This book provides an interdisciplinary introduction to the notion of fractal time, starting from scratch with a philosophical and perceptual puzzle. How subjective duration varies, depending on the way we embed current content into contexts, is explained.The complexity of our temporal perspective depends on the number of nestings performed, i.e. on the number of contexts taken into account. This temporal contextualization is described against the background of the notion of fractal time. Our temporal interface, the Now, is portrayed as a fractal structure which arises from the distribution of content and contexts in two dimensions: the length and the depth of time. The leitmotif of the book is the notion of simultaneity, which determines the temporal structure of our interfaces. Recent research results are described which present and discuss a number of distorted temporal perspectives. It is suggested that dynamical diseases arise from unsuccessful nesting attempts, i.e. from failed contextualization. Successful nesting, by contrast, manifests itself in a "win-win handshake" between the observer-participant and his chosen context. The answer as to why a watched kettle never boils has repercussions in many a discipline. It would be of immense interest to anyone who works in the fields of cognitive and complexity sciences, psychology and the neurosciences, social medicine, philosophy and the arts.

The nature of time has long puzzled physicists and philosophers. Time potentially has very fundamental yet unknown properties. In 1993 a new model of multi-dimensional time was found to relate closely to properties of the cosmological redshift. An international conference was subsequently convened in April 1996 to examine past, current and new concepts of time as they relate to physics and cosmology. These proceedings incorporate 34 reviews and contributed papers from the conference. The major reviews include observational properties of the redshift, alternative cosmologies, critical problems in cosmology, alternative viewpoints and problems in gravitation theory and particle physics, and new approaches to mathematical models of time. Professionals and students with an interest in cosmology and the structure of the universe should find that this book raises critical problems and explores challenging alternatives to classical viewpoints.

This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statistical mechanics. This will interest specialists of various fields, especially the (classical and quantum) plasma physics. However, quantum physics - to which a major part is devoted - will be of more interest since, not only it applies to quantum plasma physics, but also to nuclear matter and to strong magnetic field, cosmology, etc. Although the domain of gauge theory is not covered in this book, the topic is not completely forgotten, in particular in the domain of plasma physics. This book is particularly readable for graduate students and a fortiori to young researchers for whom it offers methods and also appropriate schemes to deal with the current problems encountered in astrophysics, in strong magnetic, in nuclear or even in high energy physics.

New Edition: Introductory Quantum Physics and Relativity (2nd Edition)This book is based on the lecture courses taught by Dunningham and Vedral at the University of Leeds. The book contains all the necessary material for quantum physics and relativity in the first two years of a typical physics degree course. The choice of topics complies fully with the Institute of Physics guidelines, but the coverage also includes more interesting and up-to-date applications, such as Bose condensation and quantum teleportation.

This book examines the rise and proliferation of 'Supermaxes', large prisons dedicated to holding prisoners in prolonged and strict solitary confinement, in the United States since the late 1980s.

Drawing on unique access to two Supermax prisons and on in-depth interviews with prison officials, prison architects, current and former prisoners, mental health professionals, penal, legal, and human rights experts, it provides a holistic view of the theory, practice and consequences of these prisons. Given the historic uses of solitary confinement, the book also traces continuities and discontinuities in its use on both sides of the Atlantic over the last two centuries.

It argues that rather than being an entirely 'new' form of imprisonment, Supermax prisons draw on principles of architecture, surveillance and control which were set out in the early 19th century but which are now enhanced by the most advanced technologies available to current day prison planners and administrators. It asks why a form of confinement which had been discredited in the past is now proposed as the best solution for dealing with 'difficult', 'dangerous' or 'disruptive' prisoners, and assesses the true costs of Supermax confinement.

