Einstein and the universe E-Book

Charles Nordmann

• Herausgeber: Librorium Editions
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2023

Beschreibung

Have you read Baruch?” La Fontaine used to cry, enthusiastically. To-day he would have troubled his friends with the question “Have you read Einstein?”
But, whereas one needs only a little Latin to gain access to Spinoza, frightful monsters keep guard before Einstein, and their horrible grimaces seem to forbid us to approach him. They stand behind strange moving bars, sometimes rectangular and sometimes curvilinear, which are known as “co-ordinates.” They bear names as frightful as themselves—“contravariant and covariant vectors, tensors, scalars, determinants, orthogonal vectors, generalised symbols of three signs,” and so on.
These strange beings, brought from the wildest depths of the mathematical jungle, join together or part from each other with a remarkable promiscuity, by means of some astonishing surgery which is called integration and differentiation.
In a word, Einstein may be a treasure, but there is a fearsome troop of mathematical reptiles keeping inquisitive folk away from it; though there can be no doubt that they have, like our Gothic gargoyles, a hidden beauty of their own. Let us, however, drive them off with the whip of simple terminology, and approach the splendour of Einstein’s theory.

Leseprobe

EINSTEIN AND THE UNIVERSE

A Popular Exposition of the Famous Theory

By CHARLES NORDMANN

Astronomer to the Paris Observatory.

Translated by JOSEPH McCABE

1922

© 2023 Librorium Editions

ISBN : 9782383839767

PREFACE

A distinguished German authority on mathematical physics, writing recently on the theory of Relativity, declared that if his publishers had been willing to allow him sufficient paper and print he could have explained what he wished to convey without using a single mathematical formula. Such success is conceivable. Mathematical methods present, however, two advantages. Their terminology is precise and concentrated, in a fashion which ordinary language cannot afford to adopt. Further, the symbols which result from their employment have implications which, when brought to light, yield new knowledge. This is deductively reached, but it is none the less new knowledge. With greater precision than is usual, ordinary language may be made to do some, if not a great deal, of this work for which mathematical methods are alone quite appropriate. If ordinary language can do part of it an advantage may be gained. The difficulty that attends mathematical symbolism is the accompanying tendency to take the symbol as exhaustively descriptive of reality. Now it is not so descriptive. It always embodies an abstraction. It accordingly leads to the use of metaphors which are inadequate and generally untrue. It is only qualification by descriptive language of a wider range that can keep this tendency in check. A new school of mathematical physicists, still, however, small in number, is beginning to appreciate this.

But for English and German writers the new task is very difficult. Neither Anglo-Saxon nor Saxon genius lends itself readily in this direction. Nor has the task as yet been taken in hand completely, so far as I am aware, in France. Still, in France there is a spirit and a gift of expression which makes the approach to it easier than either for us or for the Germans. Lucidity in expression is an endowment which the best French writers possess in a higher degree than we do. Some of us have accordingly awaited with deep interest French renderings of the difficult doctrine of Einstein.

M. Nordmann, in addition to being a highly qualified astronomer and mathematical-physicist, possesses the gift of his race. The Latin capacity for eliminating abstractness from the description of facts is everywhere apparent in his writing. Individual facts take the places of general conceptions, of Begriffe. The language is that of the Vorstellung, in a way that would hardly be practicable in German. Nor is our own language equal to that of France in delicacy of distinctive description. This book could hardly have been written by an Englishman. But the difficulty in his way would have been one as much of spirit as of letter. It is the lucidity of the French author, in combination with his own gift of expression, that has made it possible for the translator to succeed so well in overcoming the obstacles to giving the exposition in our own tongue this book contains. The rendering seems to me, after reading the book both in French and in English, admirable.

