Project Gutenberg’s Space, Time and Gravitation, by A. S. Eddington This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: Space, Time and Gravitation An Outline of the General Relativity Theory Author: A. S. Eddington Release Date: August 24, 2009 [EBook #29782] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK SPACE, TIME AND GRAVITATION *** Produced by David Clarke, Andrew D. Hwang and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/American Libraries.) transcriber’s note Figures may have been moved with respect to the surrounding text. Minor typographical corrections and presentational changes have been made without comment. This PDF file is formatted for printing, but may be easily formatted for screen viewing. Please see the preamble of the L A T E X source file for instructions. SPACE TIME AND GRAVITATION CAMBRIDGE UNIVERSITY PRESS C. F. CLAY, Manager LONDON : FETTER LANE, E.C. 4 NEW YORK : THE MACMILLAN CO. BOMBAY CALCUTTA  MACMILLAN AND CO., Ltd. MADRAS TORONTO : THE MACMILLAN CO. OF CANADA, Ltd. TOKYO : MARUZEN-KABUSHIKI-KAISHA ALL RIGHTS RESERVED C. Davidson Frontispiece See page 107 eclipse instruments at sobral SPACE TIME AND GRAVITATION AN OUTLINE OF THE GENERAL RELATIVITY THEORY BY A. S. EDDINGTON, M.A., M.Sc., F.R.S. PLUMIAN PROFESSOR OF ASTRONOMY AND EXPERIMENTAL PHILOSOPHY, CAMBRIDGE CAMBRIDGE AT THE UNIVERSITY PRESS 1920 Perhaps to move His laughter at their quaint opinions wide Hereafter, when they come to model heaven And calculate the stars: how they will wield The mighty frame: how build, unbuild, contrive To save appearances. Paradise Lost. PREFACE By his theory of relativity Albert Einstein has provoked a revolution of thought in physical science. The achievement consists essentially in this:—Einstein has succeeded in separating far more completely than hitherto the share of the observer and the share of external nature in the things we see happen. The perception of an object by an observer depends on his own situation and circum- stances; for example, distance will make it appear smaller and dimmer. We make allowance for this almost unconsciously in interpreting what we see. But it now appears that the allowance made for the motion of the ob- server has hitherto been too crude—a fact overlooked because in practice all observers share nearly the same motion, that of the earth. Physical space and time are found to be closely bound up with this motion of the observer; and only an amorphous combination of the two is left inher- ent in the external world. When space and time are relegated to their proper source—the observer—the world of nature which remains appears strangely unfamiliar; but it is in reality simplified, and the underlying unity of the principal phenomena is now clearly revealed. The deductions from this new outlook have, with one doubtful exception, been confirmed when tested by experiment. It is my aim to give an account of this work without introducing any- thing very technical in the way of mathematics, physics, or philosophy. The new view of space and time, so opposed to our habits of thought, must in any case demand unusual mental exercise. The results appear strange; and the incongruity is not without a humorous side. For the first nine chapters the task is one of interpreting a clear-cut theory, accepted in all its essentials by a large and growing school of physicists—although perhaps not everyone would accept the author’s views of its meaning. Chapters x and xi deal with very recent advances, with regard to which opinion is more fluid. As for the last chapter, containing the author’s speculations on the meaning of nature, since it touches on the rudiments of a philosophical system, it is perhaps too sanguine to hope that it can viii PREFACE ever be other than controversial. A non-mathematical presentation has necessary limitations; and the reader who wishes to learn how certain exact results follow from Einstein’s, or even Newton’s, law of gravitation is bound to seek the reasons in a mathematical treatise. But this limitation of range is perhaps less serious than the limitation of intrinsic truth. There is a relativity of truth, as there is a relativity of space.— “For is and is-not though with Rule and Line And up-and-down without, I could define.” Alas! It is not so simple. We abstract from the phenomena that which is peculiar to the position and motion of the observer; but can we abstract that which is peculiar to the limited imagination of the human brain? We think we can, but only in the symbolism of mathematics. As the language of a poet rings with a truth that eludes the clumsy explanations of his commentators, so the geometry of relativity in its perfect harmony expresses a truth of form and type in nature, which my bowdlerised version misses. But the mind is not content to leave scientific Truth in a dry husk of mathematical symbols, and demands that it shall be alloyed with famil- iar images. The mathematician, who handles x so lightly, may fairly be asked to state, not indeed the inscrutable meaning of x in nature, but the meaning which x conveys to him. Although primarily designed for readers without technical knowledge of the subject, it is hoped that the book may also appeal to those who have gone into the subject more deeply. A few notes have been added in the Appendix mainly to bridge the gap between this and more mathematical treatises, and to indicate the points of contact between the argument in the text and the parallel analytical investigation. It is impossible adequately to express my debt to contemporary lit- erature and discussion. The writings of Einstein, Minkowski, Hilbert, Lorentz, Weyl, Robb, and others, have provided the groundwork; in the give and take of debate with friends and correspondents, the extensive ramifications have gradually appeared. A. S. E. 1 May, 1920. [...]