in a tank of water may provide a better understanding of Hawking radiation leaking from black holes and, perhaps, even of quantum gravity. While quantum gravity delves into spacetime at unimaginably small scales, Lee Smolin and Sabine Hossenfelder describe how we may nevertheless find fingerprints of the quantum nature of short distance physics via experiments measuring phenomena over cosmological scales. Similarly, cosmological observations provide important clues about the physics of the very early universe, which in turn may provide hints as to the ultimate theory of nature. With this motivation, Cliff Burgess describes how we might find fingerprints of string theory through its impact on cosmic inflation. Dark energy and the present acceleration of the universe represent one of the greatest puzzles in cosmology today. They provide vital clues as to the ultimate theory and call for a radical reworking of the standard theory of cosmology, Einstein’s theory of gravity, or both. Niayesh Afshordi outlines his own efforts to rethink gravity at the largest scales, which have intriguing cosmological signatures. Particle theorists Maxim Pospelov and Brian Batell relate exciting new proposals for the properties of dark matter, the other great enigma dominating large scale phenomena in the universe, which may explain several curious new observational results. Particle physics is entering a particularly exciting new era as CERN’s Large Hadron Collider (LHC) is beginning to explore physics at a new energy frontier. Michael Trott gives us a theorist’s perspective on the motivations, challenges and possible discoveries for physics at the LHC. Freddy Cachazo describes his work on the foundations of quantum field theory which, unexpectedly, provides new tools for analyzing upcoming accelerator experiments. Alex Buchel, Rob Myers and Aninda Sinha tell us how novel techniques developed in string theory are helping us to understand a remarkable new phase of nuclear matter. The lifeblood of physics, as we all know, is brilliant young people. John Berlinsky writes about Perimeter Scholars International, an innovative graduate research training course which we launched in the fall of 2009. As you read this issue, the first class of 28 students, drawn from 16 countries, is graduating. With PSI we are attempting to reinvigorate the training of young theorists and the initial results of our experiment are highly promising. Aside from research, an equally vital part of PI’s mission is to share the joy and the power of scientific discovery with the wider community through educational programs and events, and Greg Dick and John Matlock explain why we feel outreach is so important. Rob Myers <rmyers@ perimeterinstitute.ca>, Senior Faculty member Neil Turok <nturok@ perimeterinstitute.ca>, Director Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON N2L 2Y5 We hope you enjoy this peek “inside the Perimeter”. Happy reading! —Rob Myers and Neil Turok, Guest Editors The contents of this journal, including the views expressed above, do not necessarily represent the views or policies of the Canadian Association of Physicists. Le contenu de cette revue, ainsi que les opinions exprimées ci-dessus, ne représentent pas nécessairement les opinions et les politiques de l’Association canadienne des physiciens et des physiciennes. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 67 PRÉFACE A L’INTÉRIEUR DE L’INSTITUT PERIMETER « Chaque percée importante en science est née d’une imagination audacieuse. » – John Dewey « Peu importe la beauté de votre théorie et peu importe que vous soyez brillant; si ça ne passe pas le stade de l’expérimentation, c’est que vous faites fausse route. » – Richard P. Feynman Nous avons été ravis d’accepter l’invitation de préparer cette édition thématique de La Physique au Canada et nous espérons que vous apprécierez cet aperçu des différentes activités de recherche de l’Institut Perimeter (PI). Depuis ses débuts, l’espace-temps et la théorie des quanta ont été au cour des recherches de PI. Bien que ces sujets puissent vous sembler abstraits au premier abord et un peu éloigné du monde tel qu’on le connaît, nous souhaitons qu’au fil de ces pages vous voyiez qu’à PI nous avons toujours pour maxime que la nature et l’expérimentation sont le meilleur guide du théoricien. Une des caractéristiques uniques de l’Institut est son groupe ouvrant sur les fondements quantiques. Rob Spekkens et Lucien Hardy expliquent avec éloquence les enjeux de leur domaine, en décrivant à la fois les motivations et les impacts de ces recherches. Parmi celles-ci, on souligne la récente confirmation expérimentale du paradoxe de Hardy par des groupes aux universités de Toronto et d’Osaka, qui avec le temps pourraient engendrer des applications pratiques. Christopher Fuchs présente aussi sa perspective sur une toute nouvelle approche sur le décodage des énigmes de la mécanique quantique à l’aide de la théorie des probabilités bayésienne. La science de l’information quantique a émergé en tant que ramification des fondements quantiques; son essor actuel nous promet de nouvelles technologies qui pourraient transformer notre société. PI a joué un rôle déterminant dans le lancement de l’Institute for Quantum Computing (IQC) à l’université voisine de Waterloo, deux partenaires avec lesquels PI jouit de solides relations synergiques. Dans deux des articles de cette édition, nous pouvons constater la synergie existant entre l’information quantique et les autres champs de la physique théorique. Dans leur article, Urbasi Sinha, Raymond Laflamme et leurs collègues de l’IQC présentent un compte rendu de leur expérience à triples faisceaux au cours de laquelle ils ont vérifié les principes de base de la mécanique quantique en réponse à une demande de Rafael Sorkin de PI. Un peu plus loin, vous pourrez lire l’article de Daniel Gottesman dans lequel il décrit comment son travail sur les classes de complexité algorithmiques quantiques lui a fourni des résultats inattendus sur les verres de spin. À l’égard du thème de l’espace-temps, cher à PI, nous présentons deux premiers rapports totalement différents traitant des astres occlus. Considérés à une certaine époque comme un jouet exotique dans le terrain de jeu des théoriciens, ces phénomènes de gravité ultra puissante sont devenus le cheval de bataille des astrophysiciens modernes. Dans leur article, Luis Lehner et Latham Boyle décrivent de nouvelles observations astrophysiques qui pourraient nous dévoiler davantage sur les astres occlus grâce à leur impact sur la lumière et aux gaz emprisonnés au sein de leurs immenses champs gravitationnels. En contraste, Bill Unruh, l’un des titulaires émérites de la chaire de recherche de PI, souhaite dompter ces dynamos dans sa « baignoire ». Son article raconte remarquablement bien comment ses expériences entreprises dans un bassin d’eau pourraient fournir une meilleure compréhension de la radiation de Hawking qui s’échappe des astres occlus et peut-être même de la gravité quantique. Bien que la gravité quantique explore la notion d’espace-temps à une échelle infiniment petite, Lee Smolin et Sabine Hossenfelder décrivent comment nous pourrions néanmoins y trouver des empreintes de nature quantique en physique des courtes distances par le biais d’expériences au cours desquelles on mesure le phénomène à des échelles cosmologiques. De la même façon, les expériences cosmologiques nous fournissent de précieux indices concernant la physique de l’univers à son stade primaire, qui de leurs côtés peuvent nous fournir des pistes sur la théorie ultime de la nature. Avec cette motivation, Cliff Burgess décrit comment il pourrait trouver des empreintes de la théorie des cordes par le biais de son impact sur l’inflation cosmique. L’énergie sombre et l’accélération actuelle de l’univers présentent une des plus grandes énigmes de la cosmologie actuelle. Elles procurent des indices vitaux à l’endroit de la théorie ultime et supposent une approche radicalement remodelée de la théorie standard en cosmologie, de la théorie sur la gravité de Einstein, ou des deux. Niayesh Afshordi souligne ses propres travaux à l’endroit d’un regard nouveau sur la gravité à de grandes échelles, lesquelles ont des signatures cosmologiques intrigantes. Les théoriciens des particules Maxim Pospelov et Brian Batell nous relatent de passionnantes nouvelles propositions sur les propriétés de la matière noire, l’autre grande énigme qui domine les phénomènes de grande envergure dans notre univers et qui pourrait expliquer plusieurs nouveaux résultats d’observations assez curieux. La physique des particules entre dans une ère particulièrement passionnante au moment où le grand collisionneur de hadrons (LCN) du CERN commence à explorer les nouvelles frontières de l’énergie en physique. Michael Trott nous dévoile la perspective d’un théoricien à l’égard des motivations, des défis et de possibles découvertes pour la physique que pourrait générer le LCN. Freddy Cachazo pour sa part nous décrit son travail dans le domaine de la théorie sur les fondements quantiques, lequel a fourni, alors qu’on ne s’y attendait pas, de nouveaux outils permettant l’analyse des futures expériences en accélération. Alex Buchel, Rob Myers et Aninda Sinha nous relatent comment des techniques originales développées dans le cadre de la théorie des cordes nous permettront de comprendre une nouvelle phase remarquable de la matière nucléaire. L’élément vital de la physique, on le sait, est l’humain, surtout nos jeunes gens talentueux. John Berlinsky nous propose un texte concernant le programme de bourses d’études internationales de l’Institut Perimeter (PSI), un cours novateur de formation en recherches pour étudiants de troisième cycle lancé à l’automne 2009. Au moment où vous lisez cette édition, le premier groupe de 28 étudiants venant de 16 pays ont obtenu leurs diplômes. Avec le PSI nous tentons de revigorer la formation de jeunes théoriciens et les premiers résultats de notre expérience sont très prometteurs. À part la recherche, une autre partie très importante de la mission de PI est de partager la joie et la puissance de la découverte scientifique avec la communauté élargie par l’entremise de programmes éducatifs et d’événements; et Greg Dick et John Matlock expliquent pourquoi c’est si important. Nous souhaitons que vous appréciez cette incursion au sein de l’Institut Perimeter. Bonne lecture! – Rob Myers et Neil Turok, Rédacteurs honoraires 68 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) EDITORIAL AN EXPERIMENT IN THEORETICAL PHYSICS erimeter Institute (PI) was founded just ten years ago. At the time, to outsiders, its success seemed unimaginable. Why in Canada? Why choose such an ambitious scientific focus? What could an upstart young institute contribute to such a well-established field as theoretical physics? Where is Waterloo, anyway? P The best opportunities are often only obvious after the fact. With hindsight, it is clear that Canada has everything needed to create a world leading centre for theoretical physics. It has excellent universities and a strong physics community. There is consensus in government around the need for investment in basic research and highly qualified personnel. Canada is exceptionally welcoming to people from overseas and has a deep tradition of internationalism. And, of course, Canada is an underappreciated, vast and beautiful country. Why invest in theoretical physics? Taking the big picture view, the argument is simple. Theoretical physics is a high impact, low cost field. The breakthroughs made by Newton, Maxwell, Einstein, Bohr, and their descendants nourished all the other sciences and spawned innumerable technologies, many of which form the basis for modern society. The field continues to drive the search for new quantum technologies, and a better understanding of the universe. All the researchers need is food, coffee, blackboards, computers and other researchers to talk to. Their work motivates and drives big science experiments like LHC and LIGO, and helps analyse and interpret the massive data sets generated. Theoretical physics is the most cost-effective field in all of science, for the simple reason that the human mind is simultaneously the most powerful piece of apparatus we know of and the cheapest to operate! But is there much one can do to improve the odds of progress in such a fundamental field? The great discoveries are almost always completely unplanned, resulting from a combination of daring, luck and new technical or technological opportunities or unexpected observations. Perhaps we can do no better than wait, for another Einstein or Bohr to make the next big breakthrough. PI’s founders thought we could do better. Mike Lazaridis and PI’s first Board members and supporters, and Howard Burton, the Institute’s first Director, saw a giant opportunity for Waterloo, for Canada, and for the world, precisely because no-one else had the audacity to try. Drawing on the wisdom of the world’s top theorists, they built the institution on foundations of excellence and the highest ambitions. From the start PI took as its scientific focus a better understanding, and reconciliation, of the two pillars of twentieth century physics: quantum theory and spacetime. The institute took the unusual step of deliberately promoting competing approaches within, because it is precisely through the clash of different approaches that one learns most quickly about the strengths and weaknesses of each. Thus PI has strong groups both in string theory and in quantum gravity, and the lively interaction between the two has earned the institute a reputation as an open-minded and stimulating place to visit and to work. Next, while we cannot anticipate exactly where the next breakthroughs might occur, we can certainly try to focus our efforts on the most promising areas. Here, PI’s flexibility is a huge asset. Areas which don’t fit within the traditional boundaries of a university department or centre can be easily accommodated within PI’s highly interdisciplinary community. As an example, PI’s first focus on foundational quantum theory proved remarkably far-sighted, making the institute a natural hub for the new field of quantum information and allowing us to help foster our experimental partner institute, the Institute for Quantum Computing (IQC) at the University of Waterloo. Today, PI and IQC together form a powerful magnet attracting the best researchers in this exciting field. Looking forward, I believe there are several natural research foci in which PI can become world-leading. One is what one might call “high-powered” quantum field theory, namely the attempt to develop more powerful approaches to our fundamental understanding of quantum fields. The latter describe all of nuclear and particle theory, condensed matter, and early universe cosmology. Therefore, foundational progress in quantum field theory will have an impact across all of physics. We have growing strength at PI in this area, and are well on our way to making this a world-leading effort. A second strongly emerging theme is the connection between theoretical work at PI and large experimental efforts like LHC and LIGO. Even a small number of theorists, working in a focused way, can have an enormous impact on these massive international experiments, by pointing out new signals to look for, better ways to analyse and interpret the data, and key physics targets to guide the design of new experiments. Neil Turok <nturok@ perimeterinstitute.ca>, Director, Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON N2L 2Y5 A third emerging theme is the study of black holes and gravitational waves—the next great frontier in astronomy and cosmology. Ten years from now, we hope to be routinely detecting bursts of gravitational waves emitted by The contents of this journal, including the views expressed above, do not necessarily represent the views or policies of the Canadian Association of Physicists. Le contenu de cette revue, ainsi que les opinions exprimées ci-dessus, ne représentent pas nécessairement les opinions et les politiques de l’Association canadienne des physiciens et des physiciennes. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 69 ÉDITORIAL colliding black holes, and planning even more ambitious experiments, using gravitational waves to look all the way back to the beginning of the Universe. Which, of course, is another focus of our work at PI. The fundamental unity and coherence of theoretical physics is a source of research strength, as PI expands to draw on complementary insights from across the whole spectrum of physics. We have nascent efforts in particle physics and cosmology. We are also looking to grow in condensed matter, especially in the realm of strongly quantum-correlated systems, an area which connects well to our existing strengths as well as to emerging technological frontiers. Science has become an increasingly collaborative venture. Within this context, PI seeks to be a resource for physics in Canada, and internationally. We are looking to grow our links with the strong community of physicists in Canada, with world-class theory centers like the Canadian Institute for Theoretical Astrophysics, and world-class experimental projects such as those at TRIUMF and SNOLAB. PI’s Affiliate Member program, which draws in physics faculty from across Canada to visit and participate in the institute’s research activities, now counts 96 members. By working together, I believe we can create a “win-win” situation which allows Canada to obtain maximum benefit from its support of basic physics. In a wider sense, PI is striving to be a global center and resource. It is clearly important that we collaborate with other advanced centers, but I believe it is even more vital that we support emerging centers in the developing world, where enormous pools of talent lie waiting to be unlocked. By helping to promote the cause of these centers, and by offering to share PI’s substantial institution-building expertise, I believe we can make a substantial contribution both to the future of physics and to international development. The progress of theoretical physics rests, more than anything, on brilliant young people. One of our key objectives is therefore to support a flow of youthful talent through PI. For this reason, we launched Perimeter Scholars International (PSI), an innovative Master’s program designed to attract talented students from around the world into theoretical physics, and to bring them to the cutting edge of research as quickly as possible. This year, 28 students from 16 countries will graduate, and we are delighted with their progress. Many Canadian faculty have been involved in lecturing, and in supervising projects. In the future, we hope PSI will become seen as a valuable new model for teaching theoretical physics, and a global stimulus for the field. PI already hosts the largest group of independent postdoctoral researchers in theoretical physics in the world. We are now recruiting at the highest level, competing successfully for talent with the strongest institutions internationally. We are also building our strength in terms of senior, established researchers. Over the last eighteen months, we have recruited 20 of the world’s top theoretical physicists as Distinguished Research Chairs (DRCs) at Perimeter Institute. They include both bright young stars such as Patrick Hayden (McGill) and Guifre Vidal (Queensland) and world leading figures such as Yakir Aharonov (Tel Aviv), Stephen Hawking (Cambridge) and Ashoke Sen (Harish Chandra Institute, Allahabad). They span an enormous range of expertise, from quantum foundations through particle physics, condensed matter, cosmology to quantum gravity and black holes. While retaining their permanent positions at home, our DRCs visit PI for extended periods (typically one to two months per year) to do research, collaborate and in some cases to teach on PSI. There has been excellent uptake of these positions, and the continuous flow of top international researchers adds to the excitement of working at PI. We were especially delighted that two of our DRCs were widely touted as potential Nobel prize winners last year. In the end, neither won but Willard Boyle’s prize was certainly great compensation, and his remarks about the importance of curiosity driven research, and of “special” places for science like Bell Labs in its heyday inevitably evoked comparisons with PI. To accommodate all of this growth, PI’s iconic “black box” building is now being substantially expanded with the Stephen Hawking Centre at Perimeter Institute (see cover), which will be completed next summer. Our expanded facility will allow PI to accommodate around 250 researchers, making it by some margin the largest facility for foundational theoretical physics in the world. One of the smart things that Mike Lazaridis and Howard Burton did in founding PI was to give public outreach a very high priority. The scale of these efforts—for students, teachers, and the public—is something that really sets PI apart. Just one example is our public lecture series, which attracts an audience of six hundred plus to a local high school auditorium each month. Last fall, we held a science festival called Quantum to Cosmos: Ideas for the Future. It was a huge, risky undertaking: a giant tent in Waterloo town square filled with hands-on exhibits and 3-D film narrated by Stephen Hawking, the world premiere of The Quantum Tamers, a PI-produced documentary on quantum mechanics that is anything but the usual documentary fare, concerts, and a science film festival. Last but not least, TV Ontario came and broadcast five nights of their current affairs program, “The Agenda with Steve Paikin”, right from PI’s atrium. Oh yes, and they filmed and helped broadcast 30 talks and panels with 80 presenters over 10 days, all live online in high definition, something never before attempted on this scale. As I walked down the hill to PI, to introduce the first lecture, I must admit I was nervous. So much could go wrong, but all we could do was trust to the professionalism of our team. I needn’t have worried. The festival exceeded our wildest hopes—over 40,000 people came to events here, and over a million viewers on TV and online (if you haven’t seen any of the talks yet, you can still see them at www.q2cfestival.com). At every event, questions were encouraged—whether from those present, or those online. It was an all out celebration of where curiosity can lead. Quantum to Cosmos was a stunning success, and I see it as emblematic of what PI is trying to do and where it is going: to carefully create the best initial conditions, disregard the limits of common wisdom and convention and shoot for the stars. Sometimes, magic can happen. Neil Turok Guest Editor, Physics in Canada Readers’ comments on this editorial are more than welcome. 70 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) EDITORIAL UNE EXPÉRIENCE EN PHYSIQUE THÉORIQUE Il n’y a que dix ans que l’Institut Perimeter (PI) a été créé. À ce moment-là, pour les gens de l’extérieur, son succès semblait inimaginable. Pourquoi au Canada? Pourquoi se concentrer sur un objectif scientifique aussi ambitieux? Qu’est-ce qu’un institut néophyte pouvait apporter à un secteur aussi bien établi que la physique théorique? Au fait, où se trouve Waterloo? Les meilleures perspectives ne se perçoivent souvent que devant le fait accompli. Avec le recul, il ne fait aucun doute que le Canada dispose de tout ce qu’il faut pour créer un centre de physique théorique d’envergure mondiale. Le pays est doté d’excellentes universités et d’une solide communauté dans le secteur de la physique. Un consensus se dégage au gouvernement sur les besoins d’investir dans la recherche fondamentale et dans une main-d’oeuvre hautement qualifiée. Le Canada est particulièrement accueillant à l’endroit de gens venant d’outre-mer et a une tradition internationaliste bien établie. Et bien sûr, le Canada est un pays vaste et magnifique que l’on n’apprécie pas toujours à sa juste valeur. Pourquoi investir dans la physique théorique? Vue dans son ensemble, la raison est simple. La physique théorique est un champ assez peu coûteux, dont les impacts importants se font néanmoins sentir. Les percées réussies par Newton, Maxwell, Einstein et Bohr et leurs descendants ont alimenté toutes les autres sciences et fait naître une multitude de technologies, dont plusieurs forment aujourd’hui la base de notre société moderne. Le champ est à l’avant-garde de la recherche de nouvelles technologies quantiques et d’une meilleure compréhension de l’univers. Tout ce que les chercheurs ont besoin, c’est de nourriture, de café, de tableaux noirs, d’ordinateurs et d’autres chercheurs avec qui discuter. Leur travail motive et mène à terme des expériences comme celles du LCN et du LIGO, et aide à l’analyse et à l’interprétation de l’ensemble des données qui y sont générées. La physique théorique est le champ scientifique le plus efficient pour la simple raison que le cerveau humain est à la fois l’appareil le plus puissant que l’on connaisse et le moins cher à utiliser! Par contre, y a t’il quelque chose qu’on peut faire pour améliorer les chances du progrès dans un tel champ fondamental? Les grandes découvertes se sont presque toutes produites sans quelles n’aient été planifiées, résultant de l’audace, de la chance, de nouvelles occasions fournies par la technologie ou d’observations imprévues. Peut-être que nous ne pouvons qu’attendre la venue d’un nouvel Einstein ou d’un Bohr pour parvenir aux prochaines grandes percées. Les fondateurs de PI croient plutôt qu’on peut faire mieux que çà. Mike Lazaridis et les membres du premier conseil d’administration avec ceux qui les appuient, ainsi que Howard Burton, le premier directeur de l’Institut, y ont vu une grande occasion pour Waterloo, pour le Canada et pour le monde, précisément parce que personne ne s’y était risqué. En s’appuyant sur la sagesse des théoriciens mondiaux émérites, ils ont bâti cette institution sur des bases d’excellence et d’ambitions élevées. Dès le départ, PI a choisi comme concentration scientifique une meilleure compréhension et une réconciliation des deux piliers de la physique du vingtième siècle : la théorie des quanta et de l’espace-temps. L’Institut a choisi une voie inhabituelle et délibérément audacieuse mettant de l’avant en son sein deux points de vue qui s’opposent, car c’est précisément en confrontant des approches diamétralement opposées qu’on peut apprendre plus rapidement les forces et les faiblesses de chacune de ces options. Par conséquent, l’Institut est doté de groupes forts autant du côté de la théorie des cordes que du côté de la gravité quantique; la vivacité des interactions ainsi engendrée a permis à l’Institut de se créer la réputation d’être un endroit stimulant et d’esprit ouvert qu’il est agréable de fréquenter et où il fait bon travailler. De plus, bien que ne puissions pas prévoir précisément où se produirons les prochaines percées, nous pouvons à coup sûr concentrer nos efforts dans les domaines les plus prometteurs, et c’est à ce niveau que la souplesse de PI lui procure un avantage de taille. Les domaines qui ne se trouvent pas dans le registre traditionnel des départements de physique des universités ou des centres peuvent facilement trouver leur place au sein de la communauté hautement interdisciplinaire de l’Institut. Par exemple, la vocation principale de l’Institut à l’endroit de la théorie des fondements des quanta a prouvé qu’elle était tournée vers l’avenir, faisant de l’Institut la pierre angulaire du nouveau domaine de l’information quantique et nous permettant d’aider à l’intégration de notre institut expérimental partenaire, l’Institute for Quantum Computing (IQC) à l’université de Waterloo. L’IQC et PI forment aujourd’hui un puissant pôle d’attraction auprès des meilleurs chercheurs de ce domaine passionnant. Quand je regarde ce que l’avenir nous réserve, je crois que PI pourra tenir un rôle d’avant-garde dans plusieurs domaines naturels de recherches. L’un de ceux-ci, que l’on pourrait qualifier de domaine de la théorie des champs quantifiés de « haute puissance », tente de développer des approches plus énergiques à l’égard de notre compréhension de base des champs quantifiés. Ce dernier décrit l’ensemble des théories nucléaires, des particules, de la matière condensée et de la cosmologie de l’univers primaire. Par conséquent, le progrès des bases de la théorie des champs quantifiés aura un impact sur la physique dans son ensemble. L’Institut est doté d’une force croissante dans ce domaine est sur la voie d’en devenir le fer de lance mondial. Un deuxième thème émergeant avec vigueur est la connexion entre le travail théorique de PI et les grands efforts expérimentaux comme ceux du LCN et du LIGO. Même un nombre restreint de théoriciens, travaillant en convergence, peut avoir un impact énorme sur ces expériences internationales en signalant de nouveaux éléments à surveiller, en établissant de meilleures façons d’analyser et d’interpréter les données et en précisant les objectifs physiques principaux permettant de guider la forme que prendront les nouvelles expériences. Un troisième thème qui se profile est l’étude des astres occlus et des ondes de gravité – la prochaine grande frontière en astronomie et en cosmologie. Nous souhaitons que dans une dizaine d’années, nous puissions détecter de façon routinière les vagues d’ondes de gravité émises par la collision d’astres occlus et nous planifions même des expériences encore plus ambitieuses qui nous permettront d’utiliser les ondes de gravité afin de pousser les observations aussi loin qu’au début de l’univers. Il s’agit bien sûr d’une autre facette du travail effectué à l’Institut. L’unité des fondements et la cohérence de la physique théorique sont la source d’énergie de la recherche qui permet à l’Institut de poursuivre son développement et son avance dans des sphères complémentaires venant du spectre complet de la physique. Nous faisons actuellement nos premiers pas en physique des particules et en cosmologie; nous comptons aussi évoluer du côté de la physique de la matière condensée, particulièrement dans le domaine des systèmes fortement quantifiés, une zone qui corre- PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 71 ÉDITORIAL spond bien à nos forces actuelles ainsi qu’aux frontières technologiques en émergence. La science est de plus en plus une entreprise de collaborations. Dans ce contexte, PI cherche à se positionner comme ressource dans le domaine de la physique à la fois à l’échelle canadienne et internationale. Nous voulons tisser des liens avec la vigoureuse communauté canadienne de la physique, avec des centres de physique théorique d’envergure mondiale comme l’Institut canadien d’astrophysique théorique et avec des projets expérimentaux de calibre international comme ceux du TRIUMF et du SNOLAB. Le programme pour membres affiliés de PI, qui incite les facultés de physique des universités partout au Canada à visiter l’Institut et à participer à ses activités en recherche, compte maintenant 96 membres. C’est en travaillant ensemble que nous pourrons créer une situation gagnante pour tous qui permettra au Canada de tirer le maximum de bénéfices de son soutien à la physique fondamentale. D’une façon générale, PI s’efforce à devenir un centre et une ressource mondiale dans son domaine. Il est très important que nous collaborions avec les autres centres de notre calibre, mais je crois par-dessus tout qu’il est vital que nous soutenions les centres en émergence à travers le monde où se trouve une énorme source de chercheurs talentueux qui ne demandent qu’à s’épanouir. En aidant ces centres à prendre leur envol et en offrant le savoir-faire d’établissement institutionnel de notre organisation, je crois que nous pouvons apporter une solide contribution à l’avenir de la physique ainsi qu’au développement international. Le progrès de la physique théorique repose avant tout sur de brillants jeunes gens. Un des principaux objectifs de l’Institut est notamment de soutenir l’arrivée de ces nouveaux talents. C’est pourquoi nous avons lancé le programme de bourses internationales Perimeter Scholars International (PSI), un programme international de Maîtrise novateur conçu pour attirer des étudiants talentueux d’où qu’ils viennent à la physique théorique et de rapidement les amener à la fine pointe de la recherche. Cette année, 28 étudiants venant de 16 pays obtiendront leur diplôme et nous sommes enchantés de leurs progrès. Plusieurs facultés de nos universités canadiennes ont offert des projets de conférences et de supervision. Nous espérons qu’à l’avenir, le PSI sera perçu comme un nouveau modèle valable pour l’enseignement de la physique théorique et comme un élément de stimulation dans le domaine en général. L’Institut accueille déjà le plus important groupe de chercheurs postdoctoraux indépendants en physique théorique au monde. Nous recrutons actuellement avec succès des gens talentueux dans les hautes sphères, en concurrence avec les meilleures institutions internationales. Nous bâtissons aussi notre force en matière de chercheurs établis bien aguerris. Au cours des derniers dix-huit mois, nous avons recruté 20 des meilleurs physiciens au monde en physique théorique comme titulaires émérites de la chaire de recherche de l'Institut Perimeter. On y retrouve Patrick Hayden (McGill), Guifre Vidal (Queensland) ainsi que des figures marquantes du domaine comme Yakir Aharonov (Tel-Aviv), Stephen Hawking (Cambridge) et Ashoke Sen (Harish Chandra Institute, Allahabad). Ensemble, ils embrassent une énorme étendue d’expertise, des fondements quantiques à la physique des particules, à la physique de la matière condensée, à la cosmologie, à la gravité quantique et aux astres occlus. Bien qu’ils maintiennent tous leur poste permanent chez eux, nos titulaires sont en visite à l’Institut pour de longs séjours (généralement d’une durée allant de deux mois à une année complète) pour y faire de la recherche, y collaborer et parfois même enseigner aux PSI. L’intérêt suscité par ces titulaires a été excellent, et le flot constant de chercheurs de cali- bre international a renchéri la passion de travailler à l’Institut. Nous sommes particulièrement fiers que deux de nos titulaires aient été approchés avec insistance comme récipiendaires potentiels du prix Nobel de l’année passée. Aucun d’eux n’a finalement obtenu le prix, mais le prix qu’a obtenu Willard Boyle a certainement compensé; ses remarques à l’égard de la recherche stimulée par la curiosité et des endroits de science « spéciaux » comme au cours de l’âge d’or des Bell Labs, ont inévitablement évoqué la comparaison avec PI. Afin d’accommoder tout cette croissance, « la boîte noire », l’immeuble icône de l’Institut prend maintenant une expansion importante avec l’ajout du Centre Stephen Hawking à l’Institut Perimeter (voir la couverture). Ce nouveau centre, qui sera achevé l’été prochain, permettra à PI d’accueillir environ 250 chercheurs, ce qui en fera dans une certaine mesure, le plus grand centre de physique théorique fondamentale du monde. Un des côtés brillants du projet de Mike Lazaridis et de Howard Burton lorsqu’ils ont fondé l’Institut a été d'accorder beaucoup d’importance à la proximité avec le public. La valeur de ces efforts auprès des étudiants, des professeurs et du public, positionne PI dans une classe à part. Un exemple de cette situation est notre série de conférences publiques qui attirent un auditoire de plus de six cents personnes à l’auditorium de l’école secondaire locale chaque mois. L’automne dernier, nous avons tenu un festival des sciences intitulé « Du quantum au cosmos : des idées d’avenir ». C’était une énorme entreprise, assez risquée : un chapiteau monté au square municipal rempli de stands interactifs, un film en 3D commenté par Stephen Hawking, la première mondiale du film documentaire The Quantum Tamers produit par l’Institut et traitant des mécanismes quantiques (qui n’avait rien d’un documentaire classique), des concerts et un festival de films scientifiques; et pour finir, rien de moins que TV Ontario qui était sur place pendant 5 soirées pour la diffusion de son émission d’affaires publiques « The Agenda with Steve Paikin » en direct de l’atrium de l’Institut. Ils ont d’ailleurs filmé et aidé à diffuser 30 interviews avec 80 personnes au cours des 10 journées, toutes en direct et en haute définition, rien de si important n’avait jamais été entrepris! Je dois admettre qu’alors que je descendais vers PI pour introduire ma première conférence la nervosité m’a gagné. Tant de choses pouvaient déraper, mais tout ce que l’on pouvait faire était de se fier au professionnalisme de notre équipe. Je n’aurais pas dû m’en faire. Le festival a dépassé nos attentes les plus optimistes, plus de 40 000 personnes ont participé à nos activités et plus d’un million de téléspectateurs ou d’internautes ont pu voir les interviews (si vous ne l’avez pas fait, vous pouvez les regarder au www.q2cfestival.com). Lors de toutes les activités, on incitait les participants à poser des questions, que ce soit sur place ou en ligne. Ce fut une célébration totale de la curiosité. Le festival « Du quantum au cosmos : des idées d’avenir » a obtenu un succès stupéfiant et je le considère maintenant comme le symbole de la vocation de PI et de la direction qu’il veut tracer : créer avec soin les meilleures conditions de départ, ignorer les limites habituelles des conventions et de la sagesse et viser les étoiles! Il arrive que la magie soit au rendez-vous. Neil Turok Rédacteur honoraire, La Physique au Canada Les commentaires de nos lecteurs au sujet de cet éditorial sont bienvenus. NOTE: Le genre masculin n’a été utilisé que pour alléger le texte. 72 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE WHY PHYSICS NEEDS QUANTUM FOUNDATIONS BY LUCIEN HARDY AND ROBERT SPEKKENS Q uantum theory is a peculiar creature. It was born as a theory of atomic physics early in the twentieth century, but its scope has broadened over time, to the point where it now underpins all of modern physics with the exception of gravity. It has been verified to extremely high accuracy and has never been contradicted experimentally. Yet despite its enormous suc- SUMMARY “Quantum foundations” is the field of physics that seeks to understand what quantum theory is telling us about the nature of reality. Researchers hope to answer questions such as: What do the elements of the mathematical formalism of quantum theory represent? From what physical principles can the formalism be derived? What are the precise ways in which a quantum world differs from a classical world and other possible worlds? Progress on these questions is likely to come both from an operational approach, wherein one characterizes a theory entirely in terms of the predictions for macroscopic experiments described using everyday concepts, and from a realist approach, wherein one seeks to find deeper explanations for these predictions in terms of simple entities and abstract concepts. We illustrate the practical significance of foundational research by recalling the role that it played as a spawning ground for the field of quantum information science, and we explain why we think that it will have a similar role to play in unifying quantum theory with general relativity. cess, there is still no consensus among physicists about what this theory is saying about the nature of reality. There is no question that quantum theory works well as a tool for predicting what will occur in experiments. But just as understanding how to drive a car is different from understanding how it works or how to fix it should it break down, so too is there a difference between understanding how to use quantum theory and understanding what it means. The field of quantum foundations seeks to achieve such an understanding. In particular, it seeks to determine the correct interpretation of the quantum formalism. It also seeks to determine the principles that underlie quantum theory. Why do we have a quantum world instead of a classical world or some other kind of world entirely? There are many motivations for pursuing foundational research. One is the development of quantum technologies, such as quantum computation and quantum cryptography. A better understanding of the theory facilitates the identification and development of these new technologies, the harnessing of the power of nonclassicality. Another motivation is that quantum theory is likely not the end of the road. If we are to move beyond it, then it is important to know which parts can be changed, generalized or abandoned. Finally, there are the personal motivations of individual researchers: because quantum theory is very mysterious and counterintuitive and surprising and seems to defy us to understand it. And so we take up the challenge. Lucien Hardy (lhardy@ perimeterinstitute.ca), and Robert Spekkens (rspekkens@ perimeterinstitute.ca), Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 OPERATIONALISM AND REALISM Broadly speaking, researchers in quantum foundations can be divided into two camps. There are the operationalists and there are the realists. For the operationalist, operators in Hilbert space represent preparation and measurement procedures, specified as lists of instructions of what to do PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 73 WHY PHYSICS NEEDS ... (HARDY AND SPEKKENS) in the lab. They are recipes with macroscopic activities as ingredients. The theory merely specifies what probabilities of outcomes will be observed when a given measurement follows a given preparation. For the realist, there is some deeper reality underlying the equations of quantum theory that ultimately accounts for why we see the relative frequencies we do. Does the wave function describe this reality? Or are there extra hidden variables in addition to the wave function needed to fully describe a quantum system? These are the sorts of questions the realist ponders. A classic example of the power of applying operational thinking is Einstein’s approach to special relativity. By carefully considering how to synchronise distant clocks, he was led to abandon the hitherto cherished notion of absolute simultaneity. A good example of the successful application of realism is the atomic hypothesis. In this case, John Dalton and others were right to insist on the reality of atoms (in opposition to operationalists such as Ernst Mach). It led to a theory for Brownian motion (Einstein again), the theory of statistical mechanics, and ultimately much of modern physics. Historically, both approaches were important in the development of quantum theory. Heisenberg’s 1925 paper on matrix mechanics, which ushered in the modern age of quantum theory, began with the sentence, “The present paper seeks to establish a basis for theoretical quantum mechanics founded exclusively upon relationships between quantities which in principle are observable.” This was operational thinking. In parallel to this, de Broglie posited the existence of waves to describe quantum phenomena and Schrödinger found an equation for their motion. This was realist thinking. In modern research into the foundations of quantum theory, both operationalism and realism are alive and well. By thinking operationally, a general mathematical framework has been developed which can accommodate a wide variety of probabilistic theories. Quantum theory fits very comfortably into this framework as a special case and so can be easily understood in operational terms. Much progress has been made recently in understanding the deeper mathematical structure of quantum theory in the context of this mathematics of operationalism. For example, many features of quantum theory (such as the impossibility of building a machine that can clone quantum states) turn out to be features of any non-classical probabilistic theory. These tools also contribute to the program of reconstructing quantum theory, that is, deriving its abstract mathematical formalism from natural postulates, just as the Lorentz transformations are derived from Einstein’s postulates for special relativity. But operationalism is not enough. Explanations do not end with detectors going ‘click’. Rather, the existence of detectors that click is the sort of thing that we can and should look to science to explain. Indeed, science seeks to explain far more than this, such as the existence of human agents to build these detectors, the existence of an earth and a sun to support these agents, and so on to the existence of the universe itself. The only way to meet these challenges is if explanations do not bottom out with complex entities and everyday concepts, but rather with simple entities and abstract concepts. This is the view of the realist. Without adopting some form of realism, it is unclear how one can seek a complete scientific world-view, incorporating not just laboratory physics, but all scientific disciplines, from evolutionary biology to cosmology. It is true of course that all of our evidence will come to us in the form of macroscopically observable phenomena, but we need not and should not restrict ourselves to these concepts when constructing scientific theories. For the realist, then, we need an interpretation of quantum theory. There are already plenty of candidates to choose from. There is the pilot wave model of Louis de Broglie and David Bohm in which the wave function guides the motion of actual particles according to a well defined equation. There is the many worlds interpretation of Hugh Everett III in which the universe is regarded as splitting into many copies every time the wavefunction evolves into a superposition of distinct situations. There are also collapse models in which extra terms are added to the Schrödinger equation to cause a collapse of the wavefunction when sufficiently macroscopic possibilities become superposed. Many more ideas for interpretations are in the making today. Cases have been made for each by their respective proponents, but none has yet proven sufficiently compelling to achieve a scientific consensus. So research on these issues continues. Ultimately, we expect that both operationalism and realism will play an important methodological role in future research. Operationalism is, at least, a useful exercise for freeing the mind from the baggage of preconceptions about the world, as Einstein did when he showed that the notion of absolute simultaneity was unfounded. As such it can provide a minimal interpretation, some conceptual and mathematical scaffolding on which to build. On the other hand, the extra commitments, constraints and details of a realist model can also be a virtue. Realist models are more falsifiable, they typically suggest new and interesting questions (questions that may uncover novel consequences of a theory), and they often suggest avenues for modifying and generalizing the theory. THE FOUNDATIONAL ROOTS OF QUANTUM INFORMATION THEORY The field of quantum foundations provides many examples of how basic research guided by a desire for deeper understanding can lead to discoveries of great practical interest. Quantum information science serves as the best example. To first approximation, it was born of two communities: on the one hand, computer scientists and information theorists, and on the other, physicists thinking about the foundations of quantum theory. If the name of a field indicated its parentage, then the “quantum” in “quantum information” would refer to quantum foundations. 