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    The Principle of Relativity with Applications to Physical Science
    The Principle of Relativity with Applications to Physical Science
    The Principle of Relativity with Applications to Physical Science
    Ebook300 pages1 hourDover Books on Physics

    The Principle of Relativity with Applications to Physical Science

    By Alfred North Whitehead

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    An exposition of an alternative rendering of the theory of relativity, this volume is the work of the distinguished English mathematician and philosopher, Alfred North Whitehead. Suitable for upper-level undergraduates and graduate students, its three-part treatment begins with an overview of general principles that may be described as mainly philosophical in character. Part II is devoted to physical applications and chiefly concerns the particular results deducible from the formulas assumed for the gravitation and electromagnetic fields. The final part consists of an exposition of the elementary theory of tensors.
    The author notes that the text's order proceeds naturally from general principles to particular applications, concluding with a general exposition of the mathematical theory, special examples of which have occurred in the discussion of the applications. Physicists,
    Whitehead suggests, may prefer to start with Part II, referring back to a few formulas mentioned at the end of Part I, and mathematicians may start with Part III. The whole evidence, he adds, requires a consideration of all three parts.

    LanguageEnglish
    PublisherDover Publications
    Release dateSep 20, 2012
    ISBN9780486174198
    The Principle of Relativity with Applications to Physical Science
    Author

    Alfred North Whitehead

    An English mathematician and philosopher, Alfred North Whitehead provided the foundation for the shool of thought known as process philosophy. With an academic career that spanned from Cambridge to Harvard, Whitehead wrote extensively on mathematics, metaphysis, and philosophy. He died in Massachusetts in 1947.

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      Book preview

      The Principle of Relativity with Applications to Physical Science - Alfred North Whitehead

      e9780486174198_cover.jpge9780486174198_i0001.jpg

      DOVER PHOENIX EDITIONS

      Bibliographical Note

      This Dover edition, first published in 2004, is an unabridged and unaltered republication of the work originally published by Cambridge University Press, Cambridge, England, in 1922.

      Library of Congress Cataloging-in-Publication Data

      Whitehead, Alfred North, 1861—1947.

      The principle of relativity with applications to physical science / Alfred North Whitehead.

      p. cm.—(Dover phoenix editions)

      Originally published: Cambridge, England : Cambridge University Press, 1922.

      9780486174198

      1. Relativity (Physics) I. Title. II. Series.

      QC6.W57 2004

      530.11—dc22

      2004050197

      Manufactured in the United States of America

      Dover Publications, Inc., 31 East 2nd Street, Mineola, N.Y. 11501

      TO MY WIFE

      WHOSE ENCOURAGEMENT AND COUNSEL

      HAVE MADE MY LIFE’S WORK POSSIBLE

      PREFACE

      THE present work is an exposition of an alternative rendering of the theory of relativity. It takes its rise from that ‘awakening from dogmatic slumber’—to use Kant’s phrase—which we owe to Einstein and Minkowski. But it is not an attempt to expound either Einstein’s earlier or his later theory. The metrical formulae finally arrived at are those of the earlier theory, but the meanings ascribed to the algebraic symbols are entirely different. As the result of a consideration of the character of our knowledge in general, and of our knowledge of nature in particular, undertaken in Part I of this book and in my two previous works¹ on this subject, I deduce that our experience requires and exhibits a basis of uniformity, and that in the case of nature this basis exhibits itself as the uniformity of spatio-temporal relations. This conclusion entirely cuts away the casual heterogeneity of these relations which is the essential of Einstein’s later theory. It is this uniformity which is essential to my outlook, and not the Euclidean geometry which I adopt as lending itself to the simplest exposition of the facts of nature. I should be very willing to believe that each permanent space is either uniformly elliptic or uniformly hyperbolic, if any observations are more simply explained by such a hypothesis.

      It is inherent in my theory to maintain the old division between physics and geometry. Physics is the science of the contingent relations of nature and geometry expresses its uniform relatedness.

      The book is divided into three parts. Part I is concerned with general principles and may roughly be described as mainly philosophical in character. Part II is devoted to the physical applications and deals with the particular results deducible from the formulae assumed for the gravitational and electromagnetic fields. In relation to the spectral linesthese formulae would require a ‘limb effect’ and a duplication or a triplication of individual lines, analogous to phenomena already observed. Part III is an exposition of the elementary theory of tensors. This Part has been added for one reason because it may be useful to many mathematicians who may be puzzled by some of the formulae and procedures of Part II. But this Part is also required by another reason. The theory of tensors is usually expounded under the guise of geometrical metaphors which entirely mask the type of application which I give to it in this work. For example, the whole idea of any ‘fundamental tensor’ is foreign to my purpose and impedes the comprehension of my applications.

      The order in which the parts should be studied will depend upon the psychology of the reader. I have placed them in the order natural to my own mind, namely, general principles, particular applications, and finally the general exposition of the mathematical theory of which special examples have occurred in the discussion of the applications. But a physicist may prefer to start with Part II, referring back to a few formulae which have been mentioned at the end of Part I, and a mathematician may start with Part III. The whole evidence requires a consideration of the three Parts.

      Practically the whole of the book has been delivered in the form of lectures either in America at the College of Bryn Mawr, or before the Royal Society of Edinburgh, or to my pupils in the Imperial College. I have carefully preserved the lecture form and also some reduplication of statement, particularly in Part I.

      The exposition of a novel idea which has many reactions upon diverse current modes of thought is a difficult business. The most successful example in the history of science is, I think, Galileo’s ‘Dialogues on the Two Systems of the World.’ An examination of that masterly work will show that the dialogue form is an essential element to its excellence. It allows the main expositor of the dialogues continually to restate his ideas in reference to diverse trains of thought suggested by the other interlocutors. Now the process of understanding new conceptions is essentially the process of laying the new ideas alongside of our pre-existing trains of thought. Accordingly for an author of adequate literary ability the dialogue is the natural literary form for the prolonged explanation of a tangled subject. The custom of modern presentations of science, and my own diffidence of success in the art of managing a dialogue, have led me to adopt the modified form of lectures in which the audiences—real audiences, either in America, Edinburgh or South Kensington—are to be regarded as silent interlocutors demanding explanations of the various aspects of the theory.

      Chapter II was originally delivered² in Edinburgh as a lecture to the Royal Society of Edinburgh when it did me the honour of making me the first recipient of the ‘James-Scott Prize’ for the encouragement of the philosophy of science. Chapter IV was originally delivered³ at the College of Bryn Mawr, near Philadelphia, on the occasion of a festival promoted by the former pupils and colleagues of Prof. Charlotte Angus Scott in honour of her work as Professor of Mathematics at the college since its foundation.

      My thanks are due to my colleague, Assistant-Professor Sillick, for the figure on p. 31. I am also further indebted to him for a series of beautiful slides containing the mathematical formulae of Chapter IV; even the admirable printing of the Cambridge University Press will not compensate readers of this book for the loss of the slides as used in the original lecture.

      In acknowledging my obligations to the efficiency and courtesy of the staff of the University Press, I take the opportunity of paying a respectful tribute to the work of the late Mr A. R. Waller as secretary of the Press Syndicate. The initial negotiations respecting this book were conducted through him and he died just as the printing commenced. The loss of his wisdom, his knowledge, and his charm will leave a gap in the hearts of all those who have to deal with the great Institution which he served so well.

