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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
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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
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C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 )
Normand Mousseau
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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-
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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
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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.
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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.
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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).
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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
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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
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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.
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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
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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.
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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
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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-
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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
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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
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3.
4.
5.
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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
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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.
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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.
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B. Batell, M. Pospelov and A. Ritz, Phys. Rev. D79, 115008 (2009) [arXiv:0903.0363 [hep-ph]].
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J.D. Bjorken, R. Essig, P. Schuster and N. Toro, arXiv:0906.0580 [hep-ph].
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PHYSICS
IN
CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 113
LA PHYSIQUE AU CANADA
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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
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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.
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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.
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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!
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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
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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
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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
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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.
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“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.
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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
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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
–—†‡–‘”•Š‡‡–ƒ†‡ƒ…Š‡”ǯ•‘–‡•
2. BLACK BOX DEMONSTRATION
‡–ƒ‹Ž‡††‡•…”‹’–‹‘‘ˆŠ‘™–‘…‘†—…––Š‡†‡‘•–”ƒ–‹‘ƒ†‹•–”—…–‹‘•‘ˆŠ‘™–‘„—‹Ž†›‘—”‘™„Žƒ…„‘š‘†‡Ž‘ˆ
•…‹‡…‡Ǥ
MEASURING PLANCK’S CONSTANT
INTRODUCTION
Š‹•ƒ…–‹˜‹–›’”‘˜‹†‡•ƒ•‹’Ž‡†‡‘•–”ƒ–‹‘‘ˆ–Š‡“—ƒ–‹œƒ–‹‘‘ˆŽ‹‰Š–ƒ†ƒ‡ƒ•‘ˆ‡ƒ•—”‹‰Žƒ…ǯ•…‘•–ƒ–ȋŠȌǤ
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Žƒ…ǯ•…‘•–ƒ–ȋŠα͸Ǥ͸͵šͳͲǦ͵Ͷ•Ȍ‹•ƒ—‹˜‡”•ƒŽ…‘•–ƒ––Šƒ–Ž‹‡•ƒ––Š‡Š‡ƒ”–‘ˆ“—ƒ–—’Š›•‹…•Ǥ–†‡ϐ‹‡•–Š‡•…ƒŽ‡
‘ˆ–Š‹•–Š‡‘”›Œ—•–ƒ•–Š‡•’‡‡†‘ˆŽ‹‰Š–ȋ…α͵ǤͲͲšͳͲͺȀ•Ȍ†‡ϐ‹‡•–Š‡•…ƒŽ‡‘ˆ•’‡…‹ƒŽ”‡Žƒ–‹˜‹–›Ǥ
Š‹•ƒ…–‹˜‹–›‡ƒ„Ž‡••–—†‡–•–‘‡ƒ•—”‡Žƒ…ǯ•…‘•–ƒ–—•‹‰ƒ•‹’Ž‡‡Ž‡…–”‘‹……‹”…—‹–ǤŠ‡…‹”…—‹–‹•‹‡š’‡•‹˜‡
ƒ†…‘–ƒ‹•‘Ž›ƒ͸Ǧ˜‘Ž–„ƒ––‡”›ǡƒǡƒ”‡•‹•–‘”ǡƒ˜‘Ž–‡–‡”ǡƒˆ‡™™‹”‡•ǡƒ†ƒ’‘–‡–‹‘‡–‡”Ǥ—””‡–ϐŽ‘™•™Š‡ƒ
Žƒ”‰‡‡‘—‰Š’‘–‡–‹ƒŽ†‹ˆˆ‡”‡…‡‹•ƒ’’Ž‹‡†ƒ…”‘••–Š‡ǤŠ‡‡Ž‡…–”‹…ƒŽ‡‡”‰›Ž‘•–„›‡ƒ…Š‡Ž‡…–”‘‹•…‘˜‡”–‡†‹–‘
–Š‡‡‡”‰›‘ˆƒ‹†‹˜‹†—ƒŽ’Š‘–‘ǤŠ‡‡‡”‰›‘ˆ–Š‹•’Š‘–‘‹•‰‹˜‡„›–Š‡ˆ‘”—ŽƒαŠˆǡ™Š‡”‡ˆ‹•–Š‡’Š‘–‘ǯ•
ˆ”‡“—‡…›Ǥ›‡ƒ•—”‹‰–Š‡’‘–‡–‹ƒŽ†‹ˆˆ‡”‡…‡ƒ…”‘••ƒ—„‡”‘ˆ†‹ˆˆ‡”‡–…‘Ž‘—”‡†•ǡ•–—†‡–•…ƒ…ƒŽ…—Žƒ–‡ŠǤ
›’‹…ƒŽŽ›ǡ–Š‹•ƒ…–‹˜‹–›…ƒ„‡…‘’Ž‡–‡†™‹–Š‹ƒŠ‘—”ƒ†‡ƒ•—”‡Žƒ…ǯ•…‘•–ƒ––‘™‹–Š‹ƒƒ……—”ƒ…›‘ˆŽ‡••–Šƒ
ʹͲΨǤ‹•–”—…–‹‘•‘ˆŠ‘™–‘„—‹Ž†›‘—”‘™„Žƒ…„‘š‘†‡Ž‘ˆ•…‹‡…‡Ǥ
ǣ–—†‡–•‹˜‡•–‹‰ƒ–‡–Š‡“—ƒ–‹œƒ–‹‘‘ˆŽ‹‰Š–ƒ†‡ƒ•—”‡Žƒ…ǯ•…‘•–ƒ–—•‹‰•Ǥ
PHYSICS
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MEASURING PLANCK’S CONSTANT
STUDENT WORKSHEET
AIM
‘†‡‘•–”ƒ–‡–Š‡“—ƒ–‹œƒ–‹‘‘ˆŽ‹‰Š–ƒ†–‘‡ƒ•—”‡
Žƒ…ǯ•…‘•–ƒ–ȋŠȌǤ
BACKGROUND
Š‡‡‡”‰›Ž‘•–„›ƒ•‹‰Ž‡‡Ž‡…–”‘–Šƒ–’ƒ••‡•–Š”‘—‰Šƒ
Ž‹‰Š–Ǧ‡‹––‹‰†‹‘†‡ȋȌ‹•…‘˜‡”–‡†‹–‘–Š‡‡‡”‰›‘ˆ
‘‡’Š‘–‘Ǥ
—–‹Ž–Š‡Œ—•–„‡‰‹•–‘‰Ž‘™Ǥ‡…‘”†–Š‡’‘–‡–‹ƒŽ
†‹ˆˆ‡”‡…‡ƒ–™Š‹…Š–Š‹•Šƒ’’‡•Ǥ
‘„ƒ…™ƒ”†•ƒ†
ˆ‘”™ƒ”†•’ƒ•––Š‡’‘‹–ƒ–™Š‹…Š–Š‡Œ—•–„‡‰‹•–‘
‰Ž‘™ƒˆ‡™–‹‡•–‘Ž‘…ƒ–‡‹–ƒ•ƒ……—”ƒ–‡Ž›ƒ•’‘••‹„Ž‡Ǥ