74 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) WHY PHYSICS NEEDS ... (HARDY AND SPEKKENS)AA Since those early days, there has been a slow but steady march towards quantum technologies becoming practical. Quantum cryptographic systems, for instance, are now available commercially. Meanwhile, progress on the theoretical side has shown how one can achieve stronger forms of security than previously conceived. One of the most celebrated cryptographic applications of quantum theory is key distribution: the ability to establish a shared secret key among distant parties over a public channel in such a way that one can reliably detect the presence of an eavesdropper. Recent work has shown that under the very conservative assumption that superluminal signalling is impossible, one can achieve key distribution even if the would-be eavesdropper has the advantage of providing the very devices that are used by the communicating parties [1,2]. This is practical stuff, but the path that led to such results starts with foundational research. In 1964, John Bell was considering the question of whether there is an interpretation of quantum theory in terms of hidden variables. He had been pondering the argument by Einstein, Podolsky and Rosen in favor of the incompleteness of the quantum description and thinking about various theorems that purported to show the impossibility of such completions. He was also studying the pilot wave model of de Broglie and Bohm. He noted that this theory postulated superluminal causal influences and wondered whether this might be true of all realist models of quantum theory. Once the question was asked, it was not long before he was able to prove that this is indeed the case C a theorem that now bears his name [3]. Bell’s theorem is a profound result because it demonstrates a tension between the two pillars upon which modern physics is built C quantum physics and relativity theory. Since its discovery, physicists have been puzzling over it. One such person was Artur Ekert. In 1991, he realized that the statistical correlations central to Bell’s theorem could be used to achieve secure key distribution [4]. Although a different quantum protocol for key distribution had been developed seven years earlier by Charlie Bennett and Gilles Brassard [5], it was Ekert’s protocol that ultimately led to the results mentioned above C the possibility of achieving security regardless of the provenance of the devices. The theory of entanglement C the property of quantum states that is critical to the Einstein-Podolsky-Rosen argument and Bell’s theorem C is another example of the practical payoff of foundational thinking. In 1980, William Wootters had just completed a Ph.D. thesis on a foundational question: from what principles can the Born rule of quantum theory be derived? Important to his considerations was a task known as quantum state tomography. This is an attempt to infer the identity of a quantum state by implementing many different measurements on a large number of samples of it. In the fall of 1989, Asher Peres, another foundational researcher, asked whether joint measurements on a pair of systems might yield better tomography than separate measurements. They were able to find strong numerical evidence that this was indeed the case [6]. It seemed, therefore, that if a pair of similarly prepared particles was separated in space, an experimenter would be less able to identify their state than if they were together. In other words, there is a limit to how much information about the state can be accessed by local means C a kind of nonlocality. In 1992, Charlie Bennett heard a talk by Wootters on the subject and asked whether the nonlocality that seemed to be inherent in entangled states might provide a way of achieving state tomography on separated systems with the same success that could be achieved if they were proximate. Again, once the question was asked, it took only a few days for Wootters, Bennett, Peres and their co-workers (Gilles Brassard, Claude Crépeau and Richard Jozsa) to answer it. Yes, it could be done [7]. The key insight was that by consuming a maximally entangled state (i.e. using it in a manner that ultimately destroys it), the quantum state of a system could be transferred from one party to another distant party using only local operations and classical communication. The trick was dubbed “quantum teleportation” by its authors. Several discoveries in quantum information theory (including Ekert’s key distribution protocol) had shown that entanglement was useful, and with the discovery of teleportation, it became especially obvious: entanglement was a resource. This change in perspective prompted researchers to ask many new and interesting questions about entanglement. The result has been a dramatic increase in our understanding of the phenomena, leading to applications across all subdisciplines of quantum information science (cryptography, communication and computation) and further afield (for instance, in new density matrix renormalization group methods for simulating quantum many-body systems). One final story. Early in the history of quantum information theory, when most researchers were still thinking about quantum theory as imposing upon us additional limitations relative to what we would face in a world that was governed by a classical theory, David Deutsch was thinking differently. He was looking to identify tasks for which quantum theory provided an advantage. In the mid-eighties, his unique perspective led him to write one of the very first articles on quantum computation, an article that prepared the ground for important subsequent discoveries [8]. What led Deutsch to perform this seminal work? He was thinking about the information-processing consequences of Everett’s many worlds interpretation of quantum theory. QUANTUM FOUNDATIONS MEETS QUANTUM GRAVITY Perhaps the holy grail of modern physics is a theory of quantum gravity. We need to find a theory that reduces to quantum theory in one limit and to general relativity in another, and that makes new predictions which are subsequently verified in experiments. This has been an open problem since the birth of quantum theory, yet we still do not have a theory of quantum gravity. The problem is difficult because there are deep conceptual differences between general relativity and quantum theory. Consequently, the two theories have very different mathematical structures. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 75 WHY PHYSICS NEEDS ... (HARDY AND SPEKKENS) In the past, when two less fundamental theories have been unified into a deeper, more fundamental theory, the unification has typically required an entirely new mathematical framework, motivated by conceptual insights from the two component theories. If this is the case for quantum gravity, then foundational thinking is likely to be useful. Does quantum gravity call for a new type of probabilistic theory? Which of the postulates of quantum theory (in whatever formulation) will have to be modified or abandoned, if any? A similar type of conceptual thinking about the foundations of general relativity is also likely to be significant. If we have a mathematical framework that is rich enough to contain a theory of quantum gravity (in much the same way that the mathematics of Hilbert space is sufficient for quantum theory and the mathematics of tensor calculus is sufficient for general relativity) then we could expect that a few suitably chosen postulates would narrow us down to the right theory. It is in the construction of this framework and the selection of these postulates that the conceptual and mathematical tools of quantum foundations are likely to be useful. SEND OFF The field of quantum foundations does not merely exist to tidy up the mess left behind after the physics has been done. Rather it should be regarded as part and parcel of the great project of theoretical physics: to gain an ever better understanding of the world around us. In particular, researchers in the field are striving to achieve a deeper understanding of the conceptual and mathematical structure of quantum theory. It is a testament to the importance of this sort of pure enquiry that the ideas of quantum foundations have found such a compelling application in the field of quantum information science. It was John Bell thinking about hidden variables that ultimately led to many practical results in quantum cryptography; it was William Wootters asking “Why the Born rule?” that guided us down the last stretch of the path that culminated in understanding entanglement as a resource, and it was David Deutsch thinking about the many worlds interpretation of quantum theory that laid the foundations of quantum computing. We should not expect that quantum information theory will be the only substantial application of ideas from quantum foundations. They may well play a significant role in the construction of a theory of quantum gravity. They may even spawn entirely new fields of research that we cannot currently predict. Thinking about foundations pays off in the long run. David Mermin once summarized a popular attitude towards quantum theory as “Shut up and calculate!”. We suggest a different slogan: “Shut up and contemplate!” REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. J. Barrett, L. Hardy, and A. Kent, “No Signaling and Quantum Key Distribution”, Phys. Rev. Lett. 95, 010503 (2005). A. Acín, N. Gisin, Ll. Masanes, “From Bell’s Theorem to Secure Quantum Key Distribution”, Phys. Rev. Lett. 97, 120405 (2006). J.S. Bell, “On the Einstein-Podolsky-Rosen paradox”, Physics (Long Island City, N.Y.) 1, 195 (1964). A.K. Ekert, “Quantum cryptography based on Bells theorem”, Phys. Rev. Lett. 67, 661 (1991). C.H. Bennett and G. Brassard, “Quantum Cryptography: Public key distribution and coin tossing”, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, p. 175 (1984). A. Peres and W.K.Wootters, “Optimal detection of quantum information”, Phys. Rev. Lett. 66, 1119 (1990). C.H. Bennett, G. Brassard, C. Crpeau, R. Jozsa, A. Peres, W.K. Wootters, “Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels”, Phys. Rev. Lett. 70, 1895 (1993). D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer”, Proc. R. Soc. Lond. A 400, 97 (1985). 76 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE QUANTUM BAYESIANISM AT BY THE PERIMETER CHRISTOPHER A. FUCHS A FEARED DISEASE T he start of the new decade has just passed and so has the media frenzy over the H1N1 flu pandemic. As misplaced as the latter turned out to be, it did serve to remind us of a basic truth: That a healthy body can be stricken with a fatal disease which to outward appearances is nearly identical to a common yearly annoyance. There are lessons here for quantum mechanics. In the history of physics, there has never been a healthier body than quantum theory; no theory has ever been more all-encompassing or more powerful. Its calculations are relevant at every scale of physical experience, from subnuclear particles, to table-top lasers, to the cores of neutron stars and even the first three minutes of the universe. Yet since its founding days, many physicists have feared that quantum theory’s common annoyance C the continuing feeling that something at the bottom of it does not make sense C may one day turn out to be the symptom of something fatal. There is something about quantum theory that is different in character from any physical theory posed before. To put a finger on it, the issue is this: The basic statement of the theory C the one we have all learned from our textbooks C seems to rely on terms our intuitions balk at as having any place in a fundamental description of reality. The notions of “observer” and “measurement” are taken as primitive, the very starting point of the theory. This is an unsettling situation! Shouldn’t physics be talking about what is before it starts talking about what will be seen and who will see it? Perhaps no one has put the point more forcefully than John Stewart Bell [1]: What exactly qualifies some physical systems to play the role of ‘measurer’? Was the wavefunction of the world waiting to jump for thousands of millions of years until a single-celled living creature SUMMARY This article summarizes the Quantum Bayesian view of quantum mechanics developed by the author and collaborators over a number of years. Present work at Perimeter Institute is focused on streamlining a representation of quantum mechanics purely in terms of probabilities, without amplitudes or Hilbert-space operators. appeared? Or did it have to wait a little longer, for some better qualified system ... with a PhD? One sometimes gets the feeling that until this issue is settled, fundamental physical theory has no right to move on. Worse yet, that to the extent it does move on, it does so only as the carrier of something insidious, something that will eventually cause the whole organism to stop in its tracks. “Dark matter and dark energy? Might these be the first symptoms of something systemic? Might the problem be much deeper than getting our quantum fields wrong?” C This is the kind of fear at work here. So the field of quantum foundations is not unfounded; it is absolutely vital to physics as a whole. But what constitutes “progress” in quantum foundations? Throughout the years, it seems the most popular criterion has derived from the tenor of Bell’s quote: One should remove the observer from the theory just as quickly as possible. In practice this has generally meant to keep the mathematical structure of quantum theory as it stands (complex Hilbert spaces, etc.), but find a way to tell a story about the mathematical symbols that involves no observers. Three examples suffice to give a feel: In the de BroglieBohm “pilot wave” version of quantum theory, there are no fundamental measurements, only “particles” flying around in a 3N-dimensional configuration space, pushed around by a wave function regarded as a physical field. In “spontaneous collapse” versions, systems are endowed with quantum states that generally evolve unitarily, but from time-to-time collapse without any need for measurement. In Everettian or “many-worlds” quantum mechanics, it is only the world as a whole C they call it a multiverse C that is really endowed with an intrinsic quantum state. That quantum state evolves deterministically, with only an illusion from the inside of probabilistic “branching”. Christopher Fuchs (cfuchs@ perimeterinstitute.ca), Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 The trouble with all these interpretations as quick fixes to Bell’s complaint is that they look to be just that, really quick fixes. They look to be interpretive strategies hardly compelled by the details of the quantum formalism. This explains in part why we could exhibit three such different strategies, but it is worse: Each of these strategies gives rise to its own set of incredibilities C ones for which, if one were endowed with Bell’s gift for the pen, one could make look just as silly. Take the pilot-wave theories: They give instantaneous action at a distance, but not actions that can be harnessed to send detectable signals. If there were PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 77 QUANTUM BAYESIANISM ... (FUCHS) no equations to give the illusion of science, this would have been called counting angels on the head of a pin. QUANTUM STATES DO NOT EXIST There is another lesson from the H1N1 virus. To some perplexity, it seems people over 65 C a population usually more susceptible to fatalities with seasonal flu C fare better than younger folk with H1N1. No one knows exactly why, but the leading theory is that the older population, in its years of other exposures, has developed various latent antibodies. The antibodies are not perfect, but they are a start. And so it may be for quantum foundations. Here, the latent antibody is the concept of information, and the perfected vaccine, we believe, will arise in part from the theory of single-case, personal probabilities C the branch of probability theory called Bayesianism. Symbolically, the older population corresponds to some of the founders of quantum theory (Heisenberg, Pauli, Einstein) and some of the younger disciples of the Copenhagen school (Rudolf Peierls, John Wheeler, Asher Peres), who, though they disagreed on many details, were unified on one point: That quantum states are not something out there, in the external world, but instead are expressions of information. Before there were people using quantum theory as a branch of physics, there were no quantum states. The world may be full of stuff, composed of all kinds of things, but among all the stuff and things, there is no observer-independent, quantum-state kind of stuff. The immediate payoff of this strategy is that it eliminates the conundrums arising in the various objectified-state interpretations. James Hartle [2] put the point decisively, “The ‘reduction of the wave packet’ does take place in the consciousness of the observer, not because of any unique physical process which takes place there, but only because the state is a construct of the observer and not an objective property of the physical system.” The real substance of Bell’s fear is just that, the fear itself. To succumb to it is to block the way to understanding the theory. Moreover, the harsher notes of Bell’s rhetoric are the least of the worries: The universe didn’t have to wait billions of years to collapse its first wave function C wave functions are not part of the observer-independent world. But this much of the solution is only a somewhat ineffective antibody. Its presence is mostly a call for more research. Luckily the days for this are ripe, and it has much to do with the development of the field of quantum information C that multidisciplinary field that includes quantum cryptography and quantum computation. Terminology can say it all: A practitioner in that field is just as likely to call any *ψ, “quantum information” as “a quantum state”. “What does quantum teleportation do?” “It transfers quantum information from Alice to Bob.” What we have here is a change of mindset [3]. What the protocols and theorems of quantum information pound home is the idea that quantum states look and feel like information in the technical sense of the word. There is no more beautiful demonstration of this than Robert Spekkens’s “toy model” mimicking various features of quantum mechanics [4]. In this model, the “toys” are each equipped with four possible mechanical configurations; but the players, the manipulators of the toys, are consistently impeded from having more than one bit of information about each toy’s actual configuration (two bits about two toys, etc.). The only things the players can know are their states of uncertainty. The wonderful thing is that these states of uncertainty exhibit many of the characteristics of quantum information: from the no-cloning theorem to analogues of quantum teleportation, quantum key distribution, and even interference in a Mach-Zehnder interferometer. More than two dozen quantum phenomena are reproduced qualitatively, and all the while one can pinpoint the cause: The phenomena arise in the uncertainties, not in the mechanical configurations. What considerations like this tell the objectifiers of quantum states is that, far from being an appendage cheaply tacked on to the theory, the idea of quantum states as information has a unifying power that goes a significant way toward explaining why the theory has the mathematical structure it does. There are, however, aspects of Bell’s challenge that remain a worry. And upon these, all could still topple. Particularly, the questions Whose information? and Information about what? must be addressed before any vaccine can be declared a success. Good immunology does not come easily. But this much is sure: The glaringly obvious (that a large part of quantum theory is about information) should not be abandoned rashly: To do so is to lose grip of the theory, with no better grasp on reality in return. If on the other hand, one holds fast to the central point about information, initially frightening though it may be, one may still be able to construct a picture of reality from the perimeter of vision. QUANTUM BAYESIANISM Every area of human endeavor has its bold extremes. Ones that say, “If this is going to be done right, we must go this far. Nothing less will do.” In probability theory, the bold extreme is personalist Bayesianism [5]. It says that probability theory is of the character of formal logic C a set of criteria for testing consistency. The key similarity is that formal logic does not have within it the power to set the truth values of the propositions it manipulates. It can only show whether various truth values are inconsistent; the actual values come from another source. Whenever logic reveals a set of truth values inconsistent, one must return to their source to alleviate the discord. Precisely in which way to alleviate it, though, logic gives no guidance. The key idea of personalist Bayesian probability theory is that it too is a calculus of consistency (or “coherence” as the practitioners call it), but this time for one’s decision-making degrees of belief. Probability theory can only show whether various degrees of belief are inconsistent. The actual beliefs come from another source, and there is nowhere to pin their 78 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) QUANTUM BAYESIANISM ... (FUCHS)AA responsibility but on the agent who holds them. A probability assignment is a tool an agent uses to make gambles and decisions, but probability theory as a whole is not about a single isolated belief C rather it is about a whole mesh of them. When a belief in the mesh is found to be incoherent with the others, the theory flags the inconsistency. However, it gives no guidance for how to mend any incoherences it finds. To alleviate discord, one must return to the source of the assignments in the first place C the very agent who is attempting to sum up all his history and experience with those assignments. Where personalist Bayesianism breaks from other developments of probability theory is that it says there are no external criteria for declaring an isolated probability assignment right or wrong. The only basis for a judgment of adequacy comes from the inside, from the greater mesh of beliefs the agent accesses when appraising his coherence. Similarly for quantum mechanics. The defining feature of Quantum Bayesianism [3,6-11] is that it says, “If this is going to be done right, we must go this far”. Specifically, there can be no such thing as a right and true quantum state, if such is thought of as defined by criteria external to the agent making the assignment: Quantum states must instead be like personalist Bayesian probabilities. The connection between the two foundational issues is this. Quantum states, through the Born Rule, can be used to calculate probabilities. On the other hand, if one assigns probabilities for the outcomes of a well-selected set of measurements, then this is mathematically equivalent to making the quantum-state assignment itself. Thus, if probabilities are personal in the Bayesian sense, then so too must be quantum states. The Quantum Bayesian dispels these difficulties by being conscientiously forthright. Whose information? “Mine!” Information about what? “The consequences (for me) of my actions upon the physical system!” The point of view here is that a quantum measurement is nothing other than a wellplaced kick upon a system C a kick that leads to unpredictable consequences for the very agent who did the kicking. What of quantum theory? It is a universal single-user theory in much the same way that Bayesian probability theory is. It is a users’ manual that any agent can pick up and use to help make wise decisions in this world of inherent uncertainty. In my case, a world in which I am forced to be uncertain about the consequences of my actions; in your case, a world in which you are forced to be uncertain about the consequences of your actions. In a quantum mechanics with the understanding that each instance of its use is strictly single-user C “My measurement outcomes happen right here, to me, and I am talking about my uncertainty of them.” C there is no room for most of the perennial quantum mysteries. With this we finally pin down the way in which quantum theory is “different in character from any physical theory before”. For the Quantum Bayesian, quantum theory is not something outside probability theory C it is not a picture of the world as it is C but rather an addition to probability theory itself. As probability theory is a normative theory, not saying what one must believe, but offering rules of consistency an agent should strive to satisfy within his overall mesh of beliefs, so it is the case with quantum theory. To embrace this is all the vaccination quantum theory needs. What this buys interpretatively is that it gives each quantum state a home. Indeed, a home localized in space and time C namely, the physical site of the agent who assigns it! By this method, one expels once and for all the fear that quantum mechanics leads to “spooky action at a distance”, and expels as well any hint of a problem with “Wigner’s friend”. It does this because it removes the very last trace of confusion over whether quantum states might still be objective, agent-independent, physical properties. The innovation of Quantum Bayesianism is that, for most of the history of trying to take an informational point of view about quantum states, the supporters of the idea have tried to have it both ways: that on the one hand quantum states are not real physical properties, yet on the other there is a right quantum state after all. One hears things like, “The right quantum state is the one the agent should adopt if he had all the information”. The tension in this statement, however, leaves its holder open to immediate attack: “If there’s a right quantum state after all, then why not just be done with all this squabbling and call it a physical fact independent of the agent? And if it is a physical fact, what recourse does one have for declaring that there is no action at a distance when delocalized quantum states change instantaneously?” Fig. 1 PHYSICS In contemplating a quantum measurement, one makes a conceptual split in the world: one part is treated as an agent, and the other as a kind of catalyst. A quantum measurement consists first in the agent taking an action on the quantum system. The action is represented formally by a set of operators {Ei } C a positive-operator valued measure (POVM). The action generally leads to an incompletely predictable consequence Ek for the agent. The quantum state *ψ, appears next to the agent’s head because it captures his degrees of belief concerning the consequences of his actions. IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 79 QUANTUM BAYESIANISM ... (FUCHS) SEEKING SICS C THE BORN RULE AS FUNDAMENTAL Yet, if quantum theory is a user’s manual, one cannot forget that the world is its author. And from its writing style, one may still be able to tell something of the author herself. The question is how to tease out the motif. Something that cannot be said of the Quantum Bayesian program is that it has not had to earn its keep in the larger world of quantum interpretations. Since the beginning, the promoters of the view have been on the run proving technical theorems whenever required to close a gap in its logic or negate an awkwardness in its new way of speaking. A case in point is this question: If quantum theory is so closely allied with probability theory, why is it not written in a language that starts with probability, rather than a language that ends with it? Why does quantum theory invoke the mathematical apparatus of Hilbert spaces and linear operators, rather than probabilities outright? This brings us to present-day research at Perimeter Institute. The answer we seek hinges on a hypothetical structure called a “symmetric informationally complete positive-operator-valued measure”, or SIC for short. This is a set of d 2 rank-one projection operators Π i = *ψi , +ψi* on a d-dimensional Hilbert space such that *+ψi *ψj ,*2 = 1 d +1 whenever i =/ j . How much evidence is this that SICs exist? The reader must answer this for himself, but for the remainder of the article we will proceed as if they do for all finite dimensions d and see where it leads. Thinking of a quantum state as literally an agent’s probability assignment for the outcomes of a potential SIC measurement leads to a new way of expressing the Born Rule for all quantum probabilities. Consider the diagram in Figure 2. It depicts a SIC measurement “in the sky”, with outcomes Hi , and an arbitrary von Neumann measurement “on the ground”, with outcomes Dj = * j, + j*, for some orthonormal basis. We conceive of two possibilities (or two “paths”) for a given quantum system to get to the measurement on the ground: “Path 1” proceeds directly to the measurement. “Path 2” proceeds first to the measurement in the sky and only subsequently cascades to the measurement on the ground. Suppose now, we are given the agent’s personal probabilities P (Hi ) for the outcomes in the sky and his conditional probabilities P (Dj *Hi ) for the outcomes on the ground subsequent to the sky. That is, we are given what the agent would assign on the supposition that the system follows Path 2. Then “coherence alone” (in the Bayesian sense) is enough to tell what probabilities P (Dj ) the agent should assign for the outcomes of the (1) Because of their extreme symmetry, it turns out that such sets of operators, when they exist, have remarkable properties. Among these, two powerful ones are that they must be linearly independent (spanning the space of Hermitian operators) and sum to d times the identity. This is significant because it implies that an arbitrary state ρ can be expressed as a linear combination of the Πi. Moreover, because the operators Hi = d11Πi are positive-semidefinite and sum to the identity, these can be interpreted as labeling the outcomes of a quantum measurement device C not a von Neumann measurement device, but a measurement device of the most general kind allowed in quantum theory [12]. Finally, the Πi’s symmetry gives a simple relation between the probabilities P(Hi ) = tr(ρHi ) and the expansion coefficients for ρ: 2 d 1⎞ ⎛ ρ = ∑ ⎜ ( d + 1) P ( H i ) − ⎟ Π i . ⎝ d⎠ i =1 (2) The extreme simplicity of this formula suggests it is the best place for the Quantum Bayesian to seek his motif. Fig. 2 Before proceeding, we must reveal what is so consternating about the SICs: It is whether they exist at all. Despite 10 years of growing effort since the definition was introduced [13,14], no one has been able to show that they exist in general dimension. All that is known firmly is that they exist in dimensions 2 through 67: dimensions 2-15, 19, 24, 35, and 48 by analytic proof, and the remainder through numerical simulation [15]. 80 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) The Born Rule for calculating quantum probabilities can be thought of as a rule connecting probability assignments from two physically different scenarios. Path 1, “on the ground”, is a one-step measurement generating a probability distribution Q(Dj ). Path 2, “in the sky”, is a two-step measurement generating probability distributions P(Hi ) and P(Dj *Hi ). The enchanting thing about SICs is that they make Path 1 probabilities a function of Path 2’s, despite usual quantum mechanical intuition. QUANTUM BAYESIANISM ... (FUCHS)AA measurement on the ground C it is given by the Law of Total Probability: P ( Dj ) = ∑ P ( Hi ) P ( Dj | Hi ) (3) i That takes care of Path 2, but what of Path 1? Is this enough to recover the probability Q(Dj ) the agent would assign for the outcomes of Path 1 by the Born Rule? That is, that Q(Dj ) = tr(ρDj ) for some quantum state ρ? Clearly Q(Dj ) =/ P(Dj ), for Path 2 is not a coherent process (in the quantum sense!) with respect to Path 1. What is remarkable about the SIC representation is that it implies that, though Q(Dj ) is not equal to P(Dj ), it is nonetheless a function of it. Particularly, d2 Q ( D j ) = ( d + 1) ∑ P ( H1 ) P ( D j | H i ) − 1. (4) i =1 The Born Rule is nothing but a kind of Quantum Law of Total Probability! No complex amplitudes, no operators C only probabilities in, and probabilities out. Nonetheless, Eq. (4) does not invalidate probability theory: For the old Law of Total Probability has no jurisdiction in the setting of our diagram, which compares a “factual” experiment (Path 1) to a “counterfactual” one (Path 2). Indeed as any Bayesian would emphasize, if there is a distinguishing mark in one’s considerations, then one ought to take that into account in one’s probability assignments. Thus there is a suppressed condition in our notation: Really we should have been writing the more cumbersome P (Hi * E2), P(Dj * Hi ,E2), and Q (Dj * E1) all along. With this explicit, it is no surprise that Q (Dj * E1) =/ P (Dj * E2). The message is that quantum theory supplies something that raw probability theory does not. The Born Rule in these lights is an addition to Bayesian probability in the sense of giving an extra normative rule to guide the agent’s behavior whenever he interacts with the physical world. THE FUTURE A vaccination of Quantum Bayesianism makes a healthy body even healthier, but it is far from the last word on quantum theory. In fact it is just an indication of the great adventure that lies ahead. By rewriting the Born Rule as Eq. (4) one gets a sense of where the essence of quantum theory has been hiding all along. It is in the active power of this quantity called dimension [6]. When an agent interacts with a quantum system, its dimension determines the extent to which the agent should deviate from the Law of Total Probability when transforming his counterfactual probability calculations to factual ones. That “power” calls out for an independent characterization that makes no necessary reference to the agent using it. Can it be done? And if it can be done, what are its implications for physics as whole, from common laboratory issues to open questions in gravity and cosmology? The Quantum Bayesians at Perimeter Institute are trying their best to find out. ACKNOWLEDGEMENTS The author thanks H. C. von Baeyer for improving the presentation and M. Schlosshauer for encouragement. The “Seeking SICs” section was supported in part by the U.S. Office of Naval Research (Grant No. N00014-09-1-0247). REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. J.S. Bell, Phys. World 3, 33 (1990). J.B. Hartle, Am. J. Phys. 36, 704 (1968). C.A. Fuchs, Coming of Age with Quantum Information, (Cambridge U. Press, 2010). R.W. Spekkens, Phys. Rev. A75, 032110 (2007). J.M. Bernardo and A.F.M. Smith, Bayesian Theory, (Wiley, Chichester, 1994). C.A. Fuchs, arXiv:1003.5209v1. C.M. Caves, C.A. Fuchs and R. Schack, Phys. Rev. A65, 022305 (2002). C.A. Fuchs, arXiv:quant-ph/0205039v1. C.A. Fuchs and R. Schack, arXiv:quant-ph/ 0404156v1. C.M. Caves, C.A. Fuchs, and R. Schack, Stud. Hist. Phil. Mod. Phys. 38, 255 (2007). C.A. Fuchs and R. Schack, arXiv:0906.2187v1. M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information, (Cambridge U. Press, 2000). G. Zauner, PhD thesis, University of Vienna (1999). C.M. Caves, report, University of New Mexico (1999). A.J. Scott and M. Grassl, arXiv:0910.5784v1. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 81 CAP DEPARTMENTAL MEMBERS / MEMBRES DÉPARTEMENTAUX DE L’ACP - Physics Departments / Départements de physique (as at 2010 May 31 / au 31 mai 2010) Queen's University Royal Military College Ryerson University Saint Mary’s University Simon Fraser University St. Francis Xavier University Thompson Rivers University Trent University Trinity Western University Université de Moncton Université de Montréal Université de Sherbrooke Université du Québec à Trois-Rivières Université Laval University of Alberta University of British Columbia University of Calgary University of Guelph Acadia University Bishop's University Brandon University Brock University Carleton University Collège Ahuntsic Collège François-Xavier-Garneau Collège Montmorency Concordia University Dalhousie University École Polytechnique de Montréal Lakehead University Laurentian University McGill University McMaster University Memorial Univ. of Newfoundland Mount Allison University Okanagan University College University of Lethbridge University of Manitoba University of New Brunswick University of Northern British Columbia University of Ontario Inst. of Technology University of Ottawa University of Prince Edward Island University of Regina University of Saskatchewan (and Eng. 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INSTITUTE FOR PHOTONIC INNOVATION CANADIAN LIGHT SOURCE INSTITUTE FOR QUANTUM COMPUTING PERIMETER INSTITUTE FOR THEORETICAL PHYSICS SNOLAB TRIUMF L'Association canadienne des physiciens et physiciennes invite cordialement corporations et institutions à faire partie des membres corporatifs ou institutionnels. Renseignements auprès de la directrice exécutive. CANADIAN ASSOCATION OF PHYSICISTS / ASSOCIATION CANADIENNE DES PHYSICIENS ET PHYSICIENNES Bur. Pièce 112, Imm. McDonald Bldg., Univ. of/d’Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5 Phone / Tél : (613) 562-5614; Fax / Téléc : (613) 562-5615 ; Email / courriel : [email protected] INTERNET - HTTP://WWW.CAP.CA 82 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE A TRIPLE BY SLIT TEST FOR QUANTUM MECHANICS URBASI SINHA, CHRISTOPHE COUTEAU, FAY DOWKER, THOMAS JENNEWEIN, GREGOR WEIHS, AND RAYMOND LAFLAMME “If Born’s rule fails, everything goes to hell”. [1] Q uantum mechanics, one of the pillars of theoretical physics in the 20th century, has been tremendously successful at describing the world around us. The theory has been able to describe the world of atoms and molecules, solid state physics, particle physics, allowing us to understand the photoelectric effect, superconductivity and much more. It has led to new technologies which have transformed our lives, from Magnetic Resonance Imaging (MRI) to the laser and the transistor and might lead to new ones such as quantum computers and quantum cryptography. Despite having these resounding successes, the theory still predicts phenomena that are very much counterintuitive. Quantum mechanics seems to fundamentally change the way we understand the world, opening the door to many potential interpretations. All other theories of physics that we have encountered have ultimately disagreed with observations or predicted their own demise; it would thus be surprising if quantum mechanics were to be a final theory of nature. Many attempts have been made to complement it or generalize it, by modifying some of its axioms, such as adding hidden variables, non-linear evolution etc. One axiom of quantum mechanics is that the probability is proportional to the modulus of the wave function squared [2]. This paper describes a program to test this axiom using a generalization of the famous double slit experiment. THE TRIPLE SLIT EXPERIMENT Many people encounter quantum mechanics for the first time when reading the third volume of the Feynman SUMMARY As one of the postulates of quantum mechanics, Born’s rule tells us how to get probabilities for experimental outcomes from the complex wave function of the system. Its quadratic nature entails that interference occurs in pairs of paths. We present an experiment that sets out to test the correctness of Born’s rule by testing for the presence or absence of genuine three-path interference. This is done using single photons and a three slit aperture. Lectures in Physics [3] in which Feynman describes the double slit experiment and comments that it “has in it the heart of quantum mechanics”. This view is widely shared in the physics community so it will come as a surprise to many that, though indeed the double slit experiment exhibits, beautifully, the phenomenon of interference between two histories of a single system B the photon trajectories in this case B this phenomenon does not fully characterize “quantumness”. Quantumness, it has been discovered [4], consists not only of the existence of interference between pairs of histories but precludes interference between triples of histories. The double slit experiment demonstrates two-way interference. The probability P for the photon to be detected in an experiment at a particular position on the screen when both slits, call them A and B, are open is not equal to the probability of the photon being detected at that particular band when only A is open plus the the probability for the photon to be detected there when only B is open: P (A c B) − P (A) − P (B) /= 0 (1) where A c B is shorthand for “the photon is detected at the band when both A and B are open” etc. We call this nonzero quantity, the interference I2(A, B) and it is responsible for the famous pattern of light and dark bands. It describes the interference between two histories composed of the photon passing through slit A or slit B. If we now consider an experiment with three slits, A, B and C, we can generalize I2 to I3(A,B,C). Now, there are seven experimental situations to consider: all three slits open, any pair of slits open or any single slit open. If we write the probability of a photon landing at a specified position on the screen for these seven different experiments as P (A c B c C), P (A c B) etc. and P (A) etc. (respectively) then Quantum Mechanics tells us that the following combination is zero: P (A c B c C) − P (A c B) − P (B c C) − P (C c A) + P (A) + P (B) + P (C) = 0. (2) This is a consequence of Born’s rule. Remarkably, until the present work, this prediction of quantum theory had not yet been put to direct experimental test. PHYSICS IN U. Sinha <usinha@ uwaterloo.ca>, Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1 C. Couteau, Université de Technologie de Troyes, France F. Dowker, Imperial College, UK T. Jennewein, Institute for Quantum Computing, University of Waterloo G. Weihs, Universität Innsbruck, Austria R. Laflamme, Perimeter Institute and Director, Institute for Quantum Computing, University of Waterloo CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 83 A TRIPLE SLIT TEST ... (SINHA ET AL.) Although Born’s rule has been indirectly verified to high accuracy in other experiments, the consequences of a detection of even a small three-way interference in the quantum mechanical null prediction would be tremendous. If a non-zero result were to be obtained, it would mean that quantum mechanics is only approximate, in the same way that the double slit experiment proves that classical physics is only an approximation to the true laws of nature. This would give an important hint on how to generalize quantum mechanics and open a new window to the world. Currently we have no idea what such a theory could look like but research is already being done to explore the characteristics of and alternative ways to understand such a theory [7]. It might even give a hint towards unifying quantum mechanics and gravity, a major goal of fundamental physics today. Obviously the discovery of a three path interference would lead to the question: Is there four-way interference? There is indeed a whole hierarchy of theory types: a level k theory being one in which there is k-way interference but no k+1-way interference [4]. An interesting consequence of the violation of Born’s rule would be for computer science. In the last 40 years, computer scientists have classified sets of problems according to the difficulty with which they can be solved. They look at how these sets relate to each other and have conjectured many relationships. A well-known example is the famous question of whether or not the classes P and NP are the same [5] C finding a proof to resolve this longstanding question would earn a million dollar prize from the Clay Foundation [6]. Aaronson has shown that violating Born’s rule would have a dramatic effect on computational complexity because it would allow one to efficiently distinguish two states that are exponentially close. This would relate two complexity classes implying that NPcomplete problems could be solved in polynomial space [8] something which is not believed to be true with either classical or quantum computers and would surprise many computer scientists. A similar conclusion was reached by Meyer in [9]. He has suggested that a task that takes two steps with quantum C level k = 2 C resources could be achieved in one step with level 3 resources and so on. To realise this intriguing idea would require models for level 3 and higher k physical systems to be discovered but it shows that the implications of a detection of super-quantum theories would be very far reaching indeed, even beyond the boundaries of physics itself. BRINGING THEORY TO THE LAB ... The triple slit experiment is being performed at the Institute for Quantum Computing in the University of Waterloo, Canada. In this experiment, we evaluate the triple slit interference term given by equation (2). If Quantum Mechanics is correct, this term will be zero, if there is a further generalization to the theory, then we would get a non zero result which cannot be explained by experimental errors. Fig. 1 Pictorial representation of how the different probability terms are measured. The leftmost configuration has all slits open, whereas the rightmost has all three slits blocked. The black bars represent the slits, which are never changed or moved throughout the experiment. The thick grey bars represent the opening mask, which is moved in order to make different combinations of openings overlap with the slits, thus switching between the different combinations of open and closed slits. The experiment consists of measuring the seven probability terms in equation (2) along with an eighth term P(0) which gives the background probability (this takes care of any experimental background such as detector dark counts i.e. spurious counts measured by the detector even in the absence of a source of photons). We define a quantity ε as ε = P (A c B c C) − P (A c B) − P (B c C) − P (C c A) + P (A) + P (B) + P (C) − P (0) (3) Figure 1 shows how the various probabilities are measured in a triple slit configuration. For better comparison between possible realizations of such an experiment, we further define a normalized variant of ε called ρ, ε ,where δ δ= | IAB | + | IBC | + | ICA | = | P (A c B) − P (A) − P (B) + P (0)| + | P (B c C) − P (B) − P (C) + P (0)| + | P (A c C) − P (A) − P (C) + P (0)| . ρ = (4) (5) Since δis a measure of the regular interference contrast, ρ can be seen as the ratio of three-path interference over the regular two-path interference. (If δ= 0 then ε = 0 trivially, and we really are not dealing with quantum behavior at all, but only classical probabilities.) EXPERIMENTAL SET UP Figure 2 shows a schematic of the complete experimental setup. The laser beam passes through an arrangement of mirrors and collimators before being incident on a 50/50 beam splitter. The beam then splits into two, one of the beams is used as a reference arm for measuring fluctuations in laser power whereas the other beam is incident on the thin metal membrane , which has the slit pattern cut into it using commercial laser cutting. The beam height and wast is adjusted so that it is incident on a set of three slits, the slits being centered on the beam. There is 84 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) A TRIPLE SLIT TEST ... (SINHA ET AL.)AA Fig. 2 Schematic of experimental set-up. another membrane in front which has the corresponding blocking designs on it such that one can measure the seven probabilities in equation (2). The slit plate remains stationary whereas the blocking plate is moved up and down in front of the slits to yield the various combinations of opened slits required to measure the seven probabilities. As mentioned above, in our experimental set-up, we also measure an eighth probability which corresponds to all three slits being closed in order to account for dark counts and any background light. Figure 2 shows this pictorially. A multi-mode optical fiber is placed at a point in the diffraction pattern and connected to an avalanche photodiode (APD) single photon detector which measures the photon counts corresponding to the various probabilities. The optical fiber can be moved to different positions in the diffraction pattern in order to obtain the value of ρ at different positions in the pattern. Some of our preliminary results as well as experimental details have been published in [10]. At present we are working on using single photons as our incident photons. We have a heralded single photon source (HSPS) [11] based on parametric down conversion (a method by which a blue photon splits into two red photons when it is incident on a non linear crystal to maintain energy conservation) and the use of single photons enables us to know the exact number of events and also gives us a means of performing the same experiment using two independent sources of incidence with different statistics. Figure 3 shows a comparison between interference with three slits open obtained by using a Titanium Sapphire laser at 810 nm on one hand and a heralded single photon source on the other. CONCLUSION Quantum mechanics has been one of the most elegant and important theories in 20th century physics and has been suc- Fig. 3 Comparison between experimentally obtained triple slit interference patterns. The blue dots indicate the laser pattern and the red dots indicate the single photon pattern. The black line has been drawn to aid the eye. cessful in explaining and motivating numerous applications. However, in spite of its successes, there are still mysteries associated with the theory which hint at the possibility of the existence of more generalized versions. This makes it important to test the fundamental postulates of quantum mechanics through dedicated experiments. In this paper we have described an experiment to test Born’s rule. Some of our preliminary observations have been reported in [10] giving non-zero result for ρ, as defined in equation (5). However, this could be caused by some systematic errors that have not yet been controlled. Improvements to the experiment set-up have since been made, including performing the experiment using single photons [12]. The future will tell us whether we understand these errors or perhaps that there could be a discrepancy with the predictions of quantum mechanics. We just have to wait and watch! ACKNOWLEDGEMENTS Research at IQC and Perimeter Institute was funded in part by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. Research at IQC was also funded in part by CIFAR and NSERC. This research was partly supported by NSF grant PHY-0404646. U.S. Thanks to Aninda Sinha for useful discussions. REFERENCES 1. 