Part 1

[Illustration: _Wide World Photos._

DR. ALBERT EINSTEIN IN HIS STUDY AT BERLIN.]

EASY LESSONS IN EINSTEIN

A DISCUSSION OF THE MORE INTELLIGIBLE FEATURES OF THE THEORY OF RELATIVITY

BY

EDWIN E. SLOSSON, M.S., Ph.D.

_Literary Editor of The Independent, Associate in the Columbia School of Journalism. Author of “Great American Universities,” “Major Prophets of To-day,” “Six Major Prophets,” “Creative Chemistry,” etc._

_With an Article by Albert Einstein and a Bibliography_

ILLUSTRATED

[Illustration]

NEW YORK HARCOURT, BRACE AND HOWE 1920

COPYRIGHT, 1920, BY HARCOURT, BRACE AND HOWE, INC.

THE QUINN & BODEN COMPANY RAHWAY, N. J.

_Deepest of all illusory Appearances, for hiding Wonder, as for many other ends, are your two grand fundamental world-enveloping Appearances, Space and Time._--CARLYLE.

_Henceforth Space in itself and Time in itself sink into mere shadows and only a kind of union of the two can be maintained as self-existent._--MINKOWSKI.

A PREFATORIAL DIALOGUE

(The Purpose of which is to Prevent the Prospective Reader from buying the Book under False Pretenses)

SCENE: A street car in uniform movement of translation in any direction.

TIME: The present.

_The Reader_: (looking over the top of a morning paper): Here’s something queer--a whole page taken with a new discovery in physics--“Eclipse Observations Confirm Einstein’s Theory of Relativity.” Anything about it in your paper?

_The Author_: Yes. Here’s a cartoon on it by McCutcheon.

_The Reader_: Must be something to it then. McCutcheon always knows what’s news. (Reads on with audible fragments) “Most sensational discovery in the history of science”--“Greatest achievement of the human intellect”--“Upsets Galileo, Newton, and Euclid”--“Revolution in philosophy and theology.” It looks as though I ought to know something about this, doesn’t it?

_The Author_: I think you will have to sometime. And you might as well do it now and get it over with.

_The Reader_: (running down the column and hitting the high spots): “Parallel lines meet”--“a man moving with the speed of light never grows old”--“gravitation due to a warp in space”--“length of a measuring stick depends upon direction of its motion”--“mass is latent energy”--“time as a fourth dimension”--why, the man is crazy, isn’t he?

_The Author_: Well, definitions of insanity are so uncertain that it is not safe to say who is crazy. But it seems there’s method in his madness--otherwise how could he have hit upon the exact extent of the sun’s attraction on light?

_The Reader_: (Picks up his paper and reads aloud with concentrated attention) “Postulate I. Every law of nature which holds good with respect to a coördinate system K must also hold good for any other system K′, provided that K and K′ are in uniform movement of translation.” Say, do you know anything about this business?

_The Author_: Well, yes, a little. I have followed the controversy--at a safe distance--for a number of years.

_The Reader_: Can you tell me in plain language what it is all about?

_The Author_: Yes. Just that. I can tell you what it is _about_, though I can’t tell you what it _is_. Einstein says that there are only twelve men in the world capable of understanding his latest paper.

_The Reader_: Are you one of the twelve?

_The Author_: No, nor the thirteenth. But without plunging into the mathematics of it, we might talk over some of the interesting aspects of the theory of relativity and in the end I could put you on track of the twelve so you could read up on the subject if you liked.

_The Reader_: All right. That’s fair. This is a slow car anyhow. Go ahead.

_The Author_: (See following pages)--

EASY LESSONS IN EINSTEIN

“_A warp in nature has been found,_ _No line is straight, no circle round;_ _For Isaac Newton had unsound_ _Ideas of gravitation._”

Why is it that our newspapers are sending out their reporters to interview astronomers as well as actresses and devoting pages to speculations on the nature of space and time as well as on the state of the market? It is--to get at the bottom of it--merely because a few photographs taken during the eclipse of the sun on May 29, 1919, by two telescopes, one at Sobral in northern Brazil and the other on the island of Principe off the west coast of Africa, showed an abnormal shift of less than one-324,000th of a right angle in the position of the stars. When these photograph films were laid over films taken before the eclipse it was found that the star-images about the darkened disk of the sun did not exactly coincide with the images when the sun was not in their midst. Measured with a micrometer the displacement of the stars from their ordinary positions was found to be 1.60 seconds of arc on the African plates and 1.98 seconds on the Brazilian plates. Average these two observations and you get 1.79. This is extremely close to the 1.73 predicted by Professor Einstein of Berlin and twice as large as the deflection calculated according to Newton’s law of gravitation which would be .87 of a second.

