Part 4

Prof. Cohen's Illustration. Further bewildering possibilities are clearly outlined in this apt illustration: "If when you are going away on a long and continuous journey you write home at regular intervals, you should not be surprised that with the best possible mail service your letters will reach home at progressively longer intervals, since each letter will have a greater distance to travel than its predecessor. If you were armed with instruments to hear the home clock ticking, you would find that as your distance from home keeps on increasing, the intervals between the successive ticks (that is, its seconds) grow longer, so that if you travelled with the velocity of sound the home clock would seem to slow down to a standstill--you would never hear the next tick.

"Precisely the same is true if you substitute light rays for sound waves. If with the naked eye or with a telescope you watch a clock moving away from you, you will find that its minute hand takes a longer time to cover its five-minute intervals than does the chronometer in your hand, and if the clock travelled with the velocity of light you would forever see the minute hand at precisely the same point. That which is true of the clock is, of course, also true of all time intervals which it measures, so that if you moved away from the earth with the velocity of light everything on it would appear as still as on a painted canvas."

Your time has apparently come to a standstill in one position and is moving in another! All this seems absurd enough, but it does show that time alone has little meaning.

Minkowski's Conclusion. The relativity theory requires that we thoroughly reorganise our method of measuring time. But this is intimately associated with our method of measuring space, the distance between two points. As we proceed we find that space without time has little meaning, and vice versa. This leads Minkowski to the conclusion that "time by itself and space by itself are mere shadows; they are only two aspects of a single and indivisible manner of coordinating the facts of the physical world." Einstein incorporated this time-space idea in his theory of relativity.

How We Measure a Point in Space. Suppose I say to you that the chemical laboratory of Columbia University faces Broadway; would that locate the laboratory? Hardly, for any building along Broadway would face Broadway. But suppose I add that it is situated at Broadway and 117th Street, south-east? there could be little doubt then. But if, further, this laboratory would occupy but part of the building, say the third floor; then the situation would be specified by naming Broadway, 117th Street S. E., third floor. If Broadway represents length, 117th Street width, and third floor height, we can see what is meant when we say that three dimensions are required to locate a position in space.

The Fourth Dimension. A point on a line may be located by one dimension; a point on a wall requires two dimensions; a point in the room, like the chemical laboratory above ground, needs three. The layman cannot grasp the meaning of a fourth dimension; yet the mathematician does imagine it, and plays with it in mathematical terms. Minkowski and Einstein picture time as the fourth dimension. To them time occupies no more important position than length, breadth, or thickness, and is as intimately related to these three as the three are to one another. H. G. Wells, the novelist, has beautifully caught this spirit when in his novel, "The Time Machine," he makes his hero travel backwards and forwards along time just as a man might go north or south. When the man with his time machine goes forward he is in the future; when he goes backwards he is in the past.

In reality, if we stop to think a minute, there is no valid reason for the non-existence of a fourth dimension. If one, two and three dimensions, why not four--and five and six, for that matter? Theoretically at least there is no reason why the limit should be set at three. However, our minds become sluggish when we attempt to picture dimensions beyond three; just as an extraordinary effort on our part is needed to follow Einstein when he "juggles" with space and time.

Our difficulty in imagining four dimensions may be likened to the difficulty two-dimensioned beings would experience in imagining us, beings of the conventional three dimensions. Suppose these two-dimensional beings were living on the surface of the earth; what could they see? They could see nothing below and nothing above the surface. They would see shifting surfaces as we walked about, but being sensitive to length and breadth only, and not to height, they could gain no notion whatsoever of what we really look like. It is thus with us when we attempt to picture four-dimensional space.

Perhaps the analogy of the motion picture may help us somewhat. As everybody knows, these motion pictures consist of a series of photographs which are shown in rapid succession on the screen. Each photograph by itself conveys a sensation of space, that is, of three dimensions; but one photograph rapidly following another conveys the sensation of space and time--four dimensions. Space and time are interlinked.

The Time-space Idea Further Developed. We have already alluded to the fact that objects in space moving with different velocities build up different time intervals. Thus the velocity of the star Arcturus, if compared with reference to the earth, moves at the rate of 200 miles a second. Its motion through space is different from ours. Objects which, according to Lorentz, contract in the direction of their motion to an extent proportional to their velocity, will contract differently on the surface of Arcturus than on the earth. Our space is not Arcturus' space; neither is Arcturus' time our time. And what is true of the discrepancies existing between the space and time conceptions of the earth and Arcturus is true of any other two bodies in space moving at different velocities.

But is there no relationship existing between the space and time of one body in the universe as compared to the space and time of another? Can we not find something which holds good for all bodies in the universe? We can. We can express it mathematically. It is the concept of time and space interlinked; of time as the fourth dimension, length, breadth and thickness being the other three; of time as one of four co-ordinates and at right angles to the other three (a situation which requires a terrific stretch of the imagination to visualize). The four dimensions are sufficient to co-ordinate the time-space relationships of all bodies in the cosmos, and hence have a universality which is totally lacking when time and space are used independently of one another. The four components of our time-space are up-and-down, right-and-left, backwards-and-forwards, and sooner-and-later.

"Strain" and "Distortion" in Space. The four-dimensional unit has been given the name "world-line," for the "world-line" of any particle in space is in reality a complete history of that particle as it moves about in space. Particles, we know, attract one another. If each particle is represented by a world-line these world-lines will be deflected from their course owing to such attraction.

Imagine a bladder representing the universe, with lines on it representing world-lines. Now squeeze the bladder. The world-lines are bent in various directions; they are "distorted." This illustrates the influence of gravity on these world-lines; it is the "strain" brought about due to the force of attraction. The distorted bladder illustrates even more, for it is a true representation of the real world.