2. 3. 4. 5. 6. W.H. Zurek, Private communication. M. Born, Zeitschrift fur Physik 37, 863-867, 1926. R.P. Feynman, R.B. Leighton and M. Sands, The Feynman Lectures on Physics, Addison-Wesley, Reading, MA, USA (1965). R.D. Sorkin, “Quantum mechanics as quantum measure theory”, Mod. Phys. Lett. A9 (1994). D. Gottesman, “Spin Systems and Computational Complexity”, in this issue. See: http://www.claymath.org/millennium/ PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 85 A TRIPLE SLIT TEST ... (SINHA ET AL.) 7. 8. C. Ududec, H. Barnum and J. Emerson, “Three Slit Experiments and the Structure of Quantum Theory”, arXiv:0909.4787v1. Scott Aaronson “Quantum computing, post selection, and probabilistic polynomial-time”, Proceedings of the Royal Society, A461, 3473, (2005). 9. D. Meyer, “Probability sum rules limit the computational benefits of interference”, Talk at Canadian Institute for Advanced Research Quantum Information Processing meeting, Alton-Caledon, OT, Canada 25 May 2009. 10. U. Sinha, C. Couteau, Z. Medendorp, I. Sollner, R. Laflamme, R. Sorkin, and G. Weihs, “Testing Born’s Rule in Quantum Mechanics with a Triple Slit Experiment”, Foundations of Probability and Physics-5; L. Accardi, G. Adenier, C. Fuchs, G. Jaeger, A. Yu. Khrennikov, J. Larsson, S. Stenholm (Eds.), American Institute of Physics Conference Proceedings, Vol. 1101, pp. 200-207, New-York (2009). 11. E. Bocquillon, C. Couteau, M. Razavi, R. Laflamme, and G. Weihs,“Coherence measures for heralded single-photon sources”, Phys. Rev., A79, 035801 (2009). 12. U. Sinha et al, in preparation (2010). 86 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE SPIN SYSTEMS AND COMPUTATIONAL COMPLEXITY BY DANIEL GOTTESMAN W hat is the connection between a cathedral's stained glass window and the world's hardest Sudoku puzzle? They are more closely connected than you might think. Glass (not just stained glass) differs from most materials studied by physicists in that it has structure, but not a regular one. The elemental composition of glass is not very different from quartz, but in quartz, the atoms are arranged in a regular crystalline structure, and rearranging the atoms to change the structure incurs a large energy cost. By contrast, in glass, there are many different arrangements of atoms with about the same energy. If liquid silica is cooled slowly, it can crystallize into quartz, but if it cools rapidly, the result is glass. One atomic configuration is selected, more or less at random, when the glass cools, but it is not necessarily the lowest-energy one. A similar phenomenon can occur with “spin systems”, systems where the atoms are all stationary and only the direction of their spins varies from location to location. The direction of spin for a classical system is towards the north pole of its rotation axis, and a quantum spin similarly has a direction, though it cannot be easily interpreted as rotating. A magnet is essentially a spin system: the atoms are arranged according to the structure of iron or whatever material composes the magnet. However, each atom has a spin and an associated magnetic field. The magnetic field from each atom interacts with the spin of nearby atoms. In a “ferromagnet”, the spins and magnetic fields from different atoms tend to line up in the same direction. They therefore reinforce each other, and add together to produce a field much larger than the magnetic field of any individual atom. Iron is a ferromagnetic material, and permanent magnets result from an interaction of this type. Some other materials are “antiferromagnets”. In an antiferromagnet, the magnetic fields of neighboring atoms tend to face opposite directions, and therefore cancel out. SUMMARY A spin glass is a system of particles with spins which, when cooled, does not settle into a simple ground state, but instead gets caught for a long time with many misaligned spins. I will outline the close connections between the physics of spin glasses and the mathematics of computationally difficult problems. Fig. 1 A two-dimensional spin system with random magnetic and ferromagnetic bonds. The solid green lines indicate a ferromagnetic bond and the dotted purple lines indicate an antiferromagnetic interaction. Each spin can point up or down. This particular configuration has 15 bond conditions violated, but there are many other configurations with the same number of incorrect bonds. Antiferromagnets are less common than ferromagnets, but they do occur naturally. In a ferromagnet, the lowest-energy state (the “ground state”) is just to line up all the spins to point the same way, whereas in an antiferromagnet, the ground state is for the spins to alternate which direction they face, forming a checkerboard pattern. Spin systems can display an enormous range of possible behaviors. For instance, if we have a randomly mixed material such that some neighboring pairs of atoms have ferromagnetic interactions whereas other pairs have antiferromagnetic interactions (as in Fig. 1), the system no longer has a nice regular lowest-energy state. Instead, there is a complicated morass of different states, all of which have very similar energies. A spin system that behaves like this is called a “spin glass”. While it is a subject of dispute whether there is an actual connection between the physics of spin glasses and of window glass; spin glasses are nonetheless a fascinating subject in their own right [1]. Daniel Gottesman <dgottesman@ perimeterinstitute.ca> Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5,Canada To study spin systems, physicists generally simplify them further. We assume the atoms have truly fixed locations, perhaps on a square or cubic lattice, and only the spin state of an atom can change. Frequently, we assume that only adjacent spins can interact, and that spins which are further apart have no direct effect on each other. These idealized spin systems can be classical or quantum. In a classi- PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 87 SPIN SYSTEMS ... (GOTTESMAN) cal spin system, each spin considered by itself has a definite direction, and we can describe the system’s configuration at any given time just by specifying the direction of each spin. In a quantum spin system, the spins behave quantum mechanically, and thus can be in entangled states, where it is not possible to specify the state of just one spin, only of all the spins collectively . A spin glass does not naturally find its own ground state, but one might imagine that with the aid of a powerful computer, we could still learn the lowest possible energy state of a spin glass. Not so. Computers have advanced dramatically in power in the past few decades, but there are still problems that we do not know how to solve. Indeed, we believe that some problems, including finding the ground state energy of some spin glasses, are inherently hard to solve, and that future advances in computer engineering will still not let us solve the hardest examples. Fig. 2 An example solved Sudoku problem. The values and locations of the large bold numbers are the input to the problem. The goal is to fill in the remaining locations so that each row, column, and 3 H 3 subgrid must contain exactly one of each digit from 1 to 9. The values and locations of the small red numbers provide a witness: With them in place, it is easy to check that this is a valid solution. Given only the bold large numbers, however, it is difficult to find a solution. Sudoku is another example of a computationally hard problem. (For those who are unfamiliar with it, see Figure 2 for an example.) The examples of Sudoku presented as puzzles in newspapers and elsewhere are relatively easy C they are designed to be solvable by hand. If you consider harder examples and generalize to larger k2 H k2 grids filled with numbers from 1 to k, even the world’s largest computers will often be unable to solve the problem. Computer scientists formalize the relative difficulty of various computational problems by categorizing them into “complexity classes”. To determine what complexity class a problem belongs to, one needs to look at a collection of very big examples of the problem. Given any single input for the problem, there is just one answer C one output C and the amount of time to get that answer might depend on what information you start with and exactly how your computer works. However, when you look at larger and larger inputs for a problem, finding the answer typically gets harder and harder, and the approximate rate at which it gets harder does not depend on these details. For instance, P is the class of problems that are solvable in a time which is any polynomial in the size n of the input, be it n2 or n200. The exact polynomial rate might depend on how your computer is built, but the fact that the growth is polynomial in most cases does not 1. A problem in P is generally considered to be solvable in a reasonable time, and problems which are not in P are considered to be hard. Of course, this is just a simplification C a time scaling of n 200 is enough to make the problem hard in practice, whereas a time of exp(n / 10200 ) will be over before you know it unless n itself is ridiculously large. In addition, the scaling refers to the difficulty of solving the very hardest inputs; for many, or even most, inputs, the difficulty may be much less. Still, it seems to be a reasonable criterion, in that it is both well-defined (because P doesn’t depend on exactly how you define “computer”), and for most problems outside P, there seem to be some reasonable-size inputs for which we cannot solve the problem. Another important complexity class is NP, which, roughly speaking, is the class of problems that can be checked in a reasonable amount of time. Sudoku is an example, along with many other interesting problems. More specifically, NP is composed of “yes” or “no” questions (e.g., does this Sudoku have a solution?). If the answer for a specific input is “yes”, there must be some information, called a “witness”, that will enable you to check in polynomial time that the answer is indeed “yes”. If the answer is “no”, then no purported witness should pass this checking procedure. For Sudoku, the witness is simply the solution. Finding the solution is hard, but if you are given the solution, you can easily check that it is valid. Indeed, Sudoku is an example of an “NP-complete” problem [2]. NP-complete problems are the hardest problems in NP C if you can efficiently solve an NPcomplete problem for all inputs, you can efficiently solve any problem in NP. It is a famous open question whether P = NP. We believe it does not, and that therefore the NP-complete problems are hard. One strategy you might adopt to solve an NP-complete problem is to try different potential witnesses. If you happen upon a correct witness, it is easy to check, and therefore you know the answer is “yes”. If you are unable to find a valid witness, you might conclude the answer is “no”. Of course, the number of potential witnesses is huge; there are exponentially many in the input size. You might repeatedly modify a potential witness slightly, attempting to overcome its defects. For instance, in Sudoku, you might take a trial solution which has a column with two 9s and no 3 and change one 9 to a 3. This might create new errors, requiring further changes, but perhaps after a few changes there will be fewer errors than in your original failed solution. Some version of this strategy works quite well for many particular inputs. However, the strategy fails on the very hardest inputs, because there are very many nearly-correct witnesses, and it is very difficult to find the one true witness among the forest of false witnesses. For Sudoku, there could be 1. There is one major exception: a quantum computer can solve some problems in polynomial time which we believe cannot be solved in polynomial time on a regular classical computer. 88 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) SPIN SYSTEMS ... (GOTTESMAN)AA many arrangements with just a few violations of the rules, but the true solution might be very different from the almost-correct ones. This is precisely the phenomenon that prevents spin glasses from settling down to a single state: There are many low-energy states, but only one of those (or a few at most) has absolutely the smallest energy. Indeed, for many types of classical spin glasses, the problem of finding the ground state is an NP-complete problem. For instance, it is an NP-complete problem to find the ground state of a spin system in three dimensions with some mix of ferromagnetic, antiferromagnetic, and zero interactions [3]. Quantum mechanics adds an additional twist. A “quantum computer” is a computer whose memory and computational registers may contain quantum superpositions. By taking advantage of this capability, a quantum computer can solve some problems which seem to be too hard for classical computers. The complexity class BQP is defined as the class of problems which can be solved in polynomial time on a quantum computer, and we believe BQP is bigger than P. For instance, we believe factoring is in BQP but not in P: multiplying two large prime numbers together is easy (in P), but going the other way, finding the prime factors of a large number, is believed to be hard for a classical computer. In contrast, a quantum computer could factor numbers in polynomial time [4]. Small quantum computers have been built, but it will still be decades before we can build one large enough to factor numbers that can’t be factored with today’s classical computers. Even without quantum computers, we can study the new quantum complexity classes they suggest, such as BQP, and try to apply any new insights we gain to better understand quantum physics. There is also a quantum analogue of NP called QMA. QMA is the class of problems that can be efficiently checked on a quantum computer. Just as we believe that BQP is bigger than P, we believe that QMA is bigger than NP. In other words, QMA-complete problems are likely too hard to even be efficiently checked on a classical computer. They are probably also too hard to solve efficiently with a quantum computer. (Indeed, we believe quantum computers can’t solve every problem in NP either.) Finding the ground state energy of a quantum spin glass is QMA-complete. That is, if we could solve this problem, we could solve any problem in QMA. Thus, quantum spin glasses are even more difficult than their classical counterparts, which are only NP-complete. In addition, more quantum systems are harder than classical systems. Finding the ground state energy of a 1-D classical spin system that is in P C easy C but finding the ground state energy of a 1-D quantum spin system is QMAcomplete [5]. Now you know how a cathedral’s stained glass window and the world’s hardest Sudoku problem are related. Glass is disordered because it has a multitude of nearly-optimal configurations, the same effect that makes Sudoku and some other computational problems intractable. Of course, a stained glass window and a Sudoku puzzle are not identical: The difference is that the stained glass window is supposed to help you pray, whereas with a really hard Sudoku, you can only pray for help. ACKNOWLEDGEMENTS The author thanks Lucy Zhang for helpful comments. He is supported by CIFAR, NSERC, the Government of Canada through Industry Canada and the Province of Ontario through the Ministry of Research and Innovation. This paper was written in part while the author was visiting KITP, which is supported by the NSF under Grant No. NSF PHY05-51164. REFERENCES 1. 2. 3. 4. 5. K. Binder and A.P. Young, Rev. Mod. Physics 58, 801-976 (1986). T. Yato and T. Seta, IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences E86-A, 1052-1060 (2003). F. Barahona, J. Phys. A15, 3241-3253 (1982). P.W. Shor, SIAM Review 41, 303-332 (1999). D. Aharonov, D. Gottesman, S. Irani, and J. Kempe, Proc. FOCS, 373-383 (2007), Comm. Math. Physics 287, 41-65 (2009), arXiv:0705.4077 [quant-ph]. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 89 FÉLICITATIONS / ADDENDUM ADDENDUM CONGRATULATIONS TWO CANADIAN PHYSICISTS APPOINTED FELLOWS LONDON On 21 May 2010 the Royal Society elected 44 new Fellows and eight new Foreign Members. Experts in artificial intelligence, DNA repair, asthma and superstring theory were among the scientists newly elected. The new Fellows join the ranks of the UK and Commonwealth’s leading scientists as the Society celebrates its 350th Anniversary. Among the 44 new Fellows are Canadian physicists, Ian Affleck and Victoria Kaspi. The citations published in recognition of his honour appear below. Congratulations to these distinguished Canadian physicists. Professor Ian Affleck FRS Killam University Professor, Department of Physics and Astronomy, University of British Columbia Ian Affleck has made numerous ground-breaking contributions across a wide range of theoretical physics. His early work on dynamical supersymmetry breaking and the AffleckDine mechanism for baryogenesis had strong impact on particle physics. In mathematical physics, he contributed to important rigorous results on valence-bond groundstates in antiferromagnets. He has authored many seminal works in condensed matter theory applying field theoretic methods to systems of experimental relevance, e.g. staggered flux phases and local SU(2) gauge invariance in the theory of strongly correlated fermions relevant to high temperature superconductors and nonabelian bosonization methods in one-dimensional quantum many body problems. OF THE ROYAL SOCIETY OF Professor Victoria Michelle Kaspi FRS Professor of Physics, Department of Physics, McGill University Kaspi's research is focused on the observational study of neutron stars. She and her collaborators showed that anomalous X-ray pulsars exhibit glitches, stable spin properties, and X-ray bursts, thereby strongly suggesting that they are magnetars (neutron stars powered by magnetic fields of up to a petaguass). She used magnetospheric eclipses in a double pulsar to detect spin precession at the rate predicted by general relativity (to within 13%), one of the few tests of relativity in strong fields. Kaspi has discovered novel phenomena in binaries containing neutron stars, including the first millisecond pulsar in an eccentric orbit, the first pulsar to exhibit spin-orbit coupling, and emission from the colliding winds between a neutron star and a Be star companion. Kaspi and collaborators also introduced phase-coherent timing of pulsars in X-rays, derived strong upper limits on the cosmological density of gravitational waves and the rate of change of Newton's gravitational constant from pulsar timing, found the fastest rotating pulsar (716 Hz), and discovered many new pulsars. Most of these projects were led by Kaspi or her students or postdocs at McGill, where she has led the development of a strong astrophysics group. UNIVERSITY OF LETHBRIDGE AWARDS FIRST PHD IN PHYSICS Addendum to list of PhDs awarded in Physics at Canadian Universities between Dec. 2008 and Nov. 2009 (Vol. 66, No. 1 - January-March 2010 Physics in Canada) SPENCER, Locke, “Imaging Fourier Transform Spectroscopy from a Space Based Platform - The Herschel/SPIRE Fourier Transform Spectrometer”, (David Naylor, supervisor), June, 2009, now an NSERC Postdoctoral Fellow at the School of Physics and Astronomy, University of Cardiff, Wales (working on the Planck cosmic background mission) Congratulations to the U.Lethbridge Physics Department and Loche Spencer on this important milestone. 90 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE WARPED BY VIEWS: OBSERVING BLACK HOLES LATHAM BOYLE AND LUIS LEHNER E instein’s theory of general relativity predicts the existence of black holes: regions of spacetime that are so strongly curved that not even light can escape. Black holes have been called “the most perfect macroscopic objects”[1]: elegant and symmetric whirlpools of spacetime itself, each completely characterized by its mass and spin. But these theoretical beauties present a profound observational puzzle! In one sense, they are staring us in the face: they are believed to be the driving force behind the most violent, energetic, and easily observed phenomena in astronomy, including quasars, blazars, gamma ray bursts, radio jets, and active galactic nuclei. Yet, in another sense, they are hidden from view: clean observational probes of the true essence of a black hole C namely, the highly curved spacetime in its vicinity C have remained frustratingly elusive. Soon gravitational wave detectors will provide a completely new tool for “observing” the universe around us. These detectors, along with increasingly sensitive electromagnetic telescopes, will allow us to peek deep into black hole systems, and the insights from these new observations are likely to profoundly affect our understanding of fundamental physics and the cosmos. Here we sketch some of our efforts to develop better ways to observe black holes. We start with an idea for “seeing” single holes, and then discuss techniques for observing the electromagnetic and gravitational wave emission from a pair of holes. LIGHT LOOPS ECHOES AND BLINKING BLACK HOLES One technique that we have been investigating [2] involves looking for a particular “blinking” or “echo” signal due to light loops which wrap around the hole. Light rays travel- SUMMARY Although we can’t look inside a black hole, observing the strongly curved space-time in its vicinity would be the next best thing. In this article, we explain several ideas to do just this: by looking for light rays which are wrapped into loops as they pass near the black hole’s horizon; and by looking for the striking electromagnetic and gravitational wave signals that are generated when two black holes merge. ing to our telescopes will be bent as they pass through curved regions of spacetime C a phenonemon known as gravitational lensing. To date, physicists have only detected rays with tiny bending angles (much less than 2π, even in so-called “strongly-lensed” systems where galaxies appear to be stretched into banana-shaped arcs on the sky); but general relativity predicts that light rays that pass close to a black hole can experience very large bending angles, and can even be bent into “light loops” which wrap around the black hole once or more before proceeding to the observer [3]. If we could detect this phenomenon, we would have a new way to probe the spacetime near a black hole, and dramatic confirmation of a striking prediction of general relativity. To see how we might try to detect these light loops, we should start by understanding why, at first glance, the task seems practically impossible. Consider the usual gravitational lensing configuration, in which the lens is almost perfectly aligned between the source and the observer, and far away from both (Fig. 1a). If the lens is a non-spinning black hole then, in addition to the primary ( j = 0) image, there will also be higher-order ( j = 1, 2, 3 ... ) images due to rays that wrap around the hole j times before proceeding to the observer. Unfortunately, the higher-order images tend to be extremely dim relative to the primary image [3]: the intensity Ij of the jth higher-order image is suppressed relative to the intensity I0 of the primary image by a factor 4(9 ! 3 3 )4[(GM /c2)DS/DLDLS]3/2e!(2j+1)π (1) where G is Newton’s constant, c is the speed of light, M is the black hole mass, DL is the distance from the observer to the lens, DS is the distance from the observer to the source, and DLS is the distance from the lens to the source. At first glance, Eq. (1) is depressing for two reasons: (i) the factor in square brackets looks depressingly tiny because in ordinary gravitational lensing, the distances DL, DS, and DLS are enormous relative to the Schwarzschild radius 2GM /c 2 of the lens; and (ii) the exponential factor says that in order to see highly bent rays, we have to pay a depressingly stiff price: when the bending angle is increased by χ, the intensity of the corresponding image is suppressed by exp(!χ). But, before getting too depressed, note that we can improve the situation dramatically via the following two tricks. First, if we bring the source very close to the lens, so that DLS ∼ (GM /c2), and hence DL . DS, then the factor in square brackets will be order unity. Second, if we move the source from the PHYSICS IN Latham Boyle, <lboyle@ perimeterinstitute.ca>, Perimeter Institute, 31 Caroline St. N., Waterloo, ON N2L 2Y5 and Luis Lehner, <llehner@ perimeterinstitute.ca>, Perimeter Institute and University of Guelph CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 91 WARPED VIEWS ... (BOYLE AND LEHNER) Fig. 2 Fig. 1 Two gravitational lensing configurations: (a) the usual “straight-line” configuration, and (b) the “right-angle” or “face-on” configuration. “straight-line” configuration of ordinary gravitational lensing (Fig. 1a) to the “right-angle” configuration of Fig. 1b then, instead of successive higher order images being suppressed by the factor exp (!2π) . 0.0019, they would only be suppressed by the more palatable factor exp(!π) . 0.043. Is nature kind enough to provide us with real astronomical sources that use these two tricks? Yes! In our universe, black holes come equipped with their very own nearby source: a disk of matter (an “accretion disk”) whose innermost region produces copious electromagnetic radiation, and lies very near the black hole itself. Furthermore, many of these black holes are expected to be spinning rapidly [4], which helps by bringing the accretion disk even closer to the hole. Near such a highly-spinning hole, the accretion disk lies in the equatorial plane [5] (perpendicular to the hole’s spin axis). This means that, when we view an astrophysical black hole nearly “face-on” (that is, nearly down its spin axis), we are viewing the inner part of its accretion disk in precisely the right-angle configuration of Fig. 1b. As illustrated in Fig. 2a, when a burst of radiation I0(t) is emitted in the equatorial plane, near the hole, we (the nearly face-on observer) see a light curve I(t) with a characteristic blinking pattern as the burst reaches us via multiple paths: the primary ( j = 0) burst followed by subsequent dimmer ( j = 1,2, An example: in emission from the inner stable circular orbit of a black hole spinning at .85% of its maximal value, the blinking effect can be prominent in the light curve I(t) of a burst, or even in the autocorrelation function ξ(t) from random emission. 3, ...) “echoes”. Fig. 2b shows that, even if the emission is a random sequence of bursts, with intrinsic auto-correlation function ξ0(t), the blinking signal can still show up in the observed auto-correlation function ξ(t), for similar reasons. ELECTROMAGNETIC SIGNALS FROM BINARY BLACK HOLES General Relativity also predicts the generation of gravitational waves: traveling ripples in spacetime that are generated in a particularly strong way when two black holes orbit around each other in a binary pair. These waves should soon be detected by highly sensitive detectors like LIGO in the USA, VIRGO in Italy and Geo in Germany. In addition, a space-based detector named LISA, which will hopefully be launched in about a decade, would see gravitational waves from the furthest corners of the universe. Gravitational waves carry away energy and angular momentum, leading the two components of a binary to eventually collide or coalesce. Around the time of coalescence, in addition to producing copious gravitational waves, the black holes in the binary might also generate strong electromagnetic emissions through their influence on the surrounding plasma. One of the most exciting prospects in the coming years is the possibility of studying systems through correlated gravitational and electromagnetic wave signals. We have been investigating systems with strong prospects in this regard; two examples are described below. 92 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) WARPED VIEWS ... (BOYLE AND LEHNER)AA EMISSION DURING THE MERGER The supermassive black holes lurking at the centers of most galaxies provide ideal systems. Hierarchical models of galaxy formation indicate most galaxies have undergone mergers with other galaxies; and after two galaxies merge, their supermassive black holes are expected to sink to the center and merge as well [7]. As these black holes come together, a circumbinary disk forms around their common orbit. Such a disk will typically have magnetic fields which will be stirred by the black holes as their orbit shrinks toward merger. This process can enhance the electromagnetic fields and generate a net flux of energy that induces further emissions. To understand what might happen, we solve Maxwell’s equations coupled to Einstein’s equations and examine how the changing curvature of the spacetime through the late stages of the orbit and merger affects the electromagnetic fields. Such studies [8,6] require numerical simulations running for weeks on massively parallel computers. The resulting solutions allow us to analyse the detailed behavior of the system, as illustrated in Fig. 3, where the black holes stir and modify the fields, and generate an electric field through their dynamics. The resulting electric field is well described by two dipoles whose strength is proportional to *v H B * (where v is the orbital velocity of the black holes and B is the magnetic field in the disk near the holes). As the orbit shrinks, the fields vary with time and increase in strength, leading to the release of a net flux of electromagnetic energy. To leading order, this flux can be estimated to scale as v4B2 from the simple picture of two dipoles in a circular orbit immersed in a constant magnetic field orthogonal to their trajectory. Interestingly, this scales in the same way as the gravitational-wave energy flux produced by the system. This latter energy will propagate essentially unscattered and hopefully be detected by LISA, whereas the former energy will interact with surrounding plasma and induce possibly detectable electromagnetic emission. This indirect electromagnetic emission may retain some imprint of the dynamical merger process, making it a possible probe of the spacetime itself. Even more exciting is the possibility that tremendous amounts of rotational energy could be extracted during the merger process, and converted into electromagnetic radiation, in a binary black hole analog of the famous Blandford-Znajek process (in which rotational energy is extracted from a rotating black hole, and converted into an electromagnetic jet). This would be a direct form of emission due to particles traversing the “ergosphere” of the about-to-form or recently-formed black hole and extracting some of its rotational energy. At later times, when the black hole settles down to a quasi-stationary regime, further emissions could be induced from the standard Blandford-Znajek process. Fig. 3 Electric and magnetic fields around the orbiting black holes (left) and the resulting black hole after the merger (right). away a net linear momentum so that, to conserve momentum, the final black hole produced by the merger will have to recoil in the opposite direction. In this situation C which is the generic one C the disk of matter surrounding the two black holes will be affected by the asymmetric potential due to the moving black hole resulting from the merger. This will induce shocks that will heat up portions of the disk and induce electromagnetic emission. In order to understand the temporal and energetic characteristics of this emission, as a guide for its possible detection, we studied the dynamics of the disk as it is perturbed by the recoiling black hole with the aid of numerical simulations [9]. As illustrated in Fig. 4 (which corresponds to the case of a black hole with a recoil velocity at 45o with respect to the orbital plane) shocks develop and lead to a significant increase in the local temperature of the disk. This process will induce possibly detectable emissions over a time scale of weeks to months after the binary black hole merger. These two examples highlight the possibility that, in addition to their gravitational waves, certain binary mergers might also produce detectable electromagnetic emissions. Such systems, if they can be detected at cosmological distances, will act as so-called “standard sirens” [10] C high precision distance indicators which can be used to determine cosmological parameters and, in particular, provide a fundamentally new way to measure the mysterious “dark energy” that appears to be accelerating the expansion of the universe. Therefore binary black hole mergers may play a revolutionary role in cosmology as well. EMISSION AFTER THE MERGER When two black holes of unequal masses and/or different spin orientations merge, gravitational waves will be radiated asymmetrically. As a result, these gravitational waves will carry Fig. 4 PHYSICS Top view of the circumbinary disk intially (left) and after it becomes significantly affected due to a recoiling black hole product of a binary black hole merger (right). IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 93 WARPED VIEWS ... (BOYLE AND LEHNER) FINAL WORDS ACKNOWLEDGEMENTS Einstein’s theory of general relativity has been enormously successful in the “weak-field regime” (e.g. in the Solar System); but testing its predictions in the “strong-field regime” (e.g. near black holes) remains one of the great frontiers of science. In the coming years, new electromagnetic and gravitational wave observations will give us unprecedented views of black hole systems, and it is up to us to decode the clues about the universe which these observations will undoubtedly contain. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research & Innovation. LB acknowledges support from a CITA Post-doctoral Fellowship and a Canadian Institute for Advanced Research Junior Fellowship. LL also acknowledges support from an NSERC Discovery grant and from the Canadian Institute for Advanced Research. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. S. Chandrasekhar, The Mathematical Theory of Black Holes, Oxford University Press (1983). L. Boyle, in preparation (2009). C. Darwin, Proc. Roy. Soc. London A249, 180 (1959). J.M. Bardeen, Nature 226, 64 (1970). J.M. Bardeen and J.A. Petterson, ApJ 195, L65 (1975). C. Palenzuela, L. Lehner and S. Yoshida. in preparation (2009). M. Milosavljevic and E.S. Phinney, Astrophys. J. 622, L93 (2005). C. Palenzuela, M. Anderson, L. Lehner, S.L. Liebling and D. Neilsen, Phys. Rev. Lett. 103, 081101 (2009). M. Megevand et al., Phys. Rev. D80, 024012 (2009). D. Holz and S. Hughes, Astrophys. J. 629, 15 (2005). 94 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE ANALOG BY GRAVITY AND BLACK HOLES WILLIAM G. UNRUH H awking’s [1] theoretical discovery in 1974 that black holes are not black, but emit thermal radiation with a temperature inversely proportional to the black hole mass, raised many questions. The derivation presented by Hawking showed that the radiation emitted, with a mean wavelength roughly equal to the size of the black hole, has its origins in the vacuum fluctuations of the incoming vacuum state with energies of 3 the order of e tc / GM , where t is roughly the time since the black hole formed, G is Newton’s constant, and M is the mass of the black hole. At 1 second after the formation 5 of a solar mass black hole, this is about e10 in any units might want to use. At these frequencies (where ω is 105 about e times the mass of the universe), no one believes that the free-field field theory, on which Hawking’s analysis was based, is relevant, calling into question the whole derivation. However, in 1981, I [2] discovered that fluid flows could mimic black holes. The equations of motion of sound waves in irrotational fluid flows are identical to the equation of motion of a free scalar field in a gravitational background, which formed the basis for Hawking’s calculation. By arranging that the background fluid flow had a region in which the flow of the fluid was faster than the velocity of sound in the fluid, one could create the analog of a black hole. The equations of motion of the sound in such a fluid flow (called a critical flow in the hydrodynamics literature) are the same as those of a scalar field near a black hole, with the critical surface forming the analog of the horizon of a black hole. Thus, using the linearized Euler-Lagrange equations for the sound waves, one could follow Hawking’s derivation, step by step and derive the result that such a flow should also emit thermal radiation with a temperature of T= 4πk Boltzmann 2 2 1 d (v − c ) c dx SUMMARY Black hole evaporation, Hawking’s surprising 1974 discovery that black holes should emit thermal radiation, is still poorly understood, but the analogy with supersonic waterfalls in fluid mechanics is elucidating the origin of this radiation. where c is the velocity of sound, v is the velocity of the fluid, and x is the distance along the flow lines of the fluid. For reasonable values of these parameters for fluids 1 dv ≈ 1μm-1), this temperature is (e.g., c = 300m/s and c dx below 1K, making it unsurprising that the effect has not been seen. This fluid effect gives one the opportunity, however, to test Hawking’s prediction. The derivation of this temperature for fluids suffers from the same exponential frequency problem as does the derivation of the Hawking temperature for black holes. However for fluids, we know the fluid equations break down once the scale approaches the atomic scale. Fluids have a natural cutoff on wavelengths at the atomic scale. Does this natural cutoff destroy the thermal emission? If it did, one would have severe doubts that the thermal emission would survive the alterations that quantum gravity, for example, would produce in the propagation of physical fields on scales less than the Planck length (the length where quantum effects and gravitational effects are comparable in size). Alternatively if the thermal emission was robust to the changes in the fluid equations at the atomic scale, one would have much more faith that they would also survive the effects of quantum gravity in the black hole case. One would suspect that the thermal emission, rather than being a high frequency effect, was actually a low frequency effect, where the relevant scale is the time it takes for light to travel around a black hole. As Jacobson [3] pointed out, the primary effect of the atomicity of matter in a fluid is to alter the dispersion relation at higher wave-numbers. Numerical and analytic studies of fields with distorted dispersion relations at higher frequencies by Unruh [4], Jacobson [5], Corley [6], Schuetzhold [7] show that the thermal emission seems robust against alterations of the dispersion relations at high wave numbers. In fact in such situations, the thermal emission arises not from exponentially high frequencies in the incoming vacuum fluctuations, but can depend at most on frequencies around that at which the dispersion relation changes away from the low frequency linear form predicted by the fluid equation. The exponentially large frequencies are not necessary for the thermal emission. W.G. Unruh <unruh@ physics.ubc.ca>, CIAR Cosmology and Gravity Program, Perimeter Institute Distinguished Research Chair, Dept. of Physics, University of British Columbia, Vancouver, BC, Canada V6T 1Z1 One of the more exciting prospects is that of testing these ideas experimentally. While no small black hole is likely to be found so that Hawking’s original prediction can be directly tested, critical fluid flows can be imagined. To PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 95 ANALOG GRAVITY ... (UNRUH) directly see the thermal quantum emission would require ultra low temperatures, using either liquid Helium [9] or BoseEinstein condensates (BECs) [10]. The experimental challenges of detecting the incredibly low levels of sound waves produced by the quantum process (less than 10-23 watts for He, and 10-33 watts for BECs) [11] make direct detection of the quantum effect even in these analog systems unlikely. However, even with water one can test some of the aspects of the theory [8]. The prediction of the quantum instability relies on the behaviour of the sound waves near the horizon, and in particular the creation of “negative norm” (sometimes called “negative frequency”) waves from incident “positive norm” waves. That is, it relies on the existence of “β” Bogoliubov coefficients in the mode conversion process for the propagation of the classical waves near the horizon. The existence of these conversion coefficients for these negative norm waves from positive norm waves can be tested even in fluids far from the quantum regime. At the University of BC, a group from physicists and civil engineers, S. Weinfurtner, E. Tedford, M. Richartz, M. Penrice, G. Lawrence, and W. Unruh, are carrying out a set of experiments to detect this conversion of positive to negative norm waves in flume tanks (see also Rousseaux et al [12]) for the surface (gravity) waves on the water [8]. The dispersion relation for still water looks like that in Figure 1, ω 2 = (gk + σk3) tanh(kh), (1) where I have plotted it only for the left-going waves and where ω and k are defined so that the wave looks like ei (ωt+kx). At the lowest wave-numbers (shallow water waves), the dispersion relation is linear in k (with both the group and phase veloc- ity going as gh where g is the gravitational acceleration and h the depth of the fluid). At intermediate wave numbers (deep water waves) the dispersion relation is ω = gk with the group velocity cg and phase velocity cp given by 2cg = c p = At the highest wave numbers, where the surface tension becomes important, ω = σk 3 and 2 cg = c p = σk 3 where σ is the specific surface tension. While this dispersion relation is exact if the depth of the water is constant, it is also a reasonable approximation as long as the depth is a slowly varying function of distance along the tank, and gives us a way of thinking about the behaviour of the waves as they travel up the incline of an obstacle placed into the fluid flow. In our experiment, a long tank of water has water flowing along the tank (see Figure 2 for the downstream portion of the tank). An obstacle is placed along the bottom, so that the fluid velocity over the top the obstacle is high enough to “block” the waves travelling against the flow. As the waves moves against the flow up the incline of the obstacle, their wavelength decreases, until their group velocity drops below the velocity of the fluid, at which point they are swept away from the obstacle by the fluid flow. Fig. 2 Flume tank with barrier to create horizons for surface waves. The convective time derivative ( Fig. 1 Dispersion relation and convective time derivative for ω0 = .35, the conserved frequency in the lab frame. g . k ∂ ∂ −v ∂t ∂x ) of the flowing fluid is represented by the constant slope line, where the slope equals the velocity of the fluid. For a given lab frequency (the intercept of the line with the vertical k axis) there are a variety of wave-numbers at the intersection of the dotted straight line with the dispersion curve. In the lab frame, some frequencies have group velocity to the left (where the dispersion curve slope is higher than the slope of the straight line) and some have group velocity to the right. As one travels down the flume up the lee edge of the obstacle, both the slope of the straight line changes (the fluid velocity changes) and the low frequency (shallow water) part of the dispersion curve changes (the phase velocity is proportional to the square root of the depth of the water). Note that in the actual flume tank, the behaviour is more complex, as the water does not have uniform velocity all through its depth, and in fact becomes partially turbulent on the lee side of the obstacle, and the rate of change of depth becomes non-adiabatic for the waves. It is exactly this non-adiabaticity which allows for the creation of the negative norm waves. Furthermore, non-linearities in the wave motion become important as the wavelength decreases and the ampli- 96 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) ANALOG GRAVITY ... (UNRUH)AA tude increases as the waves travel up the slope into shallower water and come near the horizon (tsunami effect). norm waves have the peaks slanted to the right, and negative norm waves have their peaks slanted to the left. This complex form of the dispersion relation allows one to test a wide variety of predictions about the generation of negative norm waves. One example is given in Figure 2, a so-called undular jump. In this case one has a constant flow of fluid over the obstacle (seen at the bottom of the tank). As the fluid slows down after having travelled over the obstacle, one has the formation of the analog of a white hole horizon. This is a horizon out of which the waves can come, but waves cannot enter and is the time inverse of a black hole horizon (out of which waves cannot come). This “stationary wave” pattern represents the upconversion at the white hole horizon of a constant, zero frequency incoming wave from the right. It is up-converted at the horizon into an outgoing, zero frequency wave, with zero phase velocity (the peaks of the waves do not move), but large group velocity. This experiment is still in the process of being carried out, and we do not yet have any definitive evidence of the creation of negative norm waves, the classical signature of the β Bogoliubov coefficients and of the particle creation by the horizon in the quantum regime. While non-linearities in the conversion process as the wave travels up the slope are a concern, our tests indicate that we can reliably measure (to submillimeter accuracy) very small waves well within the linear regime, and initial results suggest that the Hawking effect exists in this experiment. In the experiments we are carrying out, the “positive norm” wave are represented by waves whose phase velocity in the lab frame is to the left, while the negative norm waves are represented by phase velocities going to the right. Plotting the locations of the peaks of the waves as a function of time, positive Note that this experiment is a more stringent test than it at first seems. The effective equations of motion for these surface waves over an uneven bottom are very complex. The existence of the quantum instability (as manifest in the negative norm waves) would thus demonstrate that the effect first discovered by Hawking for black holes has a far wider application in physics than that derivation might at first suggest. It is this confluence of theoretical insight and experimental realisation that is making the field of analogs to gravitational fields one of the most exciting in physics today. REFERENCES 1. 2. 3. S.W. Hawking, Nature, 248, 30 (1974); Commun. Math. Phys. 43, 199 (1975). W.G. Unruh, Phys. Rev. Lett., 46, 1351 (1981); See also V. Moncrief, Ap.J. 235 1038 (1980). T. Jacobson, “Black Hole Evaporation and Ultrashort Distances”, Phys. Rev. D44, 1731 (1991). and “Black Hole Radiation in the Presence of a Short Distance Cutoff”, Phys. Rev. D48, 728 (1993). 4. W.G. Unruh, “Sonic Analogue of Black Holes and the Effects of High Frequencies on Black Hole Evaporation”, Phys. Rev. D51, 2827 (1995). 5. S. Corley, T. Jacobson, Phys. Rev. D54, 1568 (1996); S. Corley, Phys Rev D55 6155 (1997); S. Corley, T. Jacobson, Phys. Rev. D57 6269 (1998). 