When the announcement of this result was made at the meeting of the Royal Society of London on November 6 all eyes were turned toward Sir Oliver Lodge, for last February he had been rash enough to express the hope, if not the prediction, that the results of the eclipse expedition would support Newton rather than Einstein. But instead of taking part in the discussion Sir Oliver got up and walked out. It was suspected that he had “gone off mad,” as we Americans would put it, because the starlight would not follow his preferred path. But he put a stop to any such rumors by a letter to _The Times_ in which he explains that his departure was not due to any dissatisfaction with the universe but to the necessity of catching the 6 o’clock train. He frankly acknowledges that “the eclipse result is a great victory for Einstein; the quantitative agreement is too close to allow much room for doubt” but he adds “a caution against a strengthening of great and complicated generalizations concerning space and time on the strength of this splendid result: I trust that it may be accounted for, with reasonable simplicity in terms of the ether of space.”

This caution is wise, but we cannot hold our breath till 1922, when the next eclipse comes, to see if these observations are verified and we may in the meantime consider some of the implications of Einstein’s theory of relativity.

Sir Joseph Thomson, President of the Royal Society, in making the momentous announcement in the session of the Society, said:

If his theory is right, it makes us take an entirely new view of gravitation. If it is sustained that Einstein’s reasoning holds good--and it has sustained two very severe tests in connection with the perihelion of Mercury and the present eclipse--then it is the result of one of the highest achievements of human thought. The weak point in the theory is the great difficulty in expressing it. It would seem that no one can understand the new law of gravitation without a thorough knowledge of the theory of invariants and of the calculus of variations.

What is this theory of relativity and why is it so important? The mathematics of it are too much for most of us, but we can get some notion of it by a familiar illustration.

Suppose you wake up some morning in a Pullman berth and look out of the window to see where you are. You find your view blocked by a passing train on the next track. Now if you do not feel any jar of your car and cannot catch sight of the landscape beyond the other train you cannot tell whether (1) your train is moving forward and the other train is standing still, or (2) your train is standing still and the other train is moving backward, or (3) whether both trains are moving in opposite directions, or (4) whether both trains are moving in the same direction, but your train faster. It is obvious that the trains are getting past one another. You can measure their speed of parting as accurately as you please. But all you can perceive is the relative motion of the two trains. You begin to wonder whether there is any such thing as absolute motion; whether there is any real difference between rest and motion. Is there any possible way of telling whether your train is in motion or not if all you can see out of the window is some object that itself be moving? Suppose the windows were all curtained, how could you find out whether you were moving forward or backward or standing still?

You discuss this curious question with your fellow passengers at the breakfast table and one of them makes the brilliant suggestion that it might be possible to determine the absolute motion of the car by reference to the air. If the car is moving forward the air would stream from front to rear and the reverse if it were moving backward. “Suppose,” says the ingenious experimentalist, “that you stand at one end of the car and I at the other. We will shout at each other alternately and time the passage of the sound with our stop watches. Since sound is carried by air waves it will take longer for the shout to go against the air current than with it, and from that measurement it might be possible for us not only to determine which way the car is moving but how to calculate how fast it travels, assuming, of course, that there is no wind blowing.” That strikes you as a crucial experiment, but you point out one possible difficulty, that the doors at the ends of the car may be closed and the air inside is being carried along with the car, so no difference would be observable in the speed of the sound even though the car were moving. “All right,” replies your scientific friend, “we will make a preliminary test to see if the enclosed air is carried along with the car, and if we find that it is not then we will try the second experiment with the sound signals to see which way the air current is moving. These two experiments must settle it, for either the air is moving with the car or it is moving through the car. Can you conceive of any other possibility than these two?” No, you cannot, so you proceed to try the two experiments. First you visit both ends of the car and find both doors open; the air then is not being carried along with the car. You turn then with confidence to the second experiment and you find, of course, that there is a difference in the speed of sound whether it moves with the air drift or against it.