How Einstein's Conception of Time and Space Led to a New View of Gravitation. In our conventional language we 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." [11]

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."

REFERENCES

For those lacking all astronomical knowledge, an excellent plan would be to read the first 40 pages of W. H. Snyder's Everyday Science (Allyn and Bacon), in which may be found a clear and simple account of the solar system. This could be followed with Bertrand Russell's chapter on The Nature of Matter in his little volume, The Problems of Philosophy (Henry Holt and Co.). Here the reader will be introduced to the purely philosophical side of the question--quite a necessary equipment for the understanding of Einstein's theory.

Of the non-mathematical articles which have appeared, those by Prof. A. S. Eddington (Nature, volume 101, pages 15 and 34, 1918) and Prof. M. R. Cohen (The New Republic, Jan. 21, 1920) are the best which have come to the author's notice. Other articles on Einstein's theory, some easily comprehensible, others somewhat confusing, and still others full of noise and rather empty, are by H. A. Lorentz, The New York Times, Dec. 21, 1919 (since reprinted in book form by Brentano's, New York, 1920); J. Q. Stewart, Scientific American, Jan. 3, 1920; E. Cunningham, Nature, volume 104, pages 354 and 374, 1919; F. H. Loring, Chemical News, volume 112, pages 226, 236, 248, and 260, 1915; E. B. Wilson, Scientific Monthly, volume 10, page 217, 1920; J. S. Ames, Science, volume 51, page 253, 1920 [12]; L. A. Bauer, Science, volume 51, page 301 (1920), and volume 51, page 581 (1920); Sir Oliver Lodge, Scientific Monthly, volume 10, page 378, 1920; E. E. Slosson, Independent, Nov. 29, Dec. 13, Dec. 20, Dec. 27, 1919 (since collected and published in book form by Harcourt, Brace and Howe); Isabel M. Lewis, Electrical Experimenter, Jan., 1920; A. J. Lotka, Harper's Magazine, March, 1920, page 477; and R. D. Carmichael, New York Times, March 28, 1920. Einstein himself is responsible for a brief article in English which first appeared in the London Times, and was later reprinted in Science, volume 51, page 8, 1920 (see the Appendix).

A number of books deal with the subject, and all of them are more or less mathematical. However, in every one of these volumes certain chapters, or portions of chapters, may be read with profit even by the non-mathematical reader. Some of these books are: Erwin Freundlich, The Foundations of Einstein's Theory of Gravitation (University Press, Cambridge, 1920). (A very complete list of references--up to Feb., 1920--is also given); A. S. Eddington, Report on the Relativity Theory of Gravitation for the Physical Society of London (Fleetway Press, Ltd., London, 1920); R. C. Tolman, Theory of the Relativity of Motion (University of California Press, 1917); E. Cunningham, Relativity and the Electron Theory (Longmans, Green and Co., 1915); R. D. Carmichael, The Theory of Relativity (John Wiley and Sons, 1913); L. Silberstein, The Theory of Relativity (Macmillan, 1914); and E. Cunningham, The Principle of Relativity (University Press, Cambridge, England, 1914).

To those familiar with the German language Einstein's book, Über die spezielle und die allgemeine Relativitätstheorie (Friedr. Vieweg und Sohn, Braunschweig, 1920), may be recommended. [13]

The mathematical student may be referred to a volume incorporating the more important papers of Einstein, Minkowski and Lorentz: Das Relativitätsprinzip, (B. G. Teubner, Berlin, 1913).

Einstein's papers have appeared in the Annalen der Physik, Leipzig, volume 17, page 132, 1905, volume 49, page 760, 1916, and volume 55, page 241, 1918.

APPENDIX

Note 1 (page 21)

"On this earth there is indeed a tiny corner of the universe accessible to other senses [than the sense of sight]: but feeling and taste act only at those minute distances which separate particles of matter when 'in contact:' smell ranges over, at the utmost, a mile or two, and the greatest distance which sound is ever known to have traveled (when Krakatoa exploded in 1883) is but a few thousand miles--a mere fraction of the earth's girdle."--Prof. H. H. Turner of Oxford.

Note 2 (page 27)

Huyghens and Leibniz both objected to Newton's inverse square law because it postulated "action at a distance,"--for example, the attractive force of the sun and the earth. This desire for "continuity" in physical laws led to the supposition of an "ether." We may here anticipate and state that the reason which prompted Huyghens to object to Newton's law led Einstein in our own day to raise objections to the "ether" theory. "In the formulation of physical laws, only those things were to be regarded as being in causal connection which were capable of being actually observed." And the "ether" has not been "actually observed."

The idea of "continuity" implies distances between adjacent points that are infinitesimal in extent; hence the idea of "continuity" comes in direct opposition with the finite distances of Newton.

The statement relating to causal connection--the refusal to accept an "ether" as an absolute base of reference--leads to the principle of the relativity of motion.

Note 3 (page 30)

Sir Oliver Lodge goes to the extreme of pinning his faith in the reality of this ether rather than in that of matter. Witness the following statement he made recently before a New York audience:

"To my mind the ether of space is a substantial reality with extraordinarily perfect properties, with an immense amount of energy stored up in it, with a constitution which we must discover, but a substantial reality far more impressive than that of matter. Empty space, as we call it, is full of ether, but it makes no appeal to our senses. The appearance is as if it were nothing. It is the most important thing in the material universe. I believe that matter is a modification of ether, a very porous substance, a thing more analogous to a cobweb or the Milky Way or something very slight and unsubstantial, as compared to ether."

And again: