Praxis Archives – Page 101 of 181

Gravitation: Foundations and Frontiers

By T Padmanabhan
Cambridge University Press
Hardback: £50 $85
E-book: $68

The general theory of relativity – the foundation of gravitation and cosmology – may be as widely known today as Newton’s laws were before Einstein proposed their geometric interpretation. That was around 100 years ago, yet many unanswered questions and issues are being revisited from the current perspective, such as: why is gravity described by geometry and why is the cosmological constant so extraordinarily fine-tuned in comparison with the scale of elementary particles?

In an active research field – where the universe at large meets the discoveries in particle physics – there is much need for textbooks based on research that address gravity in depth. Thanu Padmanabhan’s book fills this need well and in a unique way. Within minutes of opening the rich, heavy, full, yet succinctly written 728 pages I realized that this is a new and personal view on general relativity, which leads beyond many excellent standard textbooks and offers a challenging training ground for students with its original exercises and study topics.

In the first 340 pages, the book presents the fundamentals of relativity in an approachable style. Yet, even in this “standard” part the text goes far beyond the conventional framework in preparing the reader in depth for mastering the “frontiers”. The titles of the following chapters speak for themselves: “Black Holes”, “Gravitational Waves”, “Relativistic Cosmology” and “Evolution of Cosmological Perturbations”, all of which address key domains in present-day research. Then, on page 591, the book turns to the quantum frontier and extensions of general relativity to extra dimensions, and to efforts to view it as an effective “emergent” theory.

This research-oriented volume is written in a format that is suitable for a primary text in a year-long graduate class on general relativity, although the lecturer is likely to leave a few of the chapters to self-study. “Padmanabhan” complements the somewhat older offerings of this type, such as “The Big Black Book” (Gravitation by Charles Misner, Kip Thorne and John Wheeler, W H Freeman 1973) or “Weinberg” (Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley 1972).

Naturally, this publication differs greatly from “text and no research” offerings, such as Ta-Pei Cheng’s Relativity, Gravitation and Cosmology: A Basic Introduction (OUP 2009) or Ray d’Inverno’s Introducing Einstein’s Relativity (OUP 1992). Any lecturer using these should consider adding “Padmanabhan” as an optional text to offer a wider view to students on what is happening in research today. In comparison with “Hartle” (Gravity: An Introduction to Einstein’s General Relativity, Addison-Wesley 2003), one cannot but admire that “Padmanabhan” does not send the reader to other texts to handle details of computations; what is mentioned is also derived and explained in depth. Of course, “Hartle” is often used in a “first” course on gravity but frankly how often is there a “second” course?

“Padmanabhan” is, as noted earlier, voluminous, making it an excellent value for money because it contains the material of three contemporary books for the price of one. So who should own a copy? Certainly for any good library covering physics, the question is really not if to buy but how many copies. I also highly recommend it to anyone interested in general relativity and related fields because it offers a modern update. Students who have already had a “first” course in the subject and are considering taking up research in this field will find in “Padmanabhan” a self-study text to deepen their understanding. If you are a bookworm like me, you must have it, because it is a great read from start to finish.

The Pursuit of Quantum Gravity: Memoirs of Bryce DeWitt from 1946 to 2004 and Bryce DeWitt’s Lectures on Gravitation

The Pursuit of Quantum Gravity: Memoirs of Bryce DeWitt from 1946 to 2004

By Cécile DeWitt Morette

Springer 2011
Hardback: £31.99 €36.87 $49.95

Bryce DeWitt’s Lectures on Gravitation

By Bryce DeWitt (ed. Steven M Christensen)
Springer 2011
Paperback: £62.99 €73.80 $89.95

Bryce DeWitt made many deep contributions to quantum field theory, general relativity and quantum gravity. He generalized Richard Feynman’s original approach to quantum gravity at the one-loop level, to a fully fledged, all-order quantization of non-abelian gauge theories, including ghosts. The formalism that he developed also transformed the way that we think about quantum field theory, although it took some time before his ideas percolated the community.

The Pursuit of Quantum Gravity is a charming and remarkable book put together by Cécile Morette, who became his wife and was to share his life for more than 50 years. Here we meet the man and his science. It is a remarkable story of vision, passion, independence and determination that led this scientist along such a difficult road, against all odds.

