Einstein's Theories of Relativity and Gravitation / A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000

Dr. Albert Einstein,
Originator of the Special and General Theories of Relativity

Einstein’s Theories of Relativity and Gravitation

A SELECTION OF MATERIAL FROM THE ESSAYS SUBMITTED IN THE COMPETITION FOR THE EUGENE HIGGINS PRIZE OF $5,000

COMPILED AND EDITED,
AND INTRODUCTORY MATTER SUPPLIED
BY
J. MALCOLM BIRD,
Associate Editor, Scientific American

NEW YORK
SCIENTIFIC AMERICAN PUBLISHING CO.,
MUNN & CO.
1921

Copyright 1921
by
Scientific American Publishing Company

All rights reserved

Great Britain copyright secured

The right of translation is reserved in all languages, including the Scandinavian

Swedish rights secured by Thall and Carlsson, Stockholm

PREFACE

The obstacles which the layman finds to understanding Einstein’s relativity theories lie not so much in the inherent difficulty of these theories themselves as in the difficulty of preparing the mind for their reception. The theory is no more difficult than any scientific development of comparable depth; it is not so difficult as some of these. But it is a fact that for a decent understanding of it, a large background of scientific knowledge and scientific habit of thought is essential. The bulk of the writers who have attempted to explain Einstein to the general reader have not realized the great gulf which lies between the mental processes of the trained mathematician and those of the man in the street. They have not perceived that the lay reader must be personally conducted for a long distance from the vestibule of the temple of science before he comes to Einstein, and that he cannot by any possibility make this journey unaided. The result has been to pitchfork the reader into the intricacies of the subject without adequate preparation.

The present volume avoids this mistake with the utmost care. It avoids it, in fact, with such deliberation as to make it in order to say a word in explanation of what will at first glance seem an extraordinary arrangement of material. It was to be expected, doubtless, that this book would open with a brief statement of the genesis and the outcome of the Einstein Prize Essay Contest for the $5,000 prize offered by Mr. Eugene Higgins. It was doubtless to be expected that, after this had been dismissed, the winning essay would be given the post of honor in advance of all other material bearing actually on the Einstein theories. When the reader observes that this has not been done, he will by all means expect a word of explanation; and it is mainly for the purpose of giving this that we make these introductory remarks.

The essays submitted in the contest, and in particular the comments of a few disappointed readers upon Mr. Bolton’s prize essay, make quite plain what might have been anticipated—that in the small compass of 3,000 words it is not possible both to prepare the reader’s mind for a discussion of Relativity and to give a discussion that shall be adequate. Mr. Bolton himself, in replying to a protest that he had not done all this, has used the word “miracle”—we think it a well-advised one. No miracle was expected as a result of the contest, and none has been achieved. But in awarding the prize, the Judges had to decide whether it was the best preliminary exposition or the best discussion that was wanted. They decided, and rightly we believe, that the award should go to an actual statement of what the Einstein theories are and what they do, rather than to a mere introduction, however well conceived and well executed the latter might be. Nevertheless, we should be closing our eyes to a very obvious fact if we did not recognize that, without something in the way of preparation, the general reader is not going to pursue Mr. Bolton’s essay, or any other essay on this subject, with profit. It is in order the more forcefully to hold out inducements to him to subject himself to this preparation that we place at the head of the book the chapters designed to give it to him.

Chapter II. is intended so to bring the mind of the reader into contact with certain philosophical problems presented to us by our experiences with the external world and our efforts to learn the facts about it, that he may approach the subject of relativity with an appreciation of the place it occupies as a phase of human thought and a pillar of the scientific structure. Until the reader is aware of the existence of these problems and the directions taken by the efforts, successful and unsuccessful, to unravel them, he is not equipped to comprehend the doctrine of relativity at all; he is in much the same case as a child whose education had reached only the primer stage, if asked to read the masterpieces of literature. He lacks not alone the vocabulary, but equally the mental background on which the vocabulary is based.

It will be noted that in this and the chapters immediately following it, the Editor has supplied material freely. The obvious interpretation is that satisfactory material covering the desired ground was not found in any of the essays; for we are sure the scope and number of the credited excerpts will make it clear that all contributions were adequately scrutinized in search of available passages. This “inadequacy” of the competing essays has been severely commented upon by several correspondents, and the inference drawn that as a whole the offerings were not up to the mark. Such a viewpoint is wholly unjust to the contestants. The essays which paid serious attention to the business of paving the way to relativity necessarily did so at the expense of completeness in the later paragraphs where specific explanation of the Einstein theories was in order. Mr. Law, whose essay was by all means the best of those that gave much space to introductory remarks, found himself left with only 600 words in which to tell what it was that he had been introducing. The majority of the contestants appear to have faced the same question as to subject matter which the Judges faced, and to have reached the same decision. They accordingly devoted their attention toward the prize, rather than toward the production of an essay that would best supplement that of the winner. It is for this very reason that, in these preliminary chapters, so large a proportion of the material has had to be supplied by the Editor; and this very circumstance is a tribute to the good judgment of the competitors, rather than ground for criticism of their work.

The general introduction of Chapter II. out of the way, Chapters III. and IV. take up the business of leading the reader into the actual subject of relativity. The subject is here developed in what may be called the historical order—the order in which it took form in Einstein’s own mind. Both in and outside the contest of which this book is the outcome, a majority of those who have written on relativity have followed this order, which is indeed a very natural one and one well calculated to give to the rather surprising assumptions of relativity a reasonableness which they might well appear to the lay mind to lack if laid down more arbitrarily. In these two chapters no effort is made to carry the argument beyond the formulation of the Special Principle of the relativity of uniform motion, but this principle is developed in considerably more detail than would be the case if it were left entirely to the competing essayists. The reason for this is again that we are dealing with a phase of the subject which is of subordinate importance so far as a complete statement of the General Theory of Relativity is concerned, but which is of the greatest significance in connection with the effort of the layman to acquire the proper preliminary orientation toward the larger subject.

Chapter V. goes back again to general ground. Among the ideas which the competing essayists were forced to introduce into their text on a liberal scale is that of non-Euclidean geometry. The entire formulation of the General Theory of Relativity is in fact an exercise in this. The essayists—good, bad and indifferent alike—were quite unanimous in their decision that this was one thing which the reader would have to assume the responsibility of acquiring for himself. Certainly they were justified in this; for the Editor has been able to explain what non-Euclidean geometry is only by using up considerably more space than the contestants had for an entire essay. No effort has been made to set forth any of the details of any of the various non-Euclidean geometries; it has simply been the aim to draw the dividing line between Euclidean and non-Euclidean, and to make the existence of the latter appear reasonable, so that when the essayists come to talk about it the reader will not feel hopelessly at sea. In other words, this is another case of providing the mental background, but on such a scale that it has seemed necessary to give a separate chapter to it.

Chapter VI. completes the preliminary course in the fundamentals of relativity by tying up together the findings of Chapter V. and those of Chapters III. and IV. It represents more or less of a last-minute change of plan; for while it had been the Editor’s intent from the beginning to place the material of Chapters II.–V. in its present position, his preliminary impression would have been that the work of the present Chapter VI. would be adequately done by the essayists themselves. His reading of the essays, however, convinced him that it had not so been done—that with the possible exception of Mr. Francis, the essayists did not make either a serious or a successful effort to show the organic connection between the Special Theory of Relativity and the Minkowski space-time structure, or the utter futility of trying to reconcile ourselves to the results of the former without employing the ideas of the latter. So Chapter VI. was supplied to make good this deficiency, and to complete the mental equipment which the reader requires for his battle with the General Theory.

In laying down a set of general principles to govern the award of the prize, one of the first things considered by the Judges was the relative importance of the Special and the General Theories. It was their opinion that no essay could possibly qualify for the prize which did not very distinctly give to the General Theory the center of the stage; and that in fact discussion of the Special Theory was pertinent only so long as it contributed, in proportion to the space assigned it, to the attack upon the main subject. The same principle has been employed in selecting essays for complete or substantially complete reproduction in this volume. Writers who dealt with the Special Theory in any other sense than as a preliminary step toward the General Theory have been relegated to the introductory chapters, where such excerpts from their work have been used as were found usable. The distinction of publication under name and title is reserved for those who wrote consistently and specifically upon the larger subject—with the one exception of Dr. Russell, whose exposition of the Special Theory is so far the best of those submitted and at the same time so distinctive that we have concluded it will appear to better advantage by itself than as a part of Chapters III. and IV.

Following after Mr. Bolton’s essay we have tried to arrange the various contributions, not at all in any order of merit, but in the order that will make connected reading of the book most nearly possible and profitable. Each essay should be made easier of reading by the examination of those preceding it; at the same time each, by the choice of ground covered and by the emphasis on points not brought out sharply by its predecessors, should throw new light upon these predecessors.

The reader will find that no two of the essays given thus in full duplicate or even come close to duplicating one another. They have of course been selected with this in view; each represents the best of several essays of substantially the same character. Not all of them require comment here, but concerning some of them a word may well be said.

Mr. Francis, we believe, has succeeded in packing more substance into his 3,000 words than any other competitor. Mr. Elliot has come closer than anybody else to really explaining relativity in terms familiar to everybody, without asking the reader to enlarge his vocabulary and with a minimum demand so far as enlarging his mental outlook is concerned. Were it not for certain conspicuous defects, his essay would probably have taken the prize. In justice to the Judges, we should state that we have taken the liberty of eliminating Mr. Elliot’s concluding paragraph, which was the most objectionable feature of his essay.

Dr. Dushman chose for his title the one which we adopted for this book. It became necessary, therefore, for us to find a new title for his essay; aside from this instance, the main titles appearing at the heads of the various complete essays are those of the authors. The subtitles have in practically every instance been supplied editorially.

Dr. Pickering submitted two essays, one written from the viewpoint of the physicist, the other from that of the astronomer. To make each complete, he naturally found it necessary to duplicate between them certain introductory and general material. We have run the two essays together into a single narrative, with the elimination of this duplicated material; aside from this blue-penciling no alteration has been made in Dr. Pickering’s text. This text however served as the basis of blue-penciling that of several other contestants, as indicated in the foot notes.

For the reader who is qualified or who can qualify to understand it, Dr. Murnaghan’s essay is perhaps the most illuminating of all. Even the reader who does not understand it all will realize that its author brings to the subject a freshness of viewpoint and an originality of treatment which are rather lacking in some of the published essays, and which it will readily be understood were conspicuously lacking in a good many of the unpublished ones. Dr. Murnaghan of all the competitors has come closest to making a contribution to science as well as to the semi-popular literature of science.

In the composite chapters, the brackets followed by reference numbers have been used as the most practicable means of identifying the various individual contributions. We believe that this part of the text can be read without allowing the frequent occurrence of these symbols to distract the eye. As to the references themselves, the asterisk marks the contributions of the Editor. The numbers are those attached to the essays in order of and at the time of their receipt; it has been more convenient to use these than to assign consecutive numbers to the quoted essays. The several numbers identify passages from the essays of the following contestants:

In addition to the specific credit given by these references for specifically quoted passages, the Editor feels that he ought to acknowledge his general indebtedness to the competing essayists, collectively, for the many ideas which he has taken away from their text to clothe in his own words. This does not mean that the Editor has undertaken generally to improve upon the language of the competitors, but merely that the reading of all their essays has given him many ideas of such complex origin that he could not assign credit if he would.

Table of Contents

I.—[The Einstein $5,000 Prize]: How the Contest Came to be Held, and Some of the Details of Its Conduct. By the Editor 1

II.—[The World—And Us]: An Introductory Discussion of the Philosophy of Relativity, and of the Mechanism of our Contact with Time and Space. By various contributors and the Editor 19

III.—[The Relativity of Uniform Motion]: Classical Ideas on the Subject; the Ether and the Apparent Possibility of Absolute Motion; the Michelson-Morley Experiment and the Final Negation of this possibility. By various contributors and the Editor 47

IV.—[The Special Theory of Relativity]: What Einstein’s Study of Uniform Motion Tells Us About Time and Space and the Nature of the External Reality. By various contributors and the Editor 76

V.—[That Parallel Postulate]: Modern Geometric Methods; the Dividing Line Between Euclidean and Non-Euclidean; and the Significance of the Latter. By the Editor 111

VI.—[The Space-Time Continuum]: Minkowski’s World of Events, and the Way in Which It Fits Into Einstein’s Structure. By the Editor and a few contributors 141

VII.—[Relativity]: The Winning Essay in the Contest for the Eugene Higgins $5,000 Prize. By Lyndon Bolton, British Patent Office, London 169

VIII.—[The New Concepts of Time and Space]: The Essay in Behalf of Which the Greatest Number of Dissenting Opinions Have Been Recorded. By Montgomery Francis, New York 181

IX.—[The Principle of Relativity]: A Statement of What it is All About, in Ideas of One Syllable. By Hugh Elliot, Chislehurst, Kent, England 195

X.—[Space, Time and Gravitation]: An Outline of Einstein’s Theory of General Relativity. By W. de Sitter, University of Leyden 206

XI.—[The Principle of General Relativity]: How Einstein, to a Degree Never Before Equalled, Isolates the External Reality from the Observer’s Contribution. By E. T. Bell, University of Seattle 218

XII.—[Force Vs. Geometry]: How Einstein Has Substituted the Second for the First in Connection with the Cause of Gravitation. By Saul Dushman, Schenectady 230

XIII.—[An Introduction to Relativity]: A Treatment in which the Mathematical Connections of Einstein’s Work are Brought Out More Strongly and More Successfully than Usual in a Popular Explanation. By Harold T. Davis, University of Wisconsin 240

XIV.—[New Concepts for Old]: What the World Looks Like After Einstein Has Had His Way with It. By John G. McHardy, Commander R. N., London 251

XV.—[The New World]: A Universe in Which Geometry Takes the Place of Physics, and Curvature that of Force. By George Frederick Hemens, M.C., B.Sc., London 265

XVI.—[The Quest of the Absolute]: Modern Developments in Theoretical Physics, and the Climax Supplied by Einstein. By Dr. Francis D. Murnaghan, Johns Hopkins University, Baltimore 276

XVII.—[The Physical Side of Relativity]: The Immediate Contacts between Einstein’s Theories and Current Physics and Astronomy. By Professor William H. Pickering, Harvard College Observatory, Mandeville, Jamaica 287

XVIII.—[The Practical Significance of Relativity]: The Best Discussion of the Special Theory Among All the Competing Essays. By Prof. Henry Norris Russell, Princeton University 306

XIX.—[Einstein’s Theory of Relativity]: A Simple Explanation of His Postulates and Their Consequences. By T. Royds, Kodaikanal Observatory, India 318

XX.—[Einstein’s Theory of Gravitation]: The Discussion of the General Theory and Its Most Important Application, from the Essay by Prof. W. F. G. Swann, University of Minnesota, Minneapolis 327

XXI.—[The Equivalence Hypothesis]: The Discussion of This, With Its Difficulties and the Manner in Which Einstein Has Resolved Them, from the Essay by Prof. E. N. da C. Andrade, Ordnance College, Woolwich, England 334

XXII.—[The General Theory]: Fragments of Particular Merit on This Phase of the Subject. By Various Contributors 338

Table of Contents

I.

