Arthur Jaffe

Pronob K. Mitter

Gerhard Mack

Raymond Stora

Gerard 't Hooft

The 1996 NATO Advanced Study Institute (ASI) followed the international tradi tion of the schools held in Cargese in 1976, 1979, 1983, 1987 and 1991. Impressive progress in quantum field theory had been made since the last school in 1991. Much of it is connected with the interplay of quantum theory and the structure of space time, including canonical gravity, black holes, string theory, application of noncommutative differential geometry, and quantum symmetries. In addition there had recently been important advances in quantum field theory which exploited the electromagnetic duality in certain supersymmetric gauge theories. The school reviewed these developments. Lectures were included to explain how the "monopole equations" of Seiberg and Witten can be exploited. They were presented by E. Rabinovici, and supplemented by an extra 2 hours of lectures by A. Bilal. Both the N = 1 and N = 2 supersymmetric Yang Mills theory and resulting equivalences between field theories with different gauge group were discussed in detail. There are several roads to quantum space time and a unification of quantum theory and gravity. There is increasing evidence that canonical gravity might be a consistent theory after all when treated in. a nonperturbative fashion. H. Nicolai presented a series of introductory lectures. He dealt in detail with an integrable model which is obtained by dimensional reduction in the presence of a symmetry.

Quantum Fields and Quantum Space Time

Stefan Vandoren

With a Foreword writer Steven Weinberg In this richly illustrated book, Nobel Laureate Gerard 't Hooft and Theoretical Physicist Stefan Vandoren describe the enormous diversity of natural phenomena that take place at different time scales. In the tradition of the bestseller Powers of Ten, the authors zoom in and out in time, each step with a factor of ten. Starting from one second, time scales are enlarged until processes are reached that take much longer than the age of the universe. After the largest possible eternities, the reader is treated to the shortest and fastest phenomena known. Then the authors increase with powers of ten, until again the second is reached at the end of the book. At each time scale, interesting natural phenomena occur, spread over all scientific disciplines: orbital and rotation periods of planets and stars, decay times of elementary particles and atoms, biological rhythms and evolution processes, but also the different geological time scales. Contents:Part I:100 Seconds = 1 Second101 Seconds = 10 Seconds102 Seconds = 100 Seconds = 1 Minute, 40 Seconds103 Seconds = 1,000 Seconds = 16 Minutes, 40 Seconds104 Seconds = 10,000 Seconds = 2.78 Hours105 Seconds = 100,000 Seconds = 1.16 Days = 27.78 Hours106 Seconds = 1,000,000 = 1 Million Seconds = 11.57 Days = 1.65 Weeks106.41 Seconds = 2,592,000 Seconds = 30 Days ≈ 1 Month107 Seconds = 10 Million Seconds = 115.74 Days = 3.86 Months108 Seconds = 100 Million Seconds = 3.17 Years109 Seconds = 1 Billion Seconds = 31.7 Years1010 Seconds = 10 Billion Seconds = 317 Years1011 Seconds = 100 Billion Seconds = 3,171 Years1012 Seconds = 1 Trillion Seconds = 31,710 Years1013 Seconds = 10 Trillion Seconds = 317,098 Years1014 Seconds = 100 Trillion Seconds = 3.17 Million Years1015 Seconds = 1 Quadrillion Seconds = 31.7 Million Years1016 Seconds = 10 Quadrillion Seconds = 317 Million Years1017 Seconds = 100 Quadrillion Seconds = 3.17 Billion Years1018 Seconds = 1 Quintillion Seconds = 31.7 Billion years: The Large Timescales1021 seconds = 1 Sextillion Seconds = 3.17 × 1013 Years: The Large Timescales1028 Seconds = 3.17 × 1020 Years: The Large Timescales1032 Seconds: To Infinity and Beyond: The Dark EternitiesPart II:10-44 to 10-26 Seconds: Small Timescales10-25 Seconds10-24 Seconds = 1 Yoctosecond10-23 Seconds = 10 Yoctoseconds10-22 Seconds = 100 Yoctoseconds10-21 Seconds = 1 Zeptosecond10-20 Seconds = 10 Zeptoseconds10-19 Seconds = 100 Zeptoseconds10-18 Seconds = 1 Attosecond10-17 Seconds = 10 Attoseconds10-16 Seconds = 100 Attoseconds10-15 Seconds = 1 Femtosecond10-14 Seconds = 10 Femtoseconds10-13 Seconds = 100 Femtoseconds10-12 Seconds = 1 Picosecond10-11 Seconds = 10 Picoseconds10-10 Seconds = 100 Picoseconds10-9 Seconds = 1 Nanosecond10-8 Seconds = 10 Nanoseconds10-7 Seconds = 100 Nanoseconds10-6 Seconds = 1 Microsecond10-5 Seconds = 10 Microseconds10-4 Seconds = 100 Microseconds = 0.0001 Seconds10-3 Seconds = 1 Millisecond = 0.001 Seconds10-2 Seconds = 10 Milliseconds = 0.01 Seconds10-1 Seconds = 100 Milliseconds = 0.1 Seconds100 Seconds = 1 Second -->Readership: Science enthusiasts and students. Keywords:Time;natural Phenomena;Time Scales;Age of the Universe;Powers of TenReviews: “The somewhat facetious narrating style and the abundance of illustrations are so inviting and rather addictive once you picked up the book.” European Mathematical Society “Pleasingly accessible volume that will give pleasure to academics, students, connoisseurs of coffee-table books and even the people who compile questions for Trivial Pursuit … Can be enjoyed as a source of scientific stories and images, as an unusual perspective on history, as a popular account of modern physics, and so on. Underneath them all is a wealth of serious science that will give readers insights into abstract fundamental ideas via concrete realities … Every science teacher would benefit from reading Time in Powers of Ten, but I hope it will have an even wider reach.” Times Higher Education “The authors have compiled a refreshing mix of historical anecdotes and examples from music to sport and biology to astronomy to lighten up the heavier taste of particle physics and cosmology… It is both an enjoyable read and very pleasant to browse at leisure… It fully conveys the authors' amazement at — as Feynman put it — our fantastically marvellous universe.” Nature Physics “The authors introduce the reader to the diversity of nature in a novel way by describing typical and interesting phenomena that occur or have occurred on many different time scales. The time scales considered differ by powers of ten, as the title of the book says, from the shortest times of which we have knowledge to the longest. I am sure many readers will enjoy the book as I have.” Edward Witten, Fields Medalist “Time is an essential dimension of life. Indeed, its remarkable and awesome variation of scale shapes the natural world. This book by Gerard 't Hooft and Stefan Vandoren gives us an exposé of a wide range of natural phenomena and their associated time scales, spanning the very small, the very large, and the life events of our universe. The book is elegantly illustrated and should be an enjoyable read for anyone interested in a deeper understanding of the fourth dimension, time, and how it shapes our lives.” Ahmed Zewail, Nobel Laureate in Chemistry “Like the original Powers of Ten, it is a wonderful book for flipping through and thinking about puzzles and is a good introduction to basics like how to tell a quark from a lepton.” The Dispatch “The book reveals the extraordinary complexity of our universe — it is a fascinating journey.” CERN Courier “This is a fascinating coffee-table book ranging from the unimaginably huge to the unimaginably tiny.” Ultramicroscopy “You can read the book in any direction. Delving into the index takes you on a mystery tour of the time domain. Helpfully, all the major phenomena are gathered together on an illustrated time line. This book is definitely one for your reading list.” Physics Education