M. Nordmann has presented Einstein’s principle in words which lift the average reader over many of the difficulties he must encounter in trying to take it in. Remembering Goethe’s maxim that he who would accomplish anything must limit himself, he has not aimed at covering the full field to which Einstein’s teaching is directed. But he succeeds in making many abstruse things intelligible to the layman. Perhaps the most brilliant of his efforts in this direction are Chapters V and VI, in which he explains with extraordinary lucidity the new theory of gravitation and of its relation to inertia. I think that M. Nordmann is perhaps less successful in the courageous attack he makes in his third chapter on the obscurity which attends the notion of the “Interval.” But that is because the four-dimensional world, which is the basis of experience of space and time for Einstein and Minkowski, is in itself an obscure conception. Mathematicians talk about it gaily and throw its qualities into equations, despite the essential exclusion from it of the measurement and shape which actual experience always in some form involves. They lapse on that account into unconscious metaphysics of a dubious character. This does not destroy the practical value of their equations, but it does make them very unreliable as guides to the character of reality in the meaning which the plain man attaches to it. Here, accordingly, we find the author of this little treatise to be a good man struggling with adversity. If he could make the topic clear he would. But then no one has made it clear excepting as an abstraction which works, but which, despite suggestions made to the contrary, cannot be clothed for us in images.

This, however, is the fault, not of M. Nordmann himself, but of a phase of the subject. With the subject in its other aspects he deals with the incomparable lucidity of a Frenchman. I know no book better adapted than the one now translated to give the average English reader some understanding of a principle, still in its infancy, but destined, as I believe, to transform opinion in more regions of knowledge than those merely of mathematical physics.

Haldane

CONTENTS

Preface by the Rt. Hon. Viscount Haldane, O.M.

pp. 5-8

Introduction

pp. 13-15

CHAPTER I THE METAMORPHOSES OF SPACE AND TIME

Removing the mathematical difficulties—The pillars of knowledge—Absolute time and space, from Aristotle to Newton—Relative time and space, from Epicurus to Poincaré and Einstein— Classical Relativity—Antinomy of stellar aberration and the Michelson experiment

pp. 17-31

CHAPTER II SCIENCE IN A NO-THOROUGHFARE

Scientific truth and mathematics—The precise function of Einstein—Michelson’s experiment, the Gordian knot of science—The hesitations of Poincaré—The strange, but necessary, Fitzgerald-Lorentz hypothesis—The contraction of moving bodies—Philosophical and physical difficulties

pp. 32-52

CHAPTER III EINSTEIN’S SOLUTION

Provisional rejection of ether—Relativist interpretation of Michelson’s experiment—New aspect of the speed of light—Explanation of the contraction of moving bodies—Time and the four dimensions of space—Einstein’s “Interval” the only material reality

pp. 53-72

CHAPTER IV EINSTEIN’S MECHANICS

The mechanical foundation of all the sciences— Ascending the stream of time—The speed of light an impassable limit—The addition of speeds and Fizeau’s experiment—Variability of mass— The ballistics of electrons—Gravitation and light as atomic microcosms—Matter and energy— The death of the sun

pp. 73-100

CHAPTER V GENERALISED RELATIVITY

Weight and inertia—Ambiguity of the Newtonian law—Equivalence of gravitation and accelerated movement—Jules Verne’s projectile and the principle of inertia—Why rays of light are subject to gravitation—How light from the stars is weighed—An eclipse as a source of light

pp. 101-123

CHAPTER VI THE NEW CONCEPTION OF GRAVITATION

Geometry and reality—Euclid’s geometry and others—Contingency of Poincaré’s criterion— The real universe is not Euclidean but Riemannian— The avatars of the number π—The point of view of the drunken man—Straight and geodetic lines—The new law of universal attraction—Explanation of the anomaly of the planet Mercury—Einstein’s theory of gravitation

pp. 124-147

CHAPTER VII IS THE UNIVERSE INFINITE?