THE EINSTEIN $5,000 PRIZE

How the Contest Came to be Held, and Some of the Details of its Conduct

BY THE EDITOR

In January, 1909, an anonymous donor who was interested in the spread of correct scientific ideas offered through the Scientific American a prize of $500 for the best essay explaining, in simple non-technical language, that paradise of mathematicians and bugaboo of plain ordinary folk—the fourth dimension. Many essays were submitted in this competition, and in addition to that of the winner some twenty were adjudged worthy of ultimate publication. It was felt that the competition had added distinctly to the popular understanding of this significant subject; that it had done much to clear up popular misconception of just what the mathematician means when he talks of four or even more dimensions; and that it had therefore been as successful as it was unusual in character.

In November, 1919, the world was startled by the announcement from London that examination of the photographs taken during the total solar eclipse of May 29th had been concluded, and that predictions based upon the Einstein theories of relativity had been verified. In the reaction from the long surfeit of war news an item of this sort was a thoroughly journalistic one. Long cable dispatches were carried in the news columns all over the world; Einstein and his theories were given a prominent place on the front pages day after day; leading scientists in great number were called upon to tell the public through the reportorial medium just what the excitement was all about, just in what way the classical scientific structure had been overthrown.

Instead of being a mere nine days’ wonder, the Einstein theories held their place in the public mind. The more serious periodicals devoted space to them. First and last, a very notable group of scientific men attempted to explain to the general reader the scope and content of Einstein’s system. These efforts, well considered as they were, could be no more than partially successful on account of the very radical character of the revisions which the relativity doctrine demands in our fundamental concepts. Such revisions cannot be made in a day; the average person has not the viewpoint of the mathematician which permits a sudden and complete exchange of one set of fundamentals for another. But the whole subject had caught the popular attention so strongly, that even complete initial failure to discover what it was all about did not discourage the general reader from pursuing the matter with determination to come to some understanding of what had happened to Newton and Newtonian mechanics.

The Donor and the Prize

In May, 1920, Mr. Eugene Higgins, an American citizen long resident in Paris, a liberal patron of the arts and sciences, and a lifelong friend of the Scientific American and its proprietors, suggested that the success of the Fourth Dimension Prize Contest of 1910 had been so great that it might be desirable to offer another prize in similar fashion for the best popular essay on the Einstein theories. He stated that if in the opinion of the Scientific American these theories were of sufficient importance, and the probability of getting a good number of meritorious essays were sufficiently great, and the public need and desire for enlightenment were sufficiently present, he would feel inclined to offer such a prize, leaving the conduct of the contest to the Scientific American as in the former event. It was the judgment of the editors of the Scientific American that all these provisos should be met with an affirmative, and that Mr. Higgins accordingly could with propriety be encouraged to offer the prize.

In his preliminary letter Mr. Higgins had suggested that in view of the apparent greater importance of the subject to be proposed for discussion by the contestants of 1920, the prize offered should probably be more liberal than in the former instance. This view met with the approval of the editors as well; but they were totally unprepared for the receipt, late in June, of a cablegram from Mr. Higgins stating that he had decided to go ahead with the matter, and that he was forwarding a draft for $5,000 to represent the amount of the prize. Such a sum, exceeding any award open to a professional man with the single exception of the Nobel Prize, for which he cannot specifically compete, fairly took the breath of the Editors, and made it immediately clear that the contest would attract the widest attention, and that it should score the most conspicuous success. It also made it clear that the handling of the contest would be a more serious matter than had been anticipated.

In spite of the fact that it would not for some time be possible to announce the identity of the Judges, it was felt that the prospective contestants should have every opportunity for extensive preparation; so the contest was announced, and the rules governing it printed as far as they could be determined on such short shrift, in the Scientific American for July 10, 1920. Several points of ambiguity had to be cleared up after this initial publication. In particular, it had been Mr. Higgins’ suggestion that in the very probable event of the Judges’ inability to agree upon the winning essay, the prize might, at their discretion, be divided between the contributors of the best two essays. This condition was actually printed in the first announcement, but the Post Office Department insisted upon its withdrawal, on the ground that with it in force the contestant would not know whether he were competing for $5,000 or for $2,500, and that this would introduce the “element of chance” which alone was necessary, under the Federal statutes, to make the contest a lottery. So this provision was replaced by one to the effect that in the event the Judges were not able to agree, the Einstein Editor should cast the deciding vote between the essays respectively favored by them.

The announcement attracted the widest attention, and was copied in newspapers and magazines all over the world. Inquiries poured in from all quarters, and the Einstein Editor found it almost impossible to keep himself supplied with proofs of the conditions and rules to mail in response to these inquiries. It was immediately clear that there was going to be a large number of essays submitted, and that many distinguished names would be listed among the competitors.

The Judges

In the Scientific American for September 18, announcement was carried in the following words:

“We are assured with complete certainty that the competition for the five-thousand-dollar prize will be very keen, and that many essays will be submitted which, if they bore the names of their authors, would pass anywhere as authoritative statements. The judges will confront a task of extraordinary difficulty in the effort to determine which of these efforts is the best; and we believe the difficulties are such that multiplication of judges would merely multiply the obstacles to an agreement. It is altogether likely that the initial impressions of two or three or five judges would incline toward two or three or five essays, and that any final decision would be attainable only after much consultation and discussion. It seems to us that by making the committee as small as possible while still preserving the necessary feature that its decision represent a consensus, we shall simplify both the mental and the physical problem of coming to an agreement. We believe that the award should if possible represent a unanimous decision, without any minority report, and that such a requirement is far more likely to be met among two men than among three or five. At the same time, the bringing together of two men and the details of general administration of their work together are far simpler than if there were three or five. So we have finally decided to have but two judges, and in this we have the endorsement of all the competent opinion that we have consulted.

“The gentlemen who have consented to act as Judges are Professors Leigh Page and Edwin Plimpton Adams, of the departments of physics of Yale and Princeton Universities, respectively. Both are of the younger generation of physicists that has paid special attention to those phases of mathematics and physics involved in the Einstein theories, and both have paid special attention to these theories themselves. We are gratified to be able to put forward as Judges two men so eminently qualified to act. We feel that we may here appropriately quote Professor Page, who says in his acceptance: ‘As the large prize offers a great inducement, I had thought of entering the contest. However I realize that not many people in this country have made a considerable study of Einstein’s theory, and if all who have should enter the contest, it would be difficult to secure suitable Judges.’ Without any desire to put the gentleman in the position of pleading for himself, we think this suggests very well the extent to which the Scientific American, the contestants, and the public at large, are indebted to Professors Page and Adams for their willingness to serve in the difficult capacity of Judges.”

It might appropriately have been added to this announcement that it was altogether to the credit of science and the scientific spirit that the first two gentlemen approached with the invitation to act as Judges were willing to forego their prospects as contestants in order thus to contribute to the success of the contest.

Three Thousand Words

Of the conditions, the one which evoked most comment was that stating the word limit. This limit was decided upon after the most careful discussion of the possibilities of the situation. It was not imagined for a moment that any contestant would succeed in getting within 3,000 words a complete discussion of all aspects of the Special and the General Theories of Relativity. It was however felt that for popular reading a single essay should not be much if any longer than this. Moreover, I will say quite frankly that we should never have encouraged Mr. Higgins to offer such a prize if we had supposed that the winning essay was the only thing of value that would come from the contest, or if we had not expected to find in many of the other essays material which would be altogether deserving of the light. From the beginning we had in view the present volume, and the severe restriction in length was deliberately imposed for the purpose of forcing every contestant to stick to what he considered the most significant viewpoints, and to give his best skill to displaying the theories of Einstein to the utmost advantage from these viewpoints. We felt that divergent viewpoints would be more advantageously treated in this manner than if we gave each contestant enough space to discuss the subject from all sides; and that the award of the prize to the essay which, among other requirements, seemed to the Judges to embody the best choice of material, would greatly simplify the working of the contest without effecting any injustice against those contestants who displayed with equal skill less happily chosen material. Perhaps on this point I may again quote with profit the editorial page of the Scientific American:

“An essay of three thousand words is not long enough to lose a reader more than once; if it does lose him it is a failure, and if it doesn’t it is a competitor that will go into the final elimination trials for the prize. If we can present, as a result of the contest, six or a dozen essays of this length that will not lose the lay reader at all, we shall have produced something amply worth the expenditure of Mr. Higgins’ money and our time. For such a number of essays of such character will of necessity present many different aspects of the Einstein theories, and in many different ways, and in doing so will contribute greatly to the popular enlightenment.

“Really the significant part of what has already appeared is not the part that is intelligible, but rather the part that, being unintelligible, casts the shadow of doubt and suspicion on the whole. The successful competitor for the prize and his close contestants will have written essays that, without any claim to completeness, will emphasize what seems to each author the big outstanding feature; and every one of them will be intelligible. Together they will in all probability be reasonably complete, and will retain the individual characteristic of intelligibility. They will approach the various parts of the field from various directions—we could fill this page with suggestions as to how the one item of the four-dimensional character of Einstein’s time-space might be set forth for the general reader. And when a man must say in three thousand words as much as he can of what eminent scientists have said in whole volumes—well, the result in some cases will be sheer failure, and in others a product of the first water. The best of the essays will shine through intelligent selection of what is to be said, and brilliant success in saying it. It is to get a group of essays of this character, not to get the single essay which will earn the palm, that the prize is offered.”

The Competing Essays

At all times after the first announcement the Einstein Editor had a heavy correspondence; but the first real evidence that the contest was under way came with the arrival of the first essay, which wandered into our office in the middle of September. About a week later they began to filter in at the rate of one or two per day—mostly from foreign contestants who were taking no chances on the mails. Heavy returns did not commence until about ten days before the closing date. The great avalanche, however, was reserved for the morning of Monday, November 1st. Here we had the benefit of three days’ mail; there were about 120 essays. Among those which were thrown out on the ground of lateness the honors should no doubt go to the man who mailed his offering in The Hague on October 31st.

Essays were received in greater quantity from Germany than from any other foreign country, doubtless because of the staggering value of $5,000 when converted into marks at late 1920 rates. England stood next on the list; and one or more essays were received from Austria, Czechoslovakia, Jugoslavia, France, Switzerland, the Netherlands, Denmark, Italy, Chile, Cuba, Mexico, India, Jamaica, South Africa and the Fiji Islands. Canada, of course, contributed her fair share; and few of our own states were missing on the roll-call.

The general level of English composition among the essays from non-English-speaking sources was about what might have been expected. A man may have a thorough utilitarian knowledge of a foreign tongue, but when he attempts intensive literary competition with a man who was brought up in that tongue he is at a disadvantage. We read French and German with ease and Spanish and Italian without too much difficulty, ourselves; we should never undertake serious writing in any of these languages. Not many of the foreign contributions, of course, were as ludicrous as the one we quote to some extent in our concluding chapter, but most of them were distinctly below par as literary compositions. Drs. De Sitter and Schlick were the notable exceptions to this; both showed the ability to compete on a footing of absolute equality with the best of the native product.

We dare say it was a foregone conclusion that many essays should have been over the limit, and that a few should have been over it to the point of absurdity. The winning essay contains 2,919 words, plus or minus a reasonable allowance for error in counting; that it should come so far from being on the ragged edge should be sufficient answer to those who protested against the severity of the limitation. One inquirer, by the way, wanted to know if 3,000 words was not a misprint for 30,000. Another contestant suggested that instead of disqualifying any essay that was over the line, we amputate the superfluous words at the end. This was a plausible enough suggestion, since any essay able to compete after such amputation must necessarily have been one of extreme worth; but fortunately we did not have to decide whether we should follow the scheme. Perhaps twenty of the essays submitted were so seriously in excess of the limit that it was not even necessary to count their words in detail; most of these offenders ran to 3,500 words or thereabouts, and one—a good one, too, from which we use a good deal of material in this volume—actually had 4,700. On the other extreme were a few competitors who seemed to think that the shortest essay was necessarily the best, and who tried to dismiss the subject with 500 or 1,000 words.

By a curious trick of chance there were submitted in competition for the prize exactly 300 essays. Of course a few of these did not require serious consideration—this is inevitable in a contest of such magnitude. But after excluding all the essays that were admittedly not about the Einstein theories at all, and all those whose English was so execrable as to make them quite out of the question, and all those which took the subject so lightly as not to write reasonably close to the limit of 3,000 words, and all those which were given over to explanation of the manner in which Einstein’s theories verify those of the writer, and all those in which the writer attempted to substitute his own cosmic scheme for Einstein’s—after all this, there remained some 275 essays which were serious efforts to explain in simple terms the nature and content and consequences of Special and General Relativity.

Looking for the Winner

The Einstein Editor was in sufficiently close touch with the details of the adjudication of the essays to have every realization of the difficulty of this work. The caliber of the essays submitted was on the whole high. There were many which would have been well worthy of the prize in the absence of others that were distinctly better—many which it was not possible to eliminate on the ground of specific faults, and which could only be adjudged “not the best” by detailed comparison with specific other essays. It was this detailed comparison which took time, and which so delayed the award that we were not able to publish the winning essay any sooner than February 5th. Especially difficult was this process of elimination after the number of surviving essays had been reduced to twenty or less. The advantages of plan possessed by one essay had to be weighed against those of execution exhibited in another. A certain essay had to be critically compared with another so like it in plan that the two might have been written from a common outline, and at the same time with a third as unlike it in scope and content as day and night. And all the time there was present in the background the consciousness that a prize of $5,000 hung upon the decision to be reached. For anyone who regards this as an easy task we have no worse wish than that he may some day have to attack a similar one.