6. S. Corley, “Computing the spectrum of black hole radiation in the presence of high frequency dispersion: An analytical approach”, Phys. Rev. D57, 6280 (1998); See also R. Brout, S. Massar, R. Parentani, and Ph. Spindel, Phys. Rev. D52, 4559 (1995) who make analytic arguments that the radiation should be independent of the high frequency dispersion relation. 7. W.G. Unruh and R. Schützhold, “On the universality of the Hawking effect”, Phys. Rev. D71, 024028 (2005); 8. R. Schützhold and W.G. Unruh, “Gravity wave analogues of black holes”, Phys. Rev. D66, 044019 (2002). 9. G.E. Volovik, The universe in a Helium droplet. International Series of Monographs on Physics, Oxford University Press, Jun 1 2003. 10. L.J. Garay, J.R. Anglin, J.I. Cirac, and P. Zoller, “Sonic analog of gravitational black holes in Bose-Einstein condensates”, Phys. Rev. Lett. 85:4643-4647 (2000); L.J. Garay, J.R. Anglin, J.I. Cirac, and P. Zoller, “Sonic black holes in dilute Bose-Einstein condensates”, Phys. Rev. A63:023611, 2001. 11. W.G. Unruh, “Measurability of dumb hole radiation?”, contribution to M. Novello, M. Visser, and G. Volovik (editors), Artificial Black Holes (World Scientific, Singapore, 2002). 12. For another recent experiment in fluids looking at the conversion of waves at the horizon, see Rousseaux, C. Mathis, P. Maissa, T.G. Philbin, and U. Leonhardt, “Observation of negative-frequency waves in a water tank: A classical analogue to the Hawking effect?”, NewJ.Phys. 10:053015 (2008). PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 97 INFORMATIONS CANADA COUNCIL FOR THE ARTS ANNOUNCES 2010 KILLAM PRIZES INFORMATIONS / NEWS Toronto, April 13, 2010 – Five prominent scholars have been awarded Canada’s most distinguished annual awards for outstanding career achievements in health sciences, engineering, humanities, natural sciences and social sciences. Each Prize is worth $100,000 to the recipient. The Canada Council for the Arts, which administers the Killam program, announced today the scholars include Professor Ellen Bialystok of York University, Dr. R. Mark Henkelman of University of Toronto, Dr. Ming Li of University of Waterloo, Dr. Arthur McDonald of Queen’s University, and Dr. James Tully of University of Victoria. Mr. Joseph L. Rotman, Chair of the Canada Council for the Arts, noted, “The 2010 Killam Prizes are awarded for the highest achievement in research and it is an honour to be able to provide such worthy recognition of their work and what it means for Canada. I continue to be amazed at the depth of innovation and creativity that exists within our borders.” Dr. Arthur McDonald – Queen’s University – Natural Sciences Dr. Arthur McDonald’s achievements in the areas of nuclear and particle physics span more than four decades. For the past 20 years, he has been the scientific and operational leader of the Sudbury Neutrino Observatory (SNO) project, a major experiment which has provided revolutionary insight into the properties of neutrinos and energy generation in the sun’s core. Funded by an international group of agencies, including the National Research Council, the Natural Sciences and Engineering Research Council of Canada, the Province of Ontario, the U. S. Department of Energy, and the U.K. Particle Physics and Astronomy Research Council, and including publicand private-sector partnerships with Atomic Energy of Canada Limited and Vale-INCO, the project has enabled Canada to secure a leading role internationally in neutrino physics and astrophysics. As SNO Project Director, Dr. McDonald led the extensive international collaboration to accomplish the analysis and presentation of scientific results. These results are helping to guide theoretical studies of how neutrinos are to be included in the Standard Model of Elementary particles and are motivating experiments at the new SNOLAB for further understanding neutrino properties and their effects in the early universe. Now the Gordon and Patricia Gray Chair in Particle Astrophysics at Queen’s University in Kingston, Ontario, Dr. McDonald’s numerous awards include a 1998 Killam Research Fellowship, the 2008 Benjamin Franklin Medal in Physics, the Tom W. Bonner Prize of the American Physical Society and a Medal for Lifetime Achievement from the Canadian Association of Physicists. A Fellow of the Royal Society of Canada and of the UK and Commonwealth, he holds a B.Sc. and M.Sc. in Physics from Dalhousie University in Halifax, NS, and a PhD from the California Institute of Technology. EIGHT CANADIAN SCIENTISTS AND SCHOLARS GARNER OVER $1 MILLION IN KILLAM RESEARCH FELLOWSHIPS Ottawa, March 15, 2010 – Eight outstanding Canadian researchers have been awarded a total of $1.12 million in the 43rd annual competition for Killam Research Fellowships, administered by the Canada Council for the Arts. The Fellowships provide $70,000 a year for two years to each of the researchers. The fellowships are awarded to the individual recipients to devote time to full-time research, but the funds are paid to and administered by universities or research institutes. The awards support scholars engaged in research projects of outstanding merit in the humanities, social sciences, natural sciences, health sciences, engineering and interdisciplinary studies within these fields. The recipients are chosen by the Killam Selection Committee, which comprises 15 eminent scientists and scholars representing a broad range of disciplines. After considering 83 applications, the Killam Selection Committee chose the following individuals: Engineering – Electrical/Computer Frank Kschischang, University of Toronto, Coding for Efficient Information Transmission in Long-Haul Fiber-Optic Systems and Radio Relay Networks Engineering – Mechanical Andreas Mandelis, University of Toronto, Research and development of two analytical instrumentation techniques for early osteoporotic bone loss and density variation diagnosis -- This research is expected to lead to the development of a portable laser-radar-based instrument that can be used for early detection and monitoring of osteoporosis. It will enable preventive, quantitative measurement of bone density and would be available to people living in areas with little access to hospital facilities and to astronauts on long-duration space flight missions. Humanities – Linguistics Marie-Odile Junker, Carleton University, Ontologies for Cree and Innu Dictionaries Health Sciences - Medicine Donald F. Weaver, Dalhousie University, Design and Discovery of a Curative Drug for Alzheimer’s Disease Natural Sciences – Chemistry Philip Jessop, Queen’s University, Switchable Chemistry Natural Sciences – Chemistry Eugenia Kumacheva, University of Toronto, Combining microfluidics and polymer science to create biological environments for cell studies Natural Sciences – Earth Sciences Brendan Murphy, St. Francis Xavier University, The origin of Pangea Natural Sciences – Physics/Space Science Victoria M. Kaspi, McGill University, A New Window on the High Energy Universe -- The project will focus on the study of magnetars, a small group of known neutron stars with the highest magnetic fields known in the universe that retain and occasionally release high amounts of energy. The research will form a component of the observing schedule of a new x-ray telescope, NuSTAR to be launched by NASA in 2011. 98 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE PHENOMENOLOGICAL QUANTUM GRAVITY SABINE HOSSENFELDER AND LEE SMOLIN BY I f the history of science has taught us anything, it’s that persistence and creativity makes the once impossible possible. It has long been thought experimental tests of quantum gravity are impossible. But during the last decade, several different approaches have been proposed that allow us to test, if not the fundamental theory of quantum gravity itself, at least characteristic features this theory can have. For the first time we can probe experimentally domains in which quantum physics and gravity cohabit, in spite of our failure so far to make a convincing marriage of them on a theoretical level. Gravity is a very weak interaction. The only reason why we notice it so prominently in our day-to-day lives is that, unlike the other interactions, it cannot be neutralized. For all feasible Earth-based experiments examining short-distance physics, the gravitational interaction is completely negligible. For the same reason, experimentally testing quantum effects of gravity is hard. The effects are expected to become comparable to those of the other interactions only at energy scales close to the Planck energy, EPl = c5 / G, where is Planck’s constant and G the gravitational constant. At 1016 TeV this energy is out of reach for collider experiments, and it is even far above the highest energies observed in cosmic rays. Nonetheless, the effects of quantum gravity can, in a few circumstances, become observable. A wide range of possible tests of hypotheses about quantum gravity have been proposed, and a number have even been carried out. Most of these can be understood as testing a limit of quantum gravity where effects of quantum theory alone, or gravity alone can be ignored. Still, there may be quantum gravitational phenomena since we can take 0 and G 0, while keeping their ratio, EPl = c5 / G fixed. These are then phenomena governed by two parameters, c and EPl. SUMMARY The phenomenology of quantum gravity is still a young research field accompanying the quest for a theory of quantum gravity. During the last decade, an increasing amount of effort has been invested into studying potentially observable effects. We give a brief overview of the possibilities that have been proposed. TESTS OF THE SYMMETRY OF SPACETIME Most of the tests of hypotheses about quantum gravity in this regime concern the symmetries of spacetime which are assumed in particle physics. Indeed, the most fundamental question one can ask about a physical system is what is the symmetry of its ground state. We know that in classical physics, the ground state is Lorentz-invariant and the principles of special relativity are satisfied. It is interesting to ask whether the same is the case when the effects of quantum gravity are considered. Experiments are currently probing whether Lorentz symmetry is preserved when effects of the order of the ratio of energies in the experiment to EPl are taken into account. One plausible hypothesis is that the principle of relativity breaks down at the scale EPl , so there is a preferred state of motion and rest. Those who suggest this point to the existence of a preferred cosmological rest frame, and the effect is present in a few models of quantum spacetime [1], if not in full fledged theories. There are now quite good limits on this possibility. Several come from the fact that if special relativity were false the speed of light would no longer be an invariant. So one can look for a variation in the speed of light proportional to E/EPl , where E is the energy of a photon. That is one looks for an energy dependent speed of light of the form v = c(1 ± aE/EPl ), where a is a dimensionless parameter to be determined. (Thus, this is an effect that would come in at linear order in energies, the possibility of higher order effects is harder to test and will be mentioned below.) This effect can be looked for in light coming great distances from astrophysical sources such as gamma ray bursts. Even if the effect is tiny, these gamma ray bursts are billions of light years away and the arrival time of a photon could be offset by a few seconds. The Fermi gamma-ray space telescope, which was launched in June 2008, has detected a larger number of very high energy gamma ray bursts than previously expected. The arrival of photons from these bursts also offered surprises. Several bursts have now been documented in which the higher energy photons (>GeV) arrive with a delay of more than 10 seconds after the onset of the burst has been observed in the low energy range (keVMeV). While it is still unclear whether this delay of the higher energy photons is caused at emission or during propagation, more statistics and a better analysis – in particular about the delay’s dependence on the distance to the PHYSICS IN S. Hossenfelder <[email protected]>, Nordic Institute for Theoretical Physics (NORDITA), Roslagstullsbacken 23, 106 91 Stockholm, Sweden and Lee Smolin <lsmolin@ perimeterinstitute.ca>, Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo ON N2L 2Y5 CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 99 PHENOMENOLOGICAL QUANTUM ... (HOSSENFELDER AND SMOLIN) source – will eventually allow us to narrow down the possible causes and constrain models that give rise to such features [2]. The current bound from the Fermi telescope [3] is now that the parameter a must be less than about 0.8 (at least for the minus sign). Models with a breaking of Lorentz symmetry indicate that the effect should depend on polarization, so that the sign would be plus for one polarization and minus for the opposite. The result is that the planes of polarization rotate as the photons travel, in a way that leads to polarized light becoming unpolarized. From the fact that we see polarized light coming from distant galaxies it has been shown that we must take a < 10-9 [4] in the case of a polarization dependent effect. Another test of the principle of relativity is a prediction that very high energy cosmic ray protons interact with the cosmic microwave background (CMB). Given just the principles of special relativity these interactions were predicted to take place at an energy of above 1019 eV, and the result is that the protons lose energy. This leads to what is called the GZK cutoff on the cosmic ray spectrum, which says that we should not see cosmic ray protons coming from further away than a certain distance, 75 megaparsecs, which is the mean free path for this interaction. This prediction was confirmed recently by observations at the AUGER cosmic ray detector [5]. There are also table-top experiments that remarkably turn out to be sensitive to violations of Lorentz invariance at linear order in the ratio of energy to the Planck scale, although so far the limits on a from these effects are not as good as from the astrophysical experiments [6]. These and other results make it seem very unlikely the principle of relativity breaks down at Planck scales, at least at order E/EPl . The results to date do however allow a more subtle hypothesis called “deformed special relativity”, in which the principle of relativity is preserved, but in such a way as to make all observers agree about what the special energy EPl is [7,8]. It is also possible that special relativity breaks down, but only in a way that can be seen by experiments sensitive to effects of the order of (E/EPl )2. These more subtle possibilities are harder to test experimentally, but there is reason to hope for progress here too as the experiments improve. sensitively than was previously possible. BROWNIAN MOTION AND STOCHASTIC EFFECTS A common hypothesis about quantum spacetime is that space and/or time become discrete on the Planck scale, in much the same way as matter becomes discrete when examined at the scales where atoms can be perceived. It is interesting to recall that the atomic hypothesis was confirmed, long before atoms were seen directly, by the observations of effects of their random motion. This was the great work by Einstein on Brownian motion in 1905. Similarly, it is possible to imagine that the effects of a fundamental discreteness of space and/or time would show up in random fluctuations on the propagation of light or elementary particles. There can also be other motivations besides discreteness for stochastic effects, such as the conjecture that quantum fluctuations in the geometry of spacetime cause the light cones to fluctuate, thus affecting the speed of photons in a random way [10]. Such effects would show up as noise in the incredibly sensitive interferomters that are used to measure gravitational radiation [11,12]. Remarkably, under some simple hypotheses, modern gravitational wave detectors are sensitive to this at order E/EPl. Presently there seem to be no sources of noise seen in the detectors that are not accounted for by more mundane explanation, so the evidence indicates that there are no such effects at this order. QUANTUM EFFECTS IN STRONG GRAVITATIONAL FIELDS Now we come to effects which require quantum effects themselves, so that we cannot neglect and G. The first of these to be predicted is of course Hawking radiation, and it is tantalizing to think that if primordial black holes were created in the early universe with masses of around 1015 grams (or a goodsized mountain), the last stages of their Hawking radiation would be currently visible as bursts of x-rays. It is disappointing that despite searches, no such bursts have been seen because, if they were, the precise spectra would provide tests of theories of quantum gravity, such as loop quantum gravity [13]. Another very interesting possibility is that quantum gravity effects fail to be symmetric under the discrete transformations of physics, such as parity (P) or (CP) or time reversal invariance. These might show up in high precision measurements of these effects. Even if evaporating black holes are not observed, a fascinating possibility which has been proposed is to construct analogues of them in condensed matter systems. These would not test quantum gravity directly, but they would provide tests of the reasoning which leads to the prediction of Hawking radiation [14]. The hypothesis that quantum gravitational effects break parity symmetry also has implications for observations of the CMB. It leads to predictions for a signal in the CMB spectrum, which would show up in correlations between the temperature fluctuations and certain parity odd polarization modes, called B-modes [9]. So far such an effect has not been observed, but the Planck satellite is expected to probe this effect much more The next obvious place to look is the early universe, where gravity must have been very strong. Quantum gravity could have left traces in the CMB by means of quantum effects affecting the dynamics of the universe’s expansion. This data could contain information about quantum corrections to the evolution equation, or even a possible phase transition from a pre-geometrical to a geometrical phase [15,16]. 100 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) PHENOMENOLOGICAL QUANTUM ... (HOSSENFELDER AND SMOLIN)AA Beyond that a big challenge for quantum gravity theories is an understanding of the big bang itself. Was it really the first moment of time? In this case a quantum gravity theory needs to provide initial conditions for the universe and this might, possibly, imply some predictions for cosmological observations. Or is the cosmological initial singularity predicted by general relativity only an artifact of the neglect of quantum physics, and is it really replaced by a bounce or a transition from an earlier universe [17]. A very exciting possibility is that such a bounce B and not inflation B would be the right explanation for the observed fluctuations in the CMB. If so then those observations are seeing quantum gravity effects. THE HYPOTHESIS OF LARGE EXTRA DIMENSIONS A completely different category of models studies the possibility that quantum gravitational effects could be much stronger than usually thought due to a modification of the gravitational interaction on the shortest distances. Such a modification occurs in scenarios with large additional spatial dimensions whose existence is predicted by string theory, and has the consequence that quantum gravity could become observable in Earth-based collider experiments, such as the Large Hadron Collider (LHC). If this should turn out to be a correct description of Nature, we would see the production of gravitons and black holes at the LHC [18]. The gravitons themselves would not be captured in the detector and would lead to a missing energy signal, the missing particles having spin 2. Black holes would decay via Hawking radiation. Ideally the distribution of decay products would allow one to determine the parameters of the model, the number and size of the extra dimensions. Black hole produc- tion and decay would be a striking signature, and would allow us to examine the fate of black hole information during the evaporation process in the laboratory. OUTLOOK It should be emphasized that the experiments we have discussed are described by phenomenological models that are, at least so far, not derived from any of the presently pursued approaches towards quantum gravity. The purpose of these models is to study consequences that arise from specific features the underlying theory could have and, ideally, constrain them. In such a way, we could learn about the general properties of the theory we are trying to find, for example whether it does have additional spacelike dimensions, or results in a deviation from Lorentz invariance. Nonetheless, it is remarkable that in the last few years the precision of tests of hypotheses about quantum gravity has increased dramatically, to the point that these experiments regularly probe effects at the Planck scale and beyond. Progress in physics needs two ingredients: mathematical consistency and experimental evidence. Relying entirely on mathematical consistency is a shot into the dark. It comes with the burden of connecting a new theory, and possibly a completely new mathematical framework, back to what we already know. Experimental evidence sheds light into the darkness, and helps to narrow the range of possible theories. Theory and experiment work best together. The increase of attention and effort that the phenomenology of quantum gravity has seen within the last decades is thus a very welcome and long overdue contribution to our quest of finding a unifying description for all the interactions of the standard model. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. R. Gambini and J. Pullin, Phys. Rev. D59, 124021 (1999). G. Amelino-Camelia and L. Smolin, Phys. Rev. D80, 084017 (2009). A.A. Abdo et al., Nature, 462, 331-334 (2009). L. Maccione, S. Liberati, A. Celotti and J.G. Kirk, JCAP, 0710, 013 (2007). J. Abraham et al. [Pierre Auger Collaboration], Phys. Rev. Lett., 101, 061101 (2008). R. Myers and M. Pospelov, hep-ph/0301124, G. Amelino-Camelia et al., arXiv:0806.4302. G. Amelino-Camelia, Phys. Lett. B510, 255 (2001). J. Magueijo and L. Smolin, Phys. Rev. Lett., 88, 190403 (2002). A. Lue, L.M. Wang and M. Kamionkowski, Phys. Rev. Lett., 83, 1506 (1999). L.H. Ford, Phys. Rev. D51, 1692 (1995). G. Amelino-Camelia, Nature, 398, 216 (1999). C.J. Hogan, Phys. Rev. D78, 087501 (2008). M.H. Ansari, Nucl. Phys. B783, 179 (2007). C. Barcel, S. Liberati, M. Visser C In Living Rev. Relativity, 2005 T. Konopka, F. Markopoulou and L. Smolin, arXiv:hep-th/0611197. J. Magueijo, L. Smolin and C.R. Contaldi, Class. Quant. Grav., 24, 3691 (2007). M. Bojowald, Gen. Rel. Grav., 40, 2659 (2008). G. Landsberg, arXiv:0808.1867 [hep-ex]; B Carr, S Giddings C Special Editions, 2007 C Scientific American. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 101 INFORMATIONS / NEWS INFORMATIONS CANADA EXCELLENCE RESEARCH CHAIRHOLDERS ANNOUNCED TITULAIRES Canada Excellence Research Chairs are world-class leaders in research and innovation. Chairholders and their research teams will help Canada build a critical mass of expertise in the four priority areas outlined in the Government of Canada's science and technology strategy: environmental sciences and technologies; natural resources and energy; health and related life sciences and technologies; and information and communications technologies. Les titulaires de chaire d’excellence en recherche du Canada sont des chefs de file de calibre mondial axés sur la recherche et l’innovation. Aidés de leurs équipes de recherche, ils contribuent à faire que le Canada rassemble une masse critique d’expertise dans les quatre domaines prioritaires énoncés dans la stratégie des sciences et de la technologie du gouvernement fédéral, à savoir : les sciences et technologies de l’environnement; les ressources naturelles et l’énergie; les sciences et les technologies de la santé et les sciences de la vie connexes; les technologies de l’information et des communications. For each Chair, universities will receive up to $10 million over seven years to support chairholders and their research teams in undertaking ambitious research programs. The complete list of chairholders, including the 13 universities where they will be working, appears below. Details on each chair is available at http://www.cerc.gc.ca/cpch-pctc-eng.shtml. ENVIRONMENTAL SCIENCES AND DE CHAIRE D'EXCELLENCE EN RECHERCHE DU CANADA ANNONCÉS Pour chaque chaire, les universités recevront jusqu’à dix millions de dollars sur sept ans pour appuyer les titulaires et leur équipe dans la poursuite d’ambitieux programmes de recherche. La liste complète des titulaires de chaire, y compris les 13 universités où ils travailleront, figure à l’adresse suivante : http://www.cerc.gc.ca/cpch-pctc-fra.shtml. TECHNOLOGIES Ali Emadi (McMaster University) - Canada Excellence Research Chair in Hybrid Powertrain Ian A. Gardner (University of Prince Edward Island) - Canada Excellence Research Chair in Aquatic Epidemiology Philippe Van Cappellen (University of Waterloo) - Canada Excellence Research Chair in Ecohydrology Douglas Wallace (Dalhousie University) - Canada Excellence Research Chair in Ocean Science and Technology Howard Wheater (University of Saskatchewan) - Canada Excellence Research Chair in Water Security NATURAL RESOURCES AND ENERGY Marcel Babin (Université Laval) - Canada Excellence Research Chair in Remote Sensing of Canada’s New Arctic Frontier D. Graham Pearson (University of Alberta) - Canada Excellence Research Chair in Arctic Resources Søren Rysgaard (University of Manitoba) - Canada Excellence Research Chair in Arctic Geomicrobiology and Climate Change Thomas Thundat (University of Alberta) - Canada Excellence Research Chair in Oil Sands Molecular Engineering HEALTH AND RELATED LIFE SCIENCE AND TECHNOLOGIES Oliver Ernst (University of Toronto) - Canada Excellence Research Chair in Structural Neurobiology Matthew Farrer (University of British Columbia) - Canada Excellence Research Chair in Neurogenetics and Translational Neuroscience Michael Houghton (University of Alberta) - Canada Excellence Research Chair in Virology Adrian Owen (University of Western Ontario) - Canada Excellence Research Chair in Cognitive Neuroscience and Imaging Patrik Rorsman (University of Alberta) - Canada Excellence Research Chair in Diabetes Frederick Roth (University of Toronto) - Canada Excellence Research Chair in Integrative Biology INFORMATION AND COMMUNICATIONS TECHNOLOGIES Robert W. Boyd (University of Ottawa) - Canada Excellence Research Chair in Quantum Nonlinear Optics David Cory (University of Waterloo) - Canada Excellence Research Chair in Quantum Information Processing Younès Messaddeq (Universit!é Laval) - Canada Excellence Research Chair in Enabling Photonic Innovations for Information and Communication Bertrand Reulet (Université de Sherbrooke) - Canada Excellence Research Chair in Quantum Signal Processing 102 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE GETTING A BIG BANG BY FROM STRING THEORY CLIFF BURGESS W e live in an era in which the Hot Big Bang model of cosmology has been tested with unprecedented redundancy and precision, and has emerged all the stronger for having done so. These tests are redundant inasmuch as a few parameters provide a coherent description of a much larger number of observations. This redundancy implies there are a number of independent ways of determining some of the parameters (such as the universe’s spatial curvature, or the overall baryon density), and their agreement gives confidence that the basic picture C the expansion of an initial hot primordial soup C is basically right. Much of the precision of the tests comes from studies of the properties of the temperature fluctuations that are seen in the Cosmic Microwave Background Radiation (CMBR) C the residual radiation left over from the epoch when the universe last cooled enough to allow ordinary matter to become dominated by neutral atoms, and so became transparent to photons. This precision means that the agreed-on values of the Hot Big Bang parameters are known quite accurately, including the first-ever survey of the energy content of the universe as a whole 1. Although the Big Bang picture works well, it requires the universe to start off in a very particular way: very flat and homogeneous with a specific pattern of initial perturbations in the energy density. If we perturb these initial conditions even by very small amounts, the universe that follows no longer looks at all like what we see. The theory of Cosmic Inflation [2] was invented in order to try to explain these initial conditions as the generic outcome of a much earlier epoch, during which the universe’s accelerated expansion smoothed out any initial inhomogeneities. Remarkably, this proposal turns out also to give a good explanation for the detailed properties of the primordial SUMMARY An early inflationary epoch of accelerated universal expansion could provide a simple explanation for the initial conditions required by observations for a Hot Big Bang cosmology. String theory provides our best understood candidate for the physics relevant to the very short distances required. Might the very early universe provide our first observational window onto a stringy universe? temperature fluctuations in the CMBR. But would the very early universe really inflate in the way that our later universe seems to require? Because the universe is much smaller and hotter the earlier we look, to answer this we must make assumptions about the nature of physics at energies very much higher than those we have ever had direct experience with in the lab on Earth, and almost as high as those where quantum effects for gravity are expected to become important. Although we do not yet know what the quantum theory of gravity is, so far string theory is the only proposal sufficiently well-developed to ask such precise questions about cosmology in the very early universe. This motivates searching for inflationary configurations amongst the solutions to the string-theoretic equations of motion [3]. Both string theory and inflation are around 20 years old, and success in bringing them together could teach us much about both. On one hand, inflation provides a simple phenomenological description of the initial conditions of the Hot Big Bang; yet it has so far resisted being convincingly embedded into a “realistic” high-energy field theory. On the other hand, string theory provides our first detailed picture of gravity at the small distances where quantum consistency is notoriously thorny; yet it so far lacks convincing observational support. Could string theory and inflation solve each other’s problems? Perhaps by providing the first observational window to the high energies needed to test string theory, inflationary cosmology will lead to the first real observational tests of stringy predictions. To see more precisely what can be learned requires asking in more detail how inflation works. Primordial inflation requires the cosmic expansion to accelerate 2 which is the gravitational response to a nearly constant positive energy density. But keeping an energy density approximately constant in an expanding universe requires negative pressure, such as arises when a scalar field (think: a direction-independent number C like temperature, or pressure, say C everywhere in space and time) changes so slowly and homogeneously that its kinetic energy is dominated by its potential energy (usually called a “slow roll”). C.P. Burgess <cburgess@ perimeterinstitute.ca>, McMaster University and Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo ON N2L 2Y5. 1. This contains its own surprises C Dark Matter [1] and Dark Energy C which are a fascinating story in themselves. 2. Slow contraction can also work, although the trick here is to get the universe to begin expanding again. Work on contracting cosmologies motivated by string theory also continues apace. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 103 GETTING A BIG BANG ... (BURGESS) Much searching has shown it is difficult to obtain negative pressure cleanly in a realistic quantum theory. The difficulty lies in the weakness of the forces that must act.on the scalar field required by inflation, since quantum fluctuations are notorious for generating new forces (such as Casimir energies, for example) when classical forces are absent. Although this does not mean inflation cannot be obtained from a realistic theory of high-energy physics, it does mean that it is unlikely to be generic. Evidence for its occurrence likely tells us something interesting about the properties of the high-energy physics that is relevant. Conversely, being able to identify those inflationary systems that can arise within a fundamental theory may help discriminate among the large variety of phenomenological models that can be proposed. Of course, string theory was not designed to describe cosmology, and this is part of the appeal in using it to describe features of the early universe. But because of this, inflationary constructions in string theory often seem incredibly baroque, containing a great many features that are not required by (yet significantly complicate) the search for inflationary applications. Since the observations, though impressive, are unlikely to distinguish most of these stringy details, one might ask what is to be gained from the point of view of a cosmologist by forging a connection between string theory and cosmology. It turns out there are many things one might hope to learn by understanding the physical interpretation of the scalar field involved, and the physics that determines the forces it experiences: Is inflation more common among the solutions of string theory than it is among the solutions of more generic theories? Are the observational implications of inflation more predictive when obtained from string theory than from generic field theories? Does proximity of the inflationary scale with the string scale mean there is ‘smoking gun’ evidence for string theory to be found among inflationary observables? Precisely how are primordial fluctuations generated in string theory, and does this have observable signals? Where do the elementary particles we know about reside within the string configurations considered, and how is the inflationary sector related to it? How does the energy tied up during inflation get efficiently channelled into heat for the later Hot Big Bang? How robust are the observable implications of simple inflationary models (on which most comparisons with observations rely), given the many other degrees of freedom likely to be present in string theory during inflation? SEARCH STRATEGIES Since the search for string inflation is still very new, many of these questions remain open. Yet recent work is beginning to provide preliminary answers to some of them. In particular, it has long been known that string theory predicts extra dimensions, and these dimensions have provided a huge cast of scalar fields among which inflationary actors might be sought. The physical properties of the extra dimensions B like their volume, their relative proportions, the distance between branes (which are dynamical surfaces (membranes) in space that act as gravitational sources [4]), and so on B can vary from place to place within the four usual dimensions that we can see. This means these properties are numbers that vary with position and time: from the four-dimensional point of view they are scalar fields. Could these scalars participate in a slow roll? Most of our experience with such scalars is restricted to configurations that are very symmetric (and in particular, supersymmetric C a symmetry relating particles having different spins [5]), since it is here that calculations are under the best control. They are under control because the symmetry often demands the forces acting on the various fields to be very weak. At first sight this sounds like just what the doctor ordered when seeking slow-roll inflation: scalar fields with feeble interactions that can allow the scalars to change only very slowly. Unfortunately, the supersymmetries of these configurations usually provide too much of a good thing, for two reasons. First, because the geometries involved tend to be topologically complicated, they provide not just one scalar but often hundreds. Second, because supersymmetry usually requires the forces driving the motion of the various scalar fields to vanish completely, and this vanishing persists to all finite orders in perturbation theory if one perturbs about the supersymmetric case. The second of these problems began to be addressed by identifying situations where supersymmetry breaking is calculable. For example, if the scalar field of interest describes the distance between supersymmetric branes situated about the extra dimensions, then the cancelling of forces on these branes makes their interactions vanish, with supersymmetry breaking difficult to calculate. Explicit calculations began with the observation that supersymmetry breaks if the relevant distance is between a brane and its antibrane, or branes inclined at angles relative to one another since this allows the relevant forces to be accurately computed. But the over-abundance of scalar fields remained, and serious progress finding inflation with a truly stringy provenance began once the forces that fix the shape and size of the extradimensional geometry began to be better understood. The first steps towards inflation then came with the discovery of de Sitter solutions among these flux-stabilized systems, which represent a universe that inflates forever without ever slowing down into the Hot Big Bang expansion we now find ourselves experiencing. This eventually led to a search for slowly rolling scalars describing the motion of branes within the warped extra-dimensional geometries to which this program led. Alternative constructions, with inflation driven by scalar fields describing changes to the extra-dimensional geometry itself (rather than the motion of objects, like branes and antibranes, within it) followed shortly thereafter. Although it remains early days, some preliminary insights are already emerging from these constructions: 104 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) GETTING A BIG BANG ... (BURGESS)AA Robustness: String-inflationary scenarios involve many scalar fields, whose interactions determine whether an inflationary regime arises. Yet the observational evidence for inflation relies on comparing to the predictions of very simple models, usually involving one scalar field. Does the presence of other degrees of freedom in string theory invalidate the predictions on whose success is based the inference that inflation may have occurred? A second difference can arise for brane-antibrane inflation, wherein inflation occurs as a brane and antibrane approach one another, ending with their mutual annihilation. This typically produces relic cosmic strings, and if these should be long-lived enough to survive to the present day their presence could have detectable consequences. Observation of such strings would provide considerable circumstantial evidence that this kind of inflationary mechanism is at work. The good news is that the dynamics of these extra fields seems less important for describing the primordial fluctuations that are ultimately observed. If this survives further exploration, it means stringy complications needn’t upset standard analyses of the data, yet might contribute small deviations whose presence could be observationally sought. Reheating: Nothing’s over until the fat lady sings, and for inflation the song describes how inflationary energy gets channelled into reheating the Hot Big Bang of the present epoch. This process cannot be properly understood without having the full theory (like string theory), including non-inflationary sectors. In particular, understanding reheating requires understanding how efficiently all of the sectors of the theory absorb the energy released after inflation. There is evidence that energy flow in the extra dimensions provides many novel challenges and opportunities for this process. The bad news is that inflation seems as rare amongst string solutions as it is for garden-variety theories (although a few promising corners of solution space remain to be explored). But there is an important caveat: the present state of the art can only find inflation when inflationary energies are smaller than those associated with changing extra dimensional shapes (or vibrating the underlying strings), where the inflationary evolution is four-dimensional. Yet this is not a fundamental requirement, and one wonders whether the resemblance between stringy and more prosaic versions of inflation is an artefact of looking only under the four-dimensional streetlight. New Signatures: String models can differ in their predictions from simple slow-roll models. One class that can B called ‘DBI’ inflation B involves brane motion that is fast enough to be relativistic (even though moving slow enough to inflate the universe). If this occurs it can produce observable differences in its predictions for the non-gaussianity of the statistics of CMB fluctuations. The ultimate connection between inflation and string theory remains elusive. Yet it provides a hopeful means for placing inflation on more solid theoretical foundations, and for potentially making string theory into an experimental science. ACKNOWLEDGEMENTS This research was funded in part by grants from NSERC and McMaster University. Research at Perimeter Institute is supported in part by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. REFERENCES 1. 2. 3. 4. 5. See B. Batell and M. Pospelov, this volume. A.H. Guth, Phys. Rev. D23 (1981) 347; A.D. Linde, Phys. Rev. B108 (1982) 389; A. Albrecht and P.J. Steinhardt, Phys. Rev. Lett., 48 (1982) 1220. For more complete referencing see, e.g., C.P. Burgess, PoS P2GC (2006) 008 [Class. Quant. Grav. 24 (2007), “Getting a Big Bang from String Theory” S795] [arXiv:0708.2865 [hep-th]]; D. Baumann and L. McAllister, arXiv:0901.0265 [hep-th]. See A. Buchel, R.C. Myers and A. Sinha, this volume. See M. Trott, this volume. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 105 JOIN THE FUN AMUSEZ-VOUS ART OF PHYSICS COMPETITION CONCOURS L’ART DE LA PHYSIQUE You are invited to enter the competition (open or high school categories) by capturing in a photograph a beautiful or unusual physics phenomenon and explaining it in less than 200 words in terms that everyone can understand. Vous êtes invités (es) à participer (aux catégories ouvert ou école secondaire) en photographiant un phénomène physique magnifique, ou particulier, et en rédigeant un court texte explicatif de moins de 200 mots, en termes simples et à la portée de tous. The emphasis of the contest is not so much on having a high level of physics comprehension as it is on being able to explain the general principle behind the photograph submitted. Individual (open and high school) and high school class entries are invited up until April 30, 2011 (see http://www.cap.ca /en/activities/art-physics for entry form/rules). Please note that all entries must be original artwork produced by the participant. L’accent de ce concours est de pouvoir expliquer le principe général de la photo soumise plutôt que de démontrer un niveau élevé de compréhension de la physique. L’échéance pour les inscriptions individuelles (ouvert et école secondaire) et scolaires (voir formulaire d’inscription/règlements à h t t p : / / w w w. c a p . c a / f r / activites/lart-de-physique) est fixée au 30 avril, 2011. Notez bien que toutes les inscriptions doivent être des oeuvres originales du participant ou de la participante. 1st Prize ( High School Individual Category ) 2007-08 competition “Sunset in a Bubble Film” by Dhanisha Patel, Emergy Collegiate Institute, North York, Ontario Winning entries will form part of our Art of Physics exhibition which will be on display at the Canada Science and Technology Museum, and may appear as a cover on our publication, Physics in Canada. They will also be posted on our Art of Physics website at http://www.cap.ca. We hope you will take advantage of this opportunity to explore the art of physics by submitting entries for the 2011 competition. Les articles gagnants feront partie de notre exposition L’Art de la physique au Musée des sciences et de la technologie du Canada et auront une chance de paraître sur la couverture d’un numéro de La Physique au Canada. Ils seront également affichés sous la rubrique L’Art de la physique du site web de l’ACP à l’adresse suivante: http://www.cap.ca. Nous espérons que vous profiterez de cette occasion d’explorer l’art de la physique en soumettant un travail pour la compétition de 2011. 106 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE REVIVING GRAVITY’S AETHER BY IN EINSTEIN’S UNIVERSE NIAYESH AFSHORDI A sk any good student of freshman physics and, happily quoting their textbooks, they will tell you that gravity is the weakest force of nature. After all, when you lift a pen, the electromagnetic dipoles of the molecules in your hand can easily counteract the gravitational pull from the entire planet Earth. It may thus come as a surprise that throughout history, understanding gravity has been one of the strongest drivers of breakthroughs in theoretical physics, and yet it still remains its deepest mystery. After Newton’s discovery of universal laws of gravity and mechanics, physicists and philosophers often wondered how gravitational forces could act over large distances, while other forces of nature only act in extreme proximity. In fact, this was one of Einstein’s philosophical motivations to introduce metric, or space-time geometry, as a medium that mediates gravitational forces, as “action at a distance” cannot be physical. But we are jumping ahead of ourselves! Long before Einstein’s celebrated invention of General Relativity, over the course of the 16th to 19th centuries, many mechanical models of gravity were put forth and then discarded. In these theories, an invisible medium, called “the gravitational aether”, mediated the particles, vortices, streams, or waves that exchanged gravitational force between massive bodies [1]. For example, in 1853, Riemann proposed that gravitational aether was an incompressible fluid which sinks toward massive objects where SUMMARY Einstein's theory of general relativity describes gravity as the interaction of particles with space-time geometry, as opposed to interacting with a physical fluid, as in the old gravitational aether theories. Moreover, any theoretical physicist would tell you that, despite its counter-intuitive structure, general relativity is one of the simplest, most beautiful, and successful theories in physics, that has withstood a diverse battery of precision tests over the past century. So, is there any motivation to relax its fundamental principle, and re-introduce a gravitational aether? Here, I give a short and non-technical account of why quantum gravity and cosmological constant problems provide this motivation. it is absorbed, at a rate proportional to their mass. He speculated that the absorbed aether is then emitted into another spatial dimension [2]. The most famous refutation of aether theories (even though it did not directly concern the gravitational aether) came from the Michelson-Morley experiment [3], which showed that the speed of light is constant, and independent of reference frame, as opposed to being only constant and isotropic in the aether’s frame of reference. Indeed, the absence of a preferred reference frame, otherwise known as the principle of relativity, was the key assumption in the development of special, and then general relativity. REVIVING THE INCOMPRESSIBLE GRAVITATIONAL AETHER Einstein’s theory of general relativity describes gravity as the interaction of particles with space-time geometry, as opposed to interacting with a physical fluid, as in the old gravitational aether theories. Moreover, any theoretical physicist would tell you that, despite its counterintuitive structure, general relativity is one of the simplest, most beautiful, and successful theories in physics, that has withstood a diverse battery of precision tests over the past century. So, is there any motivation to relax its fundamental principle, and re-introduce a gravitational aether? Let us consider an interesting analogy with Newtonian gravity. A hypothetical 19th century philosopher, Dr. John Smith, proposes that the laws of gravity are set by three fundamental principles: 1 - Bound orbits in the two-body problem must be closed. 