Step 5. ‡’‡ƒ––‡’Ͷˆ‘”ƒŽŽ–Š‡‘–Š‡”•ǤŽ™ƒ›•–—”
–Š‡’‘–‡–‹‘‡–‡”‘„ˆ—ŽŽ›…Ž‘…™‹•‡„‡ˆ‘”‡…Šƒ‰‹‰
••‘–Š‡‹‹–‹ƒŽ˜‘Ž–ƒ‰‡ƒ…”‘••‡ƒ…Š‹•ͲǤ
‡ȟኈ
‡α‡Ž‡‡–ƒ”›…Šƒ”‰‡αͳǤ͸šͳͲǦͳͻ
οα’‘–‡–‹ƒŽ†‹ˆˆ‡”‡…‡ƒ…”‘••
ˆαˆ”‡“—‡…›‘ˆƒ’Š‘–‘‡‹––‡†„›
MATERIALS
»
»
»
»
»
»
‡–‘ˆͷ•
͸„ƒ––‡”›
ͳπ’‘–‡–‹‘‡–‡”
͵͵Ͳ𔇕‹•–‘”
˜‘Ž–‡–‡”
ͷ…‘‡…–‹‰Ž‡ƒ†•
Step 6. —ƒ”‹œ‡›‘—””‡•—Ž–•‹ƒ–ƒ„Ž‡•‹‹Žƒ”–‘–Š‡
ˆ‘ŽŽ‘™‹‰ǣ
CAUTION - Do not stare directly at a brightly lit LED.
PROCEDURE
Step 1. ”‹‡––Š‡’‘–‡–‹‘‡–‡”•‘–Šƒ––Š‡–‡”‹ƒŽ•ƒ”‡
’‘‹–‹‰–‘™ƒ”†•›‘—Ǥ—”–Š‡‘„ˆ—ŽŽ›…Ž‘…™‹•‡Ǥ
‘‡…––Š‡‡‰ƒ–‹˜‡–‡”‹ƒŽ‘ˆ–Š‡„ƒ––‡”›–‘–Š‡Ž‡ˆ–Ǧ
Šƒ†–‡”‹ƒŽ‘ˆ–Š‡’‘–‡–‹‘‡–‡”ƒ†–Š‡’‘•‹–‹˜‡
–‡”‹ƒŽ‘ˆ–Š‡„ƒ––‡”›–‘–Š‡”‹‰Š–ǦŠƒ†–‡”‹ƒŽ‘ˆ–Š‡
’‘–‡–‹‘‡–‡”ǡƒ••Š‘™‹–Š‡†‹ƒ‰”ƒǤ
Step 2.‘‡…–ƒ›‘‡‘ˆ–Š‡•–‘–Š‡͵͵Ͳ𔇕‹•–‘”
—•‹‰ƒ™‹”‡Ǥ‘‡…–„‘–Š‘ˆ–Š‡•‡…‘’‘‡–•„‡–™‡‡
–Š‡…‡–”ƒŽƒ†”‹‰Š–ǦŠƒ†–‡”‹ƒŽ•‘ˆ–Š‡’‘–‡–‹‘‡–‡”
ƒ••Š‘™‹–Š‡†‹ƒ‰”ƒȋ™‹–Š–Š‡Ž‘‰‡”™‹”‡‘ˆ–Š‡
ƒ––ƒ…Š‡†–‘–Š‡”‹‰Š–ǦŠƒ†–‡”‹ƒŽȌǤ
Step 3.‘‡…––Š‡˜‘Ž–‡–‡”ƒ…”‘••–Š‡Ǥ
Step 4. Ž‘™Ž›‹…”‡ƒ•‡–Š‡’‘–‡–‹ƒŽ†‹ˆˆ‡”‡…‡ƒ…”‘••–Š‡
„›–—”‹‰–Š‡’‘–‡–‹‘‡–‡”‘„…‘—–‡”…Ž‘…™‹•‡
—–‹Ž–Š‡Œ—•–„‡‰‹•–‘‰Ž‘™Ǥ‡…‘”†–Š‡’‘–‡–‹ƒŽ
ANALYSIS
Step 1ǤŽ‘–ƒ‰”ƒ’Š‘ˆ’‘–‡–‹ƒŽ†‹ˆˆ‡”‡…‡ȋ›Ǧƒš‹•Ȍ˜‡”•—•
ˆ”‡“—‡…›ȋšǦƒš‹•ȌǤ
Step 2. ”ƒ™–Š‡Ž‹‡‘ˆ„‡•–ϐ‹–ƒ†‡ƒ•—”‡‹–••Ž‘’‡Ǥ
•‡–Š‹••Ž‘’‡–‘…ƒŽ…—Žƒ–‡Žƒ…ǯ•…‘•–ƒ–„›—•‹‰–Š‡
‡“—ƒ–‹‘‡ȟኈǤ
QUESTIONS
Step 1. Šƒ–‹•–Š‡’‡”…‡–ƒ‰‡‡””‘”‹›‘—”…ƒŽ…—Žƒ–‡†
˜ƒŽ—‡ˆ‘”Žƒ…ǯ•‘•–ƒ–ǫ
Step 2.‰”‡‡Žƒ•‡”’‘‹–‡”’”‘†—…‡•ͷ͵ͲŽ‹‰Š–™‹–Š
ƒ’‘™‡””ƒ–‹‰‘ˆͳǤͲǤ‘™ƒ›’Š‘–‘•†‘‡•–Š‡
Žƒ•‡”’”‘†—…‡‡ƒ…Š•‡…‘†ǫ
Step 3. ‡ƒ–Š‡””‡’‘”–•‘‹–‘”—Ž–”ƒ˜‹‘Ž‡–ȋȌŽ‹‰Š–
Ž‡˜‡Ž•ǤŠ›‹•Ž‹‰Š–ƒ…‘…‡”ǫ
136 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 )
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MEASURING PLANCK’S CONSTANT
TEACHER’S NOTES
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MATERIALS
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»
»
‡–‘ˆ•–Šƒ–’”‘†—…‡ϐ‹˜‡†‹ˆˆ‡”‡–…‘Ž‘—”•‘ˆ
Ž‹‰Š–‹–Š‡˜‹•‹„Ž‡•’‡…–”—ǡ‡‰Ǥ‹‰Š–‹–‡•
Ǧͳ͵͹ʹǡǦͳ͵ͻ͵ǡǦͳ͵ͷ͸ǡǦͳ͵͵͹ƒ†
ǦͷͲͷͺǤ
͸„ƒ––‡”›
ͳπ’‘–‡–‹‘‡–‡”
͵͵Ͳ𔇕‹•–‘”
˜‘Ž–‡–‡”
ͷ…‘‡…–‹‰Ž‡ƒ†•
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Š‡‡‡”‰›Ž‘•–„›‡ƒ…Š‡Ž‡…–”‘‹•α‡¨ǡ™Š‡”‡‡
‹•–Š‡‡Ž‡‡–ƒ”›…Šƒ”‰‡ȋͳǤ͸šͳͲǦͳͻȌƒ†¨‹•
–Š‡’‘–‡–‹ƒŽ†‹ˆˆ‡”‡…‡ƒ…”‘••–Š‡Ǥ
Š‡‡‡”‰›‘ˆƒ’Š‘–‘‘ˆˆ”‡“—‡…›ˆ‹•αŠˆǡ
™Š‡”‡Š‹•Žƒ…ǯ•…‘•–ƒ–ȋŠα͸Ǥ͸͵šͳͲǦ͵Ͷ•ȌǤ
“—ƒ–‹‰–Š‡–™‘‡‡”‰‹‡•›‹‡Ž†•‡¨αŠˆ
Ž‘––‹‰¨ƒ‰ƒ‹•–ˆˆ‘”•‘ˆ•‡˜‡”ƒŽ†‹ˆˆ‡”‡–
…‘Ž‘—”•’”‘†—…‡•ƒ•–”ƒ‹‰Š–Ž‹‡‘ˆ•Ž‘’‡ŠȀ‡Ǥ
‡ƒ•—”‹‰–Š‡‰”ƒ’Šǯ••Ž‘’‡ƒ†—Ž–‹’Ž›‹‰‹–„›
‡›‹‡Ž†•Žƒ…ǯ•…‘•–ƒ–Ǥ
USEFUL CONSTANTS
…α͵ǤͲšͳͲͺȀ•
‡αͳǤ͸šͳͲǦͳͻ
Šα͸Ǥ͸͵šͳͲǦ͵Ͷ•
EXPERIMENT SET UP
CAUTIONS
1. Students should not stare directly at LEDs when
they are brightly lit.•ƒ”‡•ƒˆ‡™Š‡–Š‡›Œ—•–„‡‰‹
–‘‰Ž‘™ǡ„—––Š‡›“—‹…Ž›„‡…‘‡„”‹‰Š–ƒ•–Š‡’‘–‡–‹ƒŽ
†‹ˆˆ‡”‡…‡ƒ…”‘••–Š‡‹…”‡ƒ•‡•ƒ„‘˜‡–Š‡–Š”‡•Š‘Ž†
˜ƒŽ—‡Ǥ‡‡•’‡…‹ƒŽŽ›…ƒ”‡ˆ—Ž™‹–Š–Š‡„Ž—‡ƒ•–Š‡
—’’‡”’ƒ”–‘ˆ‹–•ˆ”‡“—‡…›•’‡…–”—‹•˜‡”›…Ž‘•‡–‘–Š‡
—Ž–”ƒǦ˜‹‘Ž‡–”‡‰‹‘™Š‹…Š…ƒ…ƒ—•‡’‡”ƒ‡–‡›‡
†ƒƒ‰‡Ǥ–—†‡–••Š‘—Ž†‘–•–ƒ”‡ƒ––Š‡„Ž—‡
‡˜‡™Š‡‹–‹•†‹Ž›Ž‹–Ǥ
Figure 1
Diagram and photo of circuit used.