We had anticipated that the bulk of the superior essays would be among those received during the last day or two of the contest; for we felt that the men best equipped to attack the subject would be the most impressed with its seriousness. Here we were quite off the track. The seventeen essays which withstood most stubbornly the Judges’ efforts at elimination were, in order of receipt, numbers 8, 18, 28, 40, 41, 43, 92, 95, 97, 130, 181, 194, 198, 223, 267, 270, 275: a fairly even distribution. The winner was the 92nd essay received.

The Judges held their final meeting in the editorial office on January 18, 1921. The four essays which were before the committee at the start of the session were speedily cut to three, and then to two; and after an all-day session the Judges found themselves conscientiously able to agree on one of these as the best. This unanimity was especially gratifying, the more so since it by no means was to be confidently expected, on a priori grounds, that it would be possible of attainment. Even the Einstein Editor, who might have been called upon for a final decision but wasn’t, can hardly be classed as a dissenter; for with some slight mental reservations in favor of the essay by Mr. Francis which did not enter the Judges’ final discussion at all, and which he rather suspects appeals more to his personal taste than to his soundest judgment, he is entirely in accord with the verdict rendered.

The fact that the prize went to England was no surprise to those acquainted with the history of Einstein’s theories. The Special Theory, promulgated fifteen years ago, received its fair share of attention from mathematicians all over the world, and is doubtless as well known and as fully appreciated here as elsewhere. But it has never been elevated to a position of any great importance in mathematical theory, simply because of itself, in the absence of its extension to the general case, it deserves little importance. It is merely an interesting bit of abstract speculation.

The General Theory was put out by Einstein in finished form during the war. Owing to the scientific moratorium, his paper, and hence a clear understanding of the new methods and results and of the sweeping consequences if the General Theory should prevail, did not attain general circulation outside Germany until some time in 1918 or even later. Had it not been for Eddington it is doubtful that the British astronomers would have realized that the eclipse expeditions were of particular consequence. Therefore at the time of these expeditions, and even as late as the November announcement of the findings, the general body of scientific men in America had not adequately realized the immense distinction between the Special and the General Theories, had not adequately appreciated that the latter led to distinctive consequences of any import, and we fear in many cases had not even realized explicitly that the deflection of light and the behavior of Mercury were matters strictly of the General and in no sense of the Special Theory. Certainly when the American newspapers were searching frantically for somebody to interpret to their public the great stir made by the British announcement that Einstein’s predictions had been verified, they found no one to do this decently; nor were our magazines much more successful in spite of the greater time they had to devote to the search. In a word, there is not the slightest room for doubt that American science was in large measure caught asleep at the switch—perhaps for no reason within its control; and that American writers were in no such favorable case to write convincingly on the subject as were their British and continental contemporaries.

So it was quite in accord with what might have been expected to find, on opening the identifying envelopes, that not alone the winning essay, but its two most immediate rivals, come from members of that school of British thought which had been in contact with the Einstein theories in their entirety for two years longer than the average American of equal competence. This riper familiarity with the subject was bound to yield riper fruit. Indeed, had it not been for the handicap of writing in a strange language, it is reasonable to assume that the scientists of Germany would have made a showing superior to that of either Americans or British—and for the same reason that Britain showed to better advantage than America.

The Winner of the Prize

Mr. Bolton, the winner of the big prize, we suppose may fairly be referred to as unknown in a strict scientific sense. Indeed, at the time of the publication of his essay in the Scientific American nothing could be learned about him on the American side of the water beyond the bare facts that he was not a young man, and that he had for a good many years occupied a position of rank in the British Patent Office. (It will be recalled that Einstein himself was in the Swiss Patent Office for some time.) In response to the request of the Scientific American for a brief biographical sketch that would serve to introduce him better to our readers, Mr. Bolton supplied such a concise and apparently such a characteristic statement that we can do no better than quote it verbatim.

“I was born in Dublin in 1860, but I have lived in England since 1869. My family belonged to the landed gentry class, but I owe nothing to wealth or position. I was in fact put through school and college on an income which a workman would despise nowadays. After attending sundry small schools, I entered Clifton College in 1873. My career there was checkered, but it ended well. I was always fairly good at natural science and very fond of all sorts of mechanical things. I was an honest worker but no use at classics, and as I did practically nothing else for the first four years at Clifton, I came to consider myself something of a dunce. But a big public school is a little world. Everyone gets an opportunity, often seemingly by accident, and it is up to him to take it. Mine did not come till I was nearly 17. As I was intended for the engineering profession, I was sent to the military side of the school in order to learn some mathematics, at which subject I was then considered very weak. This was certainly true, as at that time I barely knew how to solve a quadratic, I was only about halfway through the third book of Euclid, and I knew no trigonometry. But the teaching was inspiring, and I took readily to mathematics. One day it came out that I had been making quite a good start with the differential calculus on my own without telling anybody. After that all was well. I left Clifton in 1880 with a School Exhibition and a mathematical scholarship at Clare College, Cambridge.

“After taking my degree in 1883 as a Wrangler, I taught science and mathematics at Wellington College, but I was attracted by what I had heard of the Patent Office and I entered it through open competition in 1885. During my official career I have been one of the Comptroller’s private secretaries and I am now a Senior Examiner. During the war I was attached to the Inventions Department of the Ministry of Munitions, where my work related mainly to anti-aircraft gunnery. I have contributed, and am still contributing to official publications on the subject.

“I have written a fair number of essays on various subjects, even on literature, but my only extra-official publications relate to stereoscopic photography. I read a paper on this subject before the Royal Photographic Society in 1903 which was favorably noticed by Dr. von Rohr of Messrs. Zeiss of Jena. I have also written in the Amateur Photographer.

“I have been fairly successful at athletics, and I am a member of the Leander Club.”

That Mr. Bolton did not take the prize through default of serious competition should be plain to any reader who examines the text from competing essays which is to be found in this volume. The reference list of these competitors, too, supplemented by the names that appear at the heads of complete essays, shows a notable array of distinguished personalities, and I could mention perhaps a dozen more very well known men of science whose excellent essays have seemed a trifle too advanced for our immediate use, but to whom I am under a good deal of obligation for some of the ideas which I have attempted to clothe in my own language.

Before leaving the subject, we wish to say here a word of appreciation for the manner in which the Judges have discharged their duties. The reader will have difficulty in realizing what it means to read such a number of essays on such a subject. We were fortunate beyond all expectation in finding Judges who combined a thorough scientific grasp of the mathematical and physical and philosophical aspects of the matter with an extremely human viewpoint which precluded any possibility of an award to an essay that was not properly a popular discussion, and with a willingness to go to meet each other’s opinions that is rare, even among those with less ground for confidence in their own views than is possessed by Drs. Page and Adams.

II.

THE WORLD—AND US

An Introductory Discussion of the Philosophy of Relativity, and of the Mechanism of Our Contact with Time and Space

BY VARIOUS CONTRIBUTORS AND THE EDITOR

From a time beyond the dawn of history, mankind has been seeking to explain the universe. At first the effort did not concern itself further probably than to make a supposition as to what were the causes of the various phenomena presented to the senses. As knowledge increased, first by observation and later by experiment also, the ideas as to these causes passed progressively through three stages—the theological (the causes were thought to be spirits or gods); the metaphysical (the causes were thought in this secondary or intermediate stage to be some inherent, animating, energizing principles); and the scientific (the causes were finally thought of as simply mechanical, chemical, and magneto-electrical attractions and repulsions, qualities or characteristics of matter itself, or of the thing of which matter is itself composed.)

With increase of knowledge, and along with the inquiry as to the nature of causes, there arose an inquiry also as to what reality was. What was the essential nature of the stuff of which the universe was made, what was matter, what were things in themselves, what were the noumena (the realities), lying back of the phenomena (the appearances)? Gradually ideas explaining motion, force, and energy were developed. At the same time inquiry was made as to the nature of man, the working of his mind, the nature of thought, the relation of his concepts (ideas) to his perceptions (knowledge gained through the sense) and the relations of both to the noumena (realities).]^[283]

[The general direction taken by this inquiry has been that of a conflict between two schools of thought which we may characterize as those of absolutism and of relativism.]* [The ancient Greek philosophers believed that they could tap a source of knowledge pure and absolute by sitting down in a chair and reasoning about the nature of time and space, and the mechanism of the physical world.]^[221] [They maintained that the mind holds in its own right certain concepts than which nothing is more fundamental. They considered it proper to conceive of time and space and matter and the other things presented to their senses by the world as having a real existence in the mind, regardless of whether any external reality could be identified with the concept as ultimately put forth. They could even dispute with significance the qualities which were to be ascribed to this abstract conceptual time and space and matter. All this was done without reference to the external reality, often in defiance of that reality. The mind could picture the world as it ought to be; if the recalcitrant facts refused to fit into the picture, so much the worse for them. We all have heard the tale of how generation after generation of Greek philosophers disputed learnedly why and how it was that a live fish could be added to a brimming pail of water without raising the level of the fluid or increasing the weight; until one day some common person conceived the troublesome idea of trying it out experimentally to learn whether it were so—and found that it was not. True or false, the anecdote admirably illustrates the subordinate place which the externals held in the absolutist system of Greek thought.]*

[Under this system a single observer is competent to examine a single phenomenon, and to write down the absolute law of nature by referring the results to his innate ideas of absolute qualities and states. The root of the word absolute signifies “taking away,” and in its philosophical sense the word implies the ability of the mind to subtract away the properties or qualities from things, and to consider these abstract qualities detached from the things; for example, to take away the coldness from ice, and to consider pure or abstract coldness apart from anything that is cold; or to take away motion from a moving body, and to consider pure motion apart from anything that moves. This assumed power is based upon the Socratic theory of innate ideas. According to this theory the mind is endowed by nature with the absolute ideas of hardness, coldness, roundness, equality, motion, and all other absolute qualities and states, and so does not have to learn them. Thus a Socratic philosopher could discuss pure or absolute being, absolute space and absolute time.]^[121]

Getting Away from the Greek Ideas

[This Greek mode of thought persisted into the late Middle Ages, at which time it was still altogether in order to dispose of a troublesome fact of the external world by quoting Aristotle against it. During the Renaissance, which intellectually at least marks the transition from ancient to modern, there came into being another type of absolutism, equally extreme, equally arbitrary, equally unjustified. The revolt against the mental slavery to Greek ideas carried the pendulum too far to the other side, and early modern science as a consequence is disfigured by what we must now recognize as gross materialism. The human mind was relegated to the position of a mere innocent bystander. The external reality was everything, and aside from his function as a recorder the observer did not in the least matter. The whole aim of science was to isolate and classify the elusive external fact. The rôle of the observer was in every possible way minimized. It was of course his duty to get the facts right, but so far as any contribution to these was concerned he did not count—he was definitely disqualified. He really played the part of an intruder; from his position outside the phenomena he was searching for the absolute truth about these phenomena. The only difference between his viewpoint and that of Aristotle was that the latter looked entirely inside himself for the elusive “truth,” while the “classical” scientist, as we call him now, looked for it entirely outside himself.

Let me illustrate the difference between the two viewpoints which I have discussed, and the third one which I am about to outline, by another concrete instance. The Greeks, and the medievals as well, were fond of discussing a question which embodies the whole of what I have been saying. This question involved, on the part of one who attempted to answer it, a choice between the observer and the external world as the seat of reality. It was put in many forms; a familiar one is the following: “If the wind blew down a great tree at a time and place where there was no conscious being to hear, would there be any noise?” The Greek had to answer this question in the negative because to him the noise was entirely a phenomenon of the listener. The classical scientist had to answer it in the affirmative because to him the noise was entirely a phenomenon of the tree and the air and the ground. Today we answer it in the negative, but for a very different reason from that which swayed the Greek. We believe that the noise is a joint phenomenon of the observer and the externals, so that in the absence of either it must fail to take existence. We believe there are sound waves produced, and all that; but what of it? There is no noise in the presence of the falling tree and the absence of the observer, any more than there would be in the presence of the observer and the absence of the tree and the wind; the noise, a joint phenomenon of the observer and the externals, exists only in their joint presence.

Relativism and Reality

This is the viewpoint of relativism. The statue is golden for one observer and silver to the other. The sun is rising here and setting in another part of the world. It is raining here and clear in Chicago. The observer in Delft hears the bombardment of Antwerp and the observer in London does not. If they were to be consistent, both the Greek and the medieval-modern absolutist would have to dispute whether the statue were “really” golden or silver, whether the sun were “really” rising or setting, whether the weather were “really” fair or foul, whether the bombardment were “really” accompanied by loud noises or not; and on each of these questions they would have to come to an agreement or confess their methods inadequate. But to the relativist the answer is simple—whether this or that be true depends upon the observer. In simple cases we understand this full well, as we have always realized it. In less simple cases we recognize it less easily or not at all, so that some of our thought is absolutist in its tendencies while the rest is relativistic. Einstein is the first ever to realize this fully—or if not this, then the first ever to realize it so fully as to be moved toward a studied effort to free human thought from the mixture of relativism and absolutism and make it consistently the one or the other.

This brings it about that the observed fact occupies a position of unexpected significance. For when we discuss matters of physical science under a strictly relativistic philosophy, we must put away as metaphysical everything that smacks of a “reality” partly concealed behind our observations. We must focus attention upon the reports of our senses and of the instruments that supplement them. These observations, which join our perceptions to their external objects, afford us our only objective manifestations; them we must accept as final—subject always to such correction as more refined observations may suggest. The question whether a “true” length or area or mass or velocity or duration or temperature exists back of the numerical determination, or in the presence of a determination that is subject to correction, or in the absence of any determination at all, is a metaphysical one and one that the physicist must not ask. Length, area, mass, velocity, duration, temperature—none of these has any meaning other than the number obtained by measurement.]* [If several different determinations are checked over and no error can be found in any of them, the fault must lie not with the observers but with the object, which we must conclude presents different values to different observers.]^[33]

[We are after all accustomed to this viewpoint; we do not demand that Pittsburgh shall present the same distance from New York and from Philadelphia, or that the New Yorker and the Philadelphian come to any agreement as to the “real” distance of Pittsburgh. The distance of Pittsburgh depends upon the position of the observer. Nor do we demand that the man who locates the magnetic pole in one spot in 1900 and in another in 1921 come to a decision as to where it “really” is; we accept his statement that its position depends upon the time of the observation.

What this really means is that the distance to Pittsburgh and the position of the magnetic pole are joint properties of the observer and the observed—relations between them, as we might put it. This is obvious enough in the case of the distance of Pittsburgh; it is hardly so obvious in the case of the position of the magnetic pole, varying with the lapse of time. But if we reflect that the observation of 1900 and that of 1921 were both valid, and both represented the true position of the pole for the observer of the date in question, we must see that this is the only explanation that shows us the way out.

I do not wish to speak too definitely of the Einstein theories in these introductory remarks, and so shall refrain from mentioning explicitly in this place the situation which they bring up and upon which what I have just said has direct bearing. It will be recognized when it arises. What must be pointed out here, however, is that we are putting the thing which the scientist calls the “observed value” on a footing of vastly greater consequence than we should have been willing offhand to concede to it. So far as any single observer is concerned, his own best observed values are themselves the external world; he cannot properly go behind the conditions surrounding his observations and speak of a real external world beyond these observations. Any world which he may think of as so existing is purely a conceptual world, one which for some reason he infers to exist behind the deceptive observations. Provided he makes this reservation he is quite privileged to speculate about this concealed world, to bestow upon it any characteristics that he pleases; but it can have no real existence for him until he becomes able to observe it. The only reality he knows is the one he can directly observe.

Laws of Nature

The observations which we have been discussing, and which we have been trying to endow with characteristics of “reality” which they are frequently not realized to possess, are the raw material of physical science. The finished product is the result of bringing together a large number of these observations.]* [The whole underlying thought behind the making of observations, in fact, is to correlate as many as possible of them, to obtain some generalization, and finally to express this in some simple mathematical form. This formulation is then called a “law of nature.”]^[35]

[Much confusion exists because of a misunderstanding in the lay mind of what is meant by a “law of nature.” It is perhaps not a well chosen term. One is accustomed to associate the word law with the idea of necessity or compulsion. In the realm of nature the term carries no such meaning. The laws of nature are man’s imperfect attempts to explain natural phenomena; they are not inherent in matter and the universe, not an iron bar of necessity running through worlds, systems and suns. Laws of nature are little more than working hypotheses, subject to change or alteration or enlargement or even abandonment, as man’s vision widens and deepens. No sanctity attaches to them, and if any one, or all, of them fail to account for any part, or all, of the phenomena of the universe, then it or they must be supplemented or abandoned.]^[102]

[The test of one of these laws is that it can be shown to include all the related phenomena hitherto known and that it enables us to predict new phenomena which can then be verified. If new facts are discovered that are not in agreement with one of these generalized statements, the assumptions on which the latter is based are examined, those which are not in accordance with the new facts are given up, and the statement is modified so as to include the new facts.]^[10] [And if one remembers that the laws of physics were formerly based on a range of observations much narrower than at present available, it seems natural that in the light of this widening knowledge one law or another may be seen to be narrow and insufficient. New theories and laws do not necessarily disprove old ones, but explain certain discrepancies in them and penetrate more deeply into their underlying principles, thereby broadening our ideas of the universe. To follow the new reasoning we must rid ourselves of the prejudice behind the old, not because it is wrong but because it is insufficient. The universe will not be distorted to fit our rules, but will teach us the rules of existence.]^[125]

[Always, however, we must guard against the too easy error of attributing to these rules anything like absolute truth.]* [The modern scientist has attained a very business-like point of view toward his “laws of nature.” To him a law is fundamentally nothing but a short-hand way of expressing the results of a large number of experiments in a single statement. And it is important to remember that this mere shortening of the description of a lot of diverse occurrences is by no means any real explanation of how and why they happened. In other words, the aim of science is not ultimately to explain but only to discover the relations that hold good among physical quantities and to embody all these relations in as few and as simple physical laws as possible.]^[221] [This is inherently the method of relativism.]* [Under it a set of phenomena is observed. There are two or many observers, and they write down their several findings. These are reviewed by a final observer or judge, who strains out the bias due to the different viewpoints of the original observers. He then writes down, not any absolute law of nature governing the observed phenomena, but a law as general as possible expressing their interrelations.]^[121] [And through this procedure modern science and philosophy reveal with increasing emphasis that we superimpose our human qualities on external nature to such an extent that]^[106] [we have at once the strongest practical justification, in addition to the arguments of reason, for our insistence that the contact between objective and subjective represented by the observation is the only thing which we shall ever be able to recognize as real. We may indulge in abstract metaphysical speculation to our heart’s content, if we be metaphysically inclined; we may not attempt to impose the dicta of metaphysics upon the physical scientist.]*

Concepts and Realities

[From the inquiry and criticism which have gone on for centuries has emerged the following present-day attitude of mind toward the sum total of our knowledge. The conceptual universe in our minds in some mysterious way parallels the real universe, but is totally unlike it. Our conceptions (ideas) of matter, molecules, atoms, corpuscles, electrons, the ether, motion, force, energy, space, and time stand in the same or similar relation to reality as the x’s and y’s of the mathematician do to the entities of his problem. Matter, molecules, atoms, corpuscles, electrons, the ether, motion, force, energy, space, and time do not exist actually and really as we conceive them, nor do they have actually and really the qualities and characteristics with which we endow them. The concepts are simply representations of things outside ourselves; things which, while real, have an essential nature not known to us. Matter, molecules, atoms, corpuscles, electrons, the ether, motion, force, energy, space and time are merely devices, symbols, which enable us to reason about reality. They are parts of a conceptual mechanism in our minds which operates, or enables our minds to operate, in the same sequence of events as the sequence of phenomena in the external universe, so that when we perceive by our senses a group of phenomena in the external universe, we can reason out what result will flow from the interaction of the realities involved, and thus predict what the situation will be at a given stage in the sequence.

But while our conceptual universe has thus a mechanical aspect, we do not regard the real universe as mechanical in its nature.]^[283] [This may be illustrated by a little story. Entering his friend’s house, a gentleman is seized unawares from behind. He turns his head but sees nothing. His hat and coat are removed and deposited in their proper places by some invisible agent, seats and tables and refreshments appear in due time where they are required, all without any apparent cause. The visitor shivers with horror and asks his host for an explanation. He is then told that the ideas “order” and “regularity” are at work, and that it is they who acquit themselves so well of their tasks. These ideas cannot be seen nor felt nor seized nor weighed; they reveal their existence only by their thoughtful care for the welfare of mankind. I think the guest, coming home, will relate that his friend’s house is haunted. The ghosts may be kind, benevolent, even useful; yet ghosts they are. Now in Newtonian mechanics, absolute space and absolute time and force and inertia and all the other apparatus, altogether imperceptible, appearing only at the proper time to make possible a proper building up of the theory, play the same mysterious part as the ideas “order” and “regularity” in my story. Classical mechanics is haunted.]^[116]

[As a matter of fact, we realize this and do not allow ourselves to be imposed upon with regard to the true nature of these agencies.]* [We use a mechanistic terminology and a mechanistic mode of reasoning only because we have found by experience that they facilitate our reasoning. They are the tools which we find produce results. They are adapted to our minds, but perhaps it would be better to say that our minds are so constructed as to render our conceptual universe necessarily mechanical in its aspect in order that our minds may reason at all. Two things antithetic are involved—subject (our perceiving mind which builds up concepts) and object (the external reality); and having neither complete nor absolute knowledge of either, we cannot affirm which is more truly to be said to be mechanistic in its nature, though we may suspect that really neither is. We no longer think of cause and effect as dictated by inherent necessity, we simply regard them as sequences in the routine of our sense-impressions of phenomena. In a word, we have at length grasped the idea that our notions of reality, at present at least, whatever they may become ultimately, are not absolute, but simply relative. We see, too, that we do not explain the universe, but only describe our perceptions of its contents.

The so-called laws of nature are simply statements of formulæ which resume or sum up the relationships and sequences of phenomena. Our effort is constantly to find formulæ which will describe the widest possible range of phenomena. As our knowledge increases, that is, as we perceive new phenomena, our laws or formulæ break down, that is, they fail to afford a description in brief terms of all of our perceptions. It is not that the old laws are untrue, but simply that they are not comprehensive enough to include all of our perceptions. The old laws are often particular or limiting instances of the new laws.]^[283]

[From what we have said of the reality of observations it follows that we must support that school of psychology, and the parallel school of philosophy, which hold that concepts originate in perceptions. But this does not impose so strong a restriction upon conceptions as might appear. The elements of all our concepts do come to us from outside; we manufacture nothing out of whole cloth. But when perception has supplied a sufficient volume of raw material, we may group its elements in ways foreign to actual occurrence in the perceptual world, and in so doing get conceptual results so entirely different from what we have consciously perceived that we are strongly tempted to look upon them as having certainly been manufactured in our minds without reference to the externals. Of even more significance is our ability to abstract from concrete objects and concrete incidents the essential features which make them alike and different. But unlike the Greeks, we see that our concept of coldness is not something with which we were endowed from the beginning, but merely an abstraction from concrete experiences with concrete objects that have been cold.

The Concepts of Space and Time

When we have formed the abstract ideas of coldness and warmth, and have had experience indicating that the occurrence of these properties varies in degree, we are in a position to form the secondary abstract notion covered by the word “temperature.” When we have formed the abstract ideas of size and position and separation, we are similarly in a position to form a secondary abstraction to which we give the name “space.” Not quite so easy to trace to its definite source but none the less clearly an abstraction based on experience, is our idea of what we call “time.” None of us are deceived as to the reality of these abstractions.]* [We do not regard space as real in the sense that we regard a chair as real; it is merely an abstract idea convenient for the location of material objects like the chair.]^[198] [Nor do we regard time as real in this sense. Things occupy space, events occupy time; space and time themselves we realize are immaterial and unreal; space does not exist and time does not happen in the same sense that material objects exist and events occur. But we find it absolutely necessary to have, among the mental machinery mentioned above as the apparatus by aid of which we keep track of the external world, these vessels for that world to exist in and move in.

Space and time, then, are concepts.]* [It is not strange, however, that when confronted with the vast and bewildering complexity of the universe and the difficulty of keeping separate and distinct in our minds our perceptions and conceptions, we should at times and as respects certain things project our conceptions illegitimately into the perpetual universe and mistake them for perceptions. The most notable example perhaps of this projection has occurred in the very case of space and time, most fundamental of all of our concepts. We got to think of these as absolute, as independent of each other and of all other things, and as always existing and continuing to exist whether or not we or anything else existed—space as a three-dimensional, uniform continuum, having the same properties in all directions; time as a one-dimensional, irreversible continuum, flowing in one direction. It is difficult to get back to the idea that space and time so described and defined are concepts merely, for the idea of their absolute existence is ingrained in us as the result probably of long ancestral experience.]^[283]

[Newton’s definitions of course represent the classical idea of time and space. He tells us that “absolute, true and mathematical time flows in virtue of its own nature, uniformly and without reference to any external object;” and that “absolute space, by virtue of its own nature and without reference to any external object, always remains the same and is immovable.” Of course from modern standpoints it is absurd to call either of these pronouncements a definition; but they represent about as well as any words can the ideas which Newton had about time and space, and they make it clear enough that he regarded both as having real existence in the external world.

If space and time are to be the vessels of our universe, and if the only thing that really matters is measured results, it is plain enough that we must have, from the very beginning, means of measuring space and time. Whether we believe space and time to have real existence or not, it is obvious that we can measure neither directly. We shall have to measure space by measuring from one material object to another; we shall have to measure time by some similar convention based on events. We shall later have something further to say about the measurement of time; for the present we need only point out that]* [Newtonian time is measured independently of space; and the existence is presupposed of a suitable timekeeper.]^[10]

[The space of Galileo and Newton was conceived of as empty, except in so far as certain parts of it were occupied by matter. Positions of bodies in this space were in general determined by reference to]^[283]

The Reference Frame for Space

The mathematician, following the lead of the great French all-around genius, Descartes, shows us very clearly how to set up, for the measurement of space, the framework known as the Cartesian coordinate system. The person of most ordinary mathematical attainments will realize that to locate a point in a plane we must have two measurements; and we could probably show this person, without too serious difficulty, that we can locate a point in any surface by two measurements. An example of this is the location of points on the earth’s surface by means of their latitude and longitude. It is equally clear that if we add a third dimension and attempt to locate points in space, we must add a third measurement. In the case of points on the earth’s surface, this might be the elevation above sea level, which would define the point not as part of the spherical surface of the earth but as part of the solid sphere. Or we may fall back on Dr. Slosson’s suggestion that in order to define completely the position of his laboratory, we must make a statement about Broadway, and one about 116th Street, and one telling how many flights of stairs there are to climb. In any event, it should be clear enough that the complete definition of a point in space calls for three measurements.

The mathematician formulates all this with the utmost precision. He asks us to]* [pick out any point whatever in space and call it O. We then draw or conceive to be drawn through this point three mutually perpendicular lines called coordinate axes, which we may designate OX, OY and OZ, respectively. Finally, we consider the three planes also mutually perpendicular like the two walls and the floor of a room that meet in one common corner, which are formed by the lines OX and OY, OY and OZ, and OZ and OX, respectively. These three planes are called coordinate planes. And then any other point P in space can be represented with respect to O by its perpendicular distances from each of the three coordinate planes—the distances x, y, z in the figure. These quantities are called the coordinates of the point.]^[272]

[To the layman there seems something altogether naive in this notion of the scientist’s setting up the three sides of a box in space and using them as the basis of all his work. The layman somehow feels that while it is perfectly all right for him to tell us that he lives at 1065 (one coordinate) 156th Street (two coordinates) on the third floor (three coordinates), it is rather trivial business for the serious-minded scientist to consider the up-and-down, the forward-and-back, the right-and-left of every point with which he has occasion to deal. There seems to the layman something particularly inane and foolish and altogether puerile about a set of coordinate axes, and you simply can’t make him believe that the serious-minded scientist has to monkey with any such funny business. He can’t be induced to take this coordinate-axis business seriously. Nevertheless, the fact is that the scientist takes it with the utmost seriousness. It is necessary for him to define the positions of points; and he does do it by means of a set of coordinate axes.