2 - There exist unbound orbits in the two-body problem. 3 - Gravitational forces obey linear superposition. These principles uniquely fix the formulation of Newtonian gravity and celestial mechanics. However, we now know that Principle (1), which fixes the inverse square law [4], is based on an accidental symmetry between radial and angular frequencies. General relativity violates this symmetry, which is the origin of Mercury’s anomalous perihelion precession. Nevertheless, Dr. Smith would have ruled out Einstein’s general relativity, as it did not respect his fundamental principles of gravitational theory, as stated above. PHYSICS IN Niayesh Afshordi (nafshordi@ perimeterinstitute.ca), Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5,Canada, and Department of Physics and Astronomy, University of Waterloo CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 107 REVIVING GRAVITY’S AETHER ... (AFSHORDI) The lesson from this story is that the underlying principles or symmetries of an effective theory might be accidental or emergent symmetries of a more fundamental theory. As powerful as the principle of relativity might have been in the development of Einstein’s theory of gravity, it might need to be broken/reexamined, e.g., by having a preferred reference frame, or a gravitational aether, in a more complete theory of gravity. While it is typical to spontaneously break Lorentz symmetry on cosmological scales, normal matter on very small scales/high energies decouples from this cosmological frame. Nevertheless, it is easy to find theories that do not behave this way, and yet are consistent, at least up to some high energy cutoff. For scalar field theories, this can be done through covariant actions that are not quadratic in field gradients. An extreme example of this is the “cuscuton action” [7,8], defined as: But is there any reason to think that general relativity is not the fundamental theory of gravity? The main motivation for this comes from quantum mechanics, the other hugely successful physical theory of the 20th century: both general relativity and quantum mechanics have been incredibly successful in describing macroscopic and microscopic phenomena respectively. However, any attempt to apply the rules of quantum mechanics to general relativity seems to lead to divergences that impair the predictive power of the theory. The effective theory of gravity breaks down when the macroscopic and microscopic worlds meet and a huge amount of energy is packed into small scales, i.e., energy densities exceeding the Planck density of 10114 Joules (or 1097 kilograms) per cubic meter. Although it is hard to achieve such densities in laboratories, Penrose and Hawking [5] showed that singularities with infinite densities are inevitable in the future and past of general relativistic dynamics. While they may not be immediately accessible to us, they should be prevalent in the universe, residing at the centers of millions of astrophysical black holes in our galaxy, and possibly present at the first moment of the cosmological big bang. It is generally believed that a fundamental theory of quantum gravity should give a self-consistent description of physics close to these singularities (and thus avoid their formation). General relativity plus quantum mechanics does not. Most physicists agree on the status of the problem at this level. However, they diverge on their approaches from this point on. One approach is the interesting possibility of relaxing the requirement of no preferred reference frame (or Lorentz invariance). While the geometric nature of gravity is ubiquitous, there might still exist a physical gravitational aether, which only interacts with geometry (or matter) at very high energies. Recently Petr Ho4rava generated a lot of excitement by suggesting that if the speed of propagation of gravitons increases with energy as E 2/3 at very high energies, then the theory of gravity might have a well-defined quantization [6]. This of course introduces a preferred frame in which the energy E is measured. While breaking Lorentz invariance may sound heretical to many physicists, it comes easily to cosmologists. After all, even though our laws don’t seem to have a preferred frame of reference, the universe hasn’t had much trouble in picking one. For example, a relativistic electron in the universe will eventually come to stop in the rest frame of the cosmic microwave background (CMB), where the CMB dipole vanishes. That is why analogues of the invisible aether, such as dark matter, dark energy, and the inflaton exist and play crucial roles in the standard model of cosmology. S = ∫ d 4 x − g ⎡ μ 2 ∂ μ ϕ ∂ μ ϕ − V ( ϕ )⎤ , ⎣ ⎦ (1) which represents an incompressible fluid, implying that perturbations around any uniform density background are nondynamical. It is interesting to note that Ho4rava’s gravity theory reduces to general relativity minimally coupled to an incompressible cuscuton fluid at low energies [9]. At this point, it is interesting to recall Riemann’s idea of an “incompressible gravitational aether”, and to entertain the possibility that after 156 years, it might turn out to be an actual ingredient of a quantum theory of gravity. There are, after all, no new ideas under the sun! GRAVITATIONAL AETHER AND THE COSMOLOGICAL CONSTANT PROBLEM Although one may decide to ignore the problem of quantizing gravity for low energy and large scale observations, there is one aspect of quantum mechanics that is disastrous for any gravitational observable: the quantum vacuum of the standard model of particle physics has a density of roughly 1033 kilograms per cubic meter! One does not need precision observations to conclude that this is not realistic, as human bodies, let alone stars and planets would be torn apart by extreme gravitational tidal forces. Incidentally, there are cosmological precision measurements of the vacuum density, which put it at [10]: ρvac = ( 7.1 ± 0.9) × 10 −27 kg / m3 , (2) i.e. some 60 orders of magnitude smaller than the standard model prediction! Of course, there could be other unknown contributions to the vacuum density, but why should they so precisely (but not completely) cancel the known contributions? This is known as the cosmological constant problem. One way to avoid the problem is to couple gravity to the traceless part of the energy-momentum tensor, effectively decoupling the vacuum energy from gravity: (8πG′ ) −1 1 ′ . Gμν [ gμν ] = Tμν − T αα gμν + T μν 4 (3) Eq. (3) is a modification of the celebrated Einstein equation, which couples the space-time curvature, represented by the Einstein tensor, Gμν on the left, to the matter energy-momentum tensor Tμν on the right. However, the last two terms on the right are new: the second term subtracts the trace of Tμν, which effectively decouples the vacuum from gravity. The last term is 108 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) REVIVING GRAVITY’S AETHER ... (AFSHORDI)AA there to ensure energy-momentum conservation Tνμ;ν = 0, as Bianchi identity enforces zero divergence for the Einstein tensor Gνμ;ν = 0. Therefore, we require 1 T μ′ν;ν = T νν,μ . 4 (4) TNμν is a new component of gravitational dynamics, which we can think of as a modern-day version of the gravitational aether [11]. Moreover, through the above argument, it is an inevitable component of a complete theory of gravity if we decide to decouple the quantum vacuum energy from geometry. Of course, one needs to know more about the properties of aether in order to make predictions in this theory. By now, it may not come to the reader as a surprise that we shall assume aether to be incompressible, or more specifically, to have zero density, but non-vanishing pressure. The main motivation, apart from its historical appeal and appearance in quantum gravity theories, is that an incompressible fluid does not introduce new dynamical degrees of freedom, which are severely constrained by precision tests of gravity. ativity, formation of singularities is shielded from the outside world by event horizons, the incompressible gravitational aether with an infinite speed of sound is not bound by the horizons. Therefore, the onset of the quantum gravity regime close to the singularity might affect aether pressure outside the black hole. In [13], it was shown that an incompressible gravitational aether ties the geometry close to the black hole horizon to cosmological scales. Assuming Planck scale physics close to the horizon, one can show that the pressure of aether at -3 , and is comparable to today’s infinity roughly scales as M BH vacuum pressure for MBH = 10 - 100M. Incidentally, this is the typical mass range for stellar black holes in our universe. Therefore, the gravitational aether scenario could potentially explain today’s acceleration of cosmic expansion, without any fine-tuning, by virtue of a quantum gravitational effect close to the horizon of stellar black holes. Furthermore, Fig. 1 shows that this model makes concrete predictions for the evolution of cosmic acceleration over time, that appear to match well with What is surprising about this theory is how similar its predictions are to those of general relativity. In fact, the two are only significantly different in objects with relativistic pressure (such as neutron stars, or the early universe) or large vorticity [11]. The main effect of the new terms on the right hand side of Eq. (3) is to create an effective Newton’s constant which depends on the equation of state of matter, ωmatt. = pmatt. / ρmatt., the ratio of pressure to density: Geff (1 + ωmatt . ) GN . (5) While this change is negligible in most astrophysical situations, it significantly changes the dynamics of the early universe, as the gravitation due to radiation is enhanced by a factor of 4/3. To a good approximation, this effect can be captured in the standard cosmological model by increasing the number of neutrinos from 3 to 5.5, while keeping the gravitational constant fixed. Surprisingly, this is exactly what is found in analysis of the Lyman-α forest in quasar spectra (Nν = 5.3 ± 1.1), even though it is marginally inconsistent with observational constraints on big bang nucleosyntheis [12]. Future cosmological observations will be able to rule out or confirm this prediction conclusively. Fig. 1 There is one final question that might be lingering in the reader’s mind. If gravity is completely decoupled from the vacuum energy, how could we measure the vacuum density as having the value in Eq. (2)? This measurement is based on the observation that the cosmic expansion appears to have started accelerating about 6 billion years ago. The easiest way to explain this is a uniform vacuum energy density which dominates today’s cosmic energy density, and is amazingly consistent with almost all the cosmological observations. It turns out that a similar phenomenon happens as black holes form in the gravitational aether scenario. While in general rel- PHYSICS From [13]: Top panel: The prediction of different astrophysical black hole formation scenarios (see below) for the effective dark energy equation of state w G (< z), given that aether pressure scales as inverse cube of the mean black -3 . This can be compared to constraints from hole mass, M BH cosmology. The unshaded area shows the region currently allowed at 68% confidence level for this parameter, as measured from cosmological observations [14]. Bottom panel: The mass-weighted geometric mean of black hole masses, MBH, in units of M as a function of redshift. Our fiducial model (solid, black line) assumes our best estimates of the evolution of the black hole mass distribution. Dashed lines indicate the range of uncertainty expected due to the unknown relative contribution of supermassive and stellarmass black holes, while the dotted lines represent the uncertainty in the shape of the star formation density evolution. These correspond to the same models used in the top panel. IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 109 REVIVING GRAVITY’S AETHER ... (AFSHORDI) current observations. Future observational probes of cosmic acceleration and galaxy formation will be able to definitively rule out or confirm this proposed connection between dark energy and astrophysical black holes over the next decade. CONCLUSIONS Unifying general relativity and quantum mechanics, the two great physical theories of the twentieth century, has fascinated and puzzled theoretical physicists for many decades. As bizarre as it may sound, recycling discarded ideas of the 19th century might provide a way forward! While gravitational aether is far from the only possibility for solving the problems of quantum gravity, the theoretical arguments and motivations for its reincarnation are simple and sound, and the coincidence of its predictions with cosmological observations is very suggestive. Many questions still remain, and need to be answered in order to have a viable physical theory on par with general relativity: Is there an action for this theory with a well-defined quantization? Can a UV completion of the theory resolve the structure of black hole horizons? What does black hole formation look like in this theory? Will there be smoking guns in the future precision tests of gravity? Is aether consistent with all cosmological observations? What about the anomalies such as those in the integrated Sachs-Wolfe [15] and large-angle CMB anisotropies [16]? Looking forward, one expects the revival of gravitational aether to lead to many new possibilities in our theoretical understanding of quantum gravity and quantum cosmology, as well as the phenomenology of astrophysical and cosmological observations. The resolution of last century’s mysteries may not be too far off after all. ACKNOWLEDGEMENTS Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. “Mechanical explanations of gravitation”, Wikipedia.org, http://en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation. B. Riemann, “Neue mathematische Prinzipien der Naturphilosophie”, Bernhard Riemanns Werke und gesammelter Nachlass, 528-538 (1876). A.A. Michelson and E.W. Morley, American Journal of Science 34, 333-345 (1887). The only closed orbits in a spherical force field are for inverse square, and linear forces. However, the latter do not have unbound orbits, thus violating Principle (2). S.W. Hawking and R. Penrose, Royal Society of London Proceedings Series A 314, 529-548 (Jan. 1970). P. Horava, Phys. Rev. D79, 084008 (2009), arXiv:0901.3775 [hep-th]. N. Afshordi, D.J.H. Chung, and G. Geshnizjani, Phys. Rev. D75, 083513 (2007), arXiv:hep-th/0609150. N. Afshordi, D.J.H. Chung, M. Doran, and G. Geshnizjani, Phys. Rev. D75, 123509 (2007), arXiv:astro-ph/0702002. N. Afshordi, Phys. Rev. D80, 081502 (2009), arXiv:0907.5201 [hep-th]. J. Dunkley et al., Astrophys. J. Suppl. 180, 306-329 (2009), arXiv:0803.0586 [astro-ph]. N. Afshordi, arXiv:0807.2639 [astro-ph]. U. Seljak, A. Slosar, and P. McDonald, JCAP 0610 (2006) 014, arXiv:astro-ph/0604335. C. Prescod-Weinstein, N. Afshordi, M.L. Balogh, N. Afshordi, and M.L. Balogh, Phys. Rev. D80, 043513 (2009), arXiv:0905.3551 [astro-ph.CO]. E. Komatsu et al., Astrophys. J. Suppl. 180, 330-376 (2009), arXiv:0803.0547 [astro-ph]. S. Ho, C. Hirata, N. Padmanabhan, U. Seljak, and N. Bahcall, Phys. Rev. D78, 043519 (2008), arXiv:0801.0642 [astro-ph]. C.J. Copi, D. Huterer, D.J. Schwarz, and G.D. Starkman, Mon. Not. Roy. Astron. Soc. 399, 295-303 (2009), arXiv:0808.3767 [astroph]. 110 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE DARK FORCES BY BRIAN BATELL AND MAXIM POSPELOV D ecades of progress in fundamental physics have resulted in a deep understanding of the nature of atoms, nuclei, elementary particles, and the forces that govern their interaction. It is precisely this understanding, combined with unprecedented progress in observational cosmology, that has led to the “missing energy” problem: 95% of the total energy density of the Universe does not consist of the atomic matter with which we are familiar, but rather a new form of matter and energy. We are aware of this missing energy only through its gravitational effects and its participation in the cosmological evolution. Understanding the nature of “dark matter”, responsible for the formation of cosmological structures such as galaxies, is one of the primary goals of particle physicists, astrophysicists and cosmologists today [1]. Although a wide variety of evidence for the gravitational interaction of dark matter exists, its connection to the micro-world of particle physics remains a mystery, and a subject of intensive experimental, observational, and theoretical research. One must keep in mind that this may be an open-ended journey, with no guarantee that the nongravitational interactions of dark matter will ever be detected. In light of this, several recent results from cosmic ray astrophysics experiments have generated considerable excitement in the physics community, as they can be interpreted as a combined effect of dark matter and dark forces. Theorists at the Perimeter Institute have pio- SUMMARY The idea of dark forces - new gauge interactions with small couplings to the Standard Model particles and interaction ranges accessible in medium energy collisions - has remained on the back burner of particle physics for almost three decades. During the last two years, however, this subject has become a focal point due to the new exciting developments that tie the combination of dark forces and particle dark matter to the newly discovered cosmic ray anomalies. Here we review this new motivation for studying dark forces, and give an account of the contribution of Perimeter Institute to the development of new search strategies of dark forces in particle physics experiments. neered many crucial ideas in this exciting new direction in dark matter research. What do we mean by dark forces? The standard model of elementary particles dictates that besides gravity, there are three fundamental forces that describe all known interactions of ordinary matter: the electromagnetic, weak, and strong forces. These forces are transmitted by the so-called gauge bosons which are elementary particles with unit spin, and can be schematically described by the Yukawa potential between point-like particles, V (r ) = ± α exp ( − r / λ ) , r (1) where α is the strength of the force and λ is its range, with a positive sign for repulsion and negative sign for attraction. For example, the photon is the gauge boson which communicates the electromagnetic force between charged matter with α ≅ 1/137 and infinite range. Analogous to these forces familiar from particle physics, it has been postulated that dark matter may be accompanied by new gauge bosons, or “dark photons”, which carry a new dark force that influences primarily dark matter particles, and to a much lesser degree ordinary particles such as electrons and protons [2,3]. The existence of dark forces can explain in a natural way the recent anomalies observed in experiments studying cosmic rays, energetic particles coming from space. The most striking result comes from PAMELA, a satelliteborne experiment that investigates charged particles in the cosmic rays and has the capacity to distinguish between types of particles and their charge, e.g. electron vs. positron. There are two important results that PAMELA has published. The first result is the observation of a stark rise in the fractional flux of positrons at energies ranging from several GeV to about 100 GeV [6], shown in Fig. 1. This suggests a new primary source of cosmic ray positrons at high energies. One possible new primary source is the annihilation of dark matter particles in the galactic halo into electron-positron pairs. However, a standard particle dark matter candidate has a characteristic annihilation cross section which is too small to obtain the measured flux. The second observation from PAMELA is the cosmic ray anti-proton fractional flux, which agrees very nicely with the predicted flux due to standard astrophysical sources [7]. Thus, if one takes seriously the possibility that dark matter annihilation is responsible for the PHYSICS IN B. Batell <bbatell@ perimeterinstitute.ca>, Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 and M. Pospelov <mpopelov@ perimeterinstitute.ca>, University of Victoria and Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 111 DARK FORCES (BATELL AND POSPELOV) enhancement of the annihilation cross section, a well-known effect in the annihilation of electron-positron pairs. To summarize, the presence of a GeV-scale dark force naturally provides an overall enhancement of the dark matter annihilation cross section, and thus a new primary source of high energy positrons which may explain the PAMELA positron flux [6]. While the notion of dark matter is somewhat exotic, even if well-accepted, the idea of dark forces may seem completely far-fetched. Nevertheless, models of dark forces make a number of concrete and striking predictions that can be tested in ongoing and upcoming particle physics and dark matter experiments, and much of the groundwork in exploring the phenomenology in this area has been carried out by researchers at Perimeter Institute [8,9]. Fig. 1 The PAMELA positron flux. The red data points indicate a rising fractional positron flux at energies above 10 GeV. The solid line is the predicted result based on known astrophysical sources. PAMELA positron anomaly, one must explain 1) the large annihilation cross section into electrons and positrons, and 2) the small annihilation cross section into protons and antiprotons. These two requirements can be naturally satisfied given the existence of a new dark force[4,5]. Let us call the dark matter particle χ and the “dark photon” (or more precisely the “massive dark force gauge boson”) V. The dominant dark matter annihilation process is χ + χ →V +V. (2) Once a dark photon V is produced, it can decay back into ordinary particles, such as electrons and protons: V → e+ + e− ; V → p+ + p− . While there exists a variety of models of dark forces, a basic framework may be characterized by two parameters. The first is the mass of the dark photon mV, which is of course one-toone related to the range of the force, mV = 1/λ. While the interaction of two dark matter particles via the dark force may have strength similar to the regular interactions, the coupling of the dark matter particles to electrons and protons is given by the coupling strength κα, where κ can be interpreted as a small mixing angle between the ordinary photon and the dark photon. How can we test the idea of dark forces experimentally? The most direct and convincing evidence would be to produce and detect dark photons directly in the laboratory, and this is the opportunity afforded by fixed-target and collider experiments. Let us first discuss fixed-target experiments, focusing on the neutrino experiments LSND [13], MiniBooNe [14], and NuMi/ MINOS [15]. The basic experimental setup is as follows: a highintensity proton beam strikes a target of material, producing particles through the strong interactions, e.g. πnmesons, ρnmesons, protons, etc. Some of these particles decay electromagnetically, e.g. π0 γγ, where γ indicates a photon. Because the dark photon V may have a small mixing angle κ with the ordinary photon, particles like the neutral pion may, very rarely, decay to a final state containing a dark photon. For example, one particular production channel may be summarized as p + A π0 + X V + γ + X. (3) However, if the dark photon is rather light, with a mass less than twice the mass of the proton, mV < 2mp , conservation of energy forbids the decay of V p+ + pn. Thus, the production of cosmic ray protons and antiprotons via dark matter annihilation is negligible provided the dark force carrier is light, mV <~ GeV, while electrons and positrons may still be produced, in accord with the results from PAMELA [6,7]. Remarkably, such a light force carrier with a mass in the GeV range may also lead to an enhancement of the total annihilation cross section due to the presence of the relatively long-range dark force. The attractive long-range force amplifies the particle wavefunctions as they scatter, leading to the Sommerfeld (4) Once a dark photon is produced, it may travel to a detector stationed meters to kilometers away from the target and decay into, e.g. an electron-positron pair. The experiments mentioned above already provide a sensitive probe to the small coupling, small mass parameter space in basic models of dark forces [9]. Although we have discussed proton-beam fixed target experiments, there are a wide variety of experimental setups. Competitive limits in the coupling-mass parameter space of dark force models are obtained from electron beam experiments. Moreover, several new experiments have been proposed specifically designed to probe new areas of the parameter space and may be carried out in upcoming years [10]. 112 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) DARK FORCES (BATELL AND POSPELOV)AA Collider experiments offer a complementary probe of models of dark forces [8,11,12]. We will focus here on electron-positron colliders. Again the main idea is to directly produce and detect the dark photon. The simplest process one may imagine is the resonant production process, e+ + en V. Unfortunately, in practice the cross section for this process is very small unless the center-of-mass energy of the collider is very close to the mass of the dark photon. Pair production offers a better chance of producing a dark photon. The simplest and most generic process in any dark force model is the pair annihilation process: e+ + en γ + V. (5) Once the V particle is produced, it may decay into a muonantimuon (μ+μn) pair. The presence of the dark photon may be recognized as a peak in the invariant mass of the μ+μn pair. The presence of additional GeV-scale particles in the dark sector can lead to very striking signals at colliders. Perhaps the most basic extension is the inclusion of a “dark Higgs” boson, hN, responsible for spontaneously breaking the dark gauge symmetry and providing the dark photon with a mass, much like the usual Higgs boson breaks the electroweak symmetry in the standard model. If the dark Higgs boson is present in the spectrum, one may consider the “Higgs-strahlung” process e+ + en V + hN. such as Belle [16] and BaBar [17] could have thousands of such events contained within their current data sets [8]. Theoretical ideas of searching for dark forces at the high-luminosity fixed target experiments and electron-positron colliders are inspiring a number of new experimental analyses and possibly new experimental set-ups where such forces can be efficiently probed. A workshop on Dark Forces held in September 2009 at the Stanford Linear Accelerator Center, as well as the earlier “New Lights on Dark Matter” workshop at Perimeter Institute, helped to advance the current understanding of dark forces and dark matter and to devise new strategies for seeking this exotic physics in the laboratory. These efforts will remain an important part of particle physics at the “intensity frontier” for many years to come. Furthermore, there has been an explosive growth in the efforts to see dark matter directly in experiments. Indeed, the CDMS collaboration just announced the observation of two events that have the properties of a nuclear recoil induced by a collision with a dark matter particle [18]. While it is entirely possible that this is a statistical fluctuation of the background, these two events may be the first sign of what is to come: a thorough measurement of the scattering of dark matter with nuclei with many events observed in upcoming direct detection experiments. ACKNOWLEDGEMENTS (6) The dark Higgs may then decay back into a pair of dark photons, hN V + V, while each dark photon can decay into a μ+μn or e+en pair. Thus, the experimental signature of the process in Eq. (6) is a six-lepton event! Such a novel signature would have gone unnoticed in previous analyses, and experiments The work of the authors was supported in part by NSERC, Canada, and research at the Perimeter Institute is supported in part by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. G. Jungman, M. Kamionkowski and K. Griest, Phys. Rept., 267, 195 (1996) [arXiv:hep-ph/9506380]; G. Bertone, D. Hooper and J. Silk, Phys. Rept., 405, 279 (2005) [arXiv:hep-ph/0404175]. B. Holdom, Phys. Lett. B, 166, 196 (1986). M. Pospelov, A. Ritz and M.B. Voloshin, Phys. Lett. B, 662, 53 (2008) [arXiv:0711.4866 [hep-ph]]. N. Arkani-Hamed, D.P. Finkbeiner, T. Slatyer and N. Weiner, arXiv:0810.0713 [hep-ph]. M. Pospelov and A. Ritz, Phys. Lett. B, 671, 391 (2009) [arXiv:0810.1502 [hep-ph]]. O. Adriani et al., arXiv:0810.4995 [astro-ph]. O. Adriani et al., Phys. Rev. Lett., 102, 051101 (2009) [arXiv:0810.4994 [astro-ph]]. B. Batell, M. Pospelov and A. Ritz, Phys. Rev. D79, 115008 (2009) [arXiv:0903.0363 [hep-ph]]. B. Batell, M. Pospelov and A. Ritz, arXiv:0906.5614 [hep-ph]. J.D. Bjorken, R. Essig, P. Schuster and N. Toro, arXiv:0906.0580 [hep-ph]. R. Essig, P. Schuster and N. Toro, arXiv:0903.3941 [hep-ph]. M. Reece and L.T. Wang, arXiv:0904.1743 [hep-ph]. A. Aguilar et al. [LSND Collaboration], Phys. Rev. D64, 112007 (2001) [arXiv:hep-ex/0104049]. A.A. Aguilar-Arevalo et al. [MiniBooNE Collaboration], Phys. Rev. D78, 012007 (2008) [arXiv:0805.1764 [hep-ex]]. P. Adamson et al. [MINOS Collaboration], Phys. Rev. D77, 072002 (2008) [arXiv:0711.0769 [hep-ex]]. Nucl. Instrum. Meth. A479, 117 (2002). B. Aubert et al. [BABAR Collaboration], Nucl. Instrum. Meth. A479, 1 (2002) [arXiv:hep-ex/0105044]. Z. Ahmed et al. [The CDMS Collaboration], arXiv:0912.3592 [astro-ph.CO]. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 113 LA PHYSIQUE AU CANADA PIC WELCOMES ARTICLES INVITATION À SOUMETTRE DES ARTICLES The Editorial Board welcomes articles from readers suitable for, and understandable to, any practising or student physicist. Review papers and contributions of general interest of up to four journal pages in length are particularly welcome. Suggestions for theme topics and guest editors are also welcome and should be sent to [email protected]. Le comité de rédaction invite les lecteurs à soumettre des articles qui intéresseraient et seraient compris par tout physicien, ou physicienne, et étudiant ou étudiante en physique. Les articles de synthèse d’une longueur d’au plus quatre pages de revue sont en particulier bienvenus. Des suggestions de sujets pour des revues à thème sont aussi bienvenues et pourront être envoyées à [email protected]. 114 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE THE EARLY LHC ERA BY MICHAEL TROTT T he era of the Large Hadron Collider (LHC) has arrived and particle physicists are excited about what this experiment will reveal about the nature of reality. The LHC took fourteen years of design/construction work and at least five billion dollars was spent to build what is the largest and most complicated physics experiment ever. Physically, the LHC is a circular tunnel twenty-seven kilometers in circumference that was dug at a level of about a hundred meters underground. The tunnel is so large it spans the Swiss-French border, and within it there are about twenty kilometers of superconducting magnets. Their purpose is to accelerate two beams of protons (one of the particles that make up the nucleus of an atom) to almost the speed of light. The thousands of experimentalists involved in the experiments at the LHC then smash these beams of protons into one another and study the debris of these collisions in giant multi-story particle detectors. They are looking for clues to answer fundamental questions such as: “What is the origin of mass?” Beset by setbacks in the form of exploding cooling systems for the giant magnets, construction delays and difficulties, and a baguette bombing run by a devious French bird (seriously) the experimentalists at LHC have persevered and, in the fall of 2009, the LHC era arrived when two proton beams collided at an energy of about a half of a tera electron volt (TeV = 1012 eV). Particle physicists use energy units such as TeV for technical reasons, but keep in mind that the amount of energy in this collision is about half the kinetic energy of a flying mosquito. However, all of this energy is packed into a space about 10G13 smaller than a mosquito and it is the density of energy that matters in these experiments. Another unit of energy/mass we will use is GeV which is 10G3 H TeV. Recently the collision energy has been increased to 2.36 TeV and a resulting col- SUMMARY We introduce the LHC experiment and discuss the physics case for this incredible machine. The Higgs mechanism is introduced and some evidence for the existence of the Higgs is presented. The possibility of new physics appearing at LHC in conjunction with the Higgs is motivated and the leading contender of New Physics, Supersymmetry, is briefly discussed. Fig. 1 A recent collision event at LHC from one of the particle detector experiments, ATLAS, where the collision is at an energy of 2.36 TeV. Each individual line is a reconstructed particle track coming from the collisions, the cones are groups of such particles classified into a “jet” structure and the boxes around the edges are measures of the total amount of energy deposited in different parts of the particle detectors from the particles. Image credit: The ATLAS experiment at CERN, http://atlas.ch lision is shown in Fig. 1. In March of 2010 the collision energy reached 7 TeV and LHC should operate at this energy for the next two years. Why has this enormous effort been expended? Will we succeed in answering the questions that drive us and uncover new and deeper mysteries? In this short review, we will discuss the physics case for this experiment and some of the practical issues and limitations of doing particle physics in the LHC collider environment. The stakes are high, but LHC is certainly worth the risk, and the effort to answer these questions is likely to be rewarded. THE STANDARD MODEL The questions that LHC has been built to answer emerge out of our understanding of the subatomic realm, which is a mysterious place far removed from our everyday experience. The model of the particles that we see when we probe very small distances with large energies is called the Standard Model (SM). The way we are able to succinctly describe the rules of the subatomic world’s constituents and interactions is to exploit the fact that symmetry is a powerful constraint on physics at any energy scale, including the energies of the subatomic realm. M. Trott <mtrott@ perimeterinstitute.ca>, Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo ON N2L 2Y5 To get the idea of how symmetry acts to constrain physics consider a sphere centered at the origin with radius r. In PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 115 THE EARLY LHC ERA (TROTT) Cartesian coordinates the equation of such a sphere is x2 + y2 + z2 = r 2. (1) This equation is actually capturing a symmetry principle. One can transform a particular (x, y, z) that satisfies this equation into another (xN, yN, zN) that also satisfies this equation. The set of all these transformations is something called the rotation group and mathematicians have a special notation for this, SO(3). Symmetry groups are critical in describing the subatomic realm, they force one to write very compact and constrained equations. The SM can be described by a different combination of groups SU(3) H SU(2) H UY(1) that describe how the properties of subatomic particles can change. The elementary particles of the SM are shown in Fig 2. If you examine this figure you will notice that the Higgs Boson is “yet to be confirmed”. This particle is central to a question that LHC was built to answer: “What is it that gives mass to the W and Z particles?” If the transformations of the SM were simply SU(3) H SU(2) H UY(1) at all energies then a physical consequence of these symmetry constraints on the theory is that the W and Z should be massless like the photon (γ) and the gluon (g) of the strong force. However we know experimentally that these particles have mass, so some mechanism must be breaking the symmetry of the SM around ~ 250 GeV in the following way SU(3) H SU(2) H UY(1) SU(3) H Uew(1). (2) Here SU(3) is a group that dictates the structure of the strong interaction known as Quantum Chromodynamics (QCD) that binds the quarks into the protons and neutrons. The Uew(1) corresponds to the symmetry that dictates the theory of electrically charged particles interacting with the photon. The SM comes with a hypothesis as to how this symmetry breaking occurs called the Higgs mechanism. It is named the Higgs mechanism even though Peter Higgs introduced the mechanism whereby a symmetry can spontaneously break giving mass to particles along with Brout, Englert, Guralnik, Hagen and Kibble [1]. The Higgs-Brout-Englert-Guralnik-HagenKibble mechanism is too much of a mouthful. It is a very simple idea. One writes a potential for the Higgs field (h) where the energy of the field is minimized when the symmetry is broken. Expanding the field around the value that corresponds to the minimum in energy, the vacuum expectation value v, the potential is very simple V (h) = 2 λ 2 h − v2 ) . ( 4! (3) The vacuum expectation value of the Higgs breaks the SM symmetry in the right way and gives the W and Z their masses through their couplings g1, g2 to the Higgs field g 2 v2 M = 2 , 4 2 W M 2 Z (g = 2 1 + g 22 ) v 2 4 . (4) The mass matrices for the quarks and charged leptons are also generated through couplings to the Higgs field. Is this how reality works? LHC should answer this question. We think that the Higgs hypothesis is right as we have already seen indirect signs of the Higgs in particle physics experiments. One can infer the mass of the Higgs through its “loop effects” on many measurements we have made over the years. By “loop” one means that this is the contribution where the Higgs is a quantum or virtual particle. For example, consider measuring the potential between an electron and a positron through a scattering experiment e+ eG γ, Z e+ eG. (5) In this experiment, one would measure the effect of γ exchanges, but one would also be sensitive to the effect of a Z exchange if the experiment was properly designed. The sensitivity to the effects of the Higgs mass enters in the following way: when the e+ eG pair smash into one another they can annihilate and emit a Z, the Z can then spit into a Z, h pair and then the Z, h pair turn back into Z before it decays back into a e+ eG pair. Particle physicists have measured many experimental signatures of the Higgs over the last twenty years. A small subset of some of these observations is given in the following Table. Source AAAS Fig. 2 Some of these observables have obvious definitions such as the MW and MZ being the mass of the W and Z boson and the Γi are the inverse lifetimes of Z bosons decaying into the final states given by i = hadrons (had) or lepton pairs (+ G). (See [2,3] for the definition of all the observables.) The theory predictions [2,3] of the Table are obtained with a Higgs mass of The elementary particles of the SM. 116 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) mh = 96+29 G24GeV. (6) THE EARLY LHC ERA (TROTT)AA very rare, it only happens about one in a thousand times when a Higgs is made at LHC, which is itself a rare event. We expect it to take approximately three years at LHC to find the Higgs in this way. What will all the particle theorists and experimentalists be doing in the meantime as they wait for the Higgs? We expect to find other particles before the Higgs is discovered. Why is this? DEFICIENCIES OF THE SM If one sets the Higgs mass to zero or takes it to infinity naively one cannot reproduce this set of measurements. However, there are some reasons to have concerns about this evidence. The two most precise measurements from which we infer the Higgs mass are not in good agreement, differing by ~ 3 σ. Retaining both of these measurements in a global fit increases the value of the Higgs mass so that there is less tension with the direct search bound of mh > 114 GeV from LEPII [4]. On the other hand, it is not surprising that some data has a significant deviation from a mean value and the quality of the fit in the SM is not obviously indicating a breakdown of the theory [2,3]. At this point, it seems likely that the SM Higgs, if it exists, will be found at LHC through TeV collisions of the gluons that bind the quarks together in the proton. If this is correct and if we have collisions (and we do, see Fig 1) why hasn’t the discovery of the Higgs boson been announced? DISCOVERING THE HIGGS The problem is that to find direct evidence for the Higgs one needs have the Higgs decay into a final state that can be experimentally measured at LHC and provide a resonance peak. This is not easy! In making the Higgs in a collision at LHC, hundreds of other particles are made in the same collision. This is the main difficulty of LHC physics. The backgrounds of other (mostly QCD) processes as the protons collide are enormous compared to the rare physics events that we are interested in. The dominant decays of a light Higgs are into b,⎯b, however, the QCD background production of b,⎯b is a factor of 107 higher at LHC than Higgs production of b,⎯b. It is not possible to pick out the one signal event from the 10 million b⎯b background events. Some decays of the Higgs can be seen over the SM background. For a light Higgs the hopes rest with the process gg h γ γ. (7) There is a large background (10 C 100 times larger than the signal) to this process as well, but it is composed of non-resonant [5] processes that give a linearly falling background while the discovery signal is a (small!) resonance peak. We believe that we will be able to find the Higgs by finding this small peak. Unfortunately, this particular decay mode of the Higgs is Despite the successes of the SM, theorists believe that it is incomplete in its description of reality at energies $ TeV. The SM alone affords no mechanism for the origin of the matterantimatter asymmetry we observe, supplies no dark matter candidate, and is silent on the cosmological constant problem. Some of these problems will be discussed in other review articles. These problems all demand solutions and some might be associated with the ~ TeV energies that we will reach at the LHC. Let us focus on a problem that is most likely to be associated with ~ TeV energies and stems from the curious nature of the Higgs known as the Hierarchy problem. When we consider the loop corrections to the bare Higgs mass (mh2 ) bare due to the other SM particles (that must couple to the Higgs if it is the origin of their mass), the results are troubling. We find that the effective mass is mh2 = ( mh2 ) bare + λ 2 3 yt2 2 Λ − 2 Λ ... 8π 2 8π (8) where λ was introduced in Eqn. 3 and we have used an energy cut off Λ $ TeV to cut off some integrals. yt is the strength of the coupling of the Higgs to the top quark. This means that what we measure for the Higgs mass is sensitive to physics at higher energies. If no physics besides the Higgs exists to be found at LHC (or higher energy scales than LHC will probe) then this implies that a light Higgs in agreement with observations to date requires that a spectacular cancellation is built into the theory. The (mh2 ) bare term and the sum of the corrections must cancel to 1028 decimal places when Λ ~ 1016 GeV to measure a Higgs mass ~ 100 GeV. This seems unlikely and many particle theorists believe that this implies there is more physics to find at LHC if the Higgs exists. This issues with the perturbative corrections to the Higgs mass and potential gets to the heart of the one aspect of the SM that is quite suspicious. The symmetry breaking in the SM is chosen to occur through the form of the potential in Eqn. (3). The corrections to the Higgs mass illustrate why we need a better mechanism. Nature might not choose a Higgs potential of the form that we have chosen, in fact the Higgs might not exist! If we do find a Higgs, these problems imply that we should find evidence of other physics that removes the need to have this spectacular cancelation in the Higgs mass. Let us consider approaches to solving this problem and some discovery possibilities in the early LHC era. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 117 THE EARLY LHC ERA (TROTT) LOWERING THE CUT OFF SCALE One way to solve the Hierarchy problem, is to lower the cut off scale of the theory, the λ of Eqn. (8) to ~ TeV. Then no spectacular cancelations are required. This can be accomplished if a new strong interaction exists and the Higgs is one of many new particles to be found along with new strong forces. By strong here we mean inter-particle forces that lead to a breakdown of perturbation theory at energies around ~ TeV. If a new strong interaction exists, we expect that many new states will exist and be produced in large numbers and spectacular deviations from the SM predictions at LHC will likely be seen in the early LHC era. SUPERSYMMETRY If no new strong interaction exists, the key to solving the hierarchy problem might lie in determining a symmetry to stabilize the Higgs mass against “loop” corrections. A popular symmetry of this form is Supersymmetry (SUSY), a spacetime symmetry that associates the spin zero Higgs field h with a spin 1/2 fermion field. SUSY uses a protecting symmetry that we know actually exists in nature for the fermions of the SM, chiral symmetry, to forbid a mass for the Higgs. In quantum mechanics a symmetry requires a conserved charge: in the case of SUSY this implies the existence of a conserved vector charge, and a powerful mathematical theorem [6] forbids any vector charges in the theory besides the vector built out of the total energy and momentum. Thus if SUSY exists in nature then all of the known particles in the SM must have Superpartners. If this were the case then the contributions to the Higgs mass from a SUSY+SM theory would be proportional to the mass splittings between the SM particles and their Super-partner, 2 C m2 δmh2 α mSM SUSY . (9) If the Super-partners can be found at LHC then this mass splitting is between energies ~ 100 GeV and ~ 1 TeV. This is much less tuning on the Higgs mass and can solve the Hierarchy problem. A solution to the hierarchy problem of this form is familiar to the prediction and discovery of antimatter. To construct a consistent theory with the symmetry required due to Einstein’s theory of Special Relativity, one had to introduce an anti-particle for every particle. The hopes for confirming SUSY at LHC lie with the partners of the gluon, the gluino g̃ or a quark partner, a squark q̃ being produced in the collisions at LHC. Estimates of how long such a discovery would take at LHC vary wildly as the super-partner masses are unknown. However, it is possible (and exciting) that a discovery of this form could occur before the Higgs is found in the first couple of years at HC. SUMMARY Particle physicists have invested an enormous amount of time and effort in building the LHC. They have compelling and exciting reasons to believe that LHC will reveal the nature of the symmetry breaking of the SM, and some supporting evidence that a Higgs particle will be discovered at LHC. It is also likely that other particles will also be made at LHC and that the LHC era will be remembered for fundamental discoveries about the nature of reality. Physicists at the Perimeter Institute will be deeply involved in the unravelling of these mysteries and are looking forward to the rest of the LHC era. ACKNOWLEDGEMENTS Research at the Perimeter Institute is supported in part by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. REFERENCES 1. 2. 3. 4. 5. 6. Englert, F. and Brout, R., Phys. Rev. Lett. 13: 321-3 (1964); Guralnik, G.S., Hagen, C.R. and Kibble, T.W.B., Phys. Rev. Lett. 13: 5857 (1964); Higgs, P.W., Phys. Rev. Lett. 13: 508-9 (1964); Higgs, P.W., Phys. Lett. 12: 132-3 (1964a). C. Amsler et al. (PDG), Physics Letters B667, 1 (2008). J. Erler, P. Langacker, S. Munir and E.R. Pena, JHEP 0908, 017 (2009). LEP Electroweak Working Group, http://lepewwg.web.cern.ch. D. Rainwater, arXiv:hep-ph/0702124. S.R. Coleman and J. Mandula, Phys. Rev. 159 (1967) 1251. 