Einstein and the universe E-Book

Nordmann Charles

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• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 227

Veröffentlichungsjahr: 2022

Beschreibung

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.

Leseprobe

Einstein and the universe

Einstein and the universePREFACEINTRODUCTIONCHAPTER ICHAPTER IICHAPTER IIICHAPTER IVCHAPTER VCHAPTER VICHAPTER VIICHAPTER VIIICHAPTER IXFootnotes:Copyright

Einstein and the universe

Charles Nordmann

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 incheck. 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, ofBegriffe. The language is that of theVorstellung, 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 ChaptersVandVI, 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 histhird chapteron 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 phaseof 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

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 thanto 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 penetratingcriticisms 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.

CHAPTER I

THE METAMORPHOSES OFSPACE AND TIMERemoving 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 calledintegrationanddifferentiation.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.Once he had removed from the structure of human knowledge what had been regarded as an indispensable wall of it, though it was really only a frail scaffolding that hid the harmony of its proportions, he began to reconstruct. He made in the structure large windows which allow us now to see the treasures it contains. In a word, Einstein showed, on the one hand, with astonishing acuteness and depth, that the foundation of our knowledge seems to be different from what we had thought, and that it needs repairing with a new kind of cement. On the other hand, he has reconstructed the edifice on this new basis, and he has given it a bold and remarkably beautiful and harmonious form.I have now to show in detail, concretely, and as accurately as possible, the meaning of these generalities. But I must first insist on a point which is of considerable importance: if Einstein had confined himself to the first part of his work, as I have described it, the part which shatters the classical ideas of time and space, he would never have attained the fame which now makes his name great in the world of thought.The point is important because most of those—apart from experts—who have written on Einstein have chiefly, often exclusively, emphasised this more or less “destructive” side of his work. But, as we shall see, from this point of view Einstein was not the first, and he is not alone. All that he has done is to sharpen, and press a little deeper between the badly joined stones of classical science, a chisel which others, especially the great Henri Poincaré, had used long before him. My next point is to explain, if I can, the real, the immortal, title ofEinstein to the gratitude of men: to show how he has by his own powers rebuilt the structure in a new and magnificent form after his critical work. In this he shares his glory with none.The whole of science, from the days of Aristotle until our own, has been based upon the hypothesis—properly speaking, the hypotheses—that there is an absolute time and an absolute space. In other words, our ideas rested upon the supposition that an interval of time and an interval of space between two given phenomena are always the same, for every observer whatsoever, and whatever the conditions of observation may be. For instance, it would never have occurred to anybody as long as classical science was predominant, that the interval of time, the number of seconds, which lies between two successive eclipses of the sun, may not be the fixed and identically same number of seconds for an observer on the earth as for an observer in Sirius (assuming that the second is defined for both by the same chronometer). Similarly, no one would have imagined that the distance in metres between two objects, for instance the distance of the earth from the sun at a given moment, measured by trigonometry, may not be the same for an observer on the earth as for an observer in Sirius (the metre being defined for both by the same rule). “ There is,” says Aristotle, “one single and invariable time, which flows in two movements in an identical and simultaneous manner; and if these two sorts of time were not simultaneous, they would nevertheless be of the same nature.... Thus, in regard to movements which take place simultaneously, there is one and the same time, whether or no the movements are equal in rapidity; and this is true even if one of them isa local movement and the other an alteration.... It follows that even if the movements differ from each other, and arise independently, the time is absolutely the same for both.”[2]This Aristotelic definition of physical time is more than two thousand years old, yet it clearly represents the idea of time which has been used in classic science, especially in the mechanics of Galileo and Newton, until quite recent years.It seems, however, that in spite of Aristotle, Epicurus outlined the position which Einstein would later adopt in antagonism to Newton. To translate liberally the words in which Lucretius expounds the teaching of Epicurus: “ Time has no existence of itself, but only in material objects, from which we get the idea of past, present, and future. It is impossible to conceive time in itself independently of the movement or rest of things.”