Kant and the number of the stars—Extinct stars and dark nebulæ—Extent and aspect of the astronomical universe—Different kinds of universes—Poincaré’s calculation—Physical definition of the infinite— The infinite and the unlimited—Stability and curvature of cosmic space-time—Real and virtual stars—Diameter of the Einsteinian universe— The hypothesis of globes of ether

pp. 148-159

CHAPTER VIII SCIENCE AND REALITY

The Einsteinian absolute—Revelation by science— Discussion of the experimental bases of Relativity— Other possible explanations—Arguments in favour of Lorentz’s real contraction—Newtonian space may be distinct from absolute space—The real is a privileged form of the possible—Two attitudes in face of the unknown

pp. 160-172

CHAPTER IX EINSTEIN OR NEWTON?

Recent discussion of Relativism at the Academy of Sciences—Traces of the privileged space of Newton—The principle of causality, the basis of science—Examination of M. Painlevé’s objections—Newtonian arguments and Relativist replies—M. Painlevé’s formulas of gravitation—Fecundity of Einstein’s theory— Two conceptions of the world—Conclusion

pp. 173-185

INTRODUCTION

This book is not a romance. Nevertheless.... If love is, as Plato says, a soaring toward the infinite, where shall we find more love than in the impassioned curiosity which impels us, with bowed heads and beating hearts, against the wall of mystery that environs our material world? Behind that wall, we feel, there is something sublime. What is it? Science is the outcome of the search for that mysterious something.

A giant blow has recently been struck, by a man of consummate ability, Albert Einstein, upon this wall which conceals reality from us. A little of the light from beyond now comes to us through the breach he has made, and our eyes are enchanted, almost dazzled, by the rays. I propose here to give, as simply and clearly as is possible, some faint reflex of the impression it has made upon us.

Einstein’s theories have brought about a profound revolution in science. In their light the world seems simpler, more co-ordinated, more in unison. We shall henceforward realise better how grandiose and coherent it is, how it is ruled by an inflexible harmony. A little of the ineffable will become clearer to us.

Men, as they pass through the universe, are like those specks of dust which dance for a moment in the golden rays of the sun, then sink into the darkness. Is there a finer or nobler way of spending this life than to fill one’s eyes, one’s mind, one’s heart with the immortal, yet so elusive, rays? What higher pleasure can there be than to contemplate, to seek, to understand, the magnificent and astounding spectacle of the universe?

There is in reality more of the marvellous and the romantic than there is in all our poor dreams. In the thirst for knowledge, in the mystic impulse which urges us toward the deep heart of the Unknown, there is more passion and more sweetness than in all the trivialities which sustain so many literatures. I may be wrong, after all, in saying that this book is not a romance.

I will endeavour in these pages to make the reader understand, accurately, yet without the aid of the esoteric apparatus of the technical writer, the revolution brought about by Einstein. I will try also to fix its limits; to state precisely what, at the most, we can really know to-day about the external world when we regard it through the translucent screen of science.

Every revolution is followed by a reaction, in virtue of the rhythm which seems to be an inherent and eternal law of the mind of man. Einstein is at once the Sieyès, the Mirabeau, and the Danton of the new revolution. But the revolution has already produced its fanatical Marats, who would say to science: “Thus far and no farther.”

Hence we find some resistance to the pretensions of over-zealous apostles of the new scientific gospel. In the Academy of Sciences M. Paul Painlevé takes his place, with all the strength of a vigorous mathematical genius, between Newton, who was supposed to be overthrown, and Einstein. In my final pages I will examine the penetrating criticisms of the great French geometrician. They will help me to fix the precise position, in the evolution of our ideas, of Einstein’s magnificent synthesis. But I would first expound the synthesis itself with all the affection which one must bestow upon things that one would understand.

Science has not completed its task with the work of Einstein. There remains many a depth that is for us unfathomable, waiting for some genius of to-morrow to throw light into it. It is the very essence of the august and lofty grandeur of science that it is perpetually advancing. It is like a torch in the sombre forest of mystery. Man enlarges every day the circle of light which spreads round him, but at the same time, and in virtue of his very advance, he finds himself confronting, at an increasing number of points, the darkness of the Unknown. Few men have borne the shaft of light so deeply into the forest as has Einstein. In spite of the sordid cares which harass us to-day, amid so many grave contingencies, his system reveals to us an element of grandeur.