The material in the book is difficult to find elsewhere and it is not only highly informative but also a pleasure to read. For instance, the way that he organized an expedition to Mauritania to check the deflection of light by the Sun and thus verify the results from the 1919 eclipse by Arthur Eddington et al. There are also documents that are not easily accessible elsewhere, such as the essay that won him the first prize of the Gravity Research Foundation in 1953. It is quite remarkable how many aspects of the vision laid out in that paper that he was able to accomplish.

This book makes us aware of how much we owe Bryce DeWitt, and how deep and broad his influence has been. It pays homage to a truly great man – through the words of the person who knew and understood him best.

Back in 1971, he delivered a series of lectures on gravitation at Stanford University, before moving to the University of Texas at Austin. It has taken 40 years for them to be available to the physics community, but finally they are here as Bryce DeWitt’s Lectures on Gravitation, thanks to the efforts of his former student Steven M Christensen. Anyone who has seen the original realizes how grateful we should be to the editor for the large amount of work required in carrying out this task.

These lectures do not represent a standard introduction to the subject but rather DeWitt’s unique way of presenting it. Along with standard topics that include special relativity, continuous groups and Riemannian manifolds, one finds a remarkable treatment of the study of asymptotic fields, the energy–momentum of the gravitational field, and above all the dynamics of the production and propagation of gravitational waves.

Many of the results found here cannot be found in other books or review articles on the subject, despite the number of years that have elapsed since they were presented. Take, for example, the treatment of the angular momentum carried by gravitational waves, where a cursory look at the relevant chapters shows why this book is different. The complexity of the algebra involved requires a combination of tenacity, wizardry and understanding that is difficult to find in any other master of general relativity. DeWitt’s head-on, uncompromising approach is unique.

The book also has high historical value, showing how this maverick maven thought of the subject. It is a great tribute to his scientific legacy.

Discovery of accelerating universe wins Nobel prize

CCnew1_09_11 — Left to Right: Perlmutter, Schmidt and Riess.
Image credits: Lawrence Berkeley National Laboratory; B Schmidt/ANU; W Kirk /Homewood Photographic Services.

Saul Perlmutter, Brian Schmidt and Adam Riess have been awarded the 2011 Nobel Prize in Physics “for the discovery of the accelerating expansion of the universe through observations of distant supernovae”. Perlmutter, professor of astrophysics at the Lawrence Berkeley National Laboratory and University of California, Berkeley, receives half of the prize, with the other half being shared between Schmidt, distinguished professor at the Australian National University, and Riess, professor of astronomy and physics at Johns Hopkins University and the Space Telescope Science Institute. Their finding led to a dramatic change in perception of the universe by providing evidence for what has become known as “dark energy”.

In 1997 the Supernova Cosmology Project (SCP), led by Perlmutter and the High-z Supernova Search Team, led by Schmidt, were working independently on observations of distant Type 1a supernovae, using them as “standard candles” to measure cosmological distances as a function of time. (All such supernovae have similar intrinsic brightness, so their apparent brightness gives a measure of distance.) They expected to find evidence for a gradual slowdown in the expansion of the universe, resulting from the influence of gravity on the matter it contains.

Instead, the measurements revealed around 50 distant supernovae that appeared to be dimmer than predicted by calculations based on the gravitational effects of matter. In 1997 Gerson Goldhaber – well known in the particle-physics community – was the first person in the SCP team to notice the unexpected effect while plotting the brightness against redshift for Type Ia supernovae that the project had discovered. The same year, Adam Riess, then a research fellow at UC Berkeley who was leading an analysis of supernovae detected by the High-z project, uncovered a similar effect.

The observations pointed to the surprising conclusion that the expansion of the universe is not slowing under the influence of gravity, but is instead accelerating. This in turn implies the existence of some form of gravitationally repulsive “substance”, uniformly distributed across the universe, which counteracts the gravitational attraction of matter. This unknown substance has become known as “dark energy“.

The two teams published their results in 1998–1999 and since then their findings have been confirmed not only by further observations of supernovae but also by detailed measurements of fluctuations in the cosmic microwave background radiation and of baryon acoustic oscillations, i.e. clustering of baryonic matter in the early universe that also serves as a “standard ruler” for cosmological distance scales. All of the evidence suggests that dark energy contributes as much as 73% of the mass-energy content of the universe, with 23% from dark matter and only about 4% from normal baryonic matter – but the nature of both dark matter and dark energy remains unknown.