PURCHASING LEDS AND POTENTIOMETERS
THEORY
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2. LEDs can be destroyed if the current flowing
through them is too large. Š‡’—”’‘•‡‘ˆ–Š‡͵͵Ͳȳ
”‡•‹•–‘”…‘‡…–‡†‹•‡”‹‡•™‹–Š–Š‡‹•–‘Ž‹‹––Š‡
…—””‡–ϐŽ‘™‹‰–Š”‘—‰Š–Š‡ǤŠ‹•…—””‡–•Š‘—Ž†„‡
‘‘”‡–Šƒƒ„‘—–ͷͲǤ
•ƒ”‡‹‡š’‡•‹˜‡ƒ†”‡ƒ†‹Ž›ƒ˜ƒ‹Žƒ„Ž‡ǤŠ‡›‘ˆ–‡
…‘•–Ž‡••–Šƒƒ†‘ŽŽƒ”ƒ†…ƒ„‡’—”…Šƒ•‡†ˆ”‘ƒ›
‡Ž‡…–”‘‹…•–‘”‡•‘”‘”†‡”‡†‘Ž‹‡Ǥ‘•–„”ƒ†•‘ˆ•
ƒ”‡•—‹–ƒ„Ž‡ˆ‘”—•‡‹–Š‹•Žƒ„‘”ƒ–‘”›ƒ…–‹˜‹–›Ǥ›•‹œ‡‘ˆ
‹•ƒŽ•‘•—‹–ƒ„Ž‡„—–‘‡‘ˆ–Š‡‘•–…‘‘•‹œ‡•‹•
ͷ‹†‹ƒ‡–‡”Ǥ‘–‡–‹‘‡–‡”•ƒ”‡ƒŽ•‘‹‡š’‡•‹˜‡
ƒ†”‡ƒ†‹Ž›ƒ˜ƒ‹Žƒ„Ž‡ǤŠ‡‘•–…‘‘–›’‡Šƒ•–Š”‡‡
–‡”‹ƒŽ•ƒ†–Š‹•‹•–Š‡–›’‡—•‡†‹–Š‹•Žƒ„ƒ…–‹˜‹–›Ǥ
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Š‡™‡ƒ’’Ž›ƒŽƒ”‰‡‡‘—‰Š’‘–‡–‹ƒŽ†‹ˆˆ‡”‡…‡
ƒ…”‘••ƒŽ‹‰Š–Ǧ‡‹––‹‰†‹‘†‡ȋȌǡ‹–‡‹–•’Š‘–‘•
–Šƒ–ƒŽŽŠƒ˜‡–Š‡•ƒ‡ˆ”‡“—‡…›Ǥ
Š‡–Š‡Œ—•–„‡‰‹•–‘‰Ž‘™ǡ–Š‡‡‡”‰›Ž‘•–
„›‡ƒ…Š‡Ž‡…–”‘ƒ•‹–’ƒ••‡•–Š”‘—‰Š–Š‡‹•
…‘˜‡”–‡†‹–‘–Š‡‡‡”‰›‘ˆƒ•‹‰Ž‡’Š‘–‘Ǥ
3. The potentiometer can be destroyed if wired
incorrectly. –—†‡–••Š‘—Ž†„‡…ƒ”‡ˆ—Ž™Š‡™‹”‹‰–Š‡
’‘–‡–‹‘‡–‡”Ǥˆ–Š‡›™‹”‡‹–‹…‘””‡…–Ž›ǡ–Š‡›…ƒ…”‡ƒ–‡ƒ
•Š‘”–…‹”…—‹–™Š‹…ŠŽ‡ƒ†•–‘ƒŽƒ”‰‡’‘–‡–‹ƒŽ†‹ˆˆ‡”‡…‡
ƒ…”‘••ƒŽ‘™”‡•‹•–ƒ…‡ǤŠ‹•…ƒ”‡•—Ž–‹–Š‡
’‘–‡–‹‘‡–‡”Š‡ƒ–‹‰—’”ƒ’‹†Ž›’”‘†—…‹‰ƒ˜‹•‹„Ž‡
“—ƒ–‹–›‘ˆ•‘‡ƒ†…‡ƒ•‹‰–‘ˆ—…–‹‘Ǥ‘’”‡˜‡–
’”‘„Ž‡•ˆ”‘‘……—””‹‰ǡ›‘—ƒ›™‹•Š–‘‹•’‡…–›‘—”
•–—†‡–•ǯ…‹”…—‹–•„‡ˆ‘”‡ƒŽŽ‘™‹‰–Š‡–‘…‘‡…––Š‡
„ƒ––‡”›Ǥ‘—ƒ›ƒŽ•‘™‹•Š–‘‰‹˜‡›‘—”•–—†‡–•‡š–”ƒ
ƒ••‹•–ƒ…‡„›Žƒ„‡ŽŽ‹‰–Š‡–‡”‹ƒŽ•‘ˆ–Š‡’‘–‡–‹‘‡–‡”
ƒ†–Š‡ȋ™‹–Š–ƒ’‡ǡˆ‘”‡šƒ’Ž‡ǡ‘”„›…‘Ž‘—”Ǧ