... length; and a third to test the second; and so ad infinitum You remind me of the incident of the clock and time- gun in Egypt The man in charge of the time- gun fired it by the clock; and the man in charge of the clock set it right by the time- gun No, you must not define length by means of a rigid scale, and define a rigid scale by means of length Phys I admit I am hazy about strict definitions There is not time. .. a metaphysical space and time which is not within reach of measurement Rel In so far as he is a psychologist our results must concern him Perception is a kind of crude physical measurement; and perceptual space and time is the same as the measured space and time, which is the subjectmatter of natural geometry In other respects he may not be so immediately concerned Physicists and philosophers have... it exactly Rel You have three hypotheses there:—(1) there is an absolute thing in nature corresponding to length, (2) the geometry of these absolute lengths is Euclidean, and (3) practical measures determine this length accurately when there is no gravitational force I see no necessity for these hypotheses, and propose to do without them Hypotheses non fingo The second hypothesis seems to me particularly... admission are not necessarily the same as this absolute thing) sometimes WHAT IS GEOMETRY? 7 obey Euclidean geometry and sometimes do not Again it would seem reasonable to doubt your third hypothesis beyond, say, the sixth decimal place; and that would play havoc with your more delicate measures But where I fundamentally differ from you is the first hypothesis Is there some absolute quantity in nature that we... of optical measures with the eyes If in a strong gravitational field optical and mechanical measures diverged, we should have to make up our minds which was the preferable standard, and afterwards abide by it So far as we can ascertain, however, they agree in all circumstances, and no such difficulty arises So, if physical measures give us a non-Euclidean space, the space of perception will be non-Euclidean... molecules have finite size, and exert special attractions on one another, and you prefer to take as standard an ideal gas with infinitely small molecules But in the present case, what is the standard you are aiming at when you propose to correct measures made with the rigid rod? Phys I see the difficulty I have no knowledge of space apart from my measures, and I have no better standard than the rigid rod... drifted down These must be in the ratio 50 to 30, and we then know from the right-angled triangle OBE that OB will correspond to 40 Since OB is 100 yards, OE is 125 yards, and the time taken is 2 1 minutes Another 2 1 minutes will be needed O 2 2 B for the return journey Total time, 5 minutes Fig 1 In still water the time would have been 4 minutes The up -and- down swim is thus longer than the transverse... speed of the aether current to the speed of light, and the contraction which compensates it must be equally definite This explanation was proposed by FitzGerald, and at first sight it seems a strange and arbitrary hypothesis But it has been rendered very plausible by subsequent theoretical researches of Larmor and Lorentz Under ordinary circumstances the form and size of a solid body is maintained by the... standard clock; but whatever definition we decide on must be a physical definition We must not dodge it by saying that a perfect clock is one which keeps perfect time Perhaps the best theoretical clock would be a pulse of light travelling in vacuum to and fro between mirrors at the ends of a rigid scale The instants of arrival at one end would define equal intervals of time Phys I think your unit of time. .. arbitrarily into space and time, just as we can split the order of space into length, breadth and thickness But space without time is as incomplete as a surface without thickness Math Do you argue that the real world behind the phenomena is fourdimensional? Rel I think that in the real world there must be a set of entities related to one another in a four-dimensional order, and that these are the basis . Project Gutenberg’s Space, Time and Gravitation, by A. S. Eddington This eBook is for the use of anyone anywhere at no cost and with almost. ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK SPACE, TIME AND GRAVITATION *** Produced by David Clarke, Andrew D. Hwang and the Online Distributed