The scientist, however, is not interested in points of empty space. The point is to him merely part again of the conceptual machinery which he uses in his effort to run along with the external world. He knows there are no real points, but it suits his convenience to keep track of certain things that are real by representing them as points. But these things are in practically every instance material bodies; and in practically every instance, instead of staying put in one spot, they insist upon moving about through space. The scientist has to use his coordinate system, not merely to define a single position of such a “point,” but to keep track of the path over which it moves and to define its position in that path at given moments.

Time and the Coordinate System

This introduces the concept of time into intimate relationship with the spatial coordinate system. And at once we feel the lack of a concrete, visualized fourth dimension.]* [If we want to fix objects in the floor alone, the edge of the room running toward the ceiling would become unnecessary and could be dropped from our coordinate system. That is, we need only two coordinates to fix the position of a point in a plane. Suppose instead of discarding the third coordinate, we use it to represent units of time. It then enables us to record the time it took a moving point in the floor to pass from position to position. Certain points in the room would be vertically above the corresponding points occupied by the moving point in its path across the floor; and the vertical height above the floor of such points corresponds to a value of the time-coordinate which indicates the time it took the point to move from position to position.]^[152] [Just as the path of the point across the floor is a continuous curve (for the mathematician, it should be understood, this term “curve” includes the straight line, as a special case in which the curvature happens to be zero); so the series of points above these in the room forms a continuous curve which records for us, not merely the path of the point across the floor, but in addition the time of its arrival at each of its successive positions. In the algebraic work connected with such a problem, the third coordinate behaves exactly the same, regardless of whether we consider it to represent time or a third spatial dimension; we cannot even tell from the algebra what it does represent.

When we come to the more general case of a point moving freely through space, we have but three coordinates at our disposal; there is not a fourth one by aid of which we can actually diagram its time-space record. Nevertheless, we can write down the numerical and algebraic relations between its three space-coordinates and the time which it takes to pass from one position to another; and by this means we can make all necessary calculations. Its motion is completely defined with regard both to space and to time. We are very apt to call attention to the fact that if we did have at our disposal a fourth, space-coordinate, we could use it to represent the time graphically, as before, and actually construct a geometric picture of the path of our moving point with regard to space and time. And on this account we are very apt to speak as though the time measurements constituted a fourth coordinate, regardless of any question of our ability to construct a picture of this coordinate. The arrival of a point in a given position constitutes an event; and this event is completely defined by means of four coordinates—three in space, which we can picture on our coordinate axes, and one in time which we cannot.

The set of coordinate axes in space, together with the zero point from which we measure time, constitute what we call a frame of reference. If we are not going to pay any attention to time, we can think of the space coordinate system alone as constituting our reference frame. This expression appears freely throughout the subsequent text, and always with one or the other of these interpretations.

We see, then, how we can keep track of a moving point by keeping track of the successive positions which it occupies in our reference frame.]* [Now we have implied that these coordinate axes are fixed in space; but there is nothing to prevent us from supposing that they move.]^[272] [If they do, they carry with them all their points; and any motion of these points which we may speak about will be merely motion with reference to the coordinate system. If we find something outside our coordinate system that is not moving, the motion of points in our system with regard to those outside it will be a combination of their motion with regard to our coordinate axes and that of these axes with regard to the external points. This will be a great nuisance; and it represents a state of affairs which we shall try to avoid. We shall avoid it, if at all, by selecting a coordinate system with reference to which we, ourselves, are not moving; one which partakes of any motion which we may have. Or perhaps we shall sometimes wish to reverse the process, in studying the behavior of some group of bodies, and seek a set of axes which is at rest with respect to these bodies; one which partakes of any motion they may have.

The Choice of a Coordinate Frame

All this emphasizes the fact that our coordinate axes are not picked out for us in advance by nature, and set down in some one particular spot. We select them for ourselves, and we select them in the most convenient way. But different observers, or perhaps the same observer studying different problems, will find it advantageous to utilize different coordinate systems.]* [The astronomer has found it possible, and highly convenient, to select a coordinate frame such that the great majority of the stars have, on the whole, no motion with respect to it.]^[283] [Such a system would be most unsuited for investigations confined to the earth; for these we naturally select a framework attached to the earth, with its origin O at the earth’s center if our investigation covers the entire globe and at some more convenient point if it does not, and in either event accompanying the earth in its rotation and revolution. But such a framework, as well as the one attached to the fixed stars, would be highly inconvenient for an investigator of the motions of the planets; he would doubtless attach his reference frame to the sun.]^[101]

[In this connection a vital question suggests itself. Is the expression of natural law independent of or dependent upon the choice of a system of coordinates? And to what extent shall we be able to reconcile the results of one observer using one reference frame, and a second observer using a different one? The answer to the second question is obvious.]* [True, if any series of events is described using two different sets of axes, the descriptions will be different, depending upon the time system adopted and the relative motion of the axes. But if the connection between the reference systems is known, it is possible by mathematical processes to deduce the quantities observed in one system if those observed in the other are known.]^[35] [This process of translating the results of one observer into those of another is known as a transformation; and the mathematical statement of the rule governing the transformation is called the equation or the equations (there are usually several of them) of the transformation.]* [Transformations of this character constitute a well-developed branch of mathematics.]^[35]

[When we inquire about the invariance of natural law it is necessary to be rather sure of just what we mean by this expression. The statement that a given body is moving with a velocity of 75 miles per hour is of course not a natural law; it is a mere numerical observation. But aside from such numerical results, we have a large number of mathematical relations which give us a more or less general statement of the relations that exist between velocities, accelerations, masses, forces, times, lengths, temperatures, pressures, etc., etc. There are some of these which we would be prepared to state at once as universally valid—distance travelled equals velocity multiplied by time, for instance. We do not believe that any conceivable change of reference systems could bring about a condition in which the product of velocity and time, as measured from a certain framework, would fail to equal distance as measured from this same framework. There are other relations more or less of the same sort which we probably believe to be in the same invariant category; there are others, perhaps, of which we might be doubtful; and presumably there are still others which we should suspect of restricted validity, holding in certain reference systems only and not in others.

The question of invariance of natural law, then, may turn out to be one which may be answered in the large by a single statement; it may equally turn out to be one that has to be answered in the small, by considering particular laws in connection with particular transformations between particular reference systems. Or, perhaps, we may find ourselves justified in taking the stand that an alleged “law of nature” is truly such a law only in the event that it is independent of the change from one reference system to another. In any event, the question may be formulated as follows:

Observer A, using the reference system R, measures certain quantities t, w, x, y, z. Observer B, using the reference system S, measures the same items and gets the values t′, w′, x′, y′, z′. The appropriate transformation equations for calculating the one set of values from the other is found. If a mathematical relation of any sort is found to exist between the values t, w, x, y, z, will the same relation exist between the values t′, w′, x′, y′, z′? If it does not, are we justified in still calling it a law of nature? And if it does not, and we refrain from calling it such a law, may we expect in every case to find some relation that will be invariant under the transformation, and that may therefore be recognized as the natural law connecting t, w, x, y and z?

I have found it advisable to discuss this point in such detail because here more than in any other single place the competing essayists betray uncertainty of thought and sloppiness of expression. It doesn’t amount to much to talk about the invariance of natural laws and their persistence as we pass from one coordinate system to another, unless we are fairly well fortified with respect to just what we mean by invariance and by natural law. We don’t expect the velocity of a train to be 60 miles per hour alike when we measure it with respect to a signal tower along the line and with respect to a moving train on the other track. We don’t expect the angular displacement of Mars to change as rapidly when he is on the other side of the sun as when he is on our side. But we do, I think, rather expect that in any phenomenon which we may observe, we shall find a natural law of some sort which is dependent for its validity neither upon the units we employ, nor the place from which we make our measurements, nor anything else external to the phenomenon itself. We shall see, later, whether this expectation is justified, or whether it will have to be discarded in the final unravelling of the absolutist from the relativistic philosophy which, with Einstein, we are to undertake.]*

III

THE RELATIVITY OF UNIFORM MOTION

Classical Ideas on the Subject; the Ether and the Apparent Possibility of Absolute Motion; the Michelson-Morley Experiment and the Final Negation of This Possibility

BY VARIOUS CONTRIBUTORS AND THE EDITOR

When we speak of a body as being “in motion,” we mean that this body is changing its position “in space.” Now it is clear that the position of an object can only be determined with reference to other objects: in order to describe the place of a material thing we must, for example, state its distances from other things. If there were no such bodies of reference, the words “position in space” would have no definite meaning for us.]^[24] [The number of such external bodies of reference which it is necessary to cite in order to define completely the position of a given body in space depends upon the character of the space dealt with. We have seen that when we visualize the space of our experience as a surface of any character, two citations are sufficient; and that when we conceive of it as surrounding us in three dimensions we require three. It will be realized that the mathematician is merely meeting this requirement when he sets up his system of coordinate axes to serve as a reference frame.]*

[What is true of “place” must be true also of “motion,” since the latter is nothing but change of place. In fact, it would be impossible to ascribe a state of motion or of rest to a body poised all alone in empty space. Whether a body is to be regarded as resting or as moving, and if the latter at what speed, depends entirely upon the objects to which we refer its positions in space.]^[24] [As Einstein sits at his desk he appears to us to be at rest; but we know that he is moving with the rotation of the earth on its axis, with the earth in its orbit about the sun, and with the solar system in its path through space—a complex motion of which the parts or the whole can be detected only by reference to appropriately chosen ones of the heavenly bodies. No mechanical test has ever been devised which will detect this motion,]^[182] [if we reserve for discussion in its proper place the Foucault pendulum experiment which will reveal the axial rotation of our globe.]* [No savage, if he were to “stand still,” could be convinced that he was moving with a very high velocity or in fact that he was moving at all.]^[30] [You drop a coin straight down a ship’s side: from the land its path appears parabolic; to a polar onlooker it whirls circle-wise; to dwellers on Mars it darts spirally about the sun; to a stellar observer it gyrates through the sky]^[263] [in a path of many complications. To you it drops in a straight line from the deck to the sea.]* [Yet its various tracks in ship-space, sea-space, earth-space, sun-space, star-space, are all equally real,]^[263] [and the one which will be singled out for attention depends entirely upon the observer, and the objects to which he refers the motion.]* [The earth moves in the solar system, which is itself approaching a distant star-cluster. But we cannot say whether we are moving toward the cluster, or the cluster toward us,]^[18] [or both, or whether we are conducting a successful stern chase of it, or it of us,]* [unless we have in mind some third body with reference to which the motions of earth and star-cluster are measured.]^[18] [And if we have this, the measurements made with reference to it are of significance with regard to it, rather than with regard to the earth and the star-cluster alone.]*

[We can express all this by saying “All motions are relative; there is no such thing as absolute motion.” This line of argument has in fact been followed by many natural philosophers. But is its result in agreement with actual experience? Is it really impossible to distinguish between rest and motion of a body if we do not take into consideration its relations to other objects? In fact it can easily be seen that, at least in many cases, no such distinction is possible.

Who Is Moving?

Imagine yourself sitting in a railroad car with veiled windows and running on a perfectly straight track with unchanging velocity: you would find it absolutely impossible to ascertain by any mechanical means whether the car were moving or not. All mechanical instruments behave exactly the same, whether the car be standing still or in motion.]^[24] [If you drop a ball you will see it fall to the floor in a straight line, just as though you had dropped it while standing on the station platform. Furthermore, if you drop the ball from the same height in the two cases, and measure the velocities with which it strikes the car floor and the station platform, or the times which it requires for the descent, you will find these identical in the two cases.]^[182]

[Any changes of speed or of direction (as when the car speeds up or slows down or rounds a curve) can be detected by observing the behavior of bodies in the car, without apparent reference to any outside objects. This becomes particularly obvious with sudden irregularities of motion, which manifest themselves by shaking everything in the car. But a uniform motion in a straight line does not reveal itself by any phenomenon within the vehicle.]^[24]

[Moreover, if we remove the veil from our window to the extent that we may observe the train on the adjoining track, we shall be able to make no decision as to whether we or it be moving. This is indeed an experience which we have all had.]* [Often when seated in a train about to leave the station, we have thought ourselves under way, only to perceive as the motion becomes no longer uniform that another train has been backing into the station on the adjoining track. Again, as we were hurried on our journey, we have, raising suddenly our eyes, been puzzled to say whether the passing train were moving with us or against us or indeed standing still; or more rarely we have had the impression that both it and we seemed to be at rest, when in truth both were moving rapidly with the same speed.]^[82] [Even this phrase “in truth” is a relative one, for it arises through using the earth as an absolute reference body. We are indeed naive if we cannot appreciate that there is no reason for doing this beyond convenience, and that to an observer detached from the earth it were just as reasonable to say that the rails are sliding under the train as that the train is advancing along the rails. One of my own most vivid childhood recollections is of the terror with which, riding on a train that passed through a narrow cut, I hid my head in the maternal lap to shut out the horrid sight of the earth rushing past my window. The absence of a background in relatively slow retrograde motion was sufficient to prevent my consciousness from drawing the accustomed conclusion that after all it was really the train that was moving.]*

Mechanical Relativity

[So we can enunciate the following principle: When a body is in uniform rectilinear motion relatively to a second body, then all phenomena take place on the first in exactly the same manner as on the second; the physical laws for the happenings on both bodies are identical.]^[24] [And between a system of bodies, nothing but relative motion may be detected by any mechanical means whatever; any attempt to discuss absolute motion presupposes a super-observer on some body external to the system. Even then, the “absolute” motion is nothing but motion relative to this super-observer. By no mechanical means is uniform straight-line motion of any other than relative character to be detected. This is the Principle of Mechanical Relativity.

