Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least time, the (...) principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

Based on the ideas of Einstein and Minkowski, this concise treatment is derived from the author's many years of teaching the mathematics of relativity at the University of Michigan. Geared toward advanced undergraduates and graduate students of physics, the text covers old physics, new geometry, special relativity, curved space, and general relativity. Beginning with a discussion of the inverse square law in terms of simple calculus, the treatment gradually introduces increasingly complicated situations and more sophisticated mathematical tools. Changes in fundamental (...) concepts, which characterize relativity theory, and the refinements of mathematical technique are incorporated as necessary. The presentation thus offers an easier approach without sacrifice of rigor. Dover (2014) republication of the edition published by John Wiley & Sons, New York, 1950. See every Dover book in print at www.doverpublications.com. (shrink)

Fundamental Theory has been called an "unfinished symphony" and "a challenge to the musicians among natural philosophers of the future". This book, written in 1944 but left unfinished because Eddington died too soon, proved to be his final effort at a vision for harmonization of quantum physics and relativity. The work is less connected and internally integrated than 'Protons and Electrons' while representing a later point in the author's thought arc. The really interested student should read both books together.The physical (...) and mathematical reasoning are very deep, but it is possible to enjoy much of the flavor of the book even without following everything. The tidbits given below illustrate Eddington's beautiful and mellifluous English style. This edition contains a clickable table of contents and some interesting illustrations.WARNING: Due to the complexity of the mathematical typesetting, the only way to reproduce this book has been as a series of scanned page images. We believe this work is scientifically and culturally important, and despite a few imperfections and the inevitably small print, have brought it back into print as part of our continuing commitment to the preservation of Eddington's work. On a portable electronic reader the pages come out pretty small, but they are legible. On a desktop computer running the Amazon app, they are perfectly fine. We appreciate your understanding, and hope you enjoy this valuable book.TIDBITS:The number of protons and electrons in the universe would, in itself, be merely a matter of idle curiosity. But N has a more general significance as a fundamental constant which enters into many physical formulae. Its special interpretation as the number of particles in the universe arises in the following way. If we consider a distribution of hydrogen in equilibrium at zero temperature, the presence of the matter produces a curvature of space, and the curvature causes the space to close when the number of particles contained in it reaches a certain total; that number is N. The present investigation seeks to determine N directly from the principles of measurement. We have to show, not that there are N particles in the universe, but that anyone who accepts certain elementary principles of measurement must, if he is consistent, think there are. We have to express in mathematical symbolism what we think we are doing when we measure things; for if we had no conception of what we were doing, the results of the measurements would not persuade us to believe anything in particular. All our results are derived from the condition that the conceptual interpretation which we place on the results of measurement must be consistent with our conceptual interpretation of the process of measurement.If we play about with a pin and a meter standard, we do not become aware of any number in particular unless the standard has been graduated, or unless we use a process of displacement which we interpret as adding pin-extensions. The fact is that, although measurement is primarily a process involving four entities, the conceptual interpretation of measurement postulates in addition the existence (in the structure contemplated) as something referred to as Z. The existence of Z is the condition that makes graduation an exact concept. In the actual universe there exists a basis which is uniform to a very high approximation, and this serves for almost all purposes; but to the much higher approximation required in the calculation of N the ideal exact basis of uniformity does not exist. The finitude of N is, in fact, the cause of the failure of the approximation.It must be remembered that we are now working to what would ordinarily be considered a fantastically high approximation. For ordinary purposes a measurable has 16 eigenvalues; but under the super-magnification here employed (which is not content to overlook 1 part in 10E39) there is a fine structure which splits each of them into 16 components. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Comprehensive coverage of the special theory (frames of reference, Lorentz transformation, relativistic mechanics of mass points, more), the general theory ...

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)