100 years of superconductivity

In November 1911, Heike Kammerlingth Onnes reported on the abrupt disappearance of resistance in mercury at 4.20 K. To mark the centenary of the discovery of superconductivity, this issue of CERN Courier looks at some of the aspects of its application – in particular in the context of particle accelerators – and at some more anniversaries. It is 75 years since type-II superconductivity was first observed in Kharkov (The discovery of type-II superconductors). Although sadly overlooked for 25 years, this made superconducting magnets a real possibility and led to the Tevatron – the first superconducting synchrotron – (Farewell to the Tevatron) and most recently the LHC, with its particular challenges (Superconductivity and the LHC: the early days), as well as to applications in medical scanners (PET and MRI: providing the full picture). First proposed 50 years ago, RF superconductivity also has an important role in many accelerators (Advances inacceleration: the superconducting way), exemplified in several of the applications of superconductivity at KEK, founded 40 years ago (Progress in applied superconductivity at KEK).

Israel to become an associate member of CERN

CCnew2_09_11 — Aharon Leshno-Yaar, left, and Rolf Heuer shake hands after signing the agreement.

On 16 September, CERN’s director-general, Rolf Heuer, and the Israeli ambassador and permanent representative of Israel to the United Nations Office and other international organizations in Geneva, Aharon Leshno-Yaar, signed a document admitting Israel to associate membership of CERN, subject to ratification by the Knesset. Following ratification, Israel will become an associate member for a minimum of 24 months. Following this period, CERN Council will decide on the admission of Israel to full membership, taking into account the recommendations of a task force to be appointed for this purpose.

Israel has a strong tradition in both experimental and theoretical particle physics, with a major involvement at CERN during the 1990s in the OPAL experiment at the Large Electron–Positron (LEP) collider. Israel’s accession to observer status in 1991 followed an agreement to contribute funds to the CERN budget to support Israeli scientists, as well as providing equipment to CERN. The Israeli fund also contributed to running LEP and supported LHC construction and R&D for future accelerators. During its association with CERN, Israel has in addition supported Palestinian students at CERN, notably sending mixed Israeli–Palestinian contingents to CERN’s summer-student programme.

“It is a vital part of our mission to build bridges between nations. This agreement enriches us scientifically and is an important step in that direction,” says CERN director-general, Rolf Heuer. “I am very pleased that CERN’s relationship with Israel is moving to a higher level.”

In 2009, Israel was accepted as a special observer state, with the right to attend restricted Council sessions for discussions of LHC matters. Israel currently has strong involvement in the ATLAS experiment at the LHC and participates in a number of other experiments at CERN.

From the Tevatron to Project X

The end of September marks the end of an era at Fermilab, with the shut down of the Tevatron after 28 years of operation at the frontiers of particle physics. The Tevatron’s far-reaching legacy spans particle physics, accelerator science and industry. The collider established Fermilab as a world leader in particle-physics research, a role that will be strengthened with a new set of facilities, programmes and projects in neutrino and rare-process physics, astroparticle physics and accelerator and detector technologies.

The Tevatron exceeded every expectation ever set for it. This remarkable machine achieved luminosities with antiprotons once considered impossible, reaching more than 4 × 10³² cm^–2s^–1 instantaneous luminosity and delivering more than 11 fb^–1 of data to the two collider experiments, CDF and DØ. Such luminosity required the development of the world’s most intense, consistent source of antiprotons. The complex process of making, capturing, storing, cooling and colliding antiprotons stands as one of the great achievements by Fermilab’s accelerator team.

As the world’s first large superconducting accelerator, the Tevatron developed the technology that allowed later accelerators – including CERN’s LHC – to push beam energy and intensity even higher. But beyond its scientific contributions, an enduring legacy to mankind is the role it played in the development of the superconducting-wire industry. The construction of the accelerator required 135,000 lb of niobium-titanium-based superconducting wire and cable at a time when annual world production of these materials was only a few hundred pounds. Fermilab brought together scientists, engineers and manufacturers who developed a large-scale manufacturing capability that quickly found huge demand in another emerging field: MRI machines.

The life of the Tevatron is marked by historic discoveries that established the Standard Model. Tevatron experiments discovered the top quark, five B baryons and the B_c meson, and observed the first τ neutrino, direct CP violation in kaon decays, and single top production. The CDF and DØ experiments measured top-quark and W-boson masses, as well as di-boson production cross-sections. Limits placed by CDF and DØ on many new phenomena and the Higgs boson guide searches elsewhere – and continuing analysis of Tevatron data may yet reveal evidence for processes beyond our current understanding. Chris Quigg’s article in this issue gives further details on the Tevatron’s scientific legacy and results still to come (Long live the Tevatron).