Natural Phenomena and Their Timescales

Time in Powers of Ten

This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The author gives examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of the wave function collapse and the measurement problem. Even the existence of an “arrow of time" can perhaps be explained in a more elegant way than usual. As well as reviewing the author’s earlier work in the field, the book also contains many new observations and calculations. It provides stimulating reading for all physicists working on the foundations of quantum theory.

The Cellular Automaton Interpretation of Quantum Mechanics

In this richly illustrated book, Nobel Laureate Gerard ''t Hooft and Theoretical Physicist Stefan Vandoren describe the enormous diversity of natural phenomena that take place at different time scales. In the tradition of the bestseller Powers of Ten, the authors zoom in and out in time, each step with a factor of ten. Starting from one second, time scales are enlarged until processes are reached that take much longer than the age of the universe. After the largest possible eternities, the reader is treated to the shortest and fastest phenomena known. Then the authors increase with powers of ten, until again the second is reached at the end of the book. At each time scale, interesting natural phenomena occur, spread over all scientific disciplines: orbital and rotation periods of planets and stars, decay times of elementary particles and atoms, biological rhythms and evolution processes, but also the different geological time scales. Readership: Science enthusiasts and students.

Emanuele Severino

Piero Coda

Fabio Scardigli

In this small book, theoretical physicist Gerard 't Hooft (Nobel prize 1999), philosopher Emanuele Severino (Lincei Academician), and theologian Piero Coda (Pontifical Lateran University) confront one another on a topic that lies at the roots of quantum mechanics and at the origin of Western thought: Determinism and Free Will. "God does not play dice" said Einstein, a tenacious determinist. Quantum Mechanics and its clash with General Relativity have reanimated ancient dilemmas about chance and necessity: Is Nature deterministic? Is Man free? The “free-will theorem” by Conway and Kochen, and the deterministic interpretation of quantum mechanics proposed by 't Hooft, revive such philosophical questions in modern Physics. Is Becoming real? Is the Elementary Event a product of the Case? The cyclopean clash between Heraclitus and Parmenides has entered a new episode, as evidenced by the essays in this volume.

New Insights from Physics, Philosophy, and Theology

Determinism and Free Will

J. Frölich

Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.

Gerard 't Hooft

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