[3]Both space and time have been regarded by science ever since Aristotle as invariable, fixed, rigid, absolute data. Newton thought that he was saying something obvious, a platitude, when he wrote in his celebrated Scholion: “Absolute, true, and mathematical time, taken in itself and without relation to any material object, flows uniformly of its own nature.... Absolute space, on the other hand, independent by its own nature of any relation to external objects, remains always unchangeable and immovable.”The whole of science, the whole of physics and mechanics, as they are still taught in our colleges and in most of our universities, are based entirely upon these propositions, these ideas of an absolute time andspace, taken by themselves and without any reference to an external object, independent by their very nature.In a word—if I may venture to use this figure—time in classical science was like a river bearing phenomena as a stream bears boats, flowing on just the same whether there were phenomena or not. Space, similarly, was rather like the bank of the river, indifferent to the ships that passed.From the time of Newton, however, if not from the time of Aristotle, any thoughtful metaphysician might have noticed that there was something wrong in these definitions. Absolute time and absolute space are “things in themselves,” and these the human mind has always regarded as not directly accessible to it. The specifications of space and time, those numbered labels which we attach to objects of the material world, as we put labels on parcels at the station so that they may not be lost (a precaution that does not always suffice), are given us by our senses, whether aided by instruments or not, only when we receive concrete impressions. Should we have any idea of them if there were no bodies attached to them, or rather to which we attach the labels? To answer this in the affirmative, as Aristotle, Newton, and classical science do, is to make a very bold assumption, and one that is not obviously justified.The only time of which we have any idea apart from all objects is the psychological time so luminously studied by M. Bergson: a time which has nothing except the name in common with the time of physicists, of science.It is really to Henri Poincaré, the great Frenchman whose death has left a void that will never be filled, that we must accord the merit ofhaving first proved, with the greatest lucidity and the most prudent audacity, that time and space, as we know them, can only be relative. A few quotations from his works will not be out of place. They will show that the credit for most of the things which are currently attributed to Einstein is, in reality, due to Poincaré. To prove this is not in any way to detract from the merit of Einstein, for that is, as we shall see, in other fields.This is how Poincaré, whose ideas still dominate the minds of thoughtful men, though his mortal frame perished years ago, expressed himself, the triumphant sweep of his wings reaching further every day: “ One cannot form any idea of empty space.... From that follows the undeniable relativity of space. Any man who talks of absolute space uses words which have no meaning. I am at a particular spot in Paris—the Place du Panthéon, let us suppose—and I say: ‘I will come backhereto-morrow.’ If anyone asks me whether I mean that I will return to the same point in space, I am tempted to reply, ‘Yes.’ I should, however, be wrong, because between this and to-morrow the earth will have travelled, taking the Place du Panthéon with it, so that to-morrow the square will be more than 2,000,000 kilometres away from where it is now. And it would be no use my attempting to use precise language, because these 2,000,000 kilometres are part of our earth’s journey round the sun, but the sun itself has moved in relation to the Milky Way, and the Milky Way in turn is doubtless moving at a speed which we cannot learn. Thus we are entirely ignorant, and always will be ignorant, how far the Place du Panthéon shifts its position in space in a single day. What I really meant to say was: ‘To-morrow I shallagain see the dome and façade of the Panthéon.’ If there were no Panthéon, there would be no meaning in my words, and space would disappear.”Poincaré works out his idea in this way: “ Suppose all the dimensions of the universe were increased a thousandfold in a night. The world would remain the same, giving the word ‘same’ the meaning it has in the third book of geometry. Nevertheless, an object that had measured a metre in length will henceforward be a kilometre in length; a thing that had measured a millimetre will now measure a metre. The bed on which I lie and the body which lies on it will increase in size to exactly the same extent. What sort of feelings will I have when I awake in the morning, in face of such an amazing transformation? Well, I shall know nothing about it. The most precise measurements would tell me nothing about the revolution, because the tape I use