…‘†‹‰–Š‡™‹–Š’ƒ‹–Ȍ–‘‹†‹…ƒ–‡™Še”‡–Š‡›•Š‘—Ž†„‡
…‘‡…–‡†Ǥ
PHYSICS
IN
CANADA / VOL. 66, NO. 2 ( Apr.-June 2010 ) C 137
E DUCATION CORNER
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MEASURING PLANCK’S CONSTANT
TEACHER’S NOTES CONTINUED
SAMPLE RESULTS
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ERRORS
Š‡”‡ƒ”‡•‡˜‡”ƒŽ’‘••‹„Ž‡•‘—”…‡•‘ˆ‡””‘”‹–Š‹•‡š’‡”‹Ǧ
‡–Ǥ‹”•–ǡ–Š‡”‡‹•–Š‡Š—ƒ‡””‘”ƒ••‘…‹ƒ–‡†™‹–Š
•‡‡‹‰–Š‡’‘‹–ƒ–™Š‹…Š–Š‡Œ—•–„‡‰‹•–‘‰Ž‘™Ǥ
Š‡”‡•—Ž–•‘„–ƒ‹‡†…ƒ˜ƒ”›†‡’‡†‹‰‘™Š‡–Š‡”‘”
‘–ƒ˜‹‡™‹‰–—„‡‹•—•‡†–‘„Ž‘…‘—–‘–Š‡”•‘—”…‡•‘ˆ
Ž‹‰Š–ǡ™Š‡–Š‡”‘”‘–”‘‘Ž‹‰Š–•ƒ”‡‘ǡ‡–…Ǥ‘”‘’–‹ƒŽ
”‡•—Ž–•ǡ—•‹‰ƒ˜‹‡™‹‰–—„‡‹•”‡…‘‡†‡†Ǥ
‘–Š‡”•‘—”…‡‘ˆ‡””‘”‹•–Š‡ˆƒ…––Šƒ–•†‘‘–‡‹–
ƒ•‹‰Ž‡ˆ”‡“—‡…›‘ˆŽ‹‰Š–Ǥ•–‡ƒ†ǡ–Š‡›‡‹–ƒƒ””‘™
•’‡…–”—™‹–Šƒ™‹†–Š‘ˆƒ’’”‘š‹ƒ–‡Ž›͸ͲǤŠ‡
ˆ”‡“—‡…›˜ƒŽ—‡•’Ž‘––‡†‘–Š‡Š‘”‹œ‘–ƒŽƒš‹•ƒ”‡–Š‡
…‡–”ƒŽˆ”‡“—‡…›‡‹––‡†„›–Š‡•ǡ„—–™Š‡–Š‡
•Œ—•–„‡‰‹–‘‰Ž‘™ǡ™‡–›’‹…ƒŽŽ›•‡‡•Ž‹‰Š–Ž›Ž‘™‡”
ˆ”‡“—‡…‹‡•Ǥ
STUDENT WORKSHEET ANSWERS
1. Š‡•ƒ’Ž‡”‡•—Ž–‘ˆŠα͹Ǥ͸šͳͲǦ͵Ͷ•‹•ͳͷΨ‰”‡ƒ–‡”
–Šƒ––Š‡‘™˜ƒŽ—‡Ǥ
2. Š‡ˆ”‡“—‡…›‘ˆ‰”‡‡Ž‹‰Š–‹•‰‹˜‡„›–Š‡ˆ‘ŽŽ‘™‹‰
‡“—ƒ–‹‘ǣ
ANALYSIS
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•Ž‘’‡‘ˆ‰”ƒ’ŠαŠȀ‡αȋͲǤͳͻȌȀȋͶǤͲšͳͲͳ͵œȌα
ͶǤ͹ͷšͳͲǦͳͷ•Ȁ
ŠαȋͶǤ͹ͷšͳͲǦͳͷ•ȀȌȋͳǤ͸šͳͲǦͳͻȌα͹Ǥ͸šͳͲǦ͵Ͷ
•
Š‹•”‡•—Ž–‹•ͳͷΨƒ„‘˜‡–Š‡–”—‡˜ƒŽ—‡ǡ™Š‹…Š‹•
”‡ƒ•‘ƒ„Ž‡ˆ‘”–Š‹•Žƒ„Ǥ””‘”•‘ˆͳͷǦʹͲΨƒ”‡
…‘‘Ǥ
‘–‡–Šƒ––Š‡‰”ƒ’ŠŠƒ•ƒˆƒŽ•‡‘”‹‰‹Ǥˆ–Š‡Ž‹‡‘ˆ„‡•–
ϐ‹–‹•‡š–‡†‡†–‘–Š‡Ž‡ˆ–‹–†‘‡•‘–’ƒ••–Š”‘—‰Š–Š‡
‘”‹‰‹ǡ„—–‹•–‡ƒ†‹–‡”…‡’–•–Š‡ȟƒš‹•ƒ–ǦͲǤͺͲǤ‡
”‡ƒ•‘ˆ‘”–Š‡‹–‡”…‡’–‘–„‡‹‰Ͳ‹•–Š‡ˆƒ…––Šƒ––Š‡
ˆ‘”—Žƒ‡ȟኈ‹•‘Ž›ƒ’’”‘š‹ƒ–‡Ǥ”‡ƒŽ‹–›ǡ‡ȟ䊈
ƒ•‡Ž‡…–”‘•‹–Š‡Šƒ˜‡•‘‡–Š‡”ƒŽ‡‡”‰›ǤŠ‡
–Š‡’‘–‡–‹ƒŽ†‹ˆˆ‡”‡…‡ƒ…”‘••–Š‡‹•Ž‡••–ŠƒŠˆǡ–Š‹•
–Š‡”ƒŽ‡‡”‰›…ƒ’”‘˜‹†‡‡‘—‰Š‡š–”ƒ‡‡”‰›ˆ‘”ƒ
’Š‘–‘™‹–Šˆ”‡“—‡…›ˆ–‘„‡…”‡ƒ–‡†Ǥ‘–‡ǡŠ‘™‡˜‡”ǡ–Šƒ–
–Š‡–Š‡”ƒŽ‡‡”‰›‘ˆ‡Ž‡…–”‘•‹•–›’‹…ƒŽŽ›•‹‰‹ϐ‹…ƒ–Ž›
Ž‡••–Šƒ‡ȟƒ†•‘…ƒ‘–ƒ……‘—–ˆ‘”–Š‡‡–‹”‡
†‡˜‹ƒ–‹‘‘ˆ–Š‡‹–‡”…‡’–ˆ”‘–Š‡‘”‹‰‹Ǥ
‡”‰›‘ˆƒ‰”‡‡’Š‘–‘ǣ
Š‡—„‡”‘ˆ’Š‘–‘•‡‹––‡†„›–Š‡Žƒ•‡”‡ƒ…Š•‡…‘†
‹•ǣ
3. Ž–”ƒǦ˜‹‘Ž‡–Ž‹‰Š–Šƒ•ƒŠ‹‰Š‡”ˆ”‡“—‡…›–Šƒ˜‹•‹„Ž‡
Ž‹‰Š–ƒ†•‘ǡ—•‹‰–Š‡ˆ‘”—ŽƒαŠˆǡ—Ž–”ƒǦ˜‹‘Ž‡–
’Š‘–‘•Šƒ˜‡‘”‡‡‡”‰›–Šƒ˜‹•‹„Ž‡‘‡•ǤŠ—•ǡ
—Ž–”ƒǦ˜‹‘Ž‡–’Š‘–‘•…ƒ…ƒ—•‡‘”‡†ƒƒ‰‡–‘–Š‡
…‡ŽŽ•‹‘—”„‘†‹‡•™Š‡–Š‡›‹’ƒ…–‘–Š‡Ǥ
138 C LA PHYSIQUE AU CANADA / Vol. 66, No. 2 ( avr. à juin 2010 )
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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
„Žƒ…„‘š†‡˜‹…‡
METHOD
1. Arrange the black box so one of the
top cords is extended. —ŽŽ–Š‡‘–Š‡”–‘’
…‘”†ƒ…”‘•••‘–Šƒ–‹–‹•‘™‡š–‡†‡†Ǥ—ŽŽ–Š‡–‘’
–™‘…‘”†•„ƒ…ƒ†ˆ‘”–Šƒˆ‡™–‹‡•ǡ‡•—”‹‰–Šƒ–ƒŽŽ
•–—†‡–•…ƒ•‡‡–Š‡ƒ’’ƒ”ƒ–—•Ǥƒ…Š–‹‡›‘—’—ŽŽ‘‡
…‘”†ǡ–Š‡‘–Š‡”™‹ŽŽ”‡–”ƒ…–‹–‘–Š‡„Žƒ…„‘šǤŠ‹•™‹ŽŽ
‰‹˜‡–Š‡•–—†‡–•–Š‡•‡•‡–Šƒ––Š‡–‘’–™‘…‘”†•ƒ”‡ǡ
‹ˆƒ…–ǡ‘Ž›‘‡…‘”†ǤŠ‡’—ŽŽ‘‡‘ˆ–Š‡„‘––‘–™‘
…‘”†•Ǥ–—†‡–•™‹ŽŽ„‡•—”’”‹•‡†–‘•‡‡–Šƒ–’—ŽŽ‹‰ƒ
„‘––‘…‘”†ƒŽ•‘…ƒ—•‡•ƒ–‘’…‘”†–‘”‡–”ƒ…–Ǥ‘–‹—‡
–Š‡†‡‘•–”ƒ–‹‘„›”ƒ†‘Ž›’—ŽŽ‹‰‡ƒ…Š…‘”†Ǥ•
•–—†‡–•–‘…ƒŽŽ‘—–’”‡†‹…–‹‘•ƒ•›‘—’—ŽŽ‘–Š‡…‘”†•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.ƒ‡•—”‡•–—†‡–•†‘–Š‹•‹†‹˜‹†—ƒŽŽ›Ǥ
4. Have several students share their sketches on the
board.