As we bid farewell to the Tevatron, what’s next for Fermilab? Over the next decades, we will develop into the foremost laboratory for the study of neutrinos and rare processes – leading the world at the intensity frontier of particle physics.

Fermilab’s accelerator complex already produces the most intense high-energy beam of neutrinos in the world. Upgrades in 2012 will allow the NOνA experiment to push neutrino oscillation measurements even further. The Long-Baseline Neutrino Experiment, which will send neutrinos 1300 km from Fermilab to South Dakota, will be another leap forward in the quest to demystify the neutrino sector and search for the origins of a matter-dominated universe.

The cornerstone for Fermilab’s leadership at the intensity frontier will be a multimegawatt continuous-beam proton-accelerator facility known as Project X. This unique facility is ideal for neutrino studies and rare-process experiments using beams of muons and kaons; it will also produce copious quantities of rare nuclear isotopes for the study of fundamental symmetries. Coupled to the existing Main Injector synchrotron, Project X will deliver megawatt beams to the Long-Baseline Neutrino Experiment. A strong programme in rare processes is developing now at Fermilab with the muon-to-electron conversion and muon g-2 experiments. A strong foundation for Project X exists at Fermilab, with expertise in high-power beams, neutrino beamlines, and superconducting RF technology.

Project X’s rare-process physics programme is complementary to the LHC

Project X’s rare-process physics programme is complementary to the LHC. If the LHC produces a host of new phenomena, then Project X experiments will help elucidate the physics behind them. Different models postulated to explain the new phenomena will have different consequences for very rare processes that will be measured with high accuracy using Project X. If no new phenomena are discovered at the LHC, the study of rare transitions at Project X may show effects beyond the direct reach of particle colliders. Project X could also serve as a foundation for the world’s first neutrino factory, or – even further in the future – as the front end of a muon collider.

In parallel with the development of its intensity frontier programme, Fermilab will remain a strong part of the LHC programme as the host US laboratory and a Tier-1 centre for the CMS experiment, as well as through participation in upgrades of the LHC accelerator and detectors. Fermilab will also continue to build on its legacy as the birthplace of the understanding of the deep connection between cosmological observations and particle physics. The Dark Energy Survey, which contains the Fermilab-built Dark Energy Camera, will see first light in 2012. Better detectors are in development for the Cryogenic Dark Matter Search, and the COUPP dark-matter search is now operating a 60 kg prototype at Fermilab.

As Fermilab’s staff and users say goodbye to the Tevatron, we look forward to working with the world community to address the field’s most critical and exciting questions at facilities in the US, at CERN and around the world.

The Poetry of Physics and the Physics of Poetry

By Robert K Logan
World Scientific
Hardback: £42 $64
Paperback: £30 $43
E-book: $83

Robert Logan is a physicist who since 1971 has taught an interdisciplinary course, “The Poetry of Physics and the Physics of Poetry”, at the University of Toronto. In this book, which grew out of the course, he introduces the evolution of ideas in physics by first briefly recalling the ancient science of Mesopotamia, Egypt and China before addressing in detail the revolutions that started in the 16th century and the more modern advances, including the birth of the Standard Model of particle physics. Sprinkled with quotations from leading physicists of the respective times, the book reports in an interesting way the historical connections that lead from one discovery to another and the impact physics had on (and received from) other branches of science, philosophy, arts, theology, etc. Thus he hopes to convey not only the poetry or beauty of physics but also how physics has influenced the humanities.

The word “physics” derives from the Greek word phusis, meaning “nature”, and Logan wonders what physics would be without the ancient Greek philosophers. However, even with them, interest in science declined as theology became the dominant concern of the day. It was mainly thanks to René Descartes, who refused to accept past philosophical truths that he could not verify for himself (“Cartesian doubt”), and to other contemporary philosophers, that a change in attitude towards science began to develop in the beginning of the 17th century. During that period, Galileo Galilei, Johannes Kepler and several other scientists uncovered many mysteries of nature, which eventually led to Isaac Newton’s breakthroughs. In return, the philosophy of the British (Locke, Berkeley, Hume) and French (Voltaire, Condillac, Diderot, Condoret) movements was heavily influenced by Newton’s physics: their reflections were based directly on the scientific method.