There might, I admit, be practical difficulties in the way of carrying out such a delicate experiment on a moving train, but we need not bother with them, for probably the current of air through the car would be so strong as to blow your hat out of the back door and that would settle the question to your satisfaction--or at least it would settle the question in the affirmative.

But imagine your amazement if this second experiment should give negative results like the first one; if you could detect no difference in time whether the sound was sent forward or back or across the car. You would then have proved by experiment (1) that the air did not move with the car and (2) that the air did not move through the car. You might suppose from this that your car is at rest, but suppose the people on the other train passing yours tried the same experiments and got the same result, namely, that they, too, were at rest as regards the air. You would then be in a quandary, for your two indisputable experiments had apparently given contradictory results. You might get out of it by saying that there was no air, but if not what carried the sound waves--and the hat?

CONTRADICTORY EXPERIMENTS

Now this is the quandary in which physicists have been in for the last thirty-three years. Is there any way of _discovering_ absolute motion among the heavenly bodies? We can observe and measure with great accuracy their relative motion. The sun is seen to pass across the sky from east to west and man at first assumed that the earth was still and the sun went around it. This is the natural and instinctive assumption, for when you first glance out of your Pullman window you get the impression that the other train is the moving one. But for the last three hundred years it has been the fashion to assume the earth was moving and not the sun. That assumption has the advantage of simplifying the calculations of the astronomers, though I never could see why we should have to give up our simple notions of sunrise and sunset to save them a little trouble figuring.

The earth moves--if it does move--so quietly and silently that we feel no jar or engine-beat to tell us of its motion. If the earth were perpetually shrouded by clouds could we find out its motion through space or even its rotation? And do we actually get any proof on this point from observation of the heavenly bodies? We see them moving about relatively to each other and we can represent their movements most easily by supposing that the moon goes around the earth and that the earth and the rest of the planets go around the sun. But is this whole solar system in motion? So it seems when we compare it with the stars. But who knows if the solar system and all the visible stars are not altogether moving off through space at the rate of a mile or a thousand miles a second? How can we tell unless we have something that is still and fixed to measure the motion by?

It seemed until recently that we had such a fixture, the ether. We know of the sun and stars only from the light that comes from them to us. Light, as we can prove by simple experiments, consists of wave motion. Now, can you have wave motion without something to wave? Sound waves are conveyed by air but there is no air between the earth and the sun. So as nothing could be found to fill this empty space scientists had to invent something to satisfy their sense of the fitness of things. The ether was the product of their excogitations. It was a British invention, devised in the Royal Institution, whence have come so many useful theories and discoveries.

The ether, as Salisbury said, is simply the nominative of the verb “to undulate.” It was conceived of as a sort of transparent jelly filling all space, more rigid than any solid, more frictionless than any fluid, more easily penetrated than any gas. It must be more elastic than steel and yet so rarefied that ordinary matter passes through it without the slightest effort. The ether is supposed to slip between the particles of the rushing earth as the wind blows through the branches of a tree.

For many years after its invention the ether had nothing to do except to carry light about from one place to another. But when the electro-magnetic waves of the wireless telegraph were produced something was needed also to carry them and this new task was laid upon the shoulders of the uncomplaining ether. When Röntgen discovered the X-rays, whose waves are 10,000 times shorter than the shortest light waves, these were turned over to the ether to run. In fact, it got so that whenever a physicist found any action that he could not explain by ordinary matter he said: “Let the ether do it,” and that hypothetical substance apparently answered every purpose until it came to this question of relative motion.

Now whatever we may think about the ether it would seem that if there is any such thing filling all “empty” space we might use it for measuring the motion of the earth through it as we did the air current in the car. If the earth is really revolving around the sun the ether must be whizzing through its pores at the rate of about nineteen miles a second.

