Certain fundamental concepts are vital to understanding the world around us, such as spacetime, covered by the special theory of relativity, and causality, the effect of random events, promoted by electromagnetism. Discussing these, the authors support a rationalist view of physics.

In any linear system, the input and the output are connected by means of a linear operator. When the input can be notionally represented by a function that is null valued everywhere except at a specific location in spacetime, the corresponding output is called the Green function in field theories. Dyadic Green functions are commonplace in electromagnetics, because both the input and the output are vector functions of space and time. This book provides a survey of the state-of-the-art knowledge of infinite space dyadic Green functions.

The 1988 Nobel Prize winner establishes the subject's mathematical background, reviews the principles of electrostatics, then introduces Einstein's special theory of relativity and applies it to topics throughout the book.

"It would be hard to imagine a better guide to this difficult subject." -- Scientific American In Three Roads to Quantum Gravity, Lee Smolin provides an accessible overview of the attempts to build a final "theory of everything." He explains in simple terms what scientists are talking about when they say the world is made from exotic entities such as loops, strings, and black holes and tells the fascinating stories behind these discoveries: the rivalries, epiphanies, and intrigues he witnessed firsthand. "Provocative, original, and unsettling." -- The New York Review of Books "An excellent writer, a creative thinker." -- Nature

This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison. Professors can request a solutions manual by email: [email protected]

Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.

This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.

When the author of Identity and Reality accepted Langevin's suggestion that Meyerson "identify the thought processes" of Einstein's relativity theory, he turned from his assured perspective as historian of the sciences to the risky bias of contemporary philosophical critic. But Emile Meyerson, the epis temologist as historian, could not find a more rigorous test of his conclusions from historical learning than the interpretation of Einstein's work, unless perhaps he were to turn from the classical revolution of Einstein's relativity to the non-classical quantum theory. Meyerson captures our sympathy in all his writings: " . . . the role of the epistemologist is . . . in following the development of science" (250); the study of the evolution of reason leads us to see that "man does not experience himself reasoning . . . which is carried on unconsciously," and as the summation of his empirical studies of the works and practices of scientists, "reason . . . behaves in an altogether predict able way: . . . first by making the consequent equivalent to the antecedent, and then by actually denying all diversity in space" (202). If logic - and to Meyerson the epistemologist is logician - is to understand reason, then "logic proceeds a posteriori. " And so we are faced with an empirically based Par menides, and, as we shall see, with an ineliminable 'irrational' within science. Meyerson's story, written in 1924, is still exciting, 60 years later.

Einstein's theory of general relativity is a theory of gravity and, as in the earlier Newtonian theory, much can be learnt about the character of gravitation and its effects by investigating particular idealised examples. This book describes the basic solutions of Einstein's equations with a particular emphasis on what they mean, both geometrically and physically. Concepts such as big bang and big crunch-types of singularities, different kinds of horizons and gravitational waves, are described in the context of the particular space-times in which they naturally arise. These notions are initially introduced using the most simple and symmetric cases. Various important coordinate forms of each solution are presented, thus enabling the global structure of the corresponding space-time and its other properties to be analysed. The book is an invaluable resource both for graduate students and academic researchers working in gravitational physics.