This monograph presents the geoscientific context arising in decorrelative gravitational exploration to determine the mass density distribution inside the Earth. First, an insight into the current state of research is given by reducing gravimetry to mathematically accessible, and thus calculable, decorrelated models. In this way, the various unresolved questions and problems of gravimetry are made available to a broad scientific audience and the exploration industry. New theoretical developments will be given, and innovative ways of modeling geologic layers and faults by mollifier regularization techniques are shown. This book is dedicated to surface as well as volume geology with potential data primarily of terrestrial origin. For deep geology, the geomathematical decorrelation methods are to be designed in such a way that depth information (e.g., in boreholes) may be canonically entered. Bridging several different geo-disciplines, this book leads in a cycle from the potential measurements made by geoengineers, to the cleansing of data by geophysicists and geoengineers, to the subsequent theory and model formation, computer-based implementation, and numerical calculation and simulations made by geomathematicians, to interpretation by geologists, and, if necessary, back. It therefore spans the spectrum from geoengineering, especially geodesy, via geophysics to geomathematics and geology, and back. Using the German Saarland area for methodological tests, important new fields of application are opened, particularly for regions with mining-related cavities or dense development in today's geo-exploration.

This book brings Einstein's general relativity into action in new ways at scales ranging from the tiny Planck scale to the scale of immense galactic clusters. It presents the case that Einstein's theory of gravity can describe the observed dynamics of galaxies without invoking the unknown "dark matter" required in models based on Newtonian gravity.

Drawing on the author's experience as a lecturer and on his own research, the book covers the essentials of Einstein's special and general relativity at a level accessible to undergraduate students. The early chapters provide a compact introduction to relativity for readers who have little or no background in the subject. Hermann Bondi's very transparent approach to special relativity is expanded to resolve the "twin paradox" using only elementary mathematics. In later chapters, general relativity is used to extend the concept of the Planck scale, to address the role of the cosmological term and to analyze the concept of "time machines."

This book presents a collection of focused review papers on the advances in topics in modern astronomy, astrophysics, cosmology and planetary science. The chapters are written by expert members of an EU-funded ERASMUS+ program of strategic partnership between several European institutes. The 13 reviews comprise the topics: Space debris, optical measurements Meteors, light from comets and asteroids Extrasolar enigmas: from disintegrating exoplanets to exo-asteroids Physical conditions and chemical abundances in photoionized nebulae from optical spectra Observational Constraints on the Common Envelope Phase A modern guide to quantitative spectroscopy of massive OB stars Explosion mechanisms of core-collapse supernovae and their observational signatures Low-mass and substellar eclipsing binaries in stellar clusters Globular cluster systems and Galaxy Formation Hot atmospheres of galaxies, groups, and clusters of galaxies The establishment of the Standard Cosmological Model through observations Exploiting solar visible-range observations by inversion techniques: from flows in the solar subsurface to a flaring atmosphere Starburst galaxies The book is intended for the general astronomical community as well as for advanced students who could use it as a guideline, inspiration and overview for their future careers in astronomy.

In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string theory / gauge theory correspondence is at work. One of the most important examples of this correspondence relates Chern-Simons theory, a topological gauge theory in three dimensions which describes knot and three-manifold invariants, to topological string theory, which is deeply related to Gromov-Witten invariants. This has led to some surprising relations between three-manifold geometry and enumerative geometry. This book gives the first coherent presentation of this and other related topics. After an introduction to matrix models and Chern-Simons theory, the book describes in detail the topological string theories that correspond to these gauge theories and develops the mathematical implications of this duality for the enumerative geometry of Calabi-Yau manifolds and knot theory. It is written in a pedagogical style and will be useful reading for graduate students and researchers in both mathematics and physics willing to learn about these developments.

A sweeping account of the century of experimentation that confirmed Einstein's general theory of relativity, bringing to life the science and scientists at the origins of relativity, the development of radio telescopes, the discovery of black holes and quasars, and the still unresolved place of gravity in quantum theory. Albert Einstein did nothing of note on May 29, 1919, yet that is when he became immortal. On that day, astronomer Arthur Eddington and his team observed a solar eclipse and found something extraordinary: gravity bends light, just as Einstein predicted. The finding confirmed the theory of general relativity, fundamentally changing our understanding of space and time. A century later, another group of astronomers is performing a similar experiment on a much larger scale. The Event Horizon Telescope, a globe-spanning array of radio dishes, is examining space surrounding Sagittarius A*, the supermassive black hole at the center of the Milky Way. As Ron Cowen recounts, the foremost goal of the experiment is to determine whether Einstein was right on the details. Gravity lies at the heart of what we don't know about quantum mechanics, but tantalizing possibilities for deeper insight are offered by black holes. By observing starlight wrapping around Sagittarius A*, the telescope will not only provide the first direct view of an event horizon-a black hole's point of no return-but will also enable scientists to test Einstein's theory under the most extreme conditions. Gravity's Century shows how we got from the pivotal observations of the 1919 eclipse to the Event Horizon Telescope, and what is at stake today. Breaking down the physics in clear and approachable language, Cowen makes vivid how the quest to understand gravity is really the quest to comprehend the universe.

This book, first appearing in German in 2004 under the title Spezielle Relativitatstheorie fur Studienanfanger, offers access to the special theory of relativity for readers with a background in mathematics and physics comparable to a high school honors degree. All mathematical and physical competence required beyond that level is gradually developed through the book, as more advanced topics are introduced. The full tensor formalism, however, is dispensed with as it would only be a burden for the problems to be dealt with. Eventually, a substantial and comprehensive treatise on special relativity emerges which, with its gray-shaded formulary, is an invaluable reference manual for students and scientists alike.Some crucial results are derived more than once with different approaches: the Lorentz transformation in one spatial direction three times, the Doppler formula four times, the Lorentz transformation in two directions twice; also twice the unification of electric and magnetic forces, the velocity addition formula, as well as the aberration formula. Beginners will be grateful to find several routes to the goal; moreover, for a theory like relativity, it is of fundamental importance to demonstrate that it is self-contained and without contradictions.Author's website: www.relativity.ch.

First published in 1973, this influential work discusses Einstein's General Theory of Relativity to show how two of its predictions arise: first, that the ultimate fate of many massive stars is to undergo gravitational collapse to form 'black holes'; and second, that there was a singularity in the past at the beginning of the universe. Starting with a precise formulation of the theory, including the necessary differential geometry, the authors discuss the significance of space-time curvature and examine the properties of a number of exact solutions of Einstein's field equations. They develop the theory of the causal structure of a general space-time, and use it to prove a number of theorems establishing the inevitability of singularities under certain conditions. A Foreword contributed by Abhay Ashtekar and a new Preface from George Ellis help put the volume into context of the developments in the field over the past fifty years.

A working knowledge of Einstein's theory of general relativity is an essential tool for every physicist today. This self-contained book is an introductory text on the subject aimed at first-year graduate students, or advanced undergraduates, in physics that assumes only a basic understanding of classical Lagrangian mechanics. The mechanics problem of a point mass constrained to move without friction on a two-dimensional surface of arbitrary shape serves as a paradigm for the development of the mathematics and physics of general relativity. After reviewing special relativity, the basic principles of general relativity are presented, and the most important applications are discussed. The final special topics section guides the reader through a few important areas of current research. This book will allow the reader to approach the more advanced texts and monographs, as well as the continual influx of fascinating new experimental results, with a deeper understanding and sense of appreciation.

A working knowledge of Einstein's theory of general relativity is an essential tool for every physicist today. This self-contained book is an introductory text on the subject aimed at first-year graduate students, or advanced undergraduates, in physics that assumes only a basic understanding of classical Lagrangian mechanics. The mechanics problem of a point mass constrained to move without friction on a two-dimensional surface of arbitrary shape serves as a paradigm for the development of the mathematics and physics of general relativity. After reviewing special relativity, the basic principles of general relativity are presented, and the most important applications are discussed. The final special topics section guides the reader through a few important areas of current research. This book will allow the reader to approach the more advanced texts and monographs, as well as the continual influx of fascinating new experimental results, with a deeper understanding and sense of appreciation.