5. Systematically test the accuracy of each student’s
ideaǡƒƒŽ›œ‹‰–Š‡†‹ƒ‰”ƒ–‘•‡‡‹ˆ‹–…‘—Ž†’”‡†‹…––Š‡
„‡Šƒ˜‹‘—”–Šƒ–‹•ƒ…–—ƒŽŽ›™‹–‡••‡†™Š‡–Š‡…‘”†•ƒ”‡
’—ŽŽ‡†Ǥƒ…Š†”ƒ™‹‰™‹ŽŽŽ‹‡Ž›Šƒ˜‡ƒ–Ž‡ƒ•–ƒ…Šƒ…‡‘ˆ
™‘”‹‰Ǥ
Š‹•†‡‘•–”ƒ–‹‘‹•‘•–‡ˆˆ‡…–‹˜‡™Š‡–Š‡”‡ƒ”‡ƒ–
Ž‡ƒ•–ͳͲ†‹ˆˆ‡”‡–†”ƒ™‹‰•‘–Š‡„‘ƒ”†ǡ‡ƒ…Š™‹–Š–Š‡
’‘–‡–‹ƒŽ‘ˆ„‡‹‰–Š‡…‘””‡…–†‡’‹…–‹‘‘ˆŠ‘™–Š‡…‘”†•
ƒ”‡ƒ…–—ƒŽŽ›ƒ––ƒ…Š‡†Ǥ
‡ϐ‹‡–Š‡‘†‡Ž•†”ƒ™‘–Š‡„‘ƒ”†„›†”ƒ™‹‰‘—–
‡™’”‡†‹…–‹‘•ȋ‡Ǥ‰Ǥǡ‘—Ž†–Š‡„Žƒ…„‘šƒ‡ƒ‘‹•‡‹ˆ
‹–‹••Šƒ‡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
…‹‡–‹•–•—•‡‘†‡Ž•–‘”‡’”‡•‡–‘”•‹’Ž‹ˆ›…‘’Ž‡š
”‡ƒŽ‹–‹‡•Ǥ‘‡–‹‡•–Š‡‘†‡Ž•ƒ”‡•‘‰‘‘†ƒ–
”‡’”‡•‡–‹‰–Š‡”‡ƒŽ‹–›–Šƒ–™‡ˆ‘”‰‡––Š‡›ƒ”‡‘†‡Ž•Ǥ
‘‡–‹‡•–Š‡”‡ƒŽ‹–›‹••‘…‘’Ž‡š–Šƒ–ƒ•‹’Ž‡’Š›•‹…ƒŽ
‘†‡Ž‹•‹ƒ†‡“—ƒ–‡Ǥ
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‡‘ˆ–Š‡…ŠƒŽŽ‡‰‡•ƒ”‹•‹‰ˆ”‘“—ƒ–—’Š›•‹…•‹•
…”‡ƒ–‹‰•‹’Ž‡‘†‡Ž•–Šƒ–ƒ‡•‡•‡‹–Š‡…Žƒ••‹…ƒŽ
™‘”Ž†™Š‹Ž‡”‡ƒ‹‹‰–”—‡–‘–Š‡”‡ƒŽ‹–›‘ˆ–Š‡“—ƒ–—
™‘”Ž†Ǥƒ˜‡Ȃ’ƒ”–‹…Ž‡†—ƒŽ‹–›‹•ƒ‡šƒ’Ž‡‘ˆ–Š‹•
…ŠƒŽŽ‡‰‡ǤŠ‡”‡ƒ”‡‘…Žƒ••‹…ƒŽƒƒŽ‘‰—‡•–Šƒ–…ƒ
ƒ……—”ƒ–‡Ž›”‡’”‡•‡––Š‡„‡Šƒ˜‹‘—”‘ˆƒ“—ƒ–—‘„Œ‡…–ǡ
•‘™‡ƒ”‡Ž‡ˆ–™‹–Šƒ‘†‡Ž–Šƒ–†‘‡•‘–”‡ƒŽŽ›ƒ‡
•‡•‡‹–Š‡…Žƒ••‹…ƒŽ™‘”Ž†Ǥ
‘–Š‡”…ŠƒŽŽ‡‰‡ƒ”‹•‹‰ˆ”‘“—ƒ–—’Š›•‹…•‹•–Šƒ–
ƒ‘†‡Ž‹•‡ƒ•—”‡†’”‹ƒ”‹Ž›„›‹–•ƒ„‹Ž‹–›–‘‡š’Žƒ‹
–Š‡‘„•‡”˜ƒ–‹‘•ǡƒ†‘„•‡”˜‹‰“—ƒ–—•›•–‡•…ƒ
„‡’”‘„Ž‡ƒ–‹…ǤŠ‡”‡ƒ”‡”‡ƒŽŽ‹‹–•–‘™Šƒ–…ƒƒ†
…ƒ‘–„‡‡ƒ•—”‡†‹–Š‡“—ƒ–—™‘”Ž†ƒ†ǡ–Š‡”‡ˆ‘”‡ǡ
ƒŽ‹‹––‘Š‘™”‡ϐ‹‡†–Š‡‘†‡Ž•…ƒ„‡Ǥ–Š‡˜‹†‡‘
™‡‡š’Ž‘”‡–Š‡˜ƒ”‹‘—•‘†‡Ž•ǡ‘”‹–‡”’”‡–ƒ–‹‘•ǡˆ‘”
™Šƒ–‹•Šƒ’’‡‹‰†—”‹‰–Š‡†‘—„Ž‡Ǧ•Ž‹–‡š’‡”‹‡–Ǥ
‘‡‹–‡”’”‡–ƒ–‹‘•ƒ›„‡’”‡ˆ‡””‡†‘˜‡”‘–Š‡”•
„‡…ƒ—•‡–Š‡›’”‘˜‹†‡—•‡ˆ—Ž‹•‹‰Š–•‘”ƒ‡†‹ˆˆ‡”‡–
ƒ••—’–‹‘•ǡ„—–‡ƒ…Š‘ˆ–Š‡’”‘˜‹†‡•ƒ…‘’Ž‡–‡
†‡•…”‹’–‹‘‘ˆ–Š‡‘„•‡”˜‡††ƒ–ƒǤ›ƒ––‡’––‘
‘„•‡”˜‡™Šƒ––Š‡‘„Œ‡…–‹•†‘‹‰†—”‹‰–Š‡†‘—„Ž‡Ǧ•Ž‹–
‡š’‡”‹‡–ƒŽ–‡”•–Š‡†ƒ–ƒƒ†’”‡˜‡–•—•ˆ”‘”‡ϐ‹‹‰