118 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE THE GEOMETRY OF TREES FREDDY CACHAZO BY THE S-MATRIX n 1937, J.A. Wheeler introduced the concept of the Scattering or S-matrix and in 1942 Heisenberg proposed to use it as a way to describe particle physics. The Scattering matrix encodes the information needed to compute the probability of a certain outcome given a particular set of incoming particles. One of the beautiful properties of quantum mechanical systems is that the S-matrix is computed using complex numbers. In particle physics, where the initial conditions are determined in terms of the four-momenta of the particles, one is naturally led to an object that is an analytic function of the initial and final data. Of course, in practice one is only interested in four-momenta which are real and thus correspond to particles used in accelerators. Each matrix element of the S-matrix is called a scattering amplitude. New methods of calculating scattering amplitudes, and what they could imply for our understanding of the underlying physics, are the subject of this article. I From the time of Rutherford scattering alpha particles against gold atoms to our modern powerful accelerators which smash subatomic particles at high energies the basic theoretical idea has been the same: to use the measurements of the outcoming particles to infer properties of short distance physics. With the Large Hadron Collider (LHC) starting operations at CERN we expect to have access to physics at distances on the order of 10n17cm. The LHC will smash protons at 14 TeV [1]. Protons are made out of quarks and gluons. The most spectacular collisions will happen when two gluons within the protons, each carrying a large fraction of the proton’s total energy, collide. Previously unseen particles are expected to be produced which will then decay into known particles. The huge CMS and ATLAS detectors will be capable of tracking and determining the properties of the final products. From these one can trace back and determine the properties of the new particles. The reader might wonder how is one supposed to know whether the interaction was the result of new physics. The answer is that one has to compute the predictions of the Standard Model [1] of particle physics, for which Glashow, Salam and Weinberg won the 1979 Nobel prize, and then find the discrepancy between the observed phenomena and the theory. Computing the predictions, also called the Standard Model background, is one motivation for finding new and efficient ways of computing scattering amplitudes. The textbook procedure for computing scattering amplitudes is very clear. One has to add up complex numbers associated with all ways of producing the final particles from the incoming ones. The rules for the allowed interactions are determined by the underlying theory, in this case the Standard Model. These are called the Feynman rules 1 of the theory and can be represented using diagrams called Feynman diagrams. The rules also give the complex number associated to each diagram. At leading order in perturbation theory, the diagrams are called Tree diagrams (see Figure 1). As mentioned, the scattering of two gluons into several gluons is of particular interest for the LHC. Gluons are massless particles which come in 8 H 2 = 16 different types. In the previous formula, 8 represents the so-called color charge while the 2 represents the helicity, which can be (±1). Unlike photons, which do not carry electric charge, gluons can interact among themselves because of their color charge! The part of the Standard Model which governs the interactions of gluons among themselves is called Quantum chromodynamics (or QCD) [2]. As usual in physics, computations and often the final answer can be simplified depending on the variables chosen. To encode the data of the initial and final gluons, the Fig. 1 SUMMARY Collisions of gluons, happening at the core of hadron colliders, have beautiful descriptions in terms of abstract mathematical spaces called Grassmannians. F. Cachazo <fcachazo@ perimeterinstitute.ca>, Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo ON N2L 2Y5 The Feynman rules for gluons tell us that they can only interact through cubic and quartic vertices. At leading order in perturbation theory, the diagrams are called Tree diagrams. Some of them are shown in the figure. 1. These rules can be formally derived by using Quantum Field Theory, but this is beyond the scope of this article. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 119 THE GEOMETRY OF TREES (CACHAZO) textbook recipe uses momenta pμ, which are null vectors for gluons, and polarization vectors εμ for each particle. With these variables the scattering amplitudes can be very lengthy and quickly get out of hand even with modern computers. A simple transformation, done using the three Pauli matrices and the identity matrix to form a four-vector σμ, which converts pμ into a 2 H 2 matrix pμσμ gives rise to a dramatic simplification. Each particle is now described by a pair of Weyl spinors which are nothing but two-component objects whose entries are complex numbers. All amplitudes become functions of the Lorentz invariant inner products of such spinors which are denoted by +i, j, for particles i and j. In the 1980’s, Parke and Taylor [3] wrote down a shockingly simple proposal for the scattering amplitude of two (+1) gluons, say particles 1 and 2, into any number of (+1) gluons, particles 3, . . ., n. The answer is given by a sum of terms of the form 3 1, 2 2, 3 3, 4 4, 5 5, 6 6, 7 ... n − 1, n n,1 (1) weighted by a factor that accounts for the color charge of the gluons participating in the interaction. This proposal was later proven by Berends and Giele [4]. Unfortunately, the simplicity observed by Parke and Taylor was not generalizable to other amplitudes and this particular set of amplitudes was considered to be very special. This point of view changed radically with the discovery of new methods, some of them inspired by a string theory living in twistor space constructed by Edward Witten in 2003 [5]. Some of these methods are the Cachazo-Svrcek-Witten (CSW) diagram expansion of amplitudes, where all scattering amplitudes are built using Parke-Taylor amplitudes as building blocks, and the Britto-Cachazo-Feng-Witten (BCFW) recursion relations [5], where scattering amplitudes of many particles are built out of those of a smaller number of particles. These new techniques, together with powerful methods developed in the past two decades, have been implemented in a very efficient computer code called BlackHat [6] which has been used to compute interesting Standard Model backgrounds for hadron colliders like the Tevatron at Fermilab and the LHC. In physics, it is often the case that when the results of computations are much simpler than expected then there is some principle or symmetry that has been missed. At the very least there is usually an alternative formulation of the theory where the simplicity is more manifest. Putting together all the clues coming from the different techniques in order to find the new formulation is a very fascinating challenge. Finding new formulations of the same theory is useful because one such formulation might be the springboard for the next breakthrough in our understanding of nature. A classic example is the Hamiltonian or Lagrangian formulation and the least action principle of Newton’s equations. TWISTOR SPACE One could say that this might have been the motivation for Roger Penrose to introduce Twistor space in 1967 as a new arena for the formulation of physical theories meant to replace space-time [7]. Twistor space takes as fundamental objects the paths followed by massless particles in space-time. Each such path is represented by a point in twistor space. The idea was that perhaps quantization in this new space would be the natural springboard for a theory of quantum gravity. Penrose was also very driven by the power of complex analysis. A problem with this was that the space of null rays is five dimensional (called PN) and thus does not admit a complex variable description (which requires an even number of real dimensions). The solution Penrose gave was beautifully physical: null rays are the trajectories of massless particles of helicity zero. If particles with non-zero helicity, say ±1/2, are considered then the solution to the wave equations can be nicely encoded into a six dimensional space which is chopped into two halves by PN. The two halves are called PT+ and PTn. Depending on the sign of the helicity, the particle is described by a point in PT+ or PTn. It turns out that the total space PNcPT+cPTn is a very familiar space for mathematicians: it is CP 3, a complex projective space, i.e., the space of complex lines in C4. As part of the twistor programme, scattering amplitudes were modeled using a construction called twistor diagrams. These diagrams were meant to encode the scattering information as multidimensional contour integrals. A puzzling fact was that, somehow, twistor diagrams were encoding the information in a different way than Feynman diagrams do. Very few people kept working on twistor diagrams for this reason and also because of their mathematical complexity. One who did was Andrew Hodges, who, after working on the subject since the 70’s, proposed a surprising connection in 2004 with the BCFW construction. In 2008, the connection was made precise. It turns out that the terms in BCFW recursion relations are, in fact, twistor diagrams! TWISTOR STRING THEORY One of the well known facts about string theory is that it lives in a space-time of 9+1 dimensions. How can one even start to think about a string theory in twistor space which only has 6 real dimensions? The answer is that a special string theory called the topological B model can live on any space which satisfies a mathematical condition called the Calabi-Yau condition. It turns out that twistor space itself does not satisfy this condition but if the space is made maximally supersymmetric [5] then it meets the requirement 2. The precise construction is delicate and beyond the scope of this article. However, the implications of the theory are remarkably simple to state. 2. Supersymmetry is usually known as a symmetry that relates bosons and fermions. Likewise, if one thinks about the usual coordinates used in geometry as “bosonic” then one can add “fermionic” coordinates in order to have a superspace! 120 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) THE GEOMETRY OF TREES (CACHAZO)AA development worth mentioning for how unexpected it is. By using the AdS/CFT correspondence [2,8] and by perturbation theory arguments as well, it was found that scattering amplitudes of gluons possess a hidden symmetry! In addition to invariance under conformal transformations 3, the new symmetry is the so-called dual conformal invariance [8], which acts just like conformal transformations but on an auxiliary spacetime where the momenta of the particles are written as the difference of two “coordinates”: p μi = x μi n x μi+1 . Is there a framework where all these developments can be seen as different faces of the same object? Could such a framework be an interesting reformulation of space-time physics? Fig. 2 CSW and connected maps into twistor space from the twistor string worldsheet. The physical amplitude is obtained by mapping the twistor space objects into space time! The map in the figure is of degree 2. The basic idea is that all scattering amplitudes are best described with a two-dimensional worldsheet and are universal. In other words, the core of all scattering amplitudes is as simple as that of the Parke-Taylor amplitudes! If this is true, how can one get the complicated answers one expects when the final gluons are not all of (+1) helicity? In fact, one expects amplitudes to get more and more complicated the larger the number of (n1) helicity gluons in the final state. Let us denote the number of (n1) gluons in the final state by m. Witten conjectured that all the complication comes from the way the core interaction is mapped into twistor space and furthermore in the mapping from twistor space into spacetime. The ways to map a sphere into twistor space are classified by their degree. For example, if f (z) = z2 is a mapping from the complex numbers to themselves we say that such a map has degree 2. The reason is that a generic point on the image, yo, comes from 2 points in the domain, for if f (zo ) is equal to yo so is f (nzo ). Witten argued that scattering amplitudes with a given m are obtained by using a map of degree m + 1. Clearly, the Parke-Taylor formula, with m = 0, corresponds to a map of degree 1 which means that the amplitude is basically the same as the core one! This striking formulation gave rise to the CSW expansion of scattering amplitudes, where the degree m + 1, is taken to produce m + 1 degree 1 spheres in twistor space, each of them with the simplicity of the original core or equivalently the ParkeTaylor one. Another form is obtained by taking the image to be a single curve of high degree, e.g., for degree 2, a conic. This led to the Roiban-Spradlin-Volovich (RSV) connected formula. THE GRASSMANNIAN UNIFICATION The answer might come from the Arkani-Hamed-CachazoCheung-Kaplan (ACCK) Grassmannian formulation [9], where the physics of scattering amplitudes in the sector containing the scattering of two (+) gluons into k n 2 (n) gluons and the remainder (+) gluons has been conjectured to be encoded in a contour integral in the space of k-planes containing the origin of Cn. This space has a name in the mathematical literature: it is called the Grassmannian G(k,n). Here n is the total number of particles. A k-plane in Cn can be specified by a matrix made out of k vectors in Cn. Let such a matrix be denoted by C. Then it is proposed that all the information needed for computing the amplitude is contained in Lk , n = ∫ k d k × nCαa δ4 4 ( CαaWa ) ∏ n ∏ i =1 ( i, i + 1, ... , i + k − 1) α =1 where Wa are points in super-(dual)-twistor space 4 which encode the data of the particles involved in the interaction and Fig. 3 We have mentioned several different constructions developed since 2004, which have led to ways of computing the amplitudes of gluons in simpler forms. There is one more recent Unification of Formulations. Center: The Grassmannian integral Lk,n . Top left: RSV. Top right: CSW. Middle left: Twistor Diagrams. Middle right: Polygon of momenta for Dual Conformal Invariance. Bottom: Feynman diagrams. 3. These are nothing but the familiar translations, rotations and Lorentz boosts together with dilations and inversions which act on space-time coordinates as xμ a xμ and xμ xμ/x2, respectively. 4. Here we are using supersymmetry in the form of super-twistors simply as a bookkeeping device but at tree-level, which is the main focus of this article, everything can be done completely within QCD! PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 121 THE GEOMETRY OF TREES (CACHAZO) (i, i + 1, . . . , i + kn1) is the k H k minor of the matrix C made out of columns i through i + k n 1. there is a single relation among the residues of a given function, in the multidimensional case there are many. Scattering amplitudes are determined by purely combinatorial data. For example, for n = 7 and k = 3 one finds the amplitude to be These relations among the residues of Lk,n , which stem from the topology of the Grassmannian, have been shown to be equivalent to relations which follow from space-time locality. An even more surprising application of the global residue theorem, as it is called, is the “duality” between Lk,n and the Grassmannian formulation of CSW and the RSV formulation. Noting that the residues of Lk,n contain all possible objects constructed from BCFW recursion relations and hence twistor diagrams, we can conclude that Lk,n leads to a unification of all known formulations! (1)[(2) + (4) + (6)] + (3)[(4) + (6)] + (5)(6) (2) where (i)( j) implies that minors starting with i and j vanish. This defines an algebraic variety in the Grassmannian and a residue can be associated with it. The form of Lk,n makes conformal invariance manifest. A Fourier transform and a simple linear algebra argument show that all residues computed using Lk,n are also dual conformal invariant. In physics we are familiar with the power of the one dimensional residue theorem or Cauchy’s theorem. It turns out that the generalization to more complex variables is even more powerful in the sense that while in the one-dimensional case ACKNOWLEDGEMENTS Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. The author also acknowledges further support provided by an NSERC Discovery grant and by an Early Researcher Award from the Province of Ontario. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. M. Trott, “The Early LHC Era”, in this issue. A. Buchel, R.C. Myers and A. Sinha, “Quark Soup: Applied Superstring Theory”, in this issue. S. Parke and T. Taylor, Phys. Rev. Lett. 56 2459 (1986). F.A. Berends and W.T. Giele, Nucl. Phys. B306 759 (1988). Reviews: F. Cachazo and P. Svrcek, PoSRTN2005:004,2005, hep-th/0504194, Z. Bern, L. Dixon and D. Kosower, AnnalsPhys. 322:1587-1634, 2007, [arXiv:0704.2798 [hep-ph]]. C.F. Berger et al., Phys. Rev. D78, 036003 (2008) [arXiv:0803.4180 [hep-ph]]. S. Huggett and K. Tod, “An Introduction to Twistor Theory”, CPU 1994, LMS. For a review see: L.F. Alday and R. Roiban, Acta Phys. Polon. B39, 2979 (2008). arXiv:0807.1889 N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, arXiv:0907.5418 [hep-th]. 122 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) FEATURE ARTICLE QUARK SOUP: APPLIED SUPERSTRING THEORY BY ALEX BUCHEL, ROBERT C. MYERS AND ANINDA SINHA M any string theorists are excited about recent experiments at the Brookhaven National Laboratory (BNL) on Long Island. Upon visiting, you would find that the BNL site is dominated by a particle accelerator running almost four kilometers in circumference, known as the Relativistic Heavy Ion Collider or RHIC, for short. In experiments at RHIC, gold nuclei are collided together with energies of up to 1011 electron-volts per nucleon n recall that each gold nucleus contains 79 protons and 118 neutrons, for a total of 197 nucleons. Each such collision produces a spectacular “explosion” sending literally thousands of subatomic particles out through the detectors enclosing the collision points (see Figure 1). The initial stages of these explosions recreate extreme high temperatures such as may have been found in the very early universe [1]. With the experiments at RHIC, physicists are seeking to better understand quantum chromodynamics (QCD), the theory of the “strong force” determining the physical properties of nuclear matter. At a superficial level, QCD looks like a simple matrix-extension of the more familiar electromagnetism. The force carriers, known as gluons, can be thought of as 3-by-3 matrix-valued photons while the charged matter, known as quarks, can be seen as 3-component vector-valued electrons. However, unlike electromagnetism, quantum fluctuations of the QCD fields play an essential role in determining the force law. In particular, at low energies or large distances (by the standards of subatomic physics), the coupling of QCD is large and SUMMARY It is believed that in the first few microseconds after the Big Bang, our universe was dominated by a strongly interacting phase of nuclear matter at extreme temperatures. An impressive experimental program at the Brookhaven National Laboratory on Long Island has been studying the properties of this nuclear plasma with some rather surprising results. We outline how there may be a deep connection between extradimensional gravity of String Theory and the fundamental theories of subatomic particles can solve the mystery of the near-ideal fluid properties of the strongly coupled nuclear plasma. Fig. 1 A high energy collision of gold ions at RHIC as seen by the Solenoidal Tracker at RHIC (STAR) detector. Each radial line indicates the path of a subatomic particle emerging from the collision. the forces are “strong”, as implied by the original name. This is exemplified by the fact that amongst thousands of particle tracks in Figure 1, not a single one corresponds to an individual quark. Rather the long-range force between quarks is so strong that they become “confined” and any experimental detectors only ever see QCD-neutral packages known as hadrons, e.g., protons and neutrons. However, in the opposite regime of very high energies or short distances, the QCD coupling becomes small and correspondingly the forces are weak. This property, known as asymptotic freedom, allows us to detect quarks and gluons, for example, inside the proton with high energy collisions at the Large Hadron Collider. Because of the strong coupling, our understanding of many aspects of QCD remains incomplete. For example, while it has now been more than thirty-five years since the discovery of asymptotic freedom (and five years since a Nobel prize was awarded to Gross, Politzer and Wilczek for its discovery), a complete theoretical understanding of confinement remains elusive. Of course, great progress has been made on various theoretical fronts. One idea was to study QCD away from its ground state. In particular, asymptotic freedom indicates interactions are weaker at short distances and high energies and so one might expect PHYSICS IN A. Buchel <abuchel@ perimeterinstitute.ca>, University of Western Ontario, and Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo ON N2L 2Y5 R.C. Myers, Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo ON N2L 2Y5 and A. Sinha, Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo ON N2L 2Y5 CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 123 QUARK SOUP ... (BUCHEL ET AL.) THE ADS/CFT CORRESPONDENCE In the 1990’s, it was realized that string theory is much more than just a theory of strings. In particular, it also contains heavy extended objects known as D-branes. In general, Dp-branes can be visualized as membrane-like objects, extended in p (spatial) dimensions, on which open strings can end (see Figure 3). Two important parameters which characterize both the strings and the D-branes are the string coupling constant gs and the string length scale s. The string coupling controls the strength of interactions of the (open and closed) strings amongst themselves and with D-branes. The string scale fixes the (rest) energy of typical excited string states as E0 ~ c / s. Fig. 2 Phase diagram of QCD according to theorists. The red arrows show caricatures of the evolution of matter in typical RHIC collisions. to find new behaviour in QCD at high densities and/or high temperatures. With this in mind, theorists mapped out the phase diagram of QCD illustrated in Figure 2. As illustrated by the red arrows in the Figure 2, the RHIC experiments are probing new regions of this phase diagram. As indicated, the collisions raise the temperature to roughly 2 H 1012 degrees Kelvin. In fact, the experiments have discovered that a surprising new phase of nuclear matter, called the strongly coupled Quark-Gluon Plasma (sQGP), emerges in this regime. In this phase, quarks (and gluons) are neither confined nor free but instead form a strongly interacting “soup”, which seems to behave like a near perfect fluid. Of course, the plasma expands (i.e., it “explodes”) and cools down again to a temperature where the quarks are again confined into hadrons which then escape out into the detectors. A precise interpretation of the RHIC experiments calls for a quantitative understanding of both strong coupling and dynamical properties of QCD. This presents a substantial challenge as few (if any) techniques exist to calculate in this regime. At this point, the reader may well be wondering what any of this has to do with superstring theory, which appears in our title. Quite surprisingly, it turns out a great deal! In a parallel set of developments, string theorists have been uncovering deep connections between gravity and strongly coupled nonabelian gauge theories (i.e., a broad class of the field theories with “matrix” structure similar to QCD). Broadly these connections are known as gauge/gravity dualities and the best understood example of such a duality is the AdS/CFT correspondence [2]. These dualities realize a holographic description of quantum gravity in which the theory has an equivalent formulation in terms of a non-gravitational theory in a spacetime with fewer dimensions. In this framework, one can study the gauge theory at strong coupling with simple calculations in classical gravity, as we will explain below. Fig. 3 D-branes are “solitonic” objects of string theory. D-branes have different descriptions, depending on where in “parameter space” we are calculating. For example, consider the low energy limit of N D3-branes sitting on top of each other, i.e., consider only processes at energies E n c / s. This physics is dominated by the massless open string excitations on the D3-branes, which it turns out can be described by a nonabelian gauge theory. This four-dimensional theory is known as N = 4 super-Yang-Mills (SYM) theory with gauge group SU(N). The matrix structure of the gauge fields, e.g., (Aμ ) i,j with i, j = 1, . . . , N, can be visualized as labeling on which D-brane the corresponding open string begins and ends. Further, the string coupling is simply related to the coupling constant of the gauge theory with g Y2 M = 4π gs. Another interesting regime to consider is the strong coupling limit. One finds that the gravitational field of N coincident D3-branes is proportional to gs N. Hence if we consider a limit where gs N becomes large, we cannot ignore how branes deform the spacetime geometry. One finds that the geometry near the D3-branes takes the form of AdS5 H S 5. The first part here is five-dimensional anti-de Sitter (AdS) space, a homogenous spacetime with fixed negative curvature. The second factor is a five-dimensional sphere. The radius of curvature for both the AdS and the sphere is given by 124 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) QUARK SOUP ... (BUCHEL ET AL.)AA R4 = 4πg s N = gY2 M N . 4s (1) In 1997, Maldacena realized that if the low energy and strong coupling limits were applied one after the other, two radically different pictures emerged depending on the order of limits, as shown in Figure 4. However, his bold conjecture was that these two pictures should still describe the same physics. Hence the AdS/CFT correspondence proposes that the four-dimensional N = 4 SYM theory at strong coupling should be equivalent to ten-dimensional superstring theory on the AdS5 H S 5 background. While this equivalence remains a conjecture, it has survived the scrutiny of hundreds of tests since it was discovered. Fig. 4 Well, so far the comparison seems hopeless then. However, we are really interested in QCD at finite temperature. The sQGP phase appears just beyond the critical temperature below which the theory becomes confining. For the SYM theory, a finite temperature breaks supersymmetry and introduces an energy scale in the theory (the temperature). Hence in this regime, both systems contain strongly coupled plasmas of gluons and various matter fields. Further we emphasize that we would like to model these plasmas with fluid dynamics and so we only care about long wavelength phenomena and not the microscopic dynamics. Therefore, it is very useful to have any model of a strongly coupled gauge theory plasma for which we can do analytic calculations. “Derivation” of the AdS/CFT correspondence. The correspondence becomes simpler upon refining the limits further. First, if we keep the curvature scale larger than the string scale, i.e., R / s o 1, then stringy corrections to the geometric side of the duality are minimized. In this regime, we may work with low energy gravity alone (rather than the full string theory). Similarly if the string coupling is kept small, i.e., gs n 1, the quantum corrections in the gravitational physics are also minimized. Hence this part of the correspondence reduces to classical gravity. Given the relation of the SYM and string couplings, one might worry that the latter limit yields a trivial gauge theory. However, comparing with eq. (1), we see that maintaining the first inequality above requires N →∞, λ≡g 2 YM N 1. index. In contrast, the matter sector of SYM contains fermions and scalars, both of which transform in the adjoint representation, i.e., they carry a pair of indices like the gluons. With these extra fields, the gauge theory becomes supersymmetric (the “S” in SYM) with a precise match of the bosonic and fermionic degrees of freedom. We should also note that four-dimensional gauge theories are Conformal Field Theories (CFT) classically, in that they do not have any intrinsic length or energy scale. However, this property is typically lost in the quantum theory. For example, QCD produces a dynamical scale which is related to the confining process. In contrast, the supersymmetry of SYM protects the conformal symmetry so that it remains a CFT even as a quantum theory. How do we calculate properties of the SYM plasma that we can then compare with the sQGP? First, we need to introduce a finite temperature into the AdS/CFT correspondence. It turns out that this corresponds to putting a black hole in AdS5 spacetime. The gauge theory temperature T then corresponds to that of the Hawking radiation emitted by the horizon. We might then use this new gravity background to calculate any of a number of properties of the dual plasma but we focus here on one in particular, the shear viscosity. In any field theory, the shear viscosity can be determined using the so-called Kubo formula η = lim ω→ 0 (2) This limit (2) is well-known in gauge theories as the 't Hooft limit, where N is taken to infinity while keeping λ fixed. Therefore, in the limit of classical gravity, the dual gauge theory has become strongly coupled in λ. CONNECTING SYM AND THE SQGP So what do we have here so far? Well, we have uncovered a remarkable new method to study the N = 4 SYM theory in the 't Hooft limit (2). However, the goal given in the introduction was to study QCD. Unfortunately, SYM is very different from QCD. In QCD, the gauge group is SU(3), i.e., N = 3, while we wish to work in the limit of large N in the SU(N) SYM theory. Further the quarks of QCD are fermions transforming in the fundamental representation, i.e., they carry a single SU(3) 1 dt d 3 x eiωt ⎡⎣Txy ( t , x ) , Txy ( 0, 0 ) ⎤⎦ . ∫ 2ω (3) The last factor in this expression is a certain correlation function of the gauge theory’s stress-energy tensor. While it is next to impossible to calculate this correlator in the gauge theory at strong coupling and finite temperature, the AdS/CFT correspondence translates this factor to a Green’s function for gravity waves in the AdS black hole. The dissipative nature of the viscosity then comes from the absorption of the gravity waves by the black hole’s event horizon. From this gravity calculation, the value of the shear viscosity of the N = 4 SYM plasma is found to be π (4) η = N 2T 3 . 8 Given the factor of N 2, the viscosity seems to be very large but one must ask: “Large compared to what?” It turns out that the natural quantity with which to make a comparison is the entropy density of the plasma. Again, the gravity theory yields PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 125 QUARK SOUP ... (BUCHEL ET AL.) a simple answer for this quantity, namely, Hawking’s black hole entropy proportional to the area of the horizon. Combining this geometric entropy with eq. (4), one finds the elegant but surprising result [3] η / s = 1/4π ~ 0.08. (5) In fact the latter is much smaller than for any material tested in the laboratory until very recently! Preliminary investigations of the experimental data from RHIC already indicated that the sQGP had an unusually low viscosity. Determining a precise value of the viscosity in the sQGP continues to be a topic of intense study and recent investigations indicate that η / s ~ 0.08 to 0.16. This unexpected (near) agreement for the viscosity combined with a lack of alternative theoretical tools to study the real-time strongly coupled dynamics of the sQGP has stimulated tremendous activity in calculating different thermal properties of strongly coupled non-abelian plasmas using the AdS/CFT correspondence. There have also been a variety of other calculations including: studying the effects of a chemical potential, investigating spectral functions, calculating the multiplicity of particles produced in collisions, examining the diffusion of heavy quarks, studying “jet quenching” and calculating the photon emission rate of the plasma, as well as extensions of this analysis to non-conformal field theories with gravity duals. To conclude then, theorists face many new challenges in developing a physical understanding of the recently discovered strongly coupled Quark-Gluon Plasma. The AdS/CFT correspondence which emerged from string theory as a new analytic tool to study certain gauge theories, e.g., N = 4 SYM, may be well-suited for this purpose. Although these holographic gauge theories differ from QCD in many details, at finite temperature, they seem to share certain features in common with the sQGP. Hence gravitational calculations are being used to gain insight into this new phase of QCD as the implications of this remarkable correspondence continue to be explored. At the same time, experimentalists are preparing to explore a new frontier with heavy ion collisions with approximately 5 H 1012 eV/nucleon at the Large Hadron Collider. Thus we can expect to see new surprises coming from both theory and experiment in the near future. ACKNOWLEDGEMENTS Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research & Innovation. AB acknowledges further support by an NSERC Discovery grant and by an Early Researcher Award from the Province of Ontario. RCM also acknowledges support from an NSERC Discovery grant and from the Canadian Institute for Advanced Research. REFERENCES 1. 2. 3. M. Riordan and W.A. Zajc, “The first few microseconds”, Sci. Am., May 2006. J.M. Maldacena, “The illusion of gravity”, Sci. Am., November 2005. S.K. Blau, “A String-Theory Calculation of Viscosity Could Have Surprising Applications”, Phys. Today, May 2005. 126 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) PHYSICS EDUCATION PERIMETER SCHOLARS INTERNATIONAL BY JOHN BERLINSKY T he idea is really simple. Top physics undergraduates from around the world are recruited into a one-year coursework Master’s program of the University of Waterloo. Students are fully supported. They are flown to Canada, housed and fed together, and take courses and tutorials at Perimeter every day. The courses are very special – taught daily in 3-week modules, two or three at a time, by top lecturers recruited from leading institutions around the world and captured on video for everyone to see. PI’s Director, Neil Turok, arrived in Waterloo in the fall of 2008 with the idea for PSI almost completely formulated. In November 2008 he recruited me to turn this idea into reality. He had already enlisted the University of Waterloo as a partner in PSI and had the assistance of Jamie Forrest, Director of the Guelph-Waterloo Physics Institute, to obtain approval of the PSI curriculum. Many lecturers had already been recruited, and a very high-tech web site was under construction. Among my first duties was approving web site design and content, which was a bit of a stretch, since my only previous experience with web sites had been navigating them. The site itself (www.perimeter scholars.org), with flash videos of Stephen Hawking, Neil, post-docs, and students, is truly awesome. I jumped in without hesitation and by January 2009 was seconded to PSI from McMaster for three days per week. Applications came pouring in from January into March. We received a total of 220, and with the help of a small, but dedicated, international admissions team, quickly surpassed our quota of 25. In the end, 28 students were admitted representing 16 countries, from Canada and the US to Cameroon, Vietnam and Cuba. One inescapable aspect of an international school is that English is not the first language of many students. Of course, physics students tend to be trained in English as well as physics and math, but they may have had limited opportunity to practice their language skills. PSI undertook to provide extra ESL training for PSI students who needed or wanted it, before the start of term in midAugust. This exposed us to another of the inescapable aspects of international education – visa problems. Three of the six students slated to take ESL training arrived after the course, while one Tutor was not able to enter Canada until early September. The decision to sign on was not difficult. I was particularly attracted by the international and diversity aspects of Neil’s vision. The idea of recruiting talented physics students, young men and women from countries around the globe, was too good to pass up. Also, coming from an Ontario university where we do as best we can with very little, it was exhilarating to undertake a project for which resources were available to do what was required. PSI students and tutors relaxing after a weekend brain-storming session at a student residence. SUMMARY This year, Perimeter launched a grand experiment for graduate students in theoretical physics. Perimeter Scholars International (PSI), the brainchild of PI’s Director, Neil Turok, has its roots in earlier educational programs, including Part III of the Cambridge Math Tripos and the African Institute for Mathematical Sciences (AIMS), but there is really nothing else quite like it, and what it is is still an evolving concept. PSI students live in close proximity to Perimeter, in suites on a common corridor in a University of Waterloo residence, equipped with both kitchens and blackboards. The suites are the venue for journal clubs and study groups as well as social activities, many of which seem to involve cooking. J. Berlinsky <jberlinsky@ perimeterinstitute.ca>, McMaster University, and Director of Academic Programs, Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo ON N2L 2Y5 One novel aspect of the program is the presence of four post-doctoral level tutors who attend the lectures, organize and staff the tutorials, answer questions and grade homeworks. The photograph above shows two Tutors, Denis Dalidovich and Tibra Ali, on the left, with a group of PSI students in one of the apartments. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 127 PERIMETER SCHOLARS ... (BERLINSKY) Nima Arkani-Hamed, of the Institute for Advanced Study, who is also a Perimeter Distinguished Research Chair, giving a lecture. An informal chat between Prof. Arkani-Hamed and students over lunch, which is brought to the building where lectures are held. The Tutors are also an international group with one from the UK, one from France, one from Bangladesh, via Cambridge and the US, and one from Russia, via the US and Canada. The continuing presence of the Tutors provides the glue which holds the program together since the high-profile lecturers fly in and out on three-week cycles. For example, the Tutors routinely contact the lecturers in advance of their course to solicit course outlines, along with homework and tutorial problems. If the outline seems too ambitious or the problems too intractable the Tutors, who have experience on their side, can feed such advice back to the lecturers. Also, since the Tutors work constantly with the students, there are open channels for student feedback and opportunities to modify how things are done, which is particularly valuable in the early years of the program. Students stop by the Institute each morning for breakfast at the Black Hole Bistro and then proceed on to the old Perimeter site on King Street, where the drill is lectures in the morning, sandwiches for lunch, and tutorials in the afternoon. Lectures are given in an old classroom on the second floor of the building. Outside the classroom is a lounge with a well-used pool table, seating for lunches and discussions, a small library, and Perimeter’s signature fixtures, blackboards and espresso machines. One high-tech feature is a recording booth linked to cameras and microphones in the classroom. All lectures, including informal “visits” by well known physicists, are recorded and made available on the web (http://pirsa.org/ C09021). The philosophy of the school is to turn students into researchers, but many students are attracted by the opportunity to learn about a broad range of theoretical physics subjects before committing to a specific area of specialization for their PhDs. In the end they get both, because interacting with so many experienced physicists, with different styles and points of view allows them to see that physics is not cut and dry, but highly varied and personal. Although there are certain commonalities (different physicists will often approach standard problems in the same way) there are also deeply held differences of opinion, all offered with perfect confidence and fiercely defended. The opportunity for beginning graduate students to experience these different perspectives put forward by so many of the top leaders in their fields is something very special that PSI has to offer. The PSI curriculum is very different from a conventional graduate program. It begins with a kind of appetizer called “Research Methods”. Kari Dalnoki-Veress first sent the students out on a Monday afternoon with cameras to observe “physics in nature” and, based on what they found, each prepared a talk, introducing and explaining that physics at the end of the week. In the interim, they learned about how to write papers and how to design and construct physics demonstrations. Nima Arkani-Hamed taught them “all of theoretical physics” the following week, including, for example, the connection between quantum entanglement and the temperature of a black hole. Leo Kadanoff, who later taught Statistical Mechanics, spent a couple of weeks at the end of August meeting the students, learning about the program and preparing his lectures. He would come to lunch and sit at the back of Nima’s lectures, asking an occasional question. Core courses started in September laying a firm foundation in Relativity, Quantum Mechanics, Quantum Field Theory and Statistical Mechanics. The eight core courses were followed by a series of review courses, of which the students take six out of nine (two at a time) in specific topics such as condensed matter and string theory. Following this were a similar number of exploration courses on current hot topics, such as quantum spin systems and cosmology. There are no exams in PSI. All courses are pass/fail. The idea is to eliminate unproductive competition and studying for the exam and to encourage learning for the sake of learning, cooperative interactions among students, and the joy of discovery and understanding. This sometimes leaves the students 128 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) PERIMETER SCHOLARS ... (BERLINSKY)AA due in early June. Each student’s Essay is supervised by a faculty member from Perimeter or some nearby or far away university. Students will do research, write up their results, and present and defend their Essay before a panel of professors. Graduation is in June and students will then go off and, for the most part, pursue PhD studies – some at Perimeter, some at nearby universities, some in their home countries, and some at other institutions around the world. Leo Kadanoff, of the University of Chicago, and also a PI Distinguished Research Chair, with PSI student John Toledo. perplexed about how they are doing, which they are used to having other people tell them, rather than setting their own objectives and measuring their own progress. The closest thing to an exam that they will experience, beyond routine grading of homeworks, is the last phase of PSI, the Essay. The Essay is a short, six week research project, starting at the end of April and Right now, the second admissions cycle has just ended. This year’s class of 32 is slightly larger than before, more balanced in gender with 13 women students, and just as internationally diverse, again with 16 countries represented. We’ve learned a great deal from the first year of PSI, which will help reshape the program. Next year there will be more introductory material at the beginning, slightly fewer courses, and extra space in the schedule for review and synthesis. Next year will also be the last at the King Street site since construction of the expansion of the Perimeter Institute building will be complete for the following year, with new and larger accommodations for a PSI class of 40 to 50 students. The PSI class of 2009-10, with Tutors and several lecturers. The 28 students came from 16 countries. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 129 ENSEIGNEMENT MISSION: OUTREACH – THE WHY AND BY THE HOW OF IT JOHN MATLOCK AND GREG DICK M otivated by James Maxwell’s equations describing electromagnetic radiation, Heinrich Hertz constructed a machine that could make a spark jump between two metal prongs separated by a finger’s width. On the far side of a room he placed a single loop of wire. Heinrich carefully cut a narrow gap into his wire loop and suspended it with some string. He then energized his spark generator, which rhythmically zapped out a series of tiny sparks between the two metal prongs. Returning to the wire loop across the room, he bent down, moved in close and inspected the little gap in the wire. There it was, a tiny spark jumping from one edge to the other. Energy was traveling through the air, across the room, from his machine to the receiving wire loop. It was transmission and reception of electromagnetic energy just as Maxwell’s mathematics had predicted. The date: 1887. As the story goes, Heinrich shared the discovery with his class of University of Karlsruhe physics undergrads. After witnessing this seemingly magical transmission of energy through space, one of his students excitedly asked what John Matlock <jmatlock@ perimeterinstitute.ca>, Director of External Relations and Communications, and Greg Dick <gdick@ perimeterinstitute.ca>, General Manager of Outreach Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON N2L 2Y5 SUMMARY Theoretical physics has, and will continue to, transform society. Perimeter Institute’s three-fold outreach focus is to communicate the importance and power of theoretical research, to develop brilliant young Canadians for the field, and to serve as an international resource for outreach expertise. Perimeter’s Outreach programming and resources are designed to engage students, teachers and the general public. Share the experience by visiting www.perimeterinstitute.ca. 130 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) was next. What did the future hold for this amazing property of nature so freshly unearthed? Heinrich responded, “Nothing, I guess.” His response typifies two distinctly different, but equally profound, aspects of theoretical physics. First, the joy of chasing our universe’s many mysteries is reason enough to commit a lifetime to the task, and second, it is not immediately obvious, even to their discoverers, what transformative uses new theoretical advances may turn out to have. But as history shows, the impact will follow. RECOGNIZING THE NEED FOR SCIENTIFIC OUTREACH Sharing the mystery, splendour, and importance of scientific research is one of the cornerstones of Perimeter Institute’s mission, and has been from the outset. Content for students, teachers and the general public not only conveys cutting-edge ideas in science, but underscores the inherent power of theoretical physics and how basic research is essential to our long-term economic and social prospects as a society. The core scientific values - of curiosity, reason, creativity, critical enquiry, and the open exchange of information - can provide anyone with the skills and habits of mind needed to build a better future for themselves and others. It seems intuitive that a scientifically literate population is an advantage for any nation, and that as the world becomes more inextricably tied to technology and the science behind it, the need for aggressive, systematic outreach becomes imperative. As NASA and CERN have demonstrated, the value to society of space exploration or high energy proton-proton collisions is not immediately obvious to some, until outreach and science communication operations bridge gaps to make the research accessible. Today, both organizations produce high quality materials explaining the basic science behind their various research activities, and showcasing the large and surprising array of spin off technologies arising from them— including food preservation techniques, Velcro, fuel cells and even the Internet. The sharing of information on modern physics at PI includes this broader context. So in tandem with learning about specific theories, we hope to give audiences an appreciation of the ability of the human mind to explore the fundamental nature of the universe and how, in time, MISSION OUTREACH: ... (MATLOCK/DICK)AA the pursuit of new understanding can give rise to a wide range of benefits and potent new technologies. “I give credit to this program for giving me the selfconfidence to believe I could become a physicist and putting me on the path I am on. It showed me that there is no reason not to try.” THE PI APPROACH TO HIGH-IMPACT OUTREACH Perimeter Institute’s three-fold outreach focus is to communicate the importance and power of theoretical research, to develop brilliant young Canadians for the field, and to serve as an international resource for outreach expertise. To do so, the Institute provides a combination of - 2008 ISSYP programming and resources. Programming participant involves face-to-face interactions with PI outreach Developing youth for the field at ISSYP. staff and scientists. Resources include hands-on kits and digitized offerings. The content within individual programs and resources typically falls into one of two categories that we think of as ‘inspiration’ and ‘exploration’. Perimeter Institute also connects with teachers through a range Inspirational content opens your mind to the mysteries and of workshops that take place across the country and in our own wonders of the universe, setting the stage for research and disresearch facility. The ‘EinsteinPlus’ science camp is held at PI covery. The exploratory strand of content is much more chalevery summer to provide educators with an opportunity to lenging and provides a deep dive into abstract ideas in far more learn about the latest developments in frontier physics. Over technical and mathematical detail, providing a rigorous experithe years the program has attracted teachers from every region ence for those who are beginning to ponder the same mysteries of Canada as well as international participants from over 20 as leading physicists. countries. Teachers grapple with fundamental questions: What are the deeper insights we want our students to have? How do A small PI Outreach team creates all of the programming and we inspire students to enter the world of scientific exploration? resources by collaborating with our resident scientists, who The range of activities provides ample time for them to deepen ensure the content is accurate and cutting-edge. In the meantheir understanding of key concepts and discuss science educatime, a growing team of teachers across Canada share their tion tools and techniques with the researchers and outreach insights and expertise on the content - from inspirations to staff at PI. explorations - and assist the PI outreach team in converting the messages into pedagogically sound presentations and Given that the reach and capacity of the teacher and student resources. workshops is inherently limited by the number of events our two outreach presenters can provide plus the actual room to YOUTH AND TEACHERS accommodate participants at various locations, we began creatPerimeter Institute programming reaches youth across Canada ing and distributing educational products that offer 24/7 benethrough on-site visits and special science camps held at PI. The fits. These in-class resources, known as ‘Perimeter trips to high schools, science fairs and public festivals provide Explorations’, provide an efficient and ongoing avenue to share the inspirational content through ‘Physica Phantastica’ sesthe wonder of science. The first two modules, entitled The sions, while the deeper exploratory content is delivered Mystery of Dark Matter and The Challenge of Quantum through ‘Go Physics’ on-location workshops. PI Outreach’s Reality, are classroom-ready kits consisting of a custom prostaff, which includes two researchers turned educators with duced 30-minute DVD presentation featuring leading scienstrong backgrounds in general relativity and quantum theory, tists, and an accompanying Teacher’s Guide containing suppleprovide many of the presentations. The most interested and mentary information, student worksheets, and hands-on activiengaged youth have the opportunity to visit PI during the ties. The kits are designed to integrate into existing curricula, International Summer School for Young Physicists (ISSYP). while proving opportunities for teachers to share cutting-edge This annual science camp attracts talented high school students physics that will challenge and motivate their students. Over from across Canada and around the world to the research cen100 teachers and researchers contributed to the creation of tre in Waterloo, Ontario for an intensive, two-week program these modules, which were then classroom tested with thouthat includes lectures on Einstein’s ideas and the quantum sands of students. Designed with both expert and novice teachworld, mentorship from PI scientists, an introduction to the ers in mind, the modules are in high demand by educators. most profound unsolved puzzles of 21st century physics, and Follow-up research shows that the lessons are now reaching visits to labs such as SNOLAB. Because this camp comes at a hundreds of thousands of students year over year across time when scientifically-minded students are actively considerCanada and beyond. ing their career paths, the experience can be life-changing. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 131 MISSION OUTREACH: ... (MATLOCK/DICK) “My students love it when I go over the quantum aspect of physics and they are quite curious about it. I could never have conveyed the excitement of theoretical and quantum physics without my experiences at PI. Likewise, my modern physics presentations to the general public (teachers, parents and students of all ages) would not have been so well received.” - Julie Lemay, École Voyageur Cold Lake, AB scientific knowledge. The flagship activity is the PI Public Lecture Series, in which visiting scientists are provided with an opportunity to share their love for research with an appreciative audience. Most events sell out within 30 minutes through an online booking system, filling a 600 seat theatre to capacity. The lecturers give eloquent and accessible insights into string theory, quantm gravity, cosmology, particle physics, quantum information and other research areas. Participating scientists have included Edward Witten, Frank Wilczek, Roger Engaging with educators and building the PI Teacher Penrose, Steven Weinberg, Nima ArkaniNetwork. Hamed, Brian Greene, Lisa Randall, Gerard t’Hooft, John Ellis and may others. In addition, PI programs some lectures to include more Engaging with teachers through workshop programming and mainstream topics – ranging from digital animation techniques resources is proving to be the most effective way for PI to reach to the death of the dinosaurs – in order to draw new audiences large numbers of youth and help lead Canadian society toward in to learn about their world through a scientific lens. The an increased awareness and appreciation for the power of theevents are professionally recorded and shared with wder oretical physics. To this end, the Institute is now developing a audiences through partnering television and cable stations as potent PI Teacher Network. This group of leading high school well as on-demand viewing over PI’s website. educators, drawn mainly from our EinsteinPlus science camp alumni, now spans across Canada. Members not only provide crucial pedagogical insights as new resources and programs are developed, they workshop PI’s existing resources for fellow teachers at home during their local professional development days. Those participants then receive full kits and, in turn, deliver the information on modern physics to their students year over year. The network is also an avenue by which PI’s expertise can transfer into provincial curricula and textbooks. The overall “train-the-trainer” approach keeps PI’s student and teacher outreach efforts focused on the science and sound pedagogy, while scaling its reach and impact in partnership with like-minded educators who embrace the instruction and professionally produced materials. THE CANADIAN PUBLIC PI outreach provides separate programming for members of the general public, who consistently demonstrate their appetite for PI Public Lecture Series, putting the power of theoretical physics into the spotlight. PI’s interactions with leading scientists, its experienc in sharing abstract ideas in creative ways, and its fruitful partnerships with broadcast experts have carried one outreach project INSPIRATIONS In an effort to inspire people of all ages to the power of ideas, PI outreach member Dr. Richard Epp recently created a series of 60-second animations called Alice & Bob in Wonderland, which are available on YouTube and other video sharing sites and will soon be available in kit form for educators. Alice is a little girl brimming with curiosity, and each episode focuses on one of her questions, such as, “Why is it dark at night? What keeps us stuck to the Earth? Why can’t we walk through walls?”. Her older brother Bob defaults to quick and easy answers he has heard elsewhere, but his little sister’s unwillingness to accept superficial replies ends up challenging Bob to think “outside the box”. The cartoons are a whimsical way to awaken children and adults alike to the scientific mysteries around us. In an age where answers are generally no further away than Wikipedia, Alice & Bob focuses on where your own mind can lead you. It is a deliberate attempt to foster curiosity and critical thinking, which are, after all, the central ingredients of Alice & Bob in Wonderland, opening science. 132 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) our minds to the mysteries around us. MISSION OUTREACH: ... (MATLOCK/DICK)A into prime time. A collaborative team has managed to convey the complexities of quantum mechanics through an entertaining made-forTV documentary called The Quantum Tamers: Revealing Our Weird & Wired Future. This program for general audiences takes viewers deep inside the sewers of Vienna (the site of groundbreaking quantum teleportation experiments) and into high-tech Quantum to Cosmos Festival, top down quantum computview of one location with panel discussion, audience and TV control room in the ing labs. Over a PI Atrium, beaming big thinkers and their dozen leading sciideas across Canada. entists, including Stephen Hawking, took part in the production in order to introduce concepts such as superposition and entanglement in novel ways that include the use of animation and even dancers. The Quantum Tamers has won several important international film festival awards and is now being distributed to television networks and education groups globally. Another activity for the general public involves special events, such as the Quantum to Cosmos: Ideas for the Future festival. This activity was held in October 2009, to mark the tenth anniversary of PI, contribute to Canada’s National Science and Technology Week, and help celebrate the Inter-national Year of Astronomy. The scope and scale of events included public lectures, panel discussions, science-in-the-pub talks, cultural activities, a sci-fi film festival, an art exhibit and a hugely popular 6,000 ft2 exhibit centre filled with demonstrations, handson activities, physics experiments, an immersive 3D tour of the universe, a scale model of the next Mars rover and much more. The ten days of inspiration and exploration attracted 40,000 to the various venues in Waterloo and, through web streaming and television broadcasts, reached over 1,000,000 viewers. The impact on this large number of participants was measured through formal online polls and informal on-site feedback. We particularly enjoyed this response received from a grade 12 student who wrote to say that after visiting the festival through the school program, she and some of her peers hosted their own “Science Play Day” for grade 9 and 10 students “to simply encourage them to take science after grade 10”. INTERNATIONAL RESOURCE Although Perimeter’s outreach activities primarily benefit youth, teachers and general public audiences across Canada, there is increasing interest from international audiences with similar interests in science as well as from formal organizations wishing to learn about or even partner with PI outreach. The Institute therefore digitizes all content – from programming such as the PI Public Lecture Series, to resources such as Perimeter Explorations in-class modules – and shares it online in a simple and efficient manner. International teachers, for example, are able to download class content in return for their contact information – such that PI outreach can remain in touch and follow-up in future with specific questions. The outreach team also provides specialized presentations upon request and has provided a wide range of plenary sessions and workshops for organizations all around the world including the American Association of Physics Teachers, the Physics Teaching Resource Agents, the UK Institute of Physics, EXPLORATIONS Described by dark matter discoverer Vera Rubin as “… imaginative, artistic and scientifically valid”, the Perimeter Explorations series fulfills the number one request from high school teachers across Canada who are seeking inclass content on modern physics in a flexible, comprehensive and simple format that can be used in classroom settings. PI Outreach member Dr. Damian Pope developed the modules for senior high school grades, and chose dark matter as the subject of the first module, since it is currently one of the hottest topics in physics and the module provides teachers with tools to show how dark matter was discovered, to explain why it remains a mystery, and to share the passion of scientists who are trying to discover what it’s made of. The resources consist of a DVD featuring leading scientists, animating equations and charts, indexed chapters to stop/start as required; a teachers manual with curriculum links; student activities with hands-on demonstrations and worksheets; and an introductory article about dark matter. The DVD also contains an electronic Word version of the printed content so that teachers can tailor the handouts and questions to suit their individual classes. The in-class resource is presently available in kit form to Canadian educators and is accessible to international educators The Mystery of Dark Matter through a digital downeducational resource, sharing load. technical content in highly visual ways. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 133 MISSION OUTREACH: ... (MATLOCK/DICK) Educational Programs Physica Phantastica Go Physics International Summer School for Young Physicists EinsteinPlus Teachers Workshop Teacher Resources PI goes on location at CERN and elsewhere upon request, sharing outreach expertise with international teachers CERN Teachers Workshop, the American Association for the Advancement of Science and even a number of customized professional development events for science writers throughout the journalism community. The Mystery of Dark Matter The Challenge of Quantum Reality Planck’s Constant Activity The Physics of Innovation Public Activities PI Public Lecture Series Festivals & Special Events The Quantum Tamers THE MISSION CONTINUES Online Activities Heinrich Hertz could not have known in 1887 that the phenomena he demonstrated as a simple curiosity to his students would usher in a new era of communication by the close of the next century. In today’s day and age, PI is trying to spark audiences of all ages to the mysteries and importance of basic research – because sharing great ideas is one of the best ways to create new ones. Select programs & resources (above) What We Research The Power of Ideas Meet a Scientist Alice & Bob in Wonderland 134 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) EDUCATION CORNER E PERIMETER INSTITUTE - OUTREACH Perimeter Institute creates and distributes classroom-ready educational resources designed by teams of educators and vetted by PI researchers. The resources share cutting-edge physics in an accessible way and are used in high schools across the country. Excerpts from two different resources are provided in this Education Corner. 1. MEASURING PLANCK’S CONSTANT ǯ 2. BLACK BOX DEMONSTRATION Ǥ MEASURING PLANCK’S CONSTANT INTRODUCTION ǯ ȋȌǤ S P A C E É D U C A T I F ǯ ȋαǤ͵ͳͲǦ͵ͶȌ Ǥϐ ȋ α͵ǤͲͲͳͲͺȀȌϐ Ǥ ǯ Ǥ ǦǡǡǡǡǡǤϐ Ǥ Ǥαǡǯ Ǥ ǡ Ǥ ǡ ǯ ʹͲΨǤ Ǥ ǣ ǯ Ǥ PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 135 E DUCATION CORNER S P A C E É D U C A T I F MEASURING PLANCK’S CONSTANT STUDENT WORKSHEET AIM ǯ ȋȌǤ BACKGROUND ǦȋȌ Ǥ Ǥ Ǥ Ǥ Step 5. ͶǤ ͲǤ ȟα α αͳǤͳͲǦͳͻ οα α MATERIALS » » » » » » ͷ ͳπ ͵͵Ͳπ ͷ Step 6. ǣ CAUTION - Do not stare directly at a brightly lit LED. PROCEDURE Step 1. Ǥ Ǥ Ǧ Ǧ ǡǤ Step 2. ͵͵Ͳπ Ǥ Ǧ ȋ ǦȌǤ Step 3. Ǥ Step 4. Ǥ ANALYSIS Step 1Ǥ ȋǦȌ ȋǦȌǤ Step 2. ϐǤ ǯ ȟαǤ QUESTIONS Step 1. ǯǫ Step 2. ͷ͵Ͳ ͳǤͲǤ ǫ Step 3. ȋȌ Ǥ ǫ 136 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) EDUCATION CORNER E MEASURING PLANCK’S CONSTANT TEACHER’S NOTES » MATERIALS » » » » » » ϐ ǡǤ Ǧͳ͵ʹǡǦͳ͵ͻ͵ǡǦͳ͵ͷǡǦͳ͵͵ ǦͷͲͷͺǤ ͳπ ͵͵Ͳπ ͷ » » » » α¨ǡ ȋͳǤͳͲǦͳͻȌ¨ Ǥ αǡ ǯ ȋαǤ͵ͳͲǦ͵ͶȌǤ ¨α ¨ ȀǤ ǯ ǯ Ǥ USEFUL CONSTANTS α͵ǤͲͳͲͺȀ αͳǤͳͲǦͳͻ αǤ͵ͳͲǦ͵Ͷ EXPERIMENT SET UP CAUTIONS 1. Students should not stare directly at LEDs when they are brightly lit. ǡ Ǥ Ǧ Ǥ Ǥ Figure 1 Diagram and photo of circuit used. PURCHASING LEDS AND POTENTIOMETERS THEORY » É D U C A T I F 2. LEDs can be destroyed if the current flowing through them is too large. ͵͵Ͳȳ ϐǤ ͷͲǤ Ǥ Ǥ Ǥ ͷǤ Ǥ Ǥ » S P A C E ǦȋȌǡ Ǥ ǡ Ǥ 3. The potentiometer can be destroyed if wired incorrectly. Ǥ ǡ Ǥ Ǥ ǡ ǯ Ǥ ȋǡǡ Ǧ Ȍ e Ǥ PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 137 E DUCATION CORNER S P A C E MEASURING PLANCK’S CONSTANT TEACHER’S NOTES CONTINUED SAMPLE RESULTS É D U C A T I F ERRORS Ǧ Ǥǡ Ǥ ǡǡ Ǥ ǡ Ǥ Ǥǡ ͲǤ ǡ ǡ Ǥ STUDENT WORKSHEET ANSWERS 1. αǤͳͲǦ͵ͶͳͷΨ Ǥ 2. ǣ ANALYSIS » » » αȀαȋͲǤͳͻȌȀȋͶǤͲͳͲͳ͵Ȍα ͶǤͷͳͲǦͳͷȀ αȋͶǤͷͳͲǦͳͷȀȌȋͳǤͳͲǦͳͻȌαǤͳͲǦ͵Ͷ ͳͷΨǡ ǤͳͷǦʹͲΨ Ǥ Ǥ ϐ ǡ ȟǦͲǤͺͲǤ Ͳ ȟαǤǡȟδ Ǥ ǡ Ǥǡǡ ϐ ȟ Ǥ ǣ ǣ 3. Ǧ ǡαǡǦ Ǥǡ Ǧ Ǥ 138 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) EDUCATION CORNER E BLACK BOX DEMONSTRATION The goal of this exercise is to show students that several different models can be created from one set of observable data and that each model is equally acceptable if it predicts the observed results. Students design a simple pencil and paper model to describe what might be happening inside the black box device. They construct their model of what is happening inside the tube from data gathered from outside the tube. Students then present their ideas to their peers. MATERIALS METHOD 1. Arrange the black box so one of the top cords is extended. Ǥ ǡ Ǥ ǡ Ǥ ǡ ǡ Ǥ Ǥ Ǥ Ǥ Ǥ 2. Allow students to try their own combinations, noting the motion and tension of the cords or anything else that might help them decipher how the cords are attached. 3. Now instruct students to complete this sketch by drawing their interpretation of how the cords might be attached.Ǥ 4. Have several students share their sketches on the board. 5. Systematically test the accuracy of each student’s ideaǡ Ǥ Ǥ ͳͲǡ Ǥ ϐ ȋǤǤǡ ǫȌǤ Note: Never divulge how the black box device is actually connected. The models must be judged primarily on their ability to explain and predict the observations. DISCUSSION Ǥ Ǥ Ǥ S P A C E É D U C A T I F ǤȂ Ǥ ǡ Ǥ ǡ Ǥ ǡǡ ϐ Ǥ ǡǡ ǦǤ ǡ Ǥ Ǧ ϐ Ǥ PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 139 E DUCATION CORNER S P A C E É D U C A T I F BLACK BOX DEMONSTRATION SUGGESTED USES Pre-video: Ǥ Ǥ Post-video: ǦǤ DzdzǦ Ǥ Dz dzǡ Ǥ HOW TO BUILD A BLACK BOX MODEL Ǥ MATERIALS » » » » ʹ ͺǡ Ͳ ͳͶͲ ͳ Ǥͷ ͵ͷ ʹ Ǥͷ TOOLS » » ͵Ȁͺdz PROCEDURE Step 1: ǡ ͷ ȋͳȌǤ ǡ ͷ Ǥ Step 2: ȋʹȌǤ Step 3: ͳͷ Ǥ Step 4:Ǥ ǡ ȋ͵ȌǤͳͷ Ǥ Step 5: Ǥ Note: Variations on the design (without a ring for example) will enrich the discussion and work equally well. You may wish to encourage students to build their own versions of the device with bathroom tissue tubes and string, but never reveal how the device is constructed. 140 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) SCIENCE POLICY CORNER CHANGES AT NSERC The CAP executive are closely monitoring this situation. An initial survey, which was coordinated by the CAP’s Director of Academic Affairs, John Dutcher, was sent to the Heads and Chairs of physics departments across Canada in July 2009 with the intention of obtaining firsthand information regarding the impacts of the implementation of the first phase of NSERC’s changes to the Discovery Grant program on the funding for Canadian researchers. Unfortunately the weak response, possibly due to the novelty of these changes, didn’t allow the CAP to draw any solid conclusions and a follow-up survey had to be sent to all physics departments at the beginning of the summer of 2010. At the same time, an adhoc committee of several physics department chairs, or former chairs, has just been established by John Dutcher. Its mandate is to analyse the effect of the new discovery grant program and to develop proposals for modifications to the system to correct any identified problems. The recommendations of this committee will be discussed directly with NSERC management through the CAP’s NSERC Liaison Committee, a group that was formed several years ago. It must be understood, however, that the lower success rate within the NSERC program is not due solely to the changes to the program, but is also because of the lack of funding for the direct expenses related to basic research; i.e. excluding the infrastructure support from the CFI program and its partners, no increases to NSERC’s budget to accommodate the increase in the number of researchers, nor for inflation. The Federal budget in March 2010 took a small step to address these issues, but it was not enough. This July, CAP members will be invited to participate in a survey and, if supported by the membership, the CAP will continue to push these points with the Federal government. We invite you to continue to respond to the surveys we send you. We understand that these “multiply” in your e-mail accounts; however, this is the only means that we have at our disposal to communicate with our members as needed. In the meantime, please do not hesitate to contact us and get involved in the activities of the CAP. by Normand Mousseau CAP Director of Communications Les résultats au dernier concours de subventions à la découverte du CRSNG viennent de rentrer, confirmant un bouleversement du financement de la recherche fondamentale au Canada. Les taux de succès continuent de diminuer et des projets ayant reçus une évaluation très positive se sont vu rejeter sans qu’on observe, pour autant, une augmentation significative de la valeur des subventions allant aux projets retenus. Comme ce programme est une des pierres d’assise de la recherche universitaire canadienne en physique depuis plusieurs décennies, il va de soit que ces changements touchent de près une grande partie des membres de l’ACP. Votre exécutif suit la situation de très près. Un premier sondage, piloté par John Dutcher, le directeur des affaires académiques, fut envoyé aux directeurs de département de physique en juillet 2009 afin de recueillir une information de première main en ce qui concernait les impacts de la première application de la nouvelle grille d’évaluation sur le financement des chercheurs. Malheureusement, le taux de réponse relativement faible, dû peut-être au fait de la nouveauté des changements, n’a pas permis à l’ACP de tirer des conclusions solides et un nouveau sondage devrait être envoyé à tous les départements de physique au début de l’été 2010 afin de faire un suivi. En parallèle, un comité ad-hoc regroupant quelques directeurs de département autour de John Dutcher, vient tout juste d’être créé avec le mandat d’analyser l’effet du nouveau régime et de suggérer des modifications corrigeant les lacunes qui pourraient être identifiées. Celles-ci pourront alors être discutées directement avec les dirigeants du CRSNG par l’intermédiaire du comité de liaison avec cet organisme créé par l’ACP, il y a quelques années. Il faut reconnaître toutefois que la baisse du taux de succès au CRSNG n’est pas seulement due aux changements à l’intérieur du programme, mais aussi au fait que le financement des dépenses courantes en recherche fondamentale, c’està-dire excluant le financement des infrastructures par la FCI et ses partenaires, n’a suivi ni l’augmentation du nombre de chercheurs ni l’inflation. Un petit pas a été fait pour contrer ces effets dans le budget fédéral de mars dernier, mais ce n’est pas suffisant. Si la communauté le veut, et elle pourra s’exprimer en répondant à un sondage qui devrait lui être envoyé en juillet, l’ACP continuera de défendre ce point encore cette année. SCIENCE POLICY CORNER The results of the latest round of NSERC Discovery Grant applications have come in, confirming a shortfall in funding for basic research in Canada. The success rates continue to diminish and some projects that received a very positive evaluation received no funding, with no obvious offsetting significant increase in funding for those projects that were funded. As this program has been one of the cornerstones of Canadian physics research at universities for several decades, by extension these changes closely affect a large proportion of the CAP members. CHANGEMENTS AU CRSNG Nous vous invitons à continuer de répondre aux sondages que nous vous envoyons. Ceux-ci se multiplient dans vos boîtes de courriel, nous en sommes bien conscients mais c’est le seul moyen à notre disposition pour échanger avec tous nos membres à la fois. Entretemps, n’hésitez pas à nous contacter et même à vous impliquer dans l’ACP. par Normand Mousseau Directeur de communications de l’ACP PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 141 BUREAU DE L’ACP SECOND SCIENCE POLICY SYMPOSIUM HELD 12-14 MAY 2010 IN GATINEAU, QUEBEC REPORT BY D.J. LOCKWOOD, CAP SECRETARY-TREASURER BUREAU DE L’ACP The theme of this conference, which was organized by the Professional Institute of the Public Service of Canada, was “Public Science in Canada: Strengthening Science and Policy to Protect Canadians”. The meeting was arranged around keynote lectures and panel presentations accompanied by three sets of three breakout sessions covering a variety of topics. The main presentations will be available later, on the conference (www.sciencesymposium2010.ca) or Institute (www.pipsc.ca) website. The opening session comprised a panel discussion of topics on the theme “Speaking Science to Power” proposed by moderator Veronique Morin followed by a general audience/panel discussion. The panelists were David Suzuki and Preston Manning, who provided provocative and sometimes opposing, but always interesting, views on how to improve communication between policy makers and scientists. This general topic turned out to be the core of the symposium, being raised again and again in various guises throughout the three days of events. Thoughtful comments and points raised by Manning were much the same as CAP has heard before in his lecture at our Annual Congress and also in his Article published in Physics in Canada. That is, science is becoming more and more relevant to public policy, there is an urgent need to communicate science to public policy makers, the scientific community needs to rethink how it communicates science because of the communications gap between the two (you have 90 s to get the message across!), the commercial community should be involved, and scientists need to be acting within Government (two or three elected members would be enough). Suzuki lamented on the lack of scientific literacy amongst our leaders and the public in general (corollary: science education at the school level is essential). He quizzed 50 parliamentarians about their scientific knowledge and those with business and legal backgrounds failed dismally (doctors, engineers and farmers were the 142 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) most knowledgeable). He also noted that the world as viewed in the media is also at fault, with prominence being given to celebrity, sport and politics – science is nowhere! Canada has no idea about where science can lead us: science has to become a part of our culture! Canada has no courage to invest in science – we need to keep active in science: it is the price we have to pay to keep in touch with what is going on in the world. Manning stressed that scientific organizations have to organize their own communities, have sessions on how to communicate better at their annual meetings, and get scientists into the public arena (provide training), as no involvement means you are left with the status quo. Suzuki echoed the latter comment, saying that we need active interest groups, but more importantly we also need a change in scientists’ attitudes. At the end of the day, the Hon. Stockwell Day, President of the Treasury Board, gave a speech outlining the state of Government funding of science, noting the increase in funding in the last budget, but emphasized the need for tight control of Government Departmental spending over the next two years, meaning cuts are coming. Stephen Lewis was the opening speaker on the second day. He described his presentation as an antidote to the talks by Manning and Suzuki! He touched on non-evidence based ideologies that abound in our society using HIV as an example, and stated that science should be heard and it should be critical – within Government too! He was concerned that we do not allow criticism and was very critical of the Government in not allowing dissenting views. He believes that evidence based information lies at the heart of public decision making. As a consequence, it was no accident that the Millennium development goals were chosen for discussion at the next G8 meeting – they have emerged as the heart of public policy worldwide and science does inform these issues. He then spent most of the remaining time evaluating the CAP OFFICE Millennium goals as they affected the developing world using examples from Africa for each goal – food supply, education, gender equality, child mortality, maternal mortality, infectious diseases, sustainable development (an apocalypse is coming in 2030-2050), and bonding between the developed and developing world (no reneging on promises). In the case of the disease topic he stressed that science has transformed global health in the last decades. He questioned why cheap drugs are not flowing to the developing countries from Canada despite Canadian Government legislation allowing it. He was indignant that principles are announced publicly, but are not supported in practice. Scientists need to speak out on this. The opening speaker on the third day was Peter Singer, Director at the McLaughlin Rotman Centre for Global Health. He gave a fascinating account of a new venture announced recently by the Hon. James Flaherty – Grand Challenges Canada – that will use innovation to solve global health issues. At present they are identifying five grand challenges, which are to be solved, with products developed and then commercialized. This is the first new innovation in 40 years in Canada for international development. Scientists are needed to develop appropriate science policy to move this project forward at a practical (and not rhetorical) level. There were three plenary panel discussions. The first was a Deputy Minister panel discussing “Federal Science in the 21st Century: Meeting the Challenge”, which emphasized the need for a national science and technology agenda, pulling and pushing science information into policy. The unanswered question was how to actually do this. The second panel comprised mostly of union representatives of Danish, UK, USA, and Canadian organizations discussed “Lessons for Canada: International Perspectives on Public Science. I was struck by how similar the science policy issues of Canada and the UK were regarding science funding cuts, and the closure, contracting out, and transfer of public science. As a result, the general civil service culture now undervalues science in the UK. The last panel discussion was on “Getting Science back on the Agenda: Signposts for Collaboration” with representatives from the Canadian Science Policy Conference (CSPCII is in Montreal next October), Partnership Group for Science and Engineering, Science Media Centre of Canada, and Canadian Association of Science Centres. There was a lively discussion of how to foster a greater understanding of and support for science. As could be expected, getting the media on ‘our side’ was seen as a crucial factor. One interesting proposal was for science graduate students to volunteer to work in the local riding offices of candidates during elections, or for MPs, to give advice on science issues. The breakout sessions comprised three or four presentations of case studies from experts followed by public discussion of topics raised therein. They covered all aspects of science policy, most of which had been introduced in the keynote addresses and plenary panels but were now covered in more detail. We were reminded by Jeff Kinder of Natural Resources Canada that a Federal framework for science and technology advice exists – it was adopted in May 2000 – but is no longer in use. It has been forgotten! The overarching message that came out of the meeting from my point of view was the proper communication of evidence based science – communicate face-to-face with science policy makers; communicate face-to-face with journalists; communicate face-to-face with MPs and MLAs – backed up with comprehensive science education of Canadians at all levels to create a Culture of Science in Canada. CAP OFFICE PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 143 IN MEMORIAM H. ROY KROUSE - (1935-2010) IN MEMORIAM January 8, 1935 to March 2, 2010 With the passing of Roy Krouse, professor emeritus in the Department of Physics and Astronomy, we have lost an outstanding scientist, a tremendous colleague, an exceptional mentor and a very dear friend. His warm and deeply inquisitive nature was shared in the classroom, in university hallways, and at numerous conferences around the globe. Krouse added insight and liveliness to events wherever he was. His generosity of spirit, inquiring mind and collegial warmth will be sorely missed. He died on Tuesday, March 2nd, 2010 after a short, courageous battle with cancer. Krouse was a patient and determined educator who transmitted his encouragement and sense of wonder about the world to students. He supervised numerous graduate students and co-supervised and participated on the committees of hundreds of students over the years. The Stable Isotope Laboratory he founded is an international entity, regularly visited by well-known scientists from around the globe. Krouse has consistently offered analyses to students and colleagues and the scientific benefits have been enormous. A large number of former students now working in industry, government and universities developed a comprehensive knowledge of isotope systematics and the ability to apply isotope data to geological and environmental problems because of Krouse’s generosity with his time and his analytical facilities. Throughout his outstanding career as scientist and educator, Krouse was always able to carve out time for his favourite hobbies. Over 50 years, he had acquired an extensive collection of model trains from around the world. On a regular basis, Krouse also played the guitar and fiddle with the Prairie Mountain Michael Wieser Fiddlers of Calgary at Stampede events, <[email protected]>, pancake breakfasts and many other occaIsotope Science sions. He and his wife Irene have comLaboratory, posed songs in traditional country style, Dept. Physics and Astronomy, some of which are featured on his CD, University of Calgary, “Calgary Country.” Krouse’s family was Calgary, Alberta, an important source of support and pride and included his loving wife Irene, sons Donald and Ian, daughter in law Kendall (Donald), and grandchildren James and Edward. Krouse received his BSc (Honours) in physics and chemistry in 1956, and a PhD in physics in 1960 from McMaster University in Ontario, Canada. He completed his PhD thesis on selenium isotopes under the direction of Harry G. 144 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) Thode. In 1960, Krouse joined the University of Alberta in Edmonton as a faculty member in the Department of Physics. There, he established an extensive multidisciplinary stable isotope research program, the second in Canada. In 1971, he moved to the University of Calgary as professor and head of the Department of Physics and Astronomy, where he established another internationally recognized stable isotope laboratory and conducted pioneering research devoted to the application of isotope techniques to numerous different disciplines throughout his scientific career. In 1997, he was awarded the honorary title of professor emeritus. At the same time, the University of Calgary appointed him to the position of faculty professor, a designation that recognizes the expertise and continuing high caliber of research being done by “retired” professors. Using and developing specialized analytical tools, complemented by home-made and commercial mass spectrometers, Krouse made significant contributions to the application of stable isotope techniques in solving environmental and geological problems. He is a worldrenowned pioneer in the application of sulfur isotopes in environmental studies. The unique situation in Alberta, with its isotopically distinct sulfur emissions from sour gas processing plants, not only allowed him to trace the fate of these emissions in the environment, but also to study many fundamental physical, chemical, and biological processes in the sulfur cycle. As a consequence he was invited to serve on a UNEP/SCOPE committee, which addressed global cycling of sulfur. One of his tasks was co-editing and contributing to a definitive book on distinguishing between natural and anthropogenic sulfur locally, regionally, and globally. Krouse was a Titular member of the Commission on Isotopic Abundances and Atomic Weights with the International Union of Pure and Applied Chemistry. This Commission has a history spanning over one hundred years evaluating the atomic weights of the elements. Krouse’s participation and leadership of a committee under the Commission to explore the natural isotope variability of several elements resulted in one of the Commission’s more significant and widely read documents on the natural isotopic variation of selected elements in the terrestrial environment. Krouse received numerous honors and awards throughout his scientific career. He was an elected fellow of the Royal Society of Canada (since 1994), the Chemical Institute of Canada (since 1990), and the Arctic Institute of North America (since 1989). In 1999, he was co-recipient of the Miroslaw Romanowski Medal of the Royal Society of Canada for significant contributions of scientific aspects of environmental problems. In 2001, Krouse received the CAP medal for outstanding achievement in Industrial and Applied Physics from the Canadian Association of Physicists (CAP). IN MEMORIAM BORIS P. STOICHEFF - (1924-2010) Boris P. Stoicheff, a CAP Past President (1983-84), a distinguished optical physicist and an emeritus university professor at the University of Toronto, passed away on April 15, 2010 in Toronto after a battle with multiple myeloma. He was 85. Stoicheff was renowned for his pioneering contributions to High Resolution Raman, Brillouin, and VUV spectroscopy; together with colleagues at NRC he built the first ruby laser in Canada. Throughout his career, Stoicheff served on numerous Canadian and international committees, including the Board of NRC, the Quantum-Electronics Council, Council of Professional Engineers of Ontario, Ontario Nuclear Safety Review Committee, International Union of Pure and Applied Physics, the Royal Society of Canada, and the Canadian Institute for Advanced Research. He also served with distinction on many committees of the Optical Society of America and became its first foreign president in 1976. A CAP member for nearly 60 years, Stoicheff was very active in the CAP’s activities. He was Chair of the Division of Atomic and Molecular Physics in 1970 and joined the presidential line in 1981, becoming President in 1983-84. One of his most important activities came during these years. He was actively involved in the CAP’s inter- In 1974, Stoicheff received the CAP’s highest honour, its Medal of Achievement. He was also the recipient of many other awards and honors. He was appointed University Professor at U of T in 1977, Officer of the Order of Canada (1982), and was elected Fellow of numerous societies including the Royal Society of London, Royal Society of Canada, American Physical Society, Optical Society of America, Australian Academy of Science, the American Academy of Arts and Sciences, the Macedonian Academy of Sciences and Arts, and the Indian Academy of Sciences. He was Henry van Driel awarded the Centennial Medal of Canada <vandriel@physics. utoronto.ca>, (1967), the Henry Marshall Tory Medal of Professor of Physics, The Royal Society of Canada, as well as University of Toronto, several honorary degrees. Stoicheff was the Toronto, Ontario. author and co-author of more than 150 papers on spectroscopy, laser physics and nonlinear optics. IN MEMORIAM Stoicheff was born in Macedonia in 1924 and emigrated to Canada with his parents and sisters in 1931. He obtained a B.A.Sc in Engineering Physics (1947) and a PhD in Molecular spectroscopy (1950) from the University of Toronto. Following an inspiring seminar by Gerhard Herzberg, Stoicheff joined what would turn out to be his life-long mentor at the National Research Council (NRC) in Ottawa where he continued his work on Raman scattering in a group that included Cec Costain, Alex Douglas, Don Ramsey and Hin Lu. Stoicheff remained at the NRC as a staff scientist from 1951-1964. He spent a sabbatical year in 1963 working with Charles Townes at MIT, and shortly thereafter, so thoroughly having enjoyed his interaction with graduate students, joined the University of Toronto as a professor of physics (1964). In his 25 years at U of T Stoicheff graduated 25 Ph.D students, his pride and joy. Although he continued to perform research after he officially retired he spent much of his time writing Herzberg’s biography, Gerhard Herzberg – An Illustrious Life in Science. The CAP has presented a copy of this biography, duly autographed by Boris Stoicheff, to its Herzberg Memorial Public Lecturer for the past several years at the CAP Congress. vention (started initially by CAP member Peter Kirkby) with respect to the efforts of the Ontario Association of Professional Engineers in the early 1980’s to modify the Ontario Professional Engineers Act to expand the definition of the practice of engineering. Stoicheff, during his year as CAP President, took responsibility for preparing the CAP’s intervention case and addressed the Standing Committee of the Ontario Legislature. At the same time, he contacted members of this Committee and other influential representatives of government and opposition. Stoicheff, accompanied by Raymond Hoff (Environment Canada), Allan Carswell (York University and Optech Inc.) and our legal advisor Brian Flood (Tory, Tory, DesLauriers and Binnington), briefly reviewed the highlights of the CAP’s written presentation. He ended with a recommendation that the committee add “but does not include practicing as a natural scientist” to the proposed definition of the practice of professional engineering. The recommendation was accepted and the three years of effort by the CAP Committee on behalf of the physics community, and the natural scientists generally, was successfully concluded. These efforts underscored the need for CAP and its members to remain vigilant to wording included in provincial engineering acts and led to the creation of the position of Director of Professional Affairs on the CAP’s Executive Committee. Boris Stoicheff is survived by his wife, Joan, a son, Peter, 2 grandchildren, and four sisters. A memorial celebration of his life was held at Massey College at the University of Toronto in May, 2010. PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 145 LIVRES BOOK REVIEW POLICY Books may be requested from the Book Review Editor, Richard Hodgson, by using the online book request form at http://www.cap.ca. CAP members are given the first opportunity to request books. Requests from non-members will only be considered one month after the distribution date of the issue of Physics in Canada in which the book was published as being available (e.g. a book listed in the January/February issue of Physics in Canada will be made available to non-members at the end of March). The Book Review Editor reserves the right to limit the number of books provided to reviewers each year. He also reserves the right to modify any submitted review for style and clarity. When rewording is required, the Book Review Editor will endeavour to preserve the intended meaning and, in so doing, may find it necessary to consult the reviewer. Reviewers submit a 300-500 word review for publication in PiC and posting on the website; however, they can choose to submit a longer review for the website together with the shorter one for PiC. LA POLITIQUE POUR LA CRITIQUE DE LIVRES Si vous voulez faire l’évaluation critique d’un ouvrage, veuillez entrer en contact avec le responsable de la critique de livres, Richard Hodgson, en utilisant le formulaire de demande électronique à http://www.cap.ca. Les membres de l'ACP auront priorité pour les demandes de livres. Les demandes des non-membres ne seront examinées qu'un mois après la date de distribution du numéro de la Physique au Canada dans lequel le livre aura été déclaré disponible (p. ex., un livre figurant dans le numéro de janvier-février de la Physique au Canada sera mis à la disposition des non-membres à la fin de mars). Le Directeur de la critique de livres se réserve le droit de limiter le nombre de livres confiés chaque année aux examinateurs. Il se réserve, en outre, le droit de modifier toute critique présentée afin d'en améliorer le style et la clarté. S'il lui faut reformuler une critique, il s'efforcera de conserver le sens voulu par l'auteur de la critique et, à cette fin, il pourra juger nécessaire de le consulter. Les critiques pour publication dans la PaC doivent être de 300 à 500 mots. Ces critiques seront aussi affichées sur le web ; s’ils le désirent les examinateurs peuvent soumettre une plus longue version pour le web. BOOKS RECEIVED / LIVRES REÇUS The following books have been received for review. Readers are invited to write reviews, in English or French, of books of interest to them. Books may be requested from the book review editor, Richard Hodgson by using the online request form at http://www.cap.ca. Les livres suivants nous sont parvenus aux fins de critique. Celle-ci peut être faite en anglais ou en français. Si vous êtes intéressé(e)s à nous communiquer une revue critique sur un ouvrage en particulier, veuillez vous mettre en rapport avec le responsable de la critique des livres, Richard Hodgson par internet à http://www.cap.ca. A list of ALL books available for review, books out for review, and copies of book reviews published since 2000 are available on-line -see the “Physics in Canada” section of the CAP's website : http://www.cap.ca. Il est possible de trouver électroniquement une liste de livres disponibles pour la revue critique, une liste de livres en voie de révision, ainsi que des exemplaires de critiques de livres publiés depuis l'an 2000, en consultant la rubrique "PiC Électronique" de la page Web de l'ACP : www.cap.ca. GENERAL INTEREST BEYOND SMOKE AND MIRRORS, BURTON RICHTER, Cambridge University Press, 2010; pp. 226; ISBN: 978-0-521-74781-3 (pbk); Price: 29.99. UNDERGRADUATE TEXTS FROM ATOMS TO GALAXIES, A CONCEPTUAL PHYSICS APPROACH TO SCIENTIFIC AWARENESS , Sadri Hassani, Taylor & Francis, 2010; pp. 723; ISBN: 978-1-4398-0849-8 (hc); Price: 89.95. QUANTUM PROCESSES SYSTEMS, & INFORMATION, Benjamin Schumacher and Michael Westmoreland, Cambridge University Press, 2010; pp. 469; ISBN: 978-0-521-87534-9 (hbk); Price: 75.00. GRADUATE TEXTS AND PROCEEDINGS ASTROPHYSICS FOR PHYSICISTS, Arnab Rai Choudhuri, Cambridge University Press, 2010; pp. 471; ISBN: 978-0-521-81553-6 (hbk); Price: 60.00. INTRODUCTION TO NANOPHOTONICS, Sergey V. Gaponenko, Cambridge University Press, 2010; pp. 465; ISBN: 978-0-521-76375-2 (hbk); Price: 78.00. INTRODUCTION TO XAFS A PRACTICAL GUIDE TO X-RAY ABSORPTION FINE STRUCTURE SPECTROSCOPY, Grant Bunker, Cabridge University Press, 2010; pp. 260; ISBN: 978-0-521-76775-0 (hbk); Price: 70.00. LINEAR PARTIAL DIFFERENCIAL EQUATIONS AND FOURIER THEORY, Marcus Pivato, Cambridge University Press, 2010; pp. 601; ISBN: 978-0-521-13659-4 (pbk); Price: 60.00. MOLECULAR FORCES AND SELF ASSEMBLY IN COLLOID, NANO SCIENCES AND BIOLOGY, Barry W. Ninham and Pierandrea Lo Nostro, Cambridge University Press, 2010; pp. 365; ISBN: 978-0-52189600-9; Price: 78.00. NON-PERTUBATIVE FIELD THEORY FROM TWO-DIMENSIONAL CONFORMAL FIELD THEORY TO QCD IN FOUR DIMENSIONS, Yitzhak Frishman and Jacob Sonnenschein, Cambridge University Press, 2010; pp. 436; ISBN: 978-0-521-66265-9 (hbk); Price: 130.00. OPTICAL QUANTUM INFORMATION PROCESSING, Pieter Kok and Brendon W. Lovett, Cambridge University Press, 2010; pp. 488; ISBN: 978-0-521-51914-4 (hbk); Price: 78.00. PARTICLE DARK MATTER OBSERVATIONS, MODELS AND SEARCHES, Gianfranco Bertone, Cambridge University Press, 2010; pp. 738; ISBN: 978-0-521-76368-4 (hbk); Price: 115.00. SUPERCONTINUUM GENERATION IN OPTICAL FIBERS, J.M. Dudley and J.R. Taylor, Cambridge University Press, 2010; pp. 404; ISBN: 978-0521-51480-4 (hbk); Price: 125.00. 