Einstein and the Universe: a Popular Exposition of the Famous Theory

CHAPTER VI. The New Conception of Gravitation

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?

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

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?

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

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. 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.

Albert Einstein, born in 1879, is a German Jew of Würtemberg. He studied in Switzerland, and was an engineer there until 1909, when he became professor at Zurich University. In 1911 he passed to Prague University, in 1912 to the Zurich Polytechnic, and in 1914 to the Prussian Academy of Science. He refused to give his name to the manifesto in which ninety-three professors of Germany and Austria defended Germany’s war-action.—Trans.

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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.

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