      A. N. W.

      15 September, 1922.

      Table of Contents

      Title Page

      Copyright Page

      Dedication

      PREFACE

      PART I - GENERAL PRINCIPLES

      CHAPTER I - PREFATORY EXPLANATIONS

      CHAPTER II - THE RELATEDNESS OF NATURE

      CHAPTER III - EQUALITY

      CHAPTER IV - SOME PRINCIPLES OF PHYSICAL SCIENCE

      PART II - PHYSICAL APPLICATIONS

      CHAPTER V - THE EQUATIONS OF MOTION

      CHAPTER VI - ON THE FORMULA FOR dJ2

      CHAPTER VII - PERMANENT GRAVITATIONAL FIELDS

      CHAPTER VIII - APPARENT MASS AND THE SPECTRAL SHIFT

      CHAPTER IX - PLANETARY MOTION

      CHAPTER X - ELECTROMAGNETIC EQUATIONS

      CHAPTER XI - GRAVITATION AND LIGHT WAVES

      CHAPTER XII - TEMPERATURE EFFECTS ON GRAVITATIONAL FORCES

      CHAPTER XIII - THE ELECTROSTATIC POTENTIAL AND SPECTRAL SHIFT

      CHAPTER XIV - THE LIMB EFFECT

      CHAPTER XV - PERMANENT DIRECTIONS OF VIBRATION AND THE DOUBLING EFFECT

      CHAPTER XVI - STEADY ELECTROMAGNETIC FIELDS

      CHAPTER XVII - THE MOON’S MOTION

      PART III - ELEMENTARY THEORY OF TENSORS

      CHAPTER XVIII - FUNDAMENTAL NOTIONS

      CHAPTER XIX - ELEMENTARY PROPERTIES

      CHAPTER XX - THE PROCESS OF RESTRICTION

      CHAPTER XXI - TENSORS OF THE SECOND ORDER

      CHAPTER XXII - THE GALILEAN TENSORS

      CHAPTER XXIII - THE DIFFERENTIATION OF TENSOR COMPONENTS

      CHAPTER XXIV - SOME IMPORTANT TENSORS

      DOVER PHOENIX EDITIONS

      PART I

      GENERAL PRINCIPLES

      CHAPTER I

      PREFATORY EXPLANATIONS

      THE doctrine of relativity affects every branch of natural science, not excluding the biological sciences. In general, however, this impact of the new doctrine on the older sciences lies in the future and will disclose itself in ways not yet apparent. Relativity, in the form of novel formulae relating time and space, first developed in connection with electromagnetism, including light phenomena. Einstein then proceeded to show its bearing on the formulae for gravitation. It so happens therefore that owing to the circumstances of its origin a very general doctrine is linked with two special applications.

      In this procedure science is evolving according to its usual mode. In that atmosphere of thought doctrines are valued for their utility as instruments of research. Only one question is asked: Has the doctrine a precise application to a variety of particular circumstances so as to determine the exact phenomena which should be then observed? In the comparative absence of these applications beauty, generality, or even truth, will not save a doctrine from neglect in scientific thought. With them, it will be absorbed.

      Accordingly a new scientific outlook clings to those fields where its first applications are to be found. They are its title deeds for consideration. But in testing its truth, if the theory have the width and depth which marks a fundamental reorganisation, we cannot wisely confine ourselves solely to the consideration of a few happy applications. The history of science is strewn with the happy applications of discarded theories. There are two gauges through which every theory must pass. There is the broad gauge which tests its consonance with the general character of our direct experience, and there is the narrow gauge which is that mentioned above as being the habitual working gauge of science. These reflections have been suggested by the advice received from two distinguished persons to whom at different times I had explained the scheme of this book. The philosopher advised me to omit the mathematics, and the mathematician urged the cutting out of the philosophy. At the moment I was persuaded: it certainly is a nuisance for philosophers to be worried with applied mathematics, and for mathematicians to be saddled with philosophy. But further reflection has made me retain my original plan. The difficulty is inherent in the subject matter.

      To expect to reorganise our ideas of Time, Space, and Measurement without some discussion which must be ranked as philosophical is to neglect the teaching of history and the inherent probabilities of the subject. On the other hand no reorganisation of these ideas can command confidence unless it supplies science with added power in the analysis of phenomena. The evidence is two-fold, and is fatally weakened if the two parts are disjoined.

      At the same time it is well to understand the limitations to the meaning of ‘philosophy’ in this connection. It has nothing to do with ethics or theology or the theory of aesthetics. It is solely engaged in determining the most general conceptions which apply to things observed by the senses. Accordingly it is not even metaphysics: it should be called pan-physics. Its task is to formulate those principles of science which are employed equally in every branch of natural science. Sir J. J. Thomson, reviewing in Nature⁴ Poynting’s Collected Papers, has quoted a statement taken from one of Poynting’s addresses:

      ‘I have no doubt whatever that our ultimate aim must be to describe the sensible in terms of the sensible.’

      Adherence to this aphorism, sanctioned by the authority of two great English physicists, is the keynote of everything in the following chapters. The philosophy of science is the endeavour to formulate the most general characters of things observed. These

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