for measuring will have changed to the same extent as the objects I wish to measure. As a matter of fact, there would be no revolution except in the mind of those who reason as if space were absolute. If I have argued for a moment as they do, it was only in order to show more clearly that their position is contradictory.”It would be easy to develop Poincaré’s argument. If all the objects in the universe were to become, for instance, a thousand times taller, a thousand times broader, we should be quite unable to detect it, because we ourselves—our retina and our measuring rod—would be transformed to the same extent at the same time. Indeed, if all the things in the universe were to experience an absolutely irregular spatial deformation—if some invisible and all-powerful spirit were to distortthe universe in any fashion, drawing it out as if it were rubber—we should have no means of knowing the fact. There could be no better proof that space is relative, and that we cannot conceive space apart from the things which we use to measure it. When there is no measuring rod, there is no space.Poincaré pushed his reasoning on this subject so far that he came to say that even the revolution of the earth round the sun is merely a more convenient hypothesis than the contrary supposition, but not a truer hypothesis, unless we imply the existence of absolute space.It may be remembered that certain unwary controversialists have tried to infer from Poincaré’s argument that the condemnation of Galileo was justified. Nothing could be more amusing than the way in which the distinguished mathematician-philosopher defended himself against this interpretation, though one must admit that his defence was not wholly convincing. He did not take sufficiently into account the agnostic element.Poincaré, in any case, is the leader of those who regard space as a mere property which we ascribe to objects. In this view our idea of it is only, so to say, the hereditary outcome of those efforts of our senses by means of which we strive to embrace the material world at a given moment.It is the same with time. Here again the objections of philosophic Relativists were raised long ago, but it was Poincaré who gave them their definitive shape. His luminous demonstrations are, however, well known, and we need not reproduce them here. It is enough to observe that, in regard to time as well as space, it is possible to imagine either a contraction or an enlargement of the scale which would becompletely imperceptible to us; and this seems to show that man cannot conceive an absolute time. If some malicious spirit were to amuse itself some night by making all the phenomena of the universe a thousand times slower, we should not, when we awake, have any means of detecting the change. The world would seem to us unchanged. Yet every hour recorded by our watches would be a thousand times longer than hours had previously been. Men would live a thousand times as long, yet they would be unaware of the fact, as their sensations would be slower in the same proportion.When Lamartine appealed to time to “suspend its flight,” he said a very charming, but perhaps meaningless, thing. If time had obeyed his passionate appeal, neither Lamartine nor Elvire would have known and rejoiced over the fact. The boatman who conducted the lovers on the Lac du Bourget would not have asked payment for a single additional hour; yet he would have dipped his oars into the pleasant waters for a far longer time.I venture to sum up all this in a sentence which will at first sight seem a paradox: in the opinion of the Relativists it is the measuring rods which create space, the clocks which create time. All this was maintained by Poincaré and others long before the time of Einstein, and one does injustice to truth in ascribing the discovery to him. I am quite aware that one lends only to the rich, but one does an injustice to the wealthy themselves in attributing to them what does not belong to them, and what they need not in order to be rich.There is, moreover, one point at which Galileo and Newton, for all their belief in the existence of absolute space and time, admitted a certain relativity. They recognised that it is impossible todistinguish between uniform movements of translation. They thus admitted the equivalence of all such movements, and therefore the impossibility of proving an absolute movement of translation.That is what is called the Principle of Classic Relativity.An unexpected fact served to bring these questions upon a new plane, and led Einstein to give a remarkable extension to the Principle of Relativity of classic mechanics. This was the issue of a famous experiment by Michelson, of which we must give a brief description.It is well known that rays of light travel across empty space from star to star, otherwise we should be unable to see the stars. From this physicists long ago concluded that the rays travelled in a medium that is devoid of mass and inertia, is infinitely elastic, and offers no resistance to the movement of material bodies, into which it penetrates. This medium has been named ether. Light travels through it as waves spread over the surface of water at a speed of something like 186,000 miles a second: a velocity which we will express by the letterV.