From Newton to Einstein - Benjamin Harrow (fox in socks read aloud txt) 📗

speak of the sun as exerting a “force” on the earth. We have seen, however, that this force brings about a “distortion” or “strain” in world-lines; or, what amounts to the same thing, a “distortion” or “strain” of time and space. The sun’s “force,” the “force” of any body in space, is the “force” due to gravity; and these “forces” may now be treated in terms of the laws of time and space. “The earth,” Prof. Eddington tells us, “moves in a curved orbit, not because the sun exerts any direct pull, but because the earth is trying to find the shortest way through a space and time which have been tangled up by an influence radiating from the sun.”8

At this point Newton’s conceptions fail, for his views and his laws do not include “strains” in space. Newton’s law of gravitation must be supplanted by one which does include such distortions. It is Einstein’s great glory to have supplied us with this new law.

Einstein’s Law of Gravitation. This appears to be the only law which meets all requirements. It includes Newton’s law, and cannot be distinguished from it if our experiments are confined to the earth and deal with relatively small velocities. But when we betake ourselves to some orbits in space, with a gravitational pull much greater than the earth’s, and when we deal with velocities comparable to that of light, the differences become marked.

Einstein’s Theory Scores Its First Great Victory. In the beginning of this chapter we referred to the elaborate eclipse expedition sent by the British to test the validity of Einstein’s new theory of gravitation. The British scientists would hardly have expended so much time and energy on this theory of Einstein’s but for the fact that Einstein had already scored one great victory. What was it?

Imagine but a single planet revolving about the sun. According to Newton’s law of gravitation, the planet’s path would be that of an ellipse—that is, oval—and the planet would travel indefinitely along this path. According to Einstein the path would also be elliptical, but before a revolution would be quite completed, the planet would start along a slightly advanced line, forming a new ellipse slightly in advance of the first. The elliptic orbit slowly turns in the direction in which the planet is moving. After many years—centuries—the orbit will be in a different direction.

The rapidity of the orbit’s change of direction depends on the velocity of the planet. Mercury moving at the rate of 30 miles a second is the fastest among the planets. It has the further advantage over Venus or the earth in that its orbit, as we have said, is an ellipse, whereas the orbits of Venus and the earth are nearly circular; and how are you going to tell in which direction a circle is pointing?

Observation tells us that the orbit of Mercury is advancing at the rate of 574 seconds (of arc) per century. We can calculate how much of this is due to the gravitational influence of other planets. It amounts to 532 seconds per century. What of the remaining 42 seconds?

You might be inclined to attribute this shortcoming to experimental error. But when all such possibilities are allowed for our mathematicians assure us that the discrepancy is 30 times greater than any possible experimental error.

This discrepancy between theory and observation remained one of the great puzzles in astronomy until Einstein cleared up the mystery. According to Einstein’s theory the mathematics of the situation is simply this: in one revolution of the planet the orbit will advance by a fraction of a revolution equal to three times the square of the ratio of the velocity of the planet to the velocity of light. When we allow mathematicians to work this out we get the figure 43, which is certainly close enough to 42 to be called identical with it.

Still Another Victory? Einstein’s third prediction—the shifting of spectral lines toward the red end of the spectrum in the case of light coming to us from the stars of appreciable mass—seems to have been confirmed recently (March, 1920). “The young physicists in Bonn,” writes Prof. Einstein to a friend, “have now as good as certainty (so gut wie sicher) proved the red displacement of the spectral lines and have cleared up the grounds of a previous disappointment.”

Summary. Velocity, or movement in space, is at the basis of Einstein’s work, as it was at the basis of Newton’s. But time and space no longer have the distinct meanings that they had when examined with the help of Newton’s equations. Time and space are not independent but interdependent. They are meaningless when treated as separate entities, giving results which may hold for one body in the universe but do not hold for any other body. To get general laws which are applicable to the cosmos as a whole the Fundamentals of Mechanics must be united.