There is nothing new in this. It was known to Galileo, it was known to Newton, it has been known ever since. But the curious persistence of the human mind in habits of thought which confuse relativity with absolutism brought about a state of affairs where we attempted to know this and to ignore it at the same time. We shall have to return to the mathematical mode of reasoning to see how this happened. The mathematician has a way all his own of putting the statement of relativity which we have made. He recalls, what we have already seen, that the observer on the earth who is measuring his “absolute” motion with respect to the earth has merely attached his reference framework to the earth; that the passenger in the train who measures all motion naively with respect to his train is merely carrying his coordinate axes along with his baggage, instead of leaving them on the solid ground; that the astronomer who deals with the motion of the earth about the sun, or with that of the “fixed” stars against one another, does so simply by the artifice of hitching his frame of reference to the sun or to one of the fixed stars. So the mathematician points out that dispute as to which of two bodies is in motion comes right down to dispute as to which of two sets of coordinate axes is the better one, the more nearly “natural” or “absolute.” He therefore phrases the mechanical principle of relativity as follows:

Among all coordinate systems that are merely in uniform straight-line motion to one another, no one occupies any position of unique natural advantage; all such systems are equivalent for the investigation of natural laws; all systems lead to the same laws and the same results.

The mathematician has thus removed the statement of relativity from its intimate association with the external observed phenomena, and transferred it to the observer and his reference frame. We must either accept the principle of relativity, or seek a set of coordinate axes that have been singled out by nature as an absolute reference frame. These axes must be in some way unique, so that when we refer phenomena to them, the laws of nature take a form of exceptional simplicity not attained through reference to ordinary axes. Where shall we look for such a preferred coordinate system?]*

The Search for the Absolute

[Older theory clung to the belief that there was such a thing as absolute motion in space.]^[197] [As the body of scientific law developed from the sixteenth century onward, the not unnatural hypothesis crept in, that these laws (that is to say, their mathematical formulations rather than their verbal statements) would reveal themselves in especially simple forms, were it possible for experimenters to make their observations from some absolute standpoint; from an absolutely fixed position in space rather than from the moving earth.]^[264] [Somewhere a set of coordinate axes incapable of motion was to be found,]^[197] absolute motion; and for two hundred years the world of science strove to find it,]^[147] [in spite of what should have been assurance that it did not exist. But the search failed, and gradually the universal applicability of the principle of relativity, so far as it concerned mechanical phenomena, grew into general acceptance.]* [And after the development, by the great mathematicians of the eighteenth century, of Newton’s laws of motion into their most complete mathematical form, it was seen that so far as these laws are concerned the absolutist hypothesis mentioned is quite unsupported. No complication is introduced into Newton’s laws if the observer has to make his measurements in a frame of reference moving uniformly through space; and for measurements in a frame like the earth, which moves with changing speed and direction about the sun and rotates on its axis at the same time, the complication is not of so decisive a nature as to give us any clue to the earth’s absolute motion in space.

But mechanics, albeit the oldest, is yet only one of the physical sciences. The great advance made in the mathematical formulation of optical and electromagnetic theory during the nineteenth century revived the hope of discovering absolute motion in space by means of the laws derived from this theory.]^[264] [Newton had supposed light to be a material emanation, and if it were so, its passage across “empty space” from sun and stars to the earth raised no problem. But against Newton’s theory Huyghens, the Dutch astronomer, advanced the idea that light was a wave motion of some sort. During the Newtonian period and for many years after, the corpuscular theory prevailed; but eventually the tables were turned.]* [Men made rays of light interfere, producing darkness (see page 61). From this, and from other phenomena like polarization, they had deduced that light was a form of wave motion similar to water ripples; for these interfere, producing level surfaces, or reinforce each other, producing waves of abnormal height. But if light were to be regarded as a form of wave motion—and the phenomena could apparently be explained on no other basis—then there must be some medium capable of undergoing this form of motion.]^[135] [Transmission of waves across empty space without the aid of an intermediary material medium would be “action at a distance,” an idea repugnant to us. Trammeled by our tactual, wire-pulling conceptions of a material universe, we could not accustom ourselves to the idea of something—even so immaterial a something as a wave—being transmitted by nothing. We needed a word—ether—to carry light if not to shed it; just as we need a word—inertia—to carry a projectile in its flight.]^[231] [It was necessary to invest this medium with properties to account for the observed facts. On the whole it was regarded as the perfect fluid.]^[235] [The ether was imagined as an all-pervading, imponderable substance filling the vast emptiness through which light reaches us, and as well the intermolecular spaces of all matter. Nothing more was known definitely, yet this much served as a good working hypothesis on the basis of which Maxwell was enabled to predict the possibility of radio communication. By its fruits the ether hypothesis justified itself; but does the ether exist?]^[231]

The Ether and Absolute Motion

[If it does exist, it seems quite necessary, on mere philosophical grounds, that it shall be eligible to serve as the long-sought reference frame for absolute motion. Surely it does not make sense to speak of a homogeneous medium filling all space, sufficiently material to serve as a means of communication between remote worlds, and in the next breath to deny that motion with respect to this medium is a concept of significance.]* [Such a system of reference as was offered by the ether, coextensive with the entire known region of the universe, must necessarily serve for all motions within our perceptions.]^[186] [The conclusion seems inescapable that motion with respect to the ether ought to be of a sufficiently unique character to stand out above all other motion. In particular, we ought to be able to use the ether to define, somewhere, a system of axes fixed with respect to the ether, the use of which would lead to natural laws of a uniquely simply description.

Maxwell’s work added fuel to this hope.]* [During the last century, after the units of electricity had been defined, one set for static electrical calculations and one for electromagnetic calculations, it was found that the ratio of the metric units of capacity for the two systems was numerically equal to what had already been found as the velocity with which light is transmitted through the hypothetical ether. One definition refers to electricity at rest, the other to electricity in motion. Maxwell, with little more working basis than this, undertook to prove that electrical and optical phenomena were merely two aspects of a common cause,]^[235] [to which the general designation of “electromagnetic waves” was applied. Maxwell treated this topic in great fullness and with complete success. In particular, he derived certain equations giving the relations between the various electrical quantities involved in a given phenomenon. But it was found, extraordinarily enough, that these relations were of such character that, when we subject the quantities involved to a change of coordinate axes, the transformed quantities did not preserve these relations if the new axes happened to be in motion with respect to the original ones. This, of course, was taken to indicate that motion really is absolute when we come to deal with electromagnetic phenomena, and that the ether which carries the electromagnetic waves really may be looked to to display the properties of an absolute reference frame.

Reference to the phenomenon of aberration, which Dr. Pickering has discussed adequately in his essay and which I need therefore mention here only by name, indicated that the ether was not dragged along by material bodies over and through which it might pass. It seemed that it must filter through such bodies, presumably via the molecular interstices, without appreciable opposition. Were this not the case, we should be in some doubt as to the possibility of observing the velocity through the ether of material bodies; if the ether adjacent to such bodies is not dragged along or thrown into eddies, but “stands still” while the bodies pass, there seems no imaginable reason for anything other than the complete success of such observations. And of course these are of the utmost importance, the moment we assign to the ether the rôle of absolute reference frame.

The Earth and the Ether

One body in motion with respect to the ether is our earth itself. We do not know in advance in what direction to expect this motion or what magnitude to anticipate that it will have. But one thing is clear.]* [In its motion around the sun, the earth has, at opposite points on its orbit, a difference in velocity with respect to the surrounding medium which is double its orbital velocity with respect to the sun. This difference comes to 37 miles per second. The earth should therefore, at some time in the year, show a velocity equal to or greater than 18½ miles per second, with reference to the universal medium. The famous Michelson-Morley experiment of 1887 was carried out with the expectation of observing this velocity.]^[267]

[The ether, of course, and hence velocities through it, cannot be observed directly. But it acts as the medium for the transmission of light.]* [If the velocity of light through the ether is C and that of the earth through the ether is v, then the velocity of light past the earth, so the argument runs, must vary from

to

, according as the light is moving exactly in the same direction as the earth, or in the opposite direction,]^[182] [or diagonally across the earth’s path so as to get the influence only of a part of the earth’s motion. This of course assumes that C has always the same value; an assumption that impresses one as inherently probable, and one that is at the same time in accord with ordinary astronomical observation.

It is not possible to measure directly the velocity of light (186,330 miles per second, more or less) with sufficient accuracy to give any meaning to the variation in this velocity which might be effected by adding or subtracting that of the earth in its orbit (a mere 18½ miles per second). It is, however, possible to play a trick on the light by sending it back and forth over several paths, and comparing (not measuring absolutely, but merely comparing) with great minuteness the times consumed in these several round trips.

A Journey Upstream and Back

The number of letters the Scientific American has received questioning the Michelson-Morley experiment indicates that many people are not acquainted with the fundamental principle on which it is based. So let us look at a simple analogous case. Suppose a swimmer or a rower make a return trip upstream and down, contending with the current as he goes up and getting its benefit when he comes down. Obviously, says snap judgment, since the two legs of the journey are equal, he derives exactly as much benefit from the current when he goes with it as he suffers handicap from it when he goes against it; so the round trip must take exactly the same time as a journey of the same length in still water, the argument applying equally in the case where the “swimmer” is a wave of light in the ether stream.

But let us look now at a numerical case. A man can row in still water at four miles per hour. He rows twelve miles upstream and back, in a current of two miles per hour. At a net speed of two miles per hour he arrives at his turning point in six hours. At a net speed of six miles per hour he makes the down-stream leg in two hours. The elapsed time for the journey is eight hours; in still water he would row the twenty-four miles in six hours.

If we were to attempt an explanation of this result in words we should say that by virtue of the very fact that it does delay him, the adverse current prolongs the time during which it operates; while by virtue of the very fact that it accelerates his progress, the favoring current shortens its venue. The careless observer realizes that distances are equal between the two legs of the journey, and unconsciously assumes that times are equal.

If the journey be made directly with and directly against the stream of water or ether or what not, retardation is effected to its fullest extent. If the course be a diagonal one, retardation is felt to an extent measurable as a component, and depending for its exact value upon the exact angle of the path. Felt, however, it must always be.

Here is where we begin to get a grip on the problem of the earth and the ether. In any problem involving the return-trip principle, there will enter two velocities—that of the swimmer and that of the medium; and the time of retardation. If we know any two of these items we can calculate the third. When the swimmer is a ray of light and the velocity of the medium is that of the ether as it flows past the earth, we know the first of these two; we hope to observe the retardation so that we may calculate the second velocity. The apparatus for the experiment is ingenious and demands description.

The Michelson-Morley Experiment

The machine is of structural steel, weighing 1,900 pounds. It has two arms which form a Greek cross. Each arm is 14 feet in length. The whole apparatus is floated in a trough containing 800 pounds of mercury.

Four mirrors are arranged on the end of each arm, sixteen in all, with a seventeenth mirror, M, set at one of the inside corners of the cross, as diagrammed. A source of light (in this case a calcium flame) is provided, and its rays directed by a lens toward the mirror M. Part of the light is allowed to pass straight through M to the opposite arm of the cross, where it strikes mirror 1. It is reflected back across the arm to mirror 2, thence to 3, and so on until it reaches mirror 8. Thence it is reflected back to mirror 7, to 6, and so on, retracing its former path, and finally is caught by the reverse side of the mirror M and is sent to an observer at O. In retracing its path the light sets up an interference phenomenon (see below) and the interference bands are visible to the observer, who is provided with a telescope to magnify the results.

A second part of the original light-beam is reflected off at right angles by the mirror M, and is passed to and fro on the adjacent arms of the machine, in exactly the same manner and over a similar path, by means of the mirrors I, II, III, … VIII. This light finally reaches the observer at the telescope, setting up a second set of interference bands, parallel to the first.

A word now about this business of light interference. Light is a wave motion. The length of a wave is but a few millionths of an inch, and the amplitude is correspondingly minute; but none the less, these waves behave in a thoroughly wave-like manner. In particular, if the crests of two waves are superposed, there is a double effect; while if a crest of one wave falls with a trough of another, there is a killing-off or “interference”.

Under ordinary circumstances interference of light waves does not occur. This is simply because under ordinary circumstances light waves are not piled up on one another. But sometimes this piling up occurs; and then, just so sure as the piled-up waves are in the same phase they reinforce one another, while if they are in opposite phase they interfere. And the conditions which we have outlined above, with the telescope and the mirrors and the ray of light retracing the path over which it went out, are conditions under which interference does occur. If the returning wave is in exact phase with the outgoing one, the effect is that of uniform double illumination; if it is in exactly opposite phase the effect is that of complete extinguishing of the light, the reversed wave exactly cancelling out the original one. If the two rays are partly in phase, there is partial reinforcement or partial cancelling out, according to whether they are nearly in phase or nearly out of phase. Finally, if the mirrors are not set absolutely parallel—as must in practice be the case when we attempt to measure their parallelism in terms of the wave-length of light—adjacent parts of the light ray will vary in the extent to which they are out of phase, since they will have travelled a fraction of a wave-length further to get to and from this, that or the other mirror. There will then appear in the telescope alternate bands of illumination and darkness, whose width and spacing depend upon all the factors entering into the problem.

If it were possible for us to make the apparatus with such a degree of refinement that the path from mirror M via mirrors 1, 2, 3, etc., back through M and into the telescope, were exactly the same length as that from flame to telescope by way of the mirrors I, II, III, etc.—exactly the same to a margin of error materially less than a single wave-length of light—why, then, the two sets of interference fringes would come out exactly superposed provided the motion of the earth through the “ether” turn out to have no influence upon the velocity of light; or, if such influence exist, these fringes would be displaced from one another to an extent measuring the influence in question. But our ability to set up this complicated pattern of mirrors at predetermined distances falls far short of the wave-length as a measure of error. So in practice all that we can say is that having once set the instrument up, and passed a beam of light through it, there will be produced two sets of parallel interference fringes. These sets will fail of superposition—each fringe of one set will be removed from the corresponding fringe of the other set—by some definite distance. Then, any subsequent variation in the speed of light along the two arms will at once be detected by a shifting of the interference bands through a distance which we shall be able to measure.

The Verdict

Under the theories and assumptions governing at the time of the original performance of this experiment, it will be readily seen that if this machine be set up in an “ether stream” with one arm parallel to the direction of the stream and the other at right angles thereto, there will be a difference in the speed of the light along the two arms. Then if the apparatus be shifted to a position oblique to the ether stream, the excess velocity of the light in the one arm would be diminished, and gradually come to zero at the 45-degree angle, after which the light traveling along the other arm would assume the greater speed. In making observations, therefore, the entire apparatus was slowly rotated, the observers walking with it, so that changes of the sort anticipated would be observed.

