Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.

Presents a complete description of homogenous and isotropic tensor-valued random fields, including the problems of continuum physics, mathematical tools and applications.

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.

This volume addresses the question of time from the perspective of the time of nature. Its aim is to provide some insights about the nature of time on the basis of the different uses of the concept of time in natural sciences. Presenting a dialogue between philosophy and science, it features a collection of papers that investigate the representation, modeling and understanding of time as they appear in physics, biology, geology and paleontology. It asks questions such as: whether or not the notions of time in the various sciences are reducible to the same physical time, what status should be given to timescale differences, or what are the specific epistemic issues raised by past facts in natural sciences. The book first explores the experience of time and its relation to time in nature in a set of chapters that bring together what human experience and physics enable metaphysicians, logicians and scientists to say about time. Next, it studies time in physics, including some puzzling paradoxes about time raised by the theory of relativity and quantum mechanics. The volume then goes on to examine the distinctive problems and conceptions of time in the life sciences. It explores the concept of deep time in paleontology and geology, time in the epistemology of evolutionary biology, and time in developmental biology. Each scientific discipline features a specific approach to time and uses distinctive methodologies for implementing time in its models. This volume seeks to define a common language to conceive of the distinct ways different scientific disciplines view time. In the process, it offers a new approach to the issue of time that will appeal to a wide range of readers: philosophers and historians of science, metaphysicians and natural scientists - be they scholars, advanced students or readers from an educated general audience.

An annual volume presenting substantive survey articles in numerical analysis and scientific computing.

Instantons, or pseudoparticles, are solutions to the equations of motion in classical field theories on a Euclidean spacetime. Instantons are found everywhere in quantum theories as they have many applications in quantum tunnelling. Diverse physical phenomena may be described through quantum tunnelling, for example: the Josephson effect, the decay of meta-stable nuclear states, band formation in tight binding models of crystalline solids, the structure of the gauge theory vacuum, confinement in 2+1 dimensions, and the decay of superheated or supercooled phases. Drawing inspiration from Sidney Coleman's Erice lectures, this volume provides an accessible, detailed introduction to instanton methods, with many applications, making it a valuable resource for graduate students in many areas of physics, from condensed matter, particle and nuclear physics, to string theory.

The structural aspects of composite quantum systems in the foundation, interpretation and application of quantum theory is an increasingly prominent topic of physics research. As an emerging field, it seeks to understand the origins of the classical world of experience from the quantum level.Quantum Structural Studies presents conceptual fundamentals and mathematical methods for investigating the structuring of quantum systems into subsystems. Split into four sections, the topics covered include the historical and philosophical aspects of quantum structures, specific interpretive approaches and ontologies, and alternative methodological approaches to quantum mechanics. Questions addressed are: Specialists, graduate students and researchers seeking an introduction to the field of emergent structures and new directions for research and experimentation can use this book to find up-to-date representative texts and reviews.