A Broader View of Relativity shows that there is still new life in old physics. The book examines the historical context and theoretical underpinnings of Einstein's theory of special relativity and describes Broad Relativity, a generalized theory of coordinate transformations between inertial reference frames that includes Einstein's special relativity as a special case. It shows how the principle of relativity is compatible with multiple concepts of physical time and how these different procedures for clock synchronization can be useful for thinking about different physical problems, including many-body systems and the development of a Lorentz-invariant thermodynamics. Broad relativity also provides new answers to old questions such as the necessity of postulating the constancy of the speed of light and the viability of Reichenbach's general concept of time. The book also draws on the idea of limiting-four-dimensional symmetry to describe coordinate transformations and the physics of particles and fields in non-inertial frames, particularly those with constant linear accelerations. This new edition expands the discussion on the role that human conventions and unit systems have played in the historical development of relativity theories and includes new results on the implications of broad relativity for clarifying the status of constants that are truly fundamental and inherent properties of our universe.

This volume of the Encyclopaedia contains three contributions in the field of complex analysis. The topics treated are mean periodicity and convolutionequations, Yang-Mills fields and the Radon-Penrose transform, and stringtheory. The latter two have strong links with quantum field theory and the theory of general relativity. In fact, the mathematical results described inthe book arose from the need of physicists to find a sound mathematical basis for their theories. The authors present their material in the formof surveys which provide up-to-date accounts of current research. The book will be immensely useful to graduate students and researchers in complex analysis, differential geometry, quantum field theory, string theoryand general relativity.

Contents:
Einstein, Albert. 'On the Electrodynamics of Moving Bodies.' In Albert Einsteins Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905-1911), translated by Arthur I. Miller (Reading, PA: Addison-Wesley Publishing Co., 1981)

Holton, Gerald. 'Mach, Einstein, and the Search for Reality'. In Gerald Holton, ed., Thematic Origins of Scientific Thought: Kepler to Einstein, rev. ed. (Cambridge, MA: Harvard University Press, 1988).

Holton, Gerald. 'Einstein and the Cultural Roots of Modern Science' Daedalus 127 (Winter 1998).

Darrigol, Oliver. 'Henri Poincaré's Criticism of Fin-de-siecle Electrodynamics'. Studies in History and Philosophy of Modern Physics 26 (1995).

Janssen, Michel. 'Reconsidering a Scientific Revolution: The Case of Einstein Versus Lorentz.' Unpublished.

Miller, Arthur I. 'The Special Relativity Theory: Einstein's Response to the Physics of 1905'. In Gerald Holton and Yehudah Elkana, eds., Albert Einstein: Historical and Cultural Perspectives (Princeton, NJ: Princeton University Press, 1982).

Galison, Peter. 'Einstein's Clocks: The Place of Time'. Critical Enquiry 26 (Winter 2000).

Cassidy, David. 'Understanding the History of Special Relativity'. Historical Studies in the Physical Sciences 16 (1986)

Pyenson, Lewis. 'The Relativity Revolution in Germany.' In The Comparitive Reception of Relativity (Dordrecht: Reidel, 1987).

Glick, Thomas. 'Cultural Issues in the Reception of Relativity (Dordrecht: Reidel, 1987)

Goldberg, Stanley. 'In Defense of the Ether: The British Response to Einstein's Special Theory of Relativity, 1905-1911.' Historical Studies in the Physical Sciences 2 (1970).

Warwick, Andrew. 'Cambridge Mathematics and Cavendish Physics: Cunningham, Campbell, and Einstein's Relativity, 1905-1911. Part I: The Uses of Theory.' Studies in History and Philosophy of Science 23 (1992).