The investigators were, however, ignorant of the position in which the apparatus ought to be set to insure that one of the arms lie across the ether drift; and they were ignorant of the time of year at which the earth’s maximum velocity through the ether was to be looked for. In particular, it is plain that if the solar system as a whole is moving through the ether at a rate less than the earth’s orbital velocity, there is a point in our orbit where our velocity through the ether and that around the sun just cancel out and leave us temporarily in a state of “absolute rest.” So it was anticipated that the experiment might have to be repeated in many orientations of the machine and at many seasons of the year in order to give a series of readings from which the true motion of the earth through the ether might be deduced.

For those who have a little algebra the demonstration which Dr. Russell gives on a subsequent page will be interesting as showing the situation in perfectly general terms. It will be realized that the more complicated arrangement of mirrors in the experiment as just described is simply an eightfold repetition of the simple experiment as outlined by Dr. Russell, and that it was done so for the mere sake of multiplying by eight the distances travelled and hence the difference in time and in phase.

And now for the grand climax. The experiment was repeated many times, with the original and with other apparatus, indoors and outdoors, at all seasons of the year, with variation of every condition that could imaginably affect the result. The apparatus was ordinarily such that a shift in the fringes of anywhere from one-tenth to one one-hundredth of that which would have followed from any reasonable value for the earth’s motion through the ether would have been systematically apparent. The result was uniformly negative. At all times and in all directions the velocity of light past the earth-bound observer was the same. The earth has no motion with reference to the ether!

[The amazing character of this result is not by any possibility to be exaggerated.]* [According to one experiment the ether was carried along by a rapidly moving body and according to another equally well-planned and well-executed experiment a rapidly moving body did not disturb the ether at all. This was the blind alley into which science had been led.]^[232]

The “Contraction” Hypothesis

[Numerous efforts were made to explain the contradiction.]* [It is indeed a very puzzling one, and it gave physicists no end of trouble. However Lorentz and Fitzgerald finally put forward an ingenious explanation, to the effect that the actual motion of the earth through the ether is balanced, as far as the ability of our measuring instruments is concerned, by a contraction of these same instruments in the direction of their motion. This contraction obviously cannot be observed directly because all bodies, including the measuring instruments themselves (which after all are only arbitrary guides), will suffer the contraction equally. According to this theory, called the Lorentz-Fitzgerald contraction theory,]^[272] [all bodies in motion suffer such contraction of their length in the direction of their motion;]^[283] [the contraction being made evident by our inability to observe the absolute motion of the earth, which it is assumed must exist.]^[272] [This would suffice to show why the Michelson-Morley experiment gave a negative result, and would preserve the concept of absolute motion with reference to the ether.]^[283]

[This proposal of Lorentz and Fitzgerald loses its startling aspect when we consider that all matter appears to be an electrical structure, and that the dimensions of the electric and magnetic fields which accompany the electrons of which it is constituted change with the velocity of motion.]^[267] [The forces of cohesion which determine the form of a rigid body are held to be electromagnetic in nature; the contraction may be regarded as due to a change in the electromagnetic forces between the molecules.]^[10] [As one writer has put it, the orientation, in the electromagnetic medium, of a body depending for its very existence upon electromagnetic forces is not necessarily a matter of indifference.]*

[Granting the plausibility of all this, on the basis of an electromagnetic theory of matter, it leaves us in an unsatisfactory position. We are left with a fixed ether with reference to which absolute motion has a meaning, but that motion remains undetected and apparently undetectable. Further, if we on shore measure the length of a moving ship, using a yard-stick which is stationary on shore, we shall obtain one result. If we take our stick aboard it contracts, and so we obtain a greater length for the ship. Not knowing our “real” motion through the ether, we cannot say which is the “true” length. Is it not, then, more satisfactory to discard all notion of true length as an inherent quality of bodies, and, by regarding length as the measure of a relation between a particular object and a particular observer, to make one length as true as the other?]^[182] [The opponents of such a viewpoint contend that Michelson’s result was due to a fluke; some mysterious counterbalancing influence was for some reason at work, concealing the result which should normally have been expected. Einstein refuses to accept this explanation;]^[192] [he refuses to believe that all nature is in a contemptible conspiracy to delude us.]*

[The Fitzgerald suggestion is further unsatisfactory because it assumes all substances, of whatever density, to undergo the same contraction; and above all for the reason that it sheds no light upon other phenomena.]^[194] [It is indeed a very special explanation; that is, it applies only to the particular experiment in question. And indeed it is only one of many possible explanations. Einstein conceived the notion that it might be infinitely more valuable to take the most general explanation possible, and then try to find from this its logical consequences. This “most general explanation” is, of course, simply that it is impossible in any way whatever to measure the absolute motion of a body in space.]^[272] [Accordingly Einstein enunciated, first the Special Theory of Relativity, and later the General Theory of Relativity. The special theory was so called because it was, limited to uniform rectilinear and non-rotary motions. The general theory, on the other hand, dealt not only with uniform rectilinear motions, but with any arbitrary motion whatever.

Taking the Bull by the Horns

The hypothesis of relativity asserts that there can be no such concept as absolute position, absolute motion, absolute time; that space and time are inter-dependent, not independent; that everything is relative to something else. It thus accords with the philosophical notion of the relativity of all knowledge.]^[283] [Knowledge is based, ultimately, upon measurement; and clearly all measurement is relative, consisting merely in the application of a standard to the magnitude measured. All metric numbers are relative; dividing the unit multiplies the metric number. Moreover, if measure and measured change proportionately, the measuring number is unchanged. Should space with all its contents swell in fixed ratio throughout, no measurement could detect this; nor even should it pulse uniformly throughout. Furthermore, were space and space-contents in any way systematically transformed (as by reflection in curved mirrors) point for point, continuously, without rending, no measurement could reveal this distortion; experience would proceed undisturbed.]^[263]

[Mark Twain said that the street in Damascus “which is called straight,” is so called because while it is not as straight as a rainbow it is straighter than a corkscrew. This expresses the basic idea of relativity—the idea of comparison. All our knowledge is relative, not absolute. Things are big or little, long or short, light or heavy, fast or slow, only by comparison. An atom may be as large, compared to an electron, as is a cathedral compared to a fly. The relativity theory of Einstein emphasizes two cases of relative knowledge; our knowledge of time and space, and our knowledge of motion.]^[216] [And in each case, instead of allowing the notions of relativity to guide us only so far as it pleases us to follow them, there abandoning them for ideas more in accord with what we find it easy to take for granted, Einstein builds his structure on the thesis that relativity must be admitted, must be followed out to the bitter end, in spite of anything that it may do to our preconceived notions. If relativity is to be admitted at all, it must be admitted in toto; no matter what else it contradicts, we have no appeal from its conclusions so long as it refrains from contradicting itself.]*

[The hypothesis of relativity was developed by Einstein through a priori methods, not the more usual a posteriori ones. That is, certain principles were enunciated as probably true, the consequences of these were developed, and these deductions tested by comparison of the predicted and the observed phenomena. It was in no sense attained by the more usual procedure of observing groups of phenomena and formulating a law or formula which would embrace them and correctly describe the routine or sequence of phenomena.

The first principle thus enunciated is that it is impossible to measure or detect absolute translatory motion through space, under any circumstances or by any means. The second is that the velocity of light in free space appears the same to all observers regardless of the relative motion of the source of light and the observer. This velocity is not affected by motion of the source toward or away from the observer,]^[283] [if we may for the moment use this expression with its implication of absolute motion.]* [But universal relativity insists that motion of the source toward the observer is identical with motion of the observer toward the source.]^[283]

[It will be seen that we are at once on the horns of a dilemma. Either we must give up relativity before we get fairly started on it, or we must overturn the foundations of common sense by admitting that time and space are so constituted that when we go to meet an advancing light-impulse, or when we retreat from it, it still reaches us with the same velocity as though we stood still waiting for it. We shall find when we are through with our investigation that common sense is at fault; that our fixed impression of the absurdity of the state of affairs just outlined springs from a confusion between relativism and absolutism which has heretofore dominated our thought and gone unquestioned. The impression of absurdity will vanish when we have resolved this confusion.]*

Questions of Common Sense

[But it is obvious from what has just been said that if we are to adopt Einstein’s theory, we must make very radical changes in some of our fundamental notions, changes that seem in violent conflict with common sense. It is unfortunate that many popularizers of relativity have been more concerned to astonish their readers with incredible paradoxes than to give an account such as would appeal to sound judgment. Many of these paradoxes do not belong essentially to the theory at all. There is nothing in the latter that an enlarged and enlightened common sense would not readily endorse. But common sense must be educated up to the necessary level.]^[141]

[There was a time when it was believed, as a result of centuries of experience, that the world was flat. This belief checked up with the known facts, and it could be used as the basis for a system of science which would account for things that had happened and that were to happen. It was entirely sufficient for the time in which it prevailed.

Then one day a man arose to point out that all the known facts were equally accounted for on the theory that the earth was a sphere. It was in order for his contemporaries to admit this, to say that so far as the facts in hand were concerned they could not tell whether the earth was flat or round—that new facts would have to be sought that would contradict one or the other hypothesis. Instead of this the world laughed and insisted that the earth could not be round because it was flat; that it could not be round because then the people would fall off the other side.

But the field of experimentation widened, and men were able to observe facts that had been hidden from them. Presently a man sailed west and arrived east; and it became clear that in spite of previously accepted “facts” to the contrary, the earth was really round. The previously accepted “facts” were then revised to fit the newly discovered truth; and finally a new system of science came into being, which accounted for all the old facts and all the new ones.

At intervals this sort of thing has been repeated. A Galileo shows that preconceived ideas with regard to the heavens are wrong, and must be revised to accord with his newly promulgated principles. A Newton does the same for physics—and people unlearn the “fact” that motion has to be supported by continued application of force, substituting the new idea that it actually requires force to stop a moving body. A Harvey shows that the things which have been “known” for generations about the human body are not so. A Lyell and a Darwin force men to throw overboard the things they have always believed about the way in which the earth and its creatures came into being. Every science we possess has passed through one or more of these periods of readjustment to new facts.

Shifting the Mental Gears

Now we are apt to lose sight of the true significance of this. It is not alone our opinions that are altered; it is our fundamental concepts. We get concepts wholly from our perceptions, making them to fit those perceptions. Whenever a new vista is opened to our perceptions, we find facts that we never could have suspected from the restricted viewpoint. We must then actually alter our concepts to make the new facts fit in with the greatest degree of harmony. And we must not hesitate to undertake this alteration, through any feeling that fundamental concepts are more sacred and less freely to be tampered with than derived facts.]* [We do, to be sure, want fundamental concepts that are easy for a human mind to conceive; but we also want our laws of nature to be simple. If the laws begin to become, intricate, why not reshape, somewhat, the fundamental concepts, in order to simplify the scientific laws? Ultimately it is the simplicity of the scientific system as a whole that is our principal aim.]^[178]

[As a fair example, see what the acceptance of the earth’s sphericity did to the idea represented by the word “down.” With a flat earth, “down” is a single direction, the same throughout the universe; with a round earth, “down” becomes merely the direction leading toward the center of the particular heavenly body on which we happen to be located. It is so with every concept we have. No matter how intrinsic a part of nature and of our being a certain notion may seem, we can never know that new facts will not develop which will show it to be a mistaken one. Today we are merely confronted by a gigantic example of this sort of thing. Einstein tells us that when velocities are attained which have just now come within the range of our close investigation, extraordinary things happen—things quite irreconcilable with our present concepts of time and space and mass and dimension. We are tempted to laugh at him, to tell him that the phenomena he suggests are absurd because they contradict these concepts. Nothing could be more rash than this.

When we consider the results which follow from physical velocities comparable with that of light, we must confess that here are conditions which have never before been carefully investigated. We must be quite as well prepared to have these conditions reveal some epoch-making fact as was Galileo when he turned the first telescope upon the skies. And if this fact requires that we discard present ideas of time and space and mass and dimension, we must be prepared to do so quite as thoroughly as our medieval fathers had to discard their notions of celestial “perfection” which demanded that there be but seven major heavenly bodies and that everything center about the earth as a common universal hub. We must be prepared to revise our concepts of these or any other fundamentals quite as severely as did the first philosopher who realized that “down” in London was not parallel to “down” in Bagdad or on Mars.]*

[In all ordinary terrestrial matters we take the earth as a fixed body, light as instantaneous. This is perfectly proper, for such matters. But we carry our earth-acquired habits with us into the celestial regions. Though we have no longer the earth to stand on, yet we assume, as on the earth, that all measurements and movements must be referred to some fixed body, and are only then valid. We cling to our earth-bound notion that there is an absolute up-and-down, back-and-forth, right-and-left, in space. We may admit that we can never find it, but we still think it is there, and seek to approach it as nearly as possible. And similarly from our earth experiences, which are sufficiently in a single place to make possible this simplifying assumption, we get the idea that there is one universal time, applicable at once to the entire universe.]^[141] [The difficulty in accepting Einstein is entirely the difficulty in getting away from these earth-bound habits of thought.]*

IV

THE SPECIAL THEORY OF RELATIVITY

What Einstein’s Study of Uniform Motion Tells Us About Time and Space and the Nature of the External Reality

BY VARIOUS CONTRIBUTORS AND THE EDITOR

Whatever the explanation adopted for the negative result of the Michelson-Morley experiment, one thing stands out clearly: the attempt to isolate absolute motion has again failed.]* [Einstein generalizes this with all the other and older negative results of similar sort into a negative deduction to the effect that no experiment is possible upon two systems which will determine that one of them is in motion and the other at rest.]^[121] [He elevates the repeated failure to detect absolute motion through space into the principle that experiment will never reveal anything in the nature of absolute velocities. He postulates that all laws of nature can and should be enunciated in such forms that they are as true in these forms for one observer as for another, even though these observers with their frames of reference be in motion relative to one another.]^[264]

[There are various ways of stating the principle of the relativity of uniform motion which has been thus arrived at, and which forms the basis of the Special Theory of Einstein. If we care to emphasize the rôle of mathematics and the reference frame we may say that]* [any coordinate system having a uniform rectilinear motion with respect to the bodies under observation may be interchangeably used with any other such system in describing their motions;]^[232] [or that the unaccelerated motion of a system of reference cannot be detected by observations made on this system alone.]^[194] [Or we can let this aspect of the matter go, and state the relativity postulate in a form more intelligible to the non-mathematician by simply insisting that it is impossible by any means whatever to distinguish any other than the relative motion between two systems that are moving uniformly. As Dr. Russell puts it on a later page, we can assume boldly that the universe is so constituted that uniform straight-ahead motion of an observer and all his apparatus will not produce any difference whatever in the result of any physical process or experiment of any kind.

