This book on the structure and role of time in physical theories addresses itself to scientists and philosophers intereste:'i in the 'no man's lard' between science and philosophy, in particular between physics and philoso phy. The p:lint of departure is physical time, Le. time as usErl 1: physicists in their theories; but the analysis is not oonfined to a purely physical level but caries the problem into the domain of philosophical in quiry. Altoough the book presupp:lses some knowledge of physics, I have avoided, wherever p:lssible, the use of advanced mathematics and technical details. Of all the people woo have been of help in writing this book, I would first of all like to mention Paul Scheurer and Guy Debrock who were my primary mentors in science and philosophy. This sttrly is a revision of my dissertation [Kroes 1982a] which I wrote under the stimulating guidance of Scheurer; many of the ideas ex posed here have their origin in his work and were developErl in frequent discussions with him. Guy Debrock not only stimulated my interest in philosophy but also made valuable suggestions. Witoout any overstatement, I dare say that without their assistence, this book would never have been written. Furthernore, I would like to thank D. Dieks, J.J.C.

At the heart of relativity theory, quantum mechanics, string theory, and much of modern cosmology lies one concept: symmetry. In Why Beauty Is Truth, world-famous mathematician Ian Stewart narrates the history of the emergence of this remarkable area of study. Stewart introduces us to such characters as the Renaissance Italian genius, rogue, scholar, and gambler Girolamo Cardano, who stole the modern method of solving cubic equations and published it in the first important book on algebra, and the young revolutionary Evariste Galois, who refashioned the whole of mathematics and founded the field of group theory only to die in a pointless duel over a woman before his work was published. Stewart also explores the strange numerology of real mathematics, in which particular numbers have unique and unpredictable properties related to symmetry. He shows how Wilhelm Killing discovered "Lie groups" with 14, 52, 78, 133, and 248 dimensions-groups whose very existence is a profound puzzle. Finally, Stewart describes the world beyond superstrings: the "octonionic" symmetries that may explain the very existence of the universe.

Gravitational Physics assesses the achievements of the field over the past decade in both theory and experiment, identifies the most promising opportunities for research in the next decade, and describes the resources necessary to realize those opportunities. A major theme running through the opportunities is the exploration of strong gravitational fields, such as those associated with black holes. The book, part of the ongoing decadal survey Physics in a New Era, examines topics such as gravitational waves and their detection, classical and quantum theory of strong gravitational fields, precision measurements, and astronomical observations relevant to the predictions of Einstein's theory of general relativity.

Shapiro argues that both realist and anti-realist accounts of mathematics are problematic. To resolve this dilemma, he articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

This is a new volume of original essays on the metaphysics of quantum mechanics. The essays address questions such as: What fundamental metaphysics is best motivated by quantum mechanics? What is the ontological status of the wave function? What is the nature of the fundamental space (or space-time manifold) of quantum mechanics?

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 book explores precisely how mathematics allows us to model and predict the behaviour of physical systems, to an amazing degree of accuracy. One of the oldest explanations for this is that, in some profound way, the structure of the world is mathematical. The ancient Pythagoreans stated that “everything is number”. However, while exploring the Pythagorean method, this book chooses to add a second principle of the universe: the mind. This work defends the proposition that mind and mathematical structure are the grounds of reality.

Emerging as a hot topic in the mid-twentieth century, causality is one of the most frequently discussed issues in contemporary philosophy. Causality has been a central concept in philosophy as well as in the sciences, especially the natural sciences, dating back to its beginning in Greek thought. David Hume famously claimed that causality is the cement of the universe. In general terms, it links eventualities, predicts the consequences of action, and is the cognitive basis for the acquisition and the use of categories and concepts in the child. Indeed, how could one answer why-questions, around which early rational thought begins to revolve, without hitting on the relationships between reason and consequence, cause and effect, or without drawing these distinctions? But a comprehensive definition of causality has been notoriously hard to provide, and virtually every aspect of causation has been subject to much debate and analysis.Thinking About Causes brings together top philosophers from the United States and Europe to focus on causality as a major force in philosophical and scientific thought. Topics addressed include: ancient Stoicism and moral philosophy; the case of sacramental causality; traditional causal concepts in Descartes; Kant on transcendental laws; the influence of J. S. Mill's politics on his concept of causation; plurality in causality; causality in modern physics; causality in economics; and the concept of free will.Taken together, the essays in this collection from the Pittsburgh -Konstanz series provide the best current thinking about causality, especially as it relates to the philosophy of science.

The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction — the direct quantisation of Einstein's general theory of relativity and string theory — are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantization of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantization, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centres around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantization of black holes, quantum cosmology, the indications of a discrete structure of spacetime, and the origin of irreversibility. This third edition contains new chapters or sections on quantum gravity phenomenology, Horava-Lifshitz quantum gravity, analogue gravity, the holographic principle, and affine quantum gravity. It will present updates on loop quantum cosmology, the LTB model, asymptotic safety, and various discrete approaches. The third edition also contains pedagogical extensions throughout the text. This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science.