Einstein’s great achievement consists in applying this revised conception of space and time to elucidate cosmical problems. “World-lines,” representing the progress of particles in space, consisting of space-time combinations (the four dimensions), are “strained” or “distorted” in space due to the attraction that bodies exhibit for one another (the force of gravitation). On the other hand, gravitation itself—more universal than anything else in the universe—may be interpreted in terms of strains on world-lines, or, what amounts to the same thing, strains of space-time combinations. This brings gravitation within the field of Einstein’s conception of time and space.

That Einstein’s conception of the universe is an improvement upon that of Newton’s is evidenced by the fact that Einstein’s law explains all that Newton’s law does, and also other facts which Newton’s law is incapable of explaining. Among these may be mentioned the distortion of the oval orbits of planets round the sun (confirmed in the case of the planet Mercury), and the deviation of light rays in a gravitational field (confirmed by the English Solar Eclipse Expedition).

Einstein’s Theories and the Inferences to be Drawn from Them. Einstein’s theories, supported as they are by very convincing experiments, will probably profoundly influence philosophic and perhaps religious thought, but they can hardly be said to be of immediate consequence to the man in the street. As I have said elsewhere, Einstein’s theories are not going to add one bushel of wheat to war-torn and devastated Europe, but in their conception of a cosmos decidedly at variance with anything yet conceived by any school of philosophy, they will attract the universal attention of thinking men in all countries. The scientist is immediately struck by the way Einstein has utilized the various achievements in physics and mathematics to build up a co-ordinated system showing connecting links where heretofore none were perceived. The philosopher is equally fascinated with a theory, which, in detail extremely complex, shows a singular beauty of unity in design when viewed as a whole. The revolutionary ideas propounded regarding time and space, the brilliant way in which the most universal property of matter, gravitation, is for the first time linked up with other properties of matter, and, above all, the experimental confirmation of several of his more startling predictions—always the finest test of scientific merit—stamps Einstein as one of those super-men who from time to time are sent to us to give us a peep into the beyond.

Some Facts about Einstein Himself. Albert Einstein was born in Germany some 45 years ago. At first he was engaged at the Patent Bureau in Berne, and later became professor at the Zürich Polytechnic. After a short stay at Prague University he accepted one of those tempting “Akademiker” professorships at the university of Berlin—professorships which insure a comfortable income to the recipient of one of them, little university work beyond, perhaps, one lecture a week, and splendid facilities for research. A similar inducement enticed the chemical philosopher, Van ’t Hoff, to leave his Amsterdam, and the Swedes came perilously near losing their most illustrious scientist, Arrhenius.

Einstein published his first paper on relativity in 1905, when not more than 30 years old. Of this paper Planck, the Nobel Laureate in physics this year, has offered this opinion: “It surpasses in boldness everything previously suggested in speculative natural philosophy and even in the philosophical theories of knowledge. The revolution introduced into the physical conceptions of the world is only to be compared in extent and depth with that brought about by the introduction of the Copernican system of the universe.”

Einstein published a full exposition of the relativity theory in 1916.

During the momentous years of 1914–19, Einstein quietly pursued his labors. There seems to be some foundation for the belief that the ways of the German High Command found little favor in his eyes. At any rate, he was not one of the forty professors who signed the famous manifesto extolling Germany’s aims. “We know for a fact,” writes Dr. O. A. Rankine, of the Imperial College of Science and Technology, London, “that Einstein never was employed on war work. Whatever may have been Germany’s mistakes in other directions, she left her men of science severely alone. In fact, they were encouraged to continue in their normal occupations. Einstein undoubtedly received a large measure of support from the Imperial Government, even when the German armies were being driven back across Belgium.”

Quite recently (June, 1920) the Barnard Medal of Columbia University was conferred on him “in recognition of his highly original and fruitful development of the fundamental concepts of physics through application of mathematics.” In acknowledging the honor, Prof. Einstein wrote to President Butler that “… quite apart from the personal satisfaction, I believe I may regard your decision [to confer the medal upon him] as a harbinger of a better time in which a sense of international solidarity will once more unite scholars of the various countries.”