As we have seen, this is entirely reasonable, on philosophical grounds, until we come to consider the assumptions of the past century with regard to light and its propagation. On the basis of these assumptions we had expected the Michelson-Morley experiment to produce a result negativing the notion of universal relativity. It refused to do this, and we agree with Einstein that the best explanation is to return to the notion of relativity, rather than to invent a forced and special hypothesis to account for the experiment’s failure. But we must now investigate the assumptions underlying the theory of light, and remove the one that requires the ether to serve as a universal standard of absolute motion.

Light and the Ether

It is among the possibilities that the wave theory of light itself will in the end be more or less seriously modified. It is even more definitely among the possibilities that the ether will be discarded.]* [Certainly when Lord Kelvin estimates that its mass per cubic centimeter is .000,000,000,000,000,001 gram, while Sir Oliver Lodge insists that the correct figure is 1,000,000,000,000,000 grams, it is quite evident that we know so little about it that it is better to get along without it if we can.]^[216] [But to avoid confusion we must emphasize that Einstein makes no mention whatsoever of the ether; his theory is absolutely independent of any theory of the ether.]^[139] [Save as he forbids us to employ the ether as a standard of absolute motion, Einstein does not in the least care what qualities we assign to it, or whether we retain it at all. His demands are going to be made upon light itself, not upon the alleged medium of light transmission.

When two observers in relative motion to one another measure their velocities with respect to a third material object, they expect to get different results. Their velocities with regard to this object properly differ, for it is no more to be taken as a universal super-observer than either of them. But if they get different results when they come to measure the velocity with which light passes their respective systems, relativity is challenged. Light is with some propriety to be regarded as a universal observer; and if it will measure our velocities against each other we cannot deny it rank as an absolute standard. If we are not prepared to abandon universal relativity, and adopt one of the “fluke” explanations for the Michelson-Morley result, we must boldly postulate that in free space light presents the same velocity C to all observers—whatever the source of the light, whatever the relative motion between source and observer, whatever the relative motion between the several observers. The departure here from the old assumption lies in the circumstance that the old physics with its ether assigned to light a velocity universally constant in this ether; we have stopped talking about the medium and have made the constant C refer to the observer’s measured value of the velocity of light with regard to himself.

We are fortified in this assumption by the Michelson-Morley result and by all other observations bearing directly upon the matter. Nevertheless, as Mr. Francis says in his essay, we feel instinctively that space and time are not so constituted as to make it possible, if I pass you at 100 miles per hour, for the same light-impulse to pass us both at the same speed C.]* [The implicit assumptions underlying this feeling, be they true or false, are now so interwoven with the commonly received notions of space and time that any theory which questions them has all the appearance of a fantastic and unthinkable thing.]^[115] [We cannot, however, go back on our relativity; so when]* [Einstein shows us that an entirely new set of time and space concepts is necessary to reconcile universe relativity with this fundamental fact of the absolute constancy of the observed velocity of light in vacuo,]^[18] [all that is left for us to do is to inquire what revisions are necessary, and submit to them.]*

[The conceptual difficulties of the theory arise principally from attributing to space and time the properties of things. No portion of space can be compared with another, save by convention; it is things which we compare. No interval of time can be compared with another, save by convention. The first has gone when the second becomes “now”.]^[149] [It is events that we compare, through the intervention of things. Our measurements are never of space or of time, but only of the things and the events that occupy space and time. And since the measurements which we deal with as though they were of space and of time lie at the foundation of all physical science, while at the same time themselves constituting, as we have seen, the only reality of which we are entitled to speak, it is in order to examine with the utmost care the assumptions underlying them. That there are such assumptions is clear—the very possibility of making measurements is itself an assumption, and every technique for carrying them out rests on an assumption. Let us inquire which of these it is that relativity asks us to revise.]*

The Measurement of Time and Space

[Time is generally conceived as perfectly uniform. How do we judge about it? What tells us that the second just elapsed is equal to the one following? By the very nature of time the superposition of its successive intervals is impossible. How then can we talk about the relative duration of these intervals? It is clear that any relationship between them can only be conventional.]^[178] [As a matter of fact, we habitually measure time in terms of moving bodies. The simplest method is to agree that some entity moves with uniform velocity. It will be considered as travelling equal distances in equal intervals of time, the distances to be measured as may be specified by our assumptions governing this department of investigation.]^[179] [The motions of the earth through which we ultimately define the length of day and year, the division of the former into 86,400 “equal” intervals as defined by the motions of pendulum or balance wheel through equal distances, are examples of this convention of time measurement. Even when we correct the motions of the earth, on the basis of what our clocks tell us of these motions, we are following this lead; the earth and the clocks fall out, it is plain that one of them does not satisfy our assumption of equal lengths in equal times, and we decide to believe the clock.]*

[The foregoing concerning time may be accepted as inherent in time itself. But concerning lengths it may be thought that we are able to verify absolutely their equality and especially their invariability. Let us have the audacity to verify this statement. We have two lengths, in the shape of two rods, which coincide perfectly when brought together. What may we conclude from this coincidence? Only that the two rods so considered have equal lengths at the same place in space and at the same moment. It may very well be that each rod has a different length at different locations in space and at different times; that their equality is purely a local matter. Such changes could never be detected if they affected all objects in the universe. We cannot even ascertain that both rods remain straight when we transport them to another location, for both can very well take the same curvature and we shall have no means of detecting it.

Euclidean geometry assumes that geometrical objects have sizes and shapes independent of position and of orientation in space, and equally invariable in time. But the properties thus presupposed are only conventional and in no way subject to direct verification. We cannot even ascertain space to be independent of time, because when comparing geometrical objects we have to conceive them as brought to the same place in space and in time.]^[178] [Even the statement that when they are made to coincide their lengths are equal is, after all, itself an assumption inherent in our ideas of what constitutes length. And certainly the notion that we can shift them from place to place and from moment to moment, for purposes of comparison, is an assumption; even Euclid, loose as he was from modern standards in this business of “axioms,” knew this and included a superposition axiom among his assumptions.

As a matter of fact, this procedure for determining equality of lengths is not always available. It assumes, it will be noted, that we have free access to the object which is to be measured—which is to say, it assumes that this object is at rest with respect to us. If it is not so at rest, we must employ at least a modification of this method; a modification that will in some manner involve the sending of signals. Even when we employ the Euclidean method of superposition directly, we must be assured that the respective ends of the lengths under comparison coincide at the same time. The observer cannot be present at both ends simultaneously; at best he can only be present at one end and receive a signal from the other end.

The Problem of Communication

Accordingly, in making the necessary assumptions to cover the matter of measuring lengths, we must make one with regard to the character of the signals which are to be employed for this purpose. If we could assume a system of signalling that would consume no time in transmission all would be simple enough. But we have no experience with such a system. Even if we believe that it ought to be possible thus to transmit signals at infinite velocity, we may not, in the absence of our present ability to do this, assume that it is possible. So we may only assume, with Einstein, that for our signals we shall employ the speediest messenger with which we are at present acquainted. This of course is light, the term including any of the electromagnetic impulses that travel at the speed C.

Of course in the vast majority of cases the distance that any light signal in which we are interested must go to reach us is so small that the time taken by its transmission can by no means be measured. We are then, to all intents and purposes, at both places—the point of origin of the signal and the point of receipt—simultaneously. But this is not the question at all. Waiving the fact that in astronomical investigations this approximation no longer holds, the fact remains that it is, in every case, merely an approximation. Approximations are all right in observations, where we know that they are approximations and act accordingly. But in the conceptual universe that parallels the external reality, computation is as good an agent of observation as visual or auditory or tactile sensation; if we can compute the error involved in a wrong procedure the error is there, regardless of whether we can see it or not. We must have methods which are conceptually free from error; and if we attempt to ignore the velocity of our light signals we do not meet this condition.

The measurement of lengths demands that we have a criterion of simultaneity between two remote points—remote in inches or remote in light-years, it does not matter which. There is no difficulty in defining simultaneity of two events that fall in the same point—or rather, in agreeing that we know what we mean by such simultaneity. But with regard to two events that occur in remote places there may be a question. A scientific definition differs from a mere description in that it must afford us a means of testing whether a given item comes under the definition or not. There is some difficulty in setting up a definition of simultaneity between distant events that satisfies this requirement. If we try simply to fall back upon our inherent ideas of what we mean by “the same instant” we see that this is not adequate. We must lay down a procedure for determining whether two events at remote points occur at “the same instant,” and check up alleged simultaneity by means of this procedure.

Einstein says, and we must agree with him, that he can find but one reasonable definition to cover this ground. An observer can tell whether he is located half way between two points of his observation; he can have mirrors set up at these points, send out light-signals, and note the time at which he gets back the reflection. He knows that the velocity of both signals, going and coming, is the same; if he observes that they return to him together so that their time of transit for the round trip is the same, he must accept the distances as equal. He is then at the mid-point of the line joining the two points under observation; and he may define simultaneity as follows, without introducing anything new or indeterminate: Two events are simultaneous if an observer midway between them sees them at the same instant, by means, of course, of light originating at the points of occurrence.]*

[It is this definition of simultaneity, coupled with the assumption that all observers, on whatever uniformly moving systems, would obtain the same experimental value for the velocity of light, that leads to the apparent paradoxes of the Special Theory of Relativity. If it be asked why we adopt it, we must in turn ask the inquirer to propose a better system for defining simultaneous events on different moving bodies.]^[198]

[There is nothing in this definition to indicate, directly, whether simultaneity persists for all observers, or whether it is relative, so that events simultaneous to one observer are not so to another. The question must then be investigated; and the answer, of course, will hinge upon the possibility of making proper allowances for the time of transit of the light signals that may be involved. It seems as though this ought to be possible; but a simple experiment will indicate that it is not, unless the observers involved are at rest with respect to one another.

An Einsteinian Experiment

Let us imagine an indefinitely long, straight railroad track, with an observer located somewhere along it at the point M. According to the convention suggested above, he has determined points A and B in opposite directions from him along the

track, and equally distant from him. We shall imagine, further, than a beneficent Providence supplies two lightning flashes, one striking at A and one at B, in such a way that observer M finds them to be simultaneous.

While all this is going on, a train is passing—a very long train, amply long enough to overlap the section AMB of the track. Among the passengers there is one, whom we may call M′, who is directly opposite M at the instant when, according to M, the lightning strikes. Observe he is not opposite M when M sees the flashes, but a brief time earlier—at the instant when, according to M’s computation, the simultaneous flashes occurred. At this instant there are definitely determined the points A′ and B′, on the train; and since we may quite well think of the two systems—train-system and track-system—as in coincidence at this instant, M′ is midway between A′ and B′, and likewise is midway between A and B.

Now if we think of the train as moving over the track in the direction of the arrow, we see very easily that M′ is running away from the light from A and toward that from B, and that, despite—or if you prefer because of—the uniform velocity of these light signals, the one from B reaches him, over a slightly shorter course, sooner than the one from A, over the slightly longer course. When the light signals reach M, M′ is no longer abreast of him but has moved along a wee bit, so that at this instant when M has the two signals, one of these has passed M′ and the other has yet to reach him. The upshot is that the events which were simultaneous to M are not so to M′.

It will probably be felt that this result is due to our having, somewhat unjustifiably and inconsistently, localized on the train the relative motion between train and track. But if we think of the track as sliding back under the train in the direction opposite to the arrow, and carrying with it the points A and B; and if we remember that this in no way affects M’s observed velocity of light or the distances AM and BM as he observes them: we can still accept his claim that the flashes were simultaneous. Then we have again the same situation: when the flashes from A and from B reach M at the same moment, in his new position a trifle to the left of his initial position of the diagram, the flash from A has not yet reached M′ in his original position while that from B has passed him. Regardless of what assumption we make concerning the motion between train-system and track-system, or more elegantly regardless of what coordinate system we use to define that motion, the event at B precedes that at A in the observation of M′. If we introduce a second train moving on the other track in the opposite direction, the observer on it will of course find that the flash at A precedes that at B—a disagreement not merely as to simultaneity but actually as to the order of two events! If we conceive the lightning as striking at the points A′ and B′ on the train, these points travel with M′ instead of with M; they are fixed to his coordinate system instead of to the other. If you carry out the argument now, you will find that when the flashes are simultaneous to M′, the one at A precedes that at B in M’s observation.

A large number of experiments more or less similar in outline to this one can be set up to demonstrate the consequences, with regard to measured values of time and space, of relative motion between two observers. I do not believe that a multiplicity of such demonstrations contributes to the intelligibility of the subject, and it is for this reason that I have cut loose from immediate dependence upon the essayists in this part of the discussion, concentrating upon the single experiment to which Einstein himself gives the place of importance.

Who Is Right?

We may permit Mr. Francis to remind us here that neither M nor M′ may correct his observation to make it accord with the other fellow’s. The one who does this is admitting that the other is at absolute rest and that he is himself in absolute motion; and this cannot be. They are simply in disagreement as to the simultaneity of two events, just as two observers might be in disagreement about the distance or the direction of a single event. This can mean nothing else than that, under the assumptions we have made, simultaneity is not an absolute characteristic as we had supposed it to be, but, like distance and direction, is in fact merely a relation between observer and objective, and therefore depends upon the particular observer who happens to be operating and upon the reference frame he is using.

But this is serious. My time measurements depend ultimately upon my space measurements; the latter, and hence both, depend closely upon my ideas of simultaneity. Yours depend upon your reading of simultaneity in precisely the same way.]* [Suppose the observer on the track, in the above experiment, wants to measure the length of something on the car, or the observer on the car something on the track. The observer, or his assistant, must be at both ends of the length to be measured at the same time, or get simultaneous reports in some way from these ends; else they will obtain false results. It is plain, then, that with different criteria of what the “same time” is, the observers in the two systems may get different values for the measured lengths in question.]^[220]