Moving on, the scientific advances of the 20th century would not have been possible without the abstract mathematical concepts developed in the 19th century or technological breakthroughs such as the invention of the vacuum pump, which paved the way for the study of all gas-discharge experiments and led to the discovery of X-rays and the electron. Logan connects these and other discoveries very naturally, claiming along the way that the distinction between physics and chemistry is artificial and a “historic accident”.

Breakthroughs in science are based on the gift of abstract thinking, astronomy being one of the earliest examples. It is interesting to realize that the structure of certain languages is intimately connected to abstract thinking. According to the Toronto school of thought in communication theory, to which Logan has contributed, “the use of a phonetic alphabet and its particular coding led the Greeks to deductive logic and abstract theoretical science”. This was probably one of the main reasons that “abstract theoretical science is a particular outgrowth of Western culture” – as opposed to Eastern cultures, which use a much more complex alphabet.

Apart from discussing major physics discoveries, Logan also triggers readers (or at least his students) to acquire a critical attitude, quoting thinkers such as Thomas Kuhn and Karl Popper: “Science cannot prove that a hypothesis is correct. It can only verify that the hypothesis explains all observed facts and has passed all experimental tests of its validity.” After all, a physics course is more than just conveying acquired knowledge.

I can gladly recommend this book to anyone wanting to refresh their physics basics or who would like to learn about the implications that physics has for other disciplines, and vice versa. I certainly enjoyed reading it and nostalgically recalled several moments from my undergraduate studies. It is a pity that there are many misprints and some unclear sentences.

Introduction to the Theory of the Universe: Hot Big Bang Theory and Introduction to the Theory of the Universe: Cosmological Perturbations and Inflationary Theory

Introduction to the Theory of the Universe: Hot Big Bang Theory
By Dmitry S Gorbunov and Valery A Rubakov
World Scientific
Hardback: £103 $158
Paperback: £51 $78
E-book: $200

Introduction to the Theory of the Universe: Cosmological Perturbations and Inflationary Theory
By Dmitry S Gorbunov and Valery A Rubakov
World Scientific
Hardback: £101 $156
Paperback: £49 $76
E-book: $203

When a field is developing as fast as modern particle astrophysics and cosmology, and in as many exciting and unexpected ways, it is difficult for textbooks to keep up. The two-volume Introduction to the Theory of the Early Universe by Dmitry Gorbunov and Valery Rubakov is an excellent addition to the field of theoretical cosmology that goes a long way towards filling the need for a fully modern pedagogical text. Rubakov, one of the outstanding masters of beyond-the-Standard Model physics, and his younger collaborator give an introduction to almost the entire field over the course of the two books.

The first book covers the basic physics of the early universe, including thorough discussions of famous successes, such as big bang nucleosynthesis, as well as more speculative topics, such as theories of dark matter and its genesis, baryogenesis, phase transitions and soliton physics – all of which receive much more coverage than is usual. As the choice of topics indicates, the approach in this volume tends to be from the perspective of particle theory, usefully complementing some of the more astrophysically and observationally oriented texts.

The second volume focuses on cosmological perturbations – where the vast amounts of data coming from cosmic-microwave background and large-scale structure observations have transformed cosmology into a precision science – and the related theory of inflation, which is our best guess for the dynamics that generate the perturbations. Both volumes contain notably insightful treatments of many topics and there is a large variety of problems for the student distributed throughout the text, in addition to extensive appendices on background material.

Naturally, there are some missing topics, particularly on the observational side, for example a discussion of direct and indirect detection of dark matter or of weak gravitational lensing. There are also some infelicities of language that a good editor would have corrected. However, for those wanting a modern successor to The Early Universe by Edward Kolb and Michael Turner (Perseus 1994) or John Peacock’s Cosmological Physics (CUP 1999), either for study of an unfamiliar topic or to recommend to PhD students to prepare them for research, the two volumes of Theory of the Early Universe are a fine choice and an excellent alternative to Steven Weinberg’s more formal Cosmology (OUP 2008).

