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

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.