‘—”‘†‡Ž•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: •‡–Š‡ƒ…–‹˜‹–›–‘‹–”‘†—…‡ƒ†‹•…—••‹‘ƒ„‘—–Š‘™’Š›•‹…‹•–•…‘•–”—…–‘†‡Ž•Ǥ”ƒ™‘—––Š‡…‘…‡’––Šƒ–
‘†‡Ž•ƒ”‡„—‹Ž–‹”‡•’‘•‡–‘‘„•‡”˜ƒ–‹‘•ƒ†•Š‘—Ž†Šƒ˜‡’”‡†‹…–‹˜‡’‘™‡”Ǥ
Post-video: •‡–Š‡ƒ…–‹˜‹–›–‘”‡˜‹•‹––Š‡’ƒ”–‘ˆ–Š‡˜‹†‡‘™Š‡”‡•…‹‡–‹•–•’”‘˜‹†‡ƒŽ–‡”ƒ–‹˜‡‹–‡”’”‡–ƒ–‹‘•ˆ‘”
–Š‡†‘—„Ž‡Ǧ•Ž‹–‡š’‡”‹‡–Ǥ—‹Ž†‘–Š‡ƒƒŽ‘‰›–Šƒ––Š‡‹•‹†‡‘ˆ–Š‡„Žƒ…„‘š‹•Ž‹‡–Š‡Dz‹•‹†‡dz‘ˆ–Š‡†‘—„Ž‡Ǧ•Ž‹–
‡š’‡”‹‡–Ǥ‡…ƒ‘–‘™™Šƒ–‹•Dzƒ…–—ƒŽŽ›dzŠƒ’’‡‹‰‹•‹†‡ǡ•‘ƒ›‘†‡Ž–Šƒ–•—……‡••ˆ—ŽŽ›‡š’Žƒ‹•–Š‡‘„•‡”˜‡†
†ƒ–ƒ…ƒ„‡…‘•‹†‡”‡†˜ƒŽ‹†Ǥ
HOW TO BUILD A BLACK BOX MODEL
Š‡Žƒ…‘š‘†‡Ž‹•ƒ‡ˆˆ‡…–‹˜‡Ž‡ƒ”‹‰–‘‘Žƒ†…ƒ„‡…‘•–”—…–‡†™‹–Š‹‹ƒŽ…‘•–ƒ†‡ˆˆ‘”–Ǥ
MATERIALS
»
»
»
»
ʹ’‹‡…‡•‘ˆͺ›Ž‘”‘’‡ǡ‡ƒ…Š͹Ͳ…Ž‘‰
ͳŠƒ”‡••”‹‰™‹–ŠƒͶͲ†‹ƒ‡–‡”
ͳ’‹‡…‡‘ˆ͹Ǥͷ…†‹ƒ‡–‡”†”ƒ‹ƒ‰‡’‹’‡͵ͷ…Ž‘‰
ʹ†”ƒ‹ƒ‰‡’‹’‡‡†…ƒ’•͹Ǥͷ…†‹ƒ‡–‡”
TOOLS
»
»
͵Ȁͺdz†”‹ŽŽ„‹–
’‘™‡”†”‹ŽŽ
PROCEDURE
Step 1: ”‹ŽŽ–Š‡–‘’Š‘Ž‡•†‹”‡…–Ž›ƒ…”‘••ˆ”‘‘‡
ƒ‘–Š‡”ǡ‡ƒ…Šͷ…ˆ”‘–Š‡–‘’ȋ‹‰—”‡ͳȌǤ‡’‡ƒ–ˆ‘”–Š‡
„‘––‘Š‘Ž‡•ǡ‡ƒ…Šͷ…ˆ”‘–Š‡„‘––‘Ǥ
Step 2:Š”‡ƒ†–Š‡‘‡Ž‡‰–Š‘ˆ”‘’‡–Š”‘—‰Š–Š‡–‘’
Š‘Ž‡•ƒ†–Š‡Šƒ”‡••”‹‰ȋ‹‰—”‡ʹȌǤ
Step 3: ‹‡ƒ‘–ͳͷ…ˆ”‘‡ƒ…Š‡†‘ˆ–Š‡”‘’‡Ǥ
Step 4:Š”‡ƒ†–Š‡‘–Š‡””‘’‡–Š”‘—‰Š–Š‡„‘––‘Š‘Ž‡•Ǥ
‰ƒ‹ǡ‡•—”‡–Šƒ––Š‡”‘’‡’ƒ••‡•–Š”‘—‰Š–Š‡Šƒ”‡••
”‹‰ƒ•‹†‹…ƒ–‡†ȋ‹‰—”‡͵ȌǤ‹‡ƒ‘–ͳͷ…ˆ”‘‡ƒ…Š
‡†‘ˆ–Š‡”‘’‡Ǥ
Step 5: ‡…—”‡‡†…ƒ’•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
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THE JULY-SEPTEMBER 2010
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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
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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.
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