Our age is like the noisy and unsubstantial froth that crowns, and hides for a moment, the gold of some generous wine. When all the transitory murmur that now fills our ears is over, Einstein’s theory will rise before us as the great lighthouse on the brink of this sad and petty twentieth century of ours.

Charles Nordmann.

EINSTEIN AND THE UNIVERSE

CHAPTER I

THE METAMORPHOSES OF SPACE AND TIME

Removing the mathematical difficulties—The pillars of knowledge—Absolute time and space, from Aristotle to Newton—Relative time and space, from Epicurus to Poincaré and Einstein—Classical Relativity—Antinomy of stellar aberration and the Michelson experiment.

“Have you read Baruch?” La Fontaine used to cry, enthusiastically. To-day he would have troubled his friends with the question “Have you read Einstein?”

But, whereas one needs only a little Latin to gain access to Spinoza, frightful monsters keep guard before Einstein, and their horrible grimaces seem to forbid us to approach him. They stand behind strange moving bars, sometimes rectangular and sometimes curvilinear, which are known as “co-ordinates.” They bear names as frightful as themselves—“contravariant and covariant vectors, tensors, scalars, determinants, orthogonal vectors, generalised symbols of three signs,” and so on.

These strange beings, brought from the wildest depths of the mathematical jungle, join together or part from each other with a remarkable promiscuity, by means of some astonishing surgery which is called integration and differentiation.

In a word, Einstein may be a treasure, but there is a fearsome troop of mathematical reptiles keeping inquisitive folk away from it; though there can be no doubt that they have, like our Gothic gargoyles, a hidden beauty of their own. Let us, however, drive them off with the whip of simple terminology, and approach the splendour of Einstein’s theory.

Who is this physicist Einstein? That is a question of no importance here. It is enough to know that he refused to sign the infamous manifesto of the professors, and thus brought upon himself persecution from the Pan-Germanists.[1] Mathematical truths and scientific discoveries have an intrinsic value, and this must be judged and appreciated impartially, whoever their author may chance to be. Had Pythagoras been the lowest of criminals, the fact would not in the least detract from the validity of the square of the hypotenuse. A theory is either true or false, whether the nose of its author has the aquiline contour of the nose of the children of Sem, or the flattened shape of that of the children of Cham, or the straightness of that of the children of Japhet. Do we feel that humanity is perfect when we hear it said occasionally: “Tell me what church you frequent, and I will tell you if your geometry is sound.” Truth has no need of a civil status. Let us get on.

All our ideas, all science, and even the whole of our practical life, are based upon the way in which we picture to ourselves the successive aspects of things. Our mind, with the aid of our senses, chiefly ranges these under the headings of time and space, which thus become the two frames in which we dispose all that is apparent to us of the material world. When we write a letter, we put at the head of it the name of the place and the date. When we open a newspaper, we find the same indications at the beginning of each piece of telegraphic news. It is the same in everything and for everything. Time and space, the situation and the period of things, are thus seen to be the twin pillars of all knowledge, the two columns which sustain the edifice of men’s understanding.

So felt Leconte de Lisle when, addressing himself to “divine death,” he wrote, in his profound, philosophic way:

Free us from time, number, and space:

Grant us the rest that life hath spoiled.

He inserts the word “number” only in order to define time and space quantitatively. What he has finely expressed in these famous and superb lines is the fact that all that there is for us in this vast universe, all that we know and see, all the ineffable and agitated flow of phenomena, presents to us no definite aspect, no precise form, until it has passed through those two filters which are interposed by the mind, time and space.

The work of Einstein derives its importance from the fact that he has shown, as we shall see, that we have entirely to revise our ideas of time and space. If that is so, the whole of science, including psychology, will have to be reconstructed. That is the first part of Einstein’s work, but it goes further. If that were the whole of his work it would be merely negative.