But wait--there is the possibility that the earth carries along with it in its flight through space a sort of atmosphere of ether as it does of air. We must first get rid of this possibility by a preliminary experiment to see if a swiftly moving mass of matter does catch up and carry along with it a little of the ether. This would cause a sort of an eddy or disturbance in the ether in the neighborhood of the moving mass as a boat disturbs the water. For instance, a ray of light passing close to a rapidly revolving wheel would be a little deflected and show a distorted image. Sir Oliver Lodge tried this experiment and got negative results. That is, moving matter does not disturb or carry with it the ether. Consequently, it would seem, we are left to the only other logical alternative, that the ether drifts through matter and we should expect to detect this drift by measuring the speed of light in the direction of the earth’s motion. It ought to take longer for light to travel from one point to another if the earth meantime is moving away from the first point and it ought to take less time if the earth is moving toward it. Well, Michelson and Morley tried this experiment--and also got negative results! It did not make any difference whether the ray of light was sent in the direction of the earth’s movement or the reverse or across the line, it traveled invariably at the same speed, 186,000 miles a second. Here then were two unquestionable experiments apparently contradicting each other. One proved that the ether did not travel with the earth. The other proved that the ether did not stand still while the earth traveled through it.

Now when we get contradictory answers to the questions we put to Nature we must assume--unless Nature is nonsensical--that we are asking nonsensical questions. If in the trial of a pickpocket one witness swears that the thief did not run up the street and another witness that he did not run down the street the lawyer does not necessarily say that one of them must be a liar. He meditates a moment and then it occurs to him that possibly the pickpocket did not move or that perhaps he disappeared into the third dimension by climbing up a fire-escape or dropping into a coalhole.

So with our ether quandary. If the ether does not move and does not stand still perhaps there isn’t any ether or perhaps there is a fourth dimension. These are two conceivable ways out of the dilemma though they are not easy to accept, either of them. If there is no ether what carries the light waves? If there is a fourth dimension in what direction does it lie? But it is no harder to believe in or conceive of a fourth dimension than it is the ether, and if the physicist finds that he needs it in his business he will have to have it. Einstein says that he needs a fourth dimension for his formulas.

THE CONUNDRUM OF THE AGES

For twenty-four hundred years philosophic thought has been concerned with the problem of the relation of space and time. Drop into any of the scientific societies of today and you will find them discussing whether space is finite or infinite, whether there is any difference between rest and motion, whether length is absolute or relative, whether time and space have real existence, which are the very questions discussed by Pythagoras and Zeno in the Greek cities of Asia Minor. Now the time spent in these speculations has not been wasted, although it has led to no definite conclusion, for out of it have grown our mathematics and physics. The Wandering Jew, who is the only mortal having the privilege of attending the schools of the Eleatics and those of the present day, would observe one difference, that modern scientists try to put their theories to the test of experiment wherever possible, while the ancients were content with thinking them out.

Of all the guesses that have been given to this riddle of the universe none has been more bold and revolutionary than that contained in a paper of four or five pages contributed in 1905 to the _Annalen der Physik_ by Albert Einstein. The controversy it precipitated has not altogether been confined to the realm of pure reason, for scientists are but human and as such are not entirely uninfluenced by patriotic prejudice.

In this brief paper he proposed a new theory of the universe based upon two postulates. The first was the principle of relativity; that all _motion is relative_. This means, for instance, that we would never know the motion of a smoothly moving train if the windows were darkened and that we could never discover the forward movement of the earth if we could not see the heavenly bodies.

Einstein’s second postulate was that _the velocity of light is independent of the motion of the source_. This is a hard one for our reason to swallow, for it means that nothing can travel faster than light, 186,000 miles a second, and that you cannot make light travel faster than that by giving it a swift send-off. It is the same as saying that if a man standing on the cowcatcher of an engine threw a ball forward, it would not make any difference with the velocity of the ball whether the train was running at full speed forward or backward or standing still. But the experiments of the American physicists, Michelson and Morley, who measured the speed of light and found it the same whether the earth was moving toward the source of the ray or away from it, or at right angles to its direction, confirm Einstein’s second assumption.

If we accept Einstein’s two primary postulates and his later “Principle of Equivalence” his theory clears up this ether-drift difficulty as well as various other riddles of the universe. It explains the shifting of the orbit of Mercury that Newton’s theory could never account for. It foretold the deflection of light by the sun’s gravitation that the observations on the eclipse of last May confirmed. A third test, the shifting of the lines of the solar spectrum toward the red end in a gravitational field, has not been met. Such technical points concern only physicists and astronomers, but Einstein’s relativity theory, which two out of the three experiments support, carries with it certain speculations as to time and space that are upsetting to current conceptions.

PARADOXES OF RELATIVITY