Nordmann Einstein and the universe

1. Auflage 2022
ISBN: 978-3-7568-2220-1
Verlag: BoD - Books on Demand
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 195 Seiten

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.

Autoren/Hrsg.

Nordmann, Charles

Leseproben

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.
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 of
Einstein 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 is
a 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...