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 — Edition Insights

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:

10: Frederick W. Shurlock, Derby, England. 18: L. L. Whyte, Cambridge, England. 24: Prof. Moritz Schlick, University of Rostock, Germany. 30: C. E. Rose, M.E., Little Rock, Ark. 33: H. Gartelmann, Bremen, Germany. 35: Prof. Joseph S. Ames, Johns Hopkins University, Baltimore. 47: James O. G. Gibbons, East Orange. N. J. 82: Charles H. Burr, Philadelphia. 101: L. F. H. de Miffonis. B.A., C.E., Ottawa, Canada. 102: Charles A. Brunn, Kansas City. 106: J. Elias Fries, Fellow A.I.E.E., Birmingham, Ala. 114: Dean W. P. Graham, Syracuse University, Syracuse, N. Y. 115: Rev. George Thomas Manley, London. 116: Prof. J. A. Schouten, Delft, Netherlands. 121: Elwyn F. Burrill, Berkeley, Cal. 125: Dorothy Burr, Bryn Mawr, Pa. 130: C. W. Kanolt, Bureau of Standards, Washington. 135: Robert Stevenson, New York. 139: Leopold Schorsch, New York. 141: Dr. M. C. Mott-Smith, Los Angeles, Calif. 147: Edward A. Clarke, Columbus, O. 149: Edward A. Partridge, Philadelphia. 150: Col. John Millis, U. S. A., Chicago. 152: George F. Marsteller, Detroit. 156: D. B. Hall, Cincinnati. 165: Francis Farquhar, York, Pa. 178: Dr. George de Bothezat, Dayton, O. 179: Professor A. E. Caswell, University of Oregon, Eugene, Ore. 182: C. E. Dimick, New London, Conn. 186: Earl R. Evans, Washington, D. C. 188: Norman E. Gilbert, Dartmouth College, Hanover, N. H. 192: A. d'Abro. New York. 194: L. M. Alexander, Cincinnati. 197: Kenneth W. Reed, East Cleveland, O. 198: Prof. E. N. da C. Andrade, Ordnance College, Woolwich, England. 216: Professor Andrew H. Patterson, University of North Carolina, Chapel Hill, N. C. 220: Prof. Arthur Gordon Webster, Clark College, Worcester, Mass. 221: Walter van B. Roberts, Princeton University, N. J. 223: Paul M. Batchelder, Austin, Tex. 227: Prof. R. W. Wood, Johns Hopkins University, Baltimore. 229: E. P. Fairbairn, M.C., B.Sc., Glasgow. 231: R. F. Deimel, Hoboken, N. J. 232: Lieut. W. Mark Angus, U. S. N., Philadelphia. 235: Edward Adams Richardson, Kansas City. 263: Prof. William Benjamin Smith, Tulane University, New Orleans. 264: James Rice, University of London, London. 267: William Hemmenway Pratt, Lynn, Mass. 272: R. Bruce Lindsay, New Bedford, Mass. 283: Frank E. Law, Montclair, N. J.

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.

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

THE EINSTEIN $5,000 PRIZE

HOW THE CONTEST CAME TO BE HELD, AND SOME OF THE DETAILS OF ITS CONDUCT

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.