Maîtriser le nucléaire : Que sait-on et que peut-on faire après Fukushima ?

par Jean Louis Basdevant

Editions Eyrolles

Broché: €17,50

Jean Louis Basdevant, ancien professeur à l’Ecole Polytechnique où il donna d’excellents cours, et auteur de nombreux livres pédagogiques, vient de réussir un tour de force en écrivant un livre sur les problèmes du nucléaire en moins d’un mois à la suite de la catastrophe de Fukushima. C’est un livre très pédagogique qui commence par un historique de la radioactivité, puis un exposé du b-a ba de la physique nucléaire, suivi d’une description des avantages et des dangers de la radioactivité dont il quantifie les effets. Suit une description de la fission, puis de la production d’énergie nucléaire présente et future (si les hommes le veulent!), y compris la proposition de fission induite par accélérateur tel que celui proposé par Carlo Rubbia. Vient alors la description de accidents : Lucens (négligeable), Three Mile Island, Tchernobyl (y compris une mise au point sur les doses reçues en France, en fait faibles), et Fukushima, avec une analyse des erreurs et même des fautes qui ont conduit à ces catastrophes.

On passe alors à la fusion, par confinement magnétique et aussi inertielle. Le diagnostic n’est pas très optimiste. Le calendrier d’ITER est sans cesse repoussé et ITER ne produira pas d’énergie électrique. Tout ceci suivi de quelques données sur l’énergie.

On passe aux armes nucléaires et thermonucléaires et leur fonctionnement ou encore les affreuses bombes à neutrons, la lutte contre la prolifération, les dangers du terrorisme, avec la facilité de construire des bombes artisanales, et aussi les bombes classiques contenant des matériaux radioactifs.

Finalement le dernier chapitre est intitulé : « que penser et que faire après Fukushima ». L’auteur se contente de donner des éléments de réponse, sans prendre explicitement parti. Les décideurs devraient certainement lire ce livre pour se faire une opinion sérieuse au lieu de se laisser aller à des réactions émotionnelles incontrôlées. Je recommande vivement la lecture de ce livre.

Bien qu’il soit en Français, je recommande également ce livre aux anglophones : le Français est simple et compréhensible.

Numerical Relativity. Solving Einstein’s Equations on the Computer

By Thomas W Baumgarte and Stuart L Shapiro

Cambridge University Press

Hardback: £55 $90

E-book: $72

Symmetries are a powerful tool for solving specific problems in all areas of physics. However, there are situations where both exact and approximate symmetries are lacking and, therefore, it is necessary to employ numerical methods. This, in essence, is the main motivation invoked for the use of large-scale simulations in relativistic systems where gravity plays a key role, such as black-hole formation, rotating stars, binary neutron-star evolution and even binary black-hole evolution.

Numerical Relativity by Thomas Baumgarte and Stuart Shapiro is an interesting and valuable contribution to the literature on this subject. Both authors are well known in the field. Shapiro, together with Saul Teukolsky, wrote a monograph on a related subject – Black Holes, White Dwarfs and Neutron Stars (John Wiley & Sons 1983) – that is familiar to students and researchers. The careful reader will recognize various similarities in the overall style of the presentation, with systematic attention to the details of the mathematical apparatus. In Numerical Relativity, 18 chapters are supplemented by a rich appendix. The first part could be used by students and practitioners for tutorials on the so-called Adler-Deser-Misner formalism and, ultimately, on the correct formulation of the Cauchy problem in general relativity.

It seems that the authors implicitly suggest that the future of numerical relativity is closely linked to our experimental ability to observe directly general relativistic effects at work. While astrophysics and gravitational waves have so far provided a rich arena for the applications, the intrinsic difficulties in detecting high-frequency gravitational waves with wide-band interferometers, such as LIGO and VIRGO, might suggest new cosmological applications of numerical techniques in the years to come. This book will take you into an exciting world populated by binary neutron stars and binary black holes.

Still, the achievements of numerical relativity (as well as those of all of the other areas of physics where large-scale computer simulations are extensively used) cannot be reduced simply to the quest for the most efficient algorithm. At the end of nearly 700 pages, the reader is led to reflect: is it wise to commit the research programme of young students and post-docs solely to the development of a complex code? After all, the lack of symmetry in a problem might just reflect the inability of physicists to see the right symmetries for the problem. A balanced perspective for potential readers can be summarized in the words of Vicky Weisskopf, when talking about the proliferation of numerical methods in all areas of physics: “[…] We should not be content with computer data. It is important to find more direct insights into what a theory says, even if such insights are insufficient to yield the numerical results obtained by computers” (Joy of Insight: Passions of a Physicist, Basic Books, 1991).

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