146 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) BOOKS BOOK REVIEWS / CRITIQUES DE LIVRES Book reviews for the following books have been received and posted to the Physics in Canada section of the CAP’s website : http://www.cap.ca. When available, the url to longer versions are listed with the book details. Des revues critiques ont été reçues pour les livres suivants et ont été affichées dans la section “La Physique au Canada” de la page web de l’ACP : http://www.cap.ca. Quand disponible, un lien url à une critique plus longue est indiqué avec les détails du livre. BUILDING SCIENTIFIC APPARATUS, 4th ed., John H. Moore, Christopher C. Davis, and Michael A. Coplan, Cambridge University Press, 2009, pp: 647, ISBN 987-0-521-87858-6 (hc). Price: US $80. When I was finishing up graduate school in the late 1980s, I came across Building Scientific Apparatus (BSA), by Moore, Davis, and Coplan, a compendium of techniques for the basics of experimental work, covering mechanical design, electronics, optics, detectors, temperature measurement, etc. I remember wishing I had known about it when I started out. Thus, it was with some anticipation that I awaited this newest, 4th edition. The strengths of the previous editions remain, and leafing through the book, I learned many new tidbits. All the chapters have been tweaked (with a new section on flexure stages in the mechanics chapter, one on non-imaging optical collectors, one on time-correlated detection techniques in electronics), and the section on detectors now fills an entire chapter, with new discussions of noise, new detector types, etc. Still, I am disappointed with this latest edition. The practice of building scientific apparatus has been profoundly changing in the last few years, and this book gives little sense of current directions. Some of the major trends that are missed include the increasing use of 1) Computers in design. BSA is filled with the kinds of rules of thumb that I learned as a graduate student in the 1980s. For example, Ch. 1 on mechanics has expressions to estimate spring constants of elastic objects of various geometries. These are good for building intuition but lousy for accurate design. Nowadays, readily available finite-element-method (FEM) software makes it possible to easily simulate the behavior of parts (or even all) of an apparatus. The design process often starts with FEM and CAD programs, with the output of the latter going directly to a computer-controlled mill. The days of “winging it” on the basis of rough estimates and hand machining are limited. The authors’ brief discussion of SPICE models just scratches the surface. Computers also make possible apparatus that was unimaginable just a few years ago. For example, diffractive optics (using a liquid-crystal spatial light modulator) allow the creation of optical beams with “designer” phases. These beams can be used to create holographic optical tweezers that simulate the action of many independent laser beams that function as micron-scale “fingers” to manipulate objects. 2) Higher-level modularity. Off-the-shelf optomechanics are now far better (and cheaper) than the devices shown in Sec. 4.3.11. Smaller, blockier shapes raise mechanical resonance frequencies, reducing coupling to external vibrations. (The elements depicted in Fig. 4.87 look dinosaur-like compared to what people now use.) Electronics is another area where the increasing sophistication of modular parts rapidly makes older techniques obsolete. For example, field programmable gate arrays (FPGAs) – digital circuits you can program – have replaced many digital circuits in industry and are starting to do the same in laboratories. 3) Micro- and nano-scale apparatus. Where students once used lathes and mills, they now use FIBS (focused ion beam) and electron-beam lithography to make structures orders of magnitude smaller. Likewise, where once students dealt with centimeter-scale pumps and valves, they now make micro- and even nanofluidics. The current technology requires new knowledge and techniques (lithography masks, resists, cleanroom protocols, etc.). Space for new material could be made by pruning obsolete techniques and descriptions. The electronics chapter, for example, discusses four different kinds of flip flops, NIM and CAMAC busses, BASIC programs, and power supplies that look like something out of a 1970s RadioShack ad but says nothing about FPGAs, USB, LabVIEW or Matlab, sigma-delta converters, and switching supplies. The chapter on glass blowing is no longer useful. If you are an experimentalist, you should have this book – despite my complaints – not as the one-stop shop for techniques that the book tries to be but for its wealth of useful tips. If you already own it, there is little to justify buying the new edition. This book has kept the same three authors for nearly 30 years. It’s time to add new blood. (eds.), Cambridge University Press, Cambridge, 1993, 310 pages, ISBN: 0-521-41439-3 (hardback), $69.95. Professor Maurice M. Shapiro is a world-leading scientist in cosmic-ray physics. He is renowned for the contributions to the development in this field. This book is a collection of a series of lectures given at a Symposium in his honor to celebrate his 75th birthday at the Naval Research Laboratory (NRL), Washington, DC. It consists of four parts: (1) Cosmic rays, (2) X-ray, gammaray and neutrino astronomy, (3) Cosmology, and (4) Reminiscences and poetic black holes. The first three cover his main research areas. Part 1 contains five articles dedicated to the observation of cosmic rays. The topics include the cosmic rays in the galaxy and galactic halo, those in distant radiogalaxies, cosmic-ray modulation boundary of the heliosphere, the origin of ultra-high-energy rays above 1 TeV, and early measurements of cosmic rays. Part 2 has nine papers. It exposes the importance of X-ray astronomy, some topics in gamma-ray astronomy, surveys in cosmic rays, cosmic gamma rays, and the Galactic structure, introduction to ultrahigh-energy gamma-ray astronomy and recent gamma-ray bursts, solar-flare high-energy astrophysics, supernovae gamma-ray radiation, history and results of neutrino detection, and studies on high-energy neutrino astronomy. Part 3 holds three papers about the cosmic quark-hadron phase transition, the development of soliton stars from the early universe, and the generation of cosmological structure related to dark matter. Part 4 is composed of four essays summarizing mainly Professor Shapiro's contributions to cosmic-ray astrophysics and his research activities at NRL. John Bechhoefer Simon Fraser University Burnaby, British Columbia, Canada Though most articles are exceptionally clearly written, and the contents were edited beautifully, the book may not be suitable to be used as a good reference for researchers. This is predominantly due to the fact that not only are the subjects discussed in the book very diverse (ranging from solar physics to cosmology), but also the levels of presentations are very diverse (ranging from original research papers to coarse poetry). There is also no topic index, and no cross-references among papers. CURRENTS IN ASTROPHYSICS AND COSMOLOGY, G.G. Fazio and R. Silberberg However, the book may be useful for students and researchers who have an interest in getting a PHYSICS IN CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 147 LIVRES general knowledge on cosmic-ray astrophysics and cosmology in their spare time. Also, as a non-textbook, it may be recommended to public libraries for popular-science purposes. John Z. G. Ma Space Science Branch Canadian Space Agency ESTUARIES. DYNAMICS, MIXING, SEDIMENTATION AND MORPHOLOGY, DAVID PRANDLE, Cambridge University Press, 2009, 236 pages. ISBN 978-0-521-88886-8 (hc), $130.00 Ce volume présente des formules pratiques et des nouvelles hypothèses pour la dynamique, le mélange, le régime des sédiments et l’évolution morphologique dans les estuaires. Le volume débute par l’introduction des notions de base utiles et présente les objectifs qui devraient être en mesure d’être répondus dans les chapitres suivants. Les objectifs sont respectivement : 1) comment la marée répond aux paramètres géométriques de l’estuaire (longueur, largeur, profondeur), 2) comment les courants de marées se comportent selon l’axe vertical principalement, 3) comment le mélange salin s’effectue sur un cycle de marée, 4) comment s’effectue le lien entre le spectre des sédiments et la dynamique estuarienne, 5) quels sont les facteurs qui déterminent la morphologie des estuaires, 6) et enfin l’adaptation des estuaires aux changements climatiques globaux. Le chapitre 2 répond au premier objectif fixé en simplifiant et linéairisant au premier ordre les équations de la dynamique du système maréeestuaire. Ceci permet d’élucider le fait que l’élévation de la surface est principalement restreinte par le ratio longueur-largueur de l’estuaire et que la propagation de la marée est alors plutôt axiale. La variation du courant de marée serait plutôt sensible à la profondeur de l’estuaire et le coefficient de friction du fond. D’autre part, des solutions pour le calcul du courant et de l’amplitude de la marée peuvent être obtenues en invoquant l’approximation d’un estuaire synchrone, c'est-àdire, un estuaire dont le gradient spatial de l’élévation de la marée est petit. Le chapitre 3 répond à la question qui consiste à savoir; comment la marée varie avec la profondeur, la friction, la latitude et la période de la marée. La structure verticale du courant de marée est simulée à l’aide d’un modèle simplifié, qui utilise l’équation de momentum et de continuité, à laquelle est introduit un terme de viscosité du remous constant ou qui varie linéairement avec la profondeur. Ce modèle permet une interprétation pouvant être validée par des observations ou des modèles tridimensionnelles. En fait, la prédiction de la structure du courant de marée devrait tenir compte du terme de viscosité du remous et la friction du fond. Par la suite, on résume les effets de la latitude, de la période de la marée, la friction du fond et le terme de viscosité du remous sur l’ellipse décrit par le courant de marée sur le plan horizontal. Le chapitre 4 nous entretient efficacement à l’intrusion saline et le mélange sur un cycle de marée. Après avoir présenté un diagramme des différents types de stratification estuarienne, l’auteur présente principalement l’intrusion dans le cas d’un estuaire partiellement mélangé. A l’aide de la théorie linéairisée permettant de représenter la moyenne de la structure verticale de la salinité et la vitesse résiduelle, un modèle numérique est formulé tenant compte de l’advection différentielle horizontale de l’intrusion saline, pouvant, dans certain cas produire une structure de densité instable et un retournement convectif. Le modèle est évalué à l’aide d’observations de six estuaires. Des expressions pour la longueur d’intrusion saline, tenant compte de l’écoulement à la tête de l’estuaire, ainsi que le temps d’évacuation, sont dérivés. Le chapitre 5 fait le lien entre le spectre des sédiments en suspension et la dynamique estuarienne. On étudie principalement l’impact des marées de vive-eau et morte-eau en intégrant l’érosion, la suspension et la déposition sédimentaire. Des solutions analytiques permettent d’obtenir des séries temporelles des sédiments en suspension et leurs structures verticales. Des paramètres d’étalonnage, incluant le type et la taille des sédiments, la vitesse du courant de marée et la profondeur de l’estuaire, permettent d’interpréter le régime sédimentaire en le comparant à des simulations numériques et aux observations. L’intérêt et l’utilité du développement des modèles proviennent du fait que ceuxci pourraient indiquer comment la morphologie des estuaires peut être modifiée suite aux aménagements possibles dans l’estuaire. Le chapitre 6 adresse plus fondamentalement la question; comment la morphologie estuarienne est déterminée et maintenue par les actions combinées de la dynamique tidale, le mélange de l’eau de rivière et l’apport salin. L’auteur se restreint ici aux fortes marées et un estuaire dit synchronisé de forme triangulaire convergente. Ainsi, avec la spécification de l’amplitude de la marée et la profondeur de l’estuaire, des solutions analytiques localisées permettent d’obtenir des valeurs du courant de marée, le rapport entre le terme de friction et d’inertie, la pente du fond, un taux de dissipation de l’énergie tidale et la différence de phase entre l’amplitude et le courant de marée. En plus, cela permet d’estimer, la longueur d’un estuaire peu profond. Cette longueur est comparée à différents estuaires britanniques et de la côte est américaine. C’est un chapitre très intéressant permettant de vérifier la théorie versus la morphologie observée des estuaires. Le chapitre suivant examine comment les sédiments sont piégés dans les estuaires et les processus qui ont pour effet de maintenir la bathymétrie de façon stable. Un émulateur analytique est construit en intégrant les solutions explicites du courant de marée, l’érosion, la suspension et la déposition des sédiments. L’émulateur estime la concentration des sédiments suspendus et le flux de sédiment net et leurs sensibilités aux paramètres tels; l’élévation de la marée, la pro- 148 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) fondeur de l’estuaire, le coefficient de friction du fond… On explique ainsi le triage des sédiments tel que communément observé dans les estuaires. Pour terminer, l’auteur évalue les risques possibles suite à l’élévation du niveau de la mer et de l’augmentation des tempêtes, résultant des changements climatiques à venir. L’auteur n’envisage pas de changements drastiques pour les estuaires suite aux changements du régime des marées ou de l’augmentation des ondes de tempêtes pour les prochaines décennies. Les ondes de tempêtes seront tout de même ressenties par les estuaires peu profonds. L’augmentation de l’écoulement de rivière et du niveau de la mer pourrait résulter en une faible augmentation de la longueur et la profondeur des estuaires. Par contre, peu d’impacts abrupts ou substantiels, seraient provoqués dans le régime des sédiments. Les changements de faune ou de flore pourraient avoir un effet sur l’érosion du fond et des berges, pouvant altérer la dynamique et la bathymétrie de l’estuaire. Une approche multidisciplinaire est toujours nécessaire pour quantifier la contribution et les effets des changements climatiques. Enfin, je considère ce volume très utile aux chercheurs et étudiants en océanographie physique et en génie maritime. C’est une source de référence et d’idées pour tous ceux qui s’intéressent aux estuaires. Il est évident que plusieurs résultats obtenus analytiquement ont été comparés principalement aux estuaires britanniques, étant donné le fait du plus grand nombre d’observations disponibles. Il pourrait être intéressant de valider ces résultats à des estuaires canadiens et de prendre en considérations le mouvement des glaces résultant de cette dynamique. Je recommande de lire, en parallèle, les articles qui sous-tendent les différents chapitres du volume, afin de mettre en lumière certains aspects, parfois mieux présentés dans les articles, que dans l’ouvrage lui-même. André April Environnement Canada FINITE-TEMPERATURE FIELD THEORY PRINCIPLES AND APPLICATIONS, SECOND EDITION, Joseph I. Kapusta, Charles Gale, Cambridge University Press, Cambridge, 2006, pp: 428, ISBN 0-521-82082-0 (hc), Price $140.00. The authors start with a series of interesting provoking questions such as “What happens when nuclear matter is heated to such great temperatures that the nucleons and pions melt into quarks and gluons…”. The answers to these questions are approached by first reviewing quantum statistical mechanics in the first chapter, and then developing in the second chapter a finite-temperature field theory using a Functional Integral representation of the Partition Function. I commend the authors, for a remarkable clear and concise exposition of the foundation from which the rest of the book flows. The chapters in this book cover subjects that in themselves are subjects of vast volumes. In roughly twenty chapters, the authors amazingly BOOKS manage to introduce the basic ideas of each area, deriving some of the key results in finite field extensions, and point out frontiers of the subject at hand. The derivations are detailed just enough so that material flows without strain but not so detailed as to create a monster text. Chapter topics that cover entire fields include Quantum electrodynamics, Linear response theory, Quantum chromodynamics, and Nucleation theory. The book also has a number of chapters devoted to particular mathematical approaches, such as Interactions and diagrammatical techniques, Renormalization, Lattice gauge theory, Resummation and hard thermal loops. Special topic chapters such as Spontaneous symmetry breaking and restoration, Dense nuclear matter, Heavy Ion collisions, Weak interactions, Hot hadronic matter and Astrophysics and cosmology give impressive coverage to the entire subject area of finite- temperature field theory. Each chapter ends with a few exercises, references, and bibliography. In a subject where the difficulty of the manipulations are legendary, the problems seem to have found a nice balance between being doable and engaging. The bibliography and reference entries range from classic texts to specialized articles in journals and appear to have been chosen with care. This book would make a strong graduate textbook on the subject for those with necessary background courses in statistical mechanics and field theory. At several places in the text, I had kind of an epiphany where facets of the subject that had eluded me suddenly became clear. This book would also be of interest to specialists in QCD, etc. that would like to broaden their understanding to related fields. While reading the book I experienced the feeling that the book was on a quest to bring one to a place where calculable results that can be compared to experiment and observed phenomena, a rare touch in a mathematical physics text. Collin Carbno Sasktel INTRODUCTION TO ELEMENTARY PARTICLE PHYSICS, Alessandro Bettini, Cambridge University Press, 2008; pp 431, ISBN 978-0521-88021-3(hc), Price $70.00. This is on the whole a nice introductory textbook to particle physics, written at the senior undergraduate or beginning graduate level. The reader is assumed to be familiar with the Dirac equation to the level of knowing its free solutions, the significance of the spinor components, and the contraction of Lorentz indices and manipulation of gamma matrices. A good working knowledge of special relativity and relativistic kinematics is also a necessary prerequisite. Many of the major topics of modern particle physics are covered here: symmetries, hadrons and quarks, QED and the running coupling constant, QCD, nucleon structure, weak interactions, neutral K and B mesons and CP violation, the Standard Model and electroweak unification, neutrinos. Perhaps to keep the book at a manageable length, some important topics are dropped. The importance of local gauge invariance and how it leads to the gauge bosons is not discussed, nor is particle physics in the early universe. The Higgs mechanism is mentioned only in passing, and there is no discussion of spontaneous symmetry breaking. The emphasis is on presenting the important results, rather than on detailed calculations; the student will not learn the details of reducing the matrix elements with trace theorems, etc., in contrast to the approach found in the book by Griffiths. There are questions embedded in the text, which the student is expected answer as he/she goes along, as well as a large number of questions at the end of each chapter, with about half of them answered at the back of the book. The pace of the book is brisk. For some topics, the author spends little time in trying to motivate the reader with descriptive introductions to the topic or to make connections with other areas of physics. Sometimes the brisk pace means that mathematical brevity trumps intuitive understanding. In the section on electromagnetic form factors (pg 201), for example, the scattering cross section is derived in half a page by using a mathematical identity, which is certainly correct, but not as intuitively appealing as drawing a set of plane waves incident on an extended target and then considering the relative phases of the waves scattered from different points in the target à la Bragg diffraction. The fact that the form factor is basically a diffraction phenomenon due to the interference of the scattered waves, and the fact that it is completely analogous to what crystallographers observe in X-ray diffraction, might be completely lost on the reader. English is not the author's first language, and despite the generally excellent English throughout, a few mistakes have slipped through. For example, “scattering amplitude” is rendered as “diffusion amplitude” (p. 163) and “scattering angle” as “diffusion angle” (p.190), and “Panofsky” becomes “Panowsky” (p.92). The sentence “If two pions are equal...as requested by Bose statistics” might be better reworded “If two pions are identical, as demanded by Bose statistics”. On p. 84, continuous transformations (as opposed to discrete transformations) are called “continuum transformations”. Some typographical errors have occurred, as might be expected for the first editions of such a lengthy book. On p.44, 5 lines from the bottom, omission of the word “not” from the intended statement “we could NOT have reconstructed it” completely reverses its meaning. On p. 90, the overbars are missing on the second “f” of the “ff” fermion-antifermion pairs. On p. 196, the text on the upper right hand part of the figure should read “(3 colours)=11/3” rather than “(1 colour)=11/3”. On p. 65, right before section 2.3, due to the omission of overbars, the Λ and the Σs are listed as having both strangeness S=+1 and S=-1. On p. 21, the author means to say that increasing distance corresponds to decreasing momentum PHYSICS IN transfer, not increasing as stated. The topic of symmetries and conservation laws is one of the most important topics in particle physics, and this is discussed in chapter 3. The author assumes that the reader is already familiar with continuous (i.e. infinitesimal) transformations of position and angle leading to conservation of linear and angular momentum; the book does not discuss these at all. This is unfortunate since any reader who lacks this background would find much of chapter 3 hard to understand. Strangely, gauge invariance is first introduced on p. 84 in the paragraph on discrete additive symmetries, even though gauge transformations are continuous transformations of the phase, and not discrete at all. On p. 84, the statement that atomic transitions with single photon emission are electric dipole is an overstatement, and the conclusion that the spin and parity of the photon must therefore be 1- does not necessarily follow. Electric dipole transitions dominate where permitted, but there are so-called “forbidden” transitions of magnetic dipole or electric quadrupole character between states of the same parity, in which case the parity of the radiated EM field would be positive, and its angular momentum would then be 1 or 2, respectively. How this relates to the intrinsic spin parity of the photon being 1- needs to be explained. In summary, this book is not without its limitations, but I enjoyed reading it nonetheless as a nice survey of most of the important topics of particle physics. With proper guidance from the instructor, to get over a few rough spots, it would make a good textbook for a first course in particle physics. Stanley Yen TRIUMF MATHEMATICS FOR PHYSICS: A GUIDED TOUR FOR GRADUATE STUDENTS, Michael Stone and Paul Goldbart, Cambridge University Press, 2009, pp: 806, ISBN 978-0-521-85403-0 (hc). Price: US $90. What makes a physicist? Despite the recent boosting of interdisciplinary research and programs, physicists continue to have a strong sense of professional identity. One reason is institutional: universities, where physicists train and may work professionally, still have physics departments, and people naturally identify with their “home”. Another reason is cultural: disciplines such as physics, mathematics, chemistry, biology, and engineering have evolved distinct cultures, with teaching and training that inculcate new members (graduate students, primarily) in the ways of their profession – in what is taught, in how to think and write, and even in stories that are transmitted from generation to generation. One place where the culture of a discipline is particularly clear is in its treatment of other disciplines. Students need to know about neighboring fields. While they may take elementary courses given by members of another discipline, the upper-level courses require such a peculiar array CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 149 LIVRES of topics that they tend to be taught within the discipline. Thus, chemists teach courses in quantum mechanics and statistical mechanics, engineers teach courses in “electromagnetics” and optics, and physicists teach courses in mathematics. In each case, the way material is presented is quite different from the presentation from “within” the discipline. In this light, Mathematics for Physics: A Guided Tour for Graduate Students, by Michael Stone and Paul Goldbart, a new textbook on mathematics written by and for physicists, is traditional. Nonetheless, it is an impressive achievement – not so much for the originality of its material but for the way in which it successfully presents mathematics in the style and feel that physicists find comfortable. By “physics style” for mathematics, I mean that the presentation is careful in that details are given and pitfalls explained while rigor for its own sake and needless generality are avoided. The language is friendly, often conversational, in contrast to the terse lemma-theoremproof style of mathematics texts. Also, the authors have integrated bits of important current problems into examples, exercises, and problems. For example, the influential work of Caldeira and Leggett (Phys. Rev. Lett. 46, 211, 1981) on dissipation in quantum systems makes several appearances. Such examples give students an “in” to contemporary research and are yet another way that the book successfully transmits physics culture. They also help to make a course fun. Similarly, the authors frequently inject historical notes that give a sense of how different mathematicians and physicists grappled with and then resolved mathematical subtleties. The history has an emphasis on story, but stories are an important part of the transmission of culture that liven up the presentation and contribute to a common ground on which members can feel comfortable. Perhaps regrettably, but in keeping with the informal style, references to historical statements are seldom supplied. In cases that I was familiar with – and in a few that I looked up – the historical statements were accurate. The book is unusual in being a graduate text, as most texts of mathematics for physicists are at the upper undergraduate level. In Canada (and the US), physics programs do not usually offer a graduate-level course dedicated to mathematical methods and, often, courses in electricity and magnetism or quantum mechanics serve that purpose. There are, however, good arguments for such a course. First, it allows physics courses to concentrate on the relevant physics, which can be obscured by a need to teach too much mathematics in parallel. Second, Stone and Goldbart present a wide range of examples, from classical mechanics to quantum physics to particle physics to fluids and elastic media to nonlinear waves. Such breadth can counteract a tendency of courses to present their own subject in isolation from others, even though “real life” problems usually involve many aspects of physics (if not other disciplines). Whatever the level, it is important that textbooks on neighboring disciplines be kept up to date. In Stone and Goldbart’s words, the goal of such a text is to present “some of the mathematical methods and concepts that [students] will find useful in their research.” But usefulness evolves, and content should be re-evaluated regularly. A good part of the material (analysis, differential and integral equations), in Stone and Goldbart is taken from the traditional syllabus of mathematic methods, e.g. Courant and Hilbert’s Methods of Mathematical Physics, first published in 1924. A more unusual feature of the book is its emphasis on geometrical and topological methods (calculus on manifolds, etc.) with a goal of increasing their prominence within the standard physics curriculum. Previous attempts to do this have generally aimed at a more specialized audience, e.g., Gravitation, by Misner, Thorne, and Wheeler or A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry, P. Sekeres, Cambridge Univ. Press, 2004, which is aimed at the much-more-limited audience of mathematical physicists. One previous, similarly evangelical attempt to teach differential forms and the like to undergraduates is Bamberg and Sternberg’s two-volume Course in Mathematics for Students of Physics, Cambridge Univ. Press, 1988 and 1990, which was perhaps overly ambitious in attempting to teach relatively difficult material to a younger audience. Of course, everyone has an opinion as to what a first-year graduate student in physics should know. I would have liked to have seen a chapter on probability, statistics, and stochastic calculus. Dealing with randomness is something required by both theorists (e.g., for statistical mechanics and Monte Carlo simulations) and experimentalists (for making inferences from experimental data). Moreover, there are subtleties that can easily lead to mistakes if the mathematical fundamentals are misunderstood. (For example, see the recent discussion clarifying the thermodynamics of spatially varying diffusion coefficients by A.W.C. Lau and T.C. Lubensky, Phys. Rev. E 76, 011123, 2007.) One small complaint: the list of references is short. That is not necessarily a bad thing, as few students will want to consult a long list of books. But the references are mostly to classic texts at a higher level. It would have been useful to include also a few references to more elementary treatments (such as the Bamberg-Sternberg books mentioned above), to help bail out a reader in trouble. In conclusion, this book is an impressive achievement and deserves a place on every physicist’s bookshelf. Like many others, my department does not have a graduate course dedicated to mathematical methods. Reading this book makes me think that we should. John Bechhoefer Simon Fraser University Burnaby, British Columbia, Canada MODERN QUANTUM FIELD THEORY: A CONCISE INTRODUCTION, Tom Banks, Cambridge University Press, 2008, pp. 280, 150 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) ISBN: 978-0521850827 (hc), $78.00. Modern Quantum Field Theory by Tom Banks, is the latest in a long line of books on the subject of QFT seeking to replace Peskin and Schroeder as the definitive QFT text. The book itself is aimed at beginning graduate students in theoretical physics, starting with the standard introduction to second quantization and Feynman diagrams before moving on to more advanced topics not necessarily covered in other books. The introductory chapters on second quantization are well written, providing clear physical insight into the many subtleties involved in QFT. The presentation is more or less the same as in other QFT texts, albeit written in slightly more modern language, and there are many useful problems for the student to tackle at the end of each chapter. The reader is assumed to have a solid grasp of non-relativistic quantum mechanics, linear algebra and complex analysis. Whilst this serves to keep the chapters short, it may deter readers with a less formal background. More advanced readers will still get something useful from these chapters however. Once past the introduction, the book gets considerably more interesting. There is an entire chapter devoted to the quantization of massive electrodynamics using the Stueckelberg formalism, providing a clear illustration of loop effects in a theory with a Higgs mechanism. Such a model is often mentioned in other books, but never explicitly considered. The book then has a nice discussion of symmetry breaking and the theory of Nambu-Goldstone bosons, before moving onto a concise discussion of non-Abelian gauge theories – including anomalies, which are often ignored in other texts. The final part of the book covers the renormalization group and topological defects. The chapter on renormalization is particularly well written, and useful for both high energy and condensed matter theorists. The presentation is very clear, with several worked examples including the oneloop renormalization of QED and running couplings in non-Abelian gauge theory. The problems at the end of the chapter provide a strong, but important test, of the reader's understanding of the material. In conclusion, although this book is not likely to topple Peskin and Schroeder, it is still a useful text for beginning graduate students – relatively self-contained and concise. The book covers the basics in a refreshing manner, whilst also discussing interesting examples that are rarely considered in other texts. The introduction to the renormalization group is particularly insightful and recommended for all high energy and condensed matter theorists – making it a welcome, and slender, addition to the bookshelf. John Ward NEWTON AND THE COUNTERFEITER: THE UNKNOWN DETECTIVE CAREER OF THE WORLD’S GREATEST SCIENTIST, Thomas BOOKS Levenson, Houghton Mifflin Harcourt, 2009; pp: xii + 318, ISBN 978-0-15-101278-7 (hc); Price: $31.50. En avril 1696, Isaac Newton quitte sa résidence de Trinity College pour Londres, où le Roi vient de le nommer Gardien de la Monnaie. Jamais il ne reviendra à Cambridge et, dans les trente dernières années de sa vie, il ne se consacrera plus à la science que de façon épisodique. Levenson amorce son ouvrage en rappelant brièvement comment Newton en est arrivé là. Orphelin de père dès sa naissance, il est séparé à deux ans de sa mère remariée. Celle-ci voudrait qu'il prenne charge de la ferme familiale après ses études secondaires, mais l'oncle de Newton et son maître d'école la persuadent de le laisser s'inscrire à Cambridge. Presque sans appui, il se plonge alors dans les mathématiques et la science avec l'obsession qu'il mettra dans tout ce qu'il entreprendra. On connaît la suite: le retour chez lui pendant la peste de 1665-67 et l'amorce de la plupart de ses découvertes futures; les Principia en 1687, sous l'impulsion de Halley. Moins connue est la dépression de 1693, après ses échecs en alchimie et la faillite de ce qui a sans doute été l'amitié la plus intime de sa vie. Quand Newton obtient le poste de Londres, il vise depuis plusieurs années l'ascension sociale que le prestige des Principia et son appui aux nouveaux souverains Guillaume et Marie devraient lui mériter. Parallèlement à la vie de Newton, Levenson retrace celle de William Chaloner: naissance dans une famille pauvre, apprentissage à Birmingham chez un fabricant de clous où il va acquérir la maîtrise du travail des métaux. Peu après 1680, Chaloner tente sa chance à Londres, ville de 600 000 habitants dont Levenson nous décrit la repoussante insalubrité. Chaloner va d'abord vivre de métiers précaires, jusqu'à ce qu'il se lance dans la fabrication de fausse monnaie et s'enrichisse ainsi rapidement. Car la fausse monnaie représente alors une véritable plaie sociale. Malgré le spectre de la peine de mort qui plane sur les faussaires, on rogne les pièces et on les contrefait à grande échelle. Newton arrive à la Monnaie au moment où l'ensemble des sept millions de livres d'argent de l'Angleterre doit être refondu et frappé de nouveau. Le Maître de la Monnaie, Thomas Neale, est un pur incompétent. Qu'à cela ne tienne, Newton réalise le travail à sa place: il fait installer de nouvelles machines et supervise éventuellement la production de cinquante ou même de cent mille livres par semaine, alors qu'on en frappait à peine quinze mille auparavant. En moins de deux ans, la tâche est complétée. Mais le Gardien de la Monnaie a aussi une autre responsabilité: pourchasser, citer en justice et faire condamner les faux-monnayeurs. La plupart de ceux-ci sont de petits brigands sans envergure incapables d'affronter le nouveau Gardien. Mais Chaloner est beaucoup plus coriace, et n'a rien d'un enfant de coeur. Il n'hésite pas à dénoncer ses propres collaborateurs pour se tirer de mauvais pas. Il persuade deux imprimeurs de reproduire des textes favorables au roi déchu Jacques II, pour les dénoncer ensuite, toucher la récompense et les faire condamner à mort. Il va jusqu'à proposer ses services pour améliorer la sécurité de l'Hôtel de la Monnaie, pour mieux la déjouer, en accusant publiquement Newton d'incompétence et de malversations. Newton désobéit à l'ordre du Parlement de le laisser entrer. Et le Gardien engage alors une lutte à finie avec le faussaire. Newton interrogera plus de cent témoins pour étayer sa preuve, n'hésitant pas à rencontrer les informateurs jusque dans les tavernes des quartiers populaires de Londres. Chaloner est finalement traduit en justice. Le procès a lieu, comme aujourd'hui encore, au tribunal de l'Old Bailey, mais selon des procédures expéditives: un jury peut entendre dix causes le même jour; l'accusé n'a pas la présomption d'innocence, il se défend lui-même et ne prend véritablement connaissance de la preuve qu'au moment du procès. La preuve de Newton est dévastatrice et, malgré des failles techniques que le juge ne retient pas, Chaloner est trouvé coupable. Il sera pendu quelques semaines plus tard. Directeur du programme de rédaction scientifique du MIT, Levenson nous a livré un ouvrage passionnant et fort bien documenté. Des notes détaillées renvoient systématiquement aux sources originales ou secondaires. La bibliographie et l'index complètent le livre. Newton and the Counterfeiter nous révèle de manière très vivante certaines facettes moins connues de la personnalité et de la vie tellement remplie de l'auteur des Principia. Louis Marchildon Université du Québec à Trois-Rivières PHYSICS OF SOLITONS, Thierry Dauxois and Michel Peyrard, Cambridge University Press, Cambridge, 2006, 411 pages, ISBN: 0-52185421-0 (hc), US $80.00. A water soliton (also called a solitary water wave) was first observed by John Scott Russell in 1834. The weakly dispersive, nonlinear structure was described in 1895 by D. Korteweg and G. de Vries, with a mathematical formulation called the KdV equation. The soliton is an exceptionally stable standing wave which appears in many areas, such as electrical lines, optical fibres, plasmas, crystals, ferroelectric materials, magnetic systems, polymers, biological molecules, etc. This book was written on the basis of the authors' graduate courses, with an emphasis on modeling nonlinearities using soliton equations. It introduces basic properties and formalisms of different classes of solitons (Part I), offers mathematical approaches for the study of solitons (Part II), and provides applications in solid state, atomic and biological physics (Parts III, IV). It also includes a few very useful appendices (Part V). Part I describes the KdV equation, the SineGordon equation, the Schrödinger equation, and ion-acoustic plasma modelings. Part II introduces linearization around a soliton, the collectivecoordinate method and the inverse-scattering transform. Part III discusses the Fermi-Pasta- PHYSICS IN Ulam problem, simple models for dislocations, ferroelectric domain walls, and incommensurate phases, and exposes solitons in magnetic systems, conducting polymers, and Bose-Einstein condensates. Part IV presents energy localization and transfer in proteins, nonlinear dynamics and statistics of DNA. After a conclusive comment on the existence of solitons, Part V derives the KdV equation for surface hydrodynamic waves, and formulates it for a continuous medium and a harmonic oscillator. A list of figures, references and an index are also included in the book. However, as a textbook produced in the 2000s, it is a pity that it does not contain the physics of large-amplitude solitons, though entitled "Physics of solitons". As a matter of fact, largeamplitude solitary waves have been developed rapidly since 1957 when I.B. Bernstein, J.M. Green, and M.D. Kruskal predicted the existence of the non-wave structures in plasmas (called the BGK mode). In particular, the book does not provide any information about the advances made in the 21st century, e.g., "oscillitons" which describes a traditional soliton the amplitude of which is violently modulated by small-amplitude oscillations. Notwithstanding this weakness, this textbook gives an instructive view of the physics of solitons. It is thus a good reference book for undergraduate students and researchers with a basic knowledge of physics, and classical and quantum mechanics. John Z. G. Ma Space Science Branch, Canadian Space Agency PRINCIPLES OF QUANTUM GENERAL RELATIVITY, Eduard Prugovecki, World Scientific, 1994, pp:351, ISBN 9810220774 (pbk), US $36.00 pbk. In 1994, and today in 2010, there was and still is no generally accepted consistent and satisfactory quantum general relativity (QGR), also known as “quantum gravity” (QG). Such a theory would be the unification of two fundamental theories of physics, namely, classical general relativity (CGR) and quantum field theory (QFT). While much progress has been achieved, with more than one promising line of attack, each of the stream of efforts seems to have fallen short of meeting all the necessary conditions. This book is the review, postulation, and development of one such stream of attack on QG, namely that of first geometrizing the quantum foundations in the absence of gravity. Eduard notes that geometrical quantization appears to be the only approach in which the concept of a fundamental length appears possible, and such an approach is known to help remove singularities from the theory. In this regard, Eduard reviews extensively through this book, but explicitly in the first chapter, various principles encountered in working on the QG problem. In the second chapter he reviews the modern formalization of CGR using classical frame bundles. CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 151 LIVRES The next several chapters develop the conception of quantum fibre bundles over a Lorentzian spacetime manifold. Within this formulation, the approach is therefore to develop a QG in a similar manner to that of the way CGR was developed from special relativity via the equivalence principle. In essence, Eduard employs a quantum equivalence principle that roughly says that locally a free falling quantum system should behave exactly as a similar system in the absence of gravity. While the program seems straightforward, it proves to be a significant task, as Eduard spends several intense mathematical chapters developing boson and fermion super fibre bundle field geometric quantization upon which transformation to curved space-time can occur. In the process, Eduard discusses an impressive diversity of considerations including topics such as quantum particles providing natural space-time clocks, various approaches to quantization, and path-integral approaches in a geometrized environment. The end result of Eduard program is a quantum gravitational field mediated by graviton of spin 2 and with zero-mass, and where quantum gravitational fluctuations manifest themselves as super local multgraviton states described on superfibre over a quantum spacetime supermanifold. Ghost states and like, are all magically removed by a quantum spacetime governed by a connection based on a quantum gravitational gauge supergroup, (i.e. BRST quantization). The final result appears to be a fundamentally consistent approach to QG. Thus, I think this book should be in the library of every researcher on QG. Having now read through this book, I am convinced that the various fuzzy space-time, noncommutative geometries, approaches currently in development for QG which flow from Eduard’s work, have much more promise than I had before realized. Colin Carbno Sasktel 152 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 ) PIC NEWS UPCOMING ISSUES NOUVELLES DE LA PAC PROCHAINS NUMÉROS THE JULY-SEPTEMBER 2010 ISSUE LE This exciting issue will feature articles related to the largest non-partnered CAP congress which was held at the University of Toronto in June 2010 (over 800 participants!). In addition to the approved feature articles, look for summaries of the Herzberg lecture given by Charles Townes, 1964 Nobel Prize in Physics the best student paper presentations, and the 2010 medal winners (including a couple of interviews). The annual report by the then CAP President, Robert Mann, will also be featured. Ce numéro fascinant comprendra des articles reliés au plus grand congrès de l’ACP sans partenaires qui a eu lieu à l’Université de Toronto en juin 2010 (avec plus de 800 participants!). En plus d’articles de fonds approuvés, vous trouverez des sommaires de la conférence de Herzberg donnée par Charles Townes, prix Nobel en physique en 1964, des meilleures présentations étudiantes, et des médaillés de 2010 (y compris deux entrevues). Le rapport annuel du président sortant de l’ACP Robert Mann sera aussi inclus. THE OCTOBER-DECEMBER 2010 ISSUE LE The CAP has partnered with APS, OSA and SPIE on LaserFest 2010 a celebration of 50th anniversary of the laser. L’ACP fut partenaire avec l’APS, OSA et SPIE dans le LaserFest 2010 – une célébration du 50 ième anniversaire du laser. As part of the CAP’s Laserfest celebration, Paul Corkum, University of Ottawa/NRC, in partnership with the PiC Editor, Béla Jóos, is producing a mini-theme issue on the 50 years of lasers in Canada. This theme will be featured as a part of the Oct-Dec. 2010 issue. Une composante de la célébration de Laserfest par l’ACP est un mininuméro à thème sur les cinquante années du laser au Canada édité par Paul Corkum de l’Université d’Ottawa et du CNRC, en partenariat avec l’ éditeur de la Physique au Canada, Béla Joós. Cette célébrationl fera partie du numéro d’octobre à décembre 2010. NUMÉRO DE JUILLET À SEPTEMBRE 2010 NUMÉRO D’OCTOBRE À DÉCEMBRE 2010 ALL UNDELIVERABLE COPIES IN CANADA / TOUTE CORRESPONDANCE NE POUVANT ETRE LIVREE AU CANADA should be returned to / devra être retournée à: Canadian Association of Physicists/ l’Association canadienne des physiciens et physiciennes Suite/bur. 112 Imm. McDonald Bldg. Canadian Publications Product Sales Agreement No. 40036324 / Numéro de convention pour les envois de publications canadiennes : 40036324 Univ. of/ d’Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5