Gravitational waves (GWs) are a hot topic and promise to play a central role in astrophysics, cosmology, and theoretical physics. Technological developments have led us to the brink of their direct observation, which could become a reality in the coming years. The direct observation of GWs will open an entirely new field: GW astronomy. This is expected to bring a revolution in our knowledge of the universe by allowing the observation of previously unseen phenomena, such as the coalescence of compact objects (neutron stars and black holes), the fall of stars into supermassive black holes, stellar core collapses, big-bang relics, and the new and unexpected.
With a wide range of contributions by leading scientists in the field, Gravitational Waves covers topics such as the basics of GWs, various advanced topics, GW detectors, astrophysics of GW sources, numerical applications, and several recent theoretical developments. The material is written at a level suitable for postgraduate students entering the field.

This book explores the use of waves on strings and sound waves to illustrate the behaviour of waves. It shows how Albert Einstein overturned Newtonian physics and predicted startling new effects such as time dilation and length contraction for objects travelling at close to the speed of light.

This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory.

There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups -- particularly the Lorentz and the SL(2, C) groups -- to the theory of general relativity. Each chapter is concluded with a set of problems.

The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2, C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed.

The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.

Spinors are used extensively in physics. It is widely accepted that they are more fundamental than tensors, and the easy way to see this is through the results obtained in general relativity theory by using spinors -- results that could not have been obtained by using tensor methods only.

The foundation of the concept of spinors is groups; spinors appear as representations of groups. This textbook expounds the relationship between spinors and representations of groups. As is well known, spinors and representations are both widely used in the theory of elementary particles.

The authors present the origin of spinors from representation theory, but nevertheless apply the theory of spinors to general relativity theory, and part of the book is devoted to curved space-time applications.

Based on lectures given at Ben Gurion University, this textbook is intended for advanced undergraduate and graduate students in physics and mathematics, as well as being a reference for researchers.

This compact yet informative Guide presents an accessible route through Special Relativity, taking a modern axiomatic and geometrical approach. It begins by explaining key concepts and introducing Einstein's postulates. The consequences of the postulates - length contraction and time dilation - are unravelled qualitatively and then quantitatively. These strands are then tied together using the mathematical framework of the Lorentz transformation, before applying these ideas to kinematics and dynamics. This volume demonstrates the essential simplicity of the core ideas of Special Relativity, while acknowledging the challenges of developing new intuitions and dealing with the apparent paradoxes that arise. A valuable supplementary resource for intermediate undergraduates, as well as independent learners with some technical background, the Guide includes numerous exercises with hints and notes provided online. It lays the foundations for further study in General Relativity, which is introduced briefly in an appendix.

This is the second volume of textbooks on atomic, molecular and optical physics, aiming at a comprehensive presentation of this highly productive branch of modern physics as an indispensable basis for many areas in physics and chemistry as well as in state of the art bio- and material-sciences. It primarily addresses advanced students (including PhD students), but in a number of selected subject areas the reader is lead up to the frontiers of present research. Thus even the active scientist is addressed. This volume 2 introduces lasers and quantum optics, while the main focus is on the structure of molecules and their spectroscopy, as well as on collision physics as the continuum counterpart to bound molecular states. The emphasis is always on the experiment and its interpretation, while the necessary theory is introduced from this perspective in a compact and occasionally somewhat heuristic manner, easy to follow even for beginners.

This book is divided into two parts. In the first part we introduce the foundations of special relativity, such as, the inertial frame of reference, the definition of simulataneity, and Einstein's two basic hypotheses. We give the main relativistic effects, e.g. the relativity of simultaneity, velocity addition, length-contraction, the apparent shape of a moving body, time-dilation, Doppler effect, and the Thomas precession, In particular, the simultaneity problem and slow transport of clocks are investigated in detail by means of the test theories of special relativity. In the second part, variant types of experiments performed up to now are analyzed and compared to the predictions of special relativity. This shows that the experiments are a test of the two-way speed of light, but not of the one-way speed of light.