Part 3

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

All three of Newton’s laws of motion are now questioned and the world is called upon to unlearn the lesson which Euclid taught it that parallel lines never meet. According to Einstein they may meet. According to Newton the action of gravitation is instantaneous throughout all space. According to Einstein no action can exceed the velocity of light. If the theory of relativity is right there can be no such thing as absolute time or way of finding whether clocks in different places are synchronous. Our yardsticks may vary according to how we hold them and the weight of a body may depend upon its velocity. The shortest distance between two points may not be a straight line. These are a few of the startling implications of Einstein’s theory of relativity. If he had put it forward as a mere metaphysical fancy, as a possible but unverifiable hypothesis, it would have aroused mere idle curiosity. But he deduced from it mathematical laws governing physical phenomena which could be put to the test of experiment. They have been tested in these two crucial cases and prove to be true.

In the preceding pages we have discussed the question of the relativity of motion and seen how impossible it is to tell, for instance, whether a train or a ship you are on is moving or not unless you can compare it with something that you are “sure” is stationary. But what are you sure is stationary? Nothing on earth surely, for the earth compared with the “fixed” stars is spinning around at the rate of about a thousand miles an hour and rushing around the sun at the rate of nearly 70,000 miles an hour. But are we sure the stars are fixed since we have nothing else to compare them with? You may remember Herbert Spencer’s illustration of the sea captain who was walking west on the deck of a ship sailing east at the same rate. Is he moving or not? If you are in the same boat, you say he is. If you are on shore when the ship is passing you say he is standing still and “marking time.” It all depends on the point of view.

Now you may readily admit that all motion is relative, not absolute, and yet you may balk at the idea that space and time are also relative, not absolute. But motion is merely simultaneous change of position in space and time, and why should we feel so certain about space and time when we have never seen either?

You may say, for instance, that you are sure your desk is so long. But if I ask you how long you have to say as long as something else. You may say it is a yard long. But how long is a yard? It is as long as some tape or stick marked “one yard,” and this in turn has been taken from some other yardstick, until you get back to the brass rod in London that is just as long as the distance from the tip of the nose of King Henry I to the end of his royal thumb. But such a standard of absolute measurement is unsatisfactory to everyone except an absolute monarchist. But apart from the difficulty of the present inaccessibility of King Henry’s nose and thumb, can we be confident that our yardstick keeps the same length while we are measuring with it? We must admit indeed that it is longer on a summer day than on a winter day, but can we be sure that it does not alter in length when we hold it upright or lay it horizontally? Or, rather, could we tell if it did change in length as it is changed in direction?

ARE YOU SURE OF YOUR SHAPE?

If you have ever been in any of those funny places at the amusement parks you will have noticed the convex mirrors there and how ridiculous they make other people look. If you cannot afford the nickel necessary for the study of optics in such an establishment you can contemplate your reflection in the side of a shiny tin cup or can. In a plane mirror you see a man who looks as you suppose yourself to be except that somehow you seem to have become left-handed. But when you look into a convex cylindrical mirror set upright you see a man thinner than you “really are.” Look into the same mirror set horizontal and you see a man shorter than you “really are.” You grin at the sight of such queer-looking creatures, but you notice that they are equally amused at your shape. Now how are you going to prove to the men in the curved glasses that they are mere caricatures and that you are not really built on the plan of either of these images? You naturally resort to measurement, as a scientist should. You cannot get into the mirror world to measure the tall man who pretends to represent you, but you can explain to him in the sign language what you want him to do and he instantly complies. You stand up a measuring rod at your side and show him that you are exactly 72 inches tall. He also sets up a rod and that also reads 72 inches. Never mind, let him use any kind of measure he likes, you will catch him when it comes to measurement of width with the same stick. You hold your rule across your shoulders and it reads 18 inches, that is, one-fourth your height. But he also measures his width with his rule and makes it just the same, 18 inches, although as you see him he looks at least six times as high as he is broad.

When the man in the middle looks at himself in a curved mirror he sees what he regards as a distorted image. The image on the right is thinner and seems taller because it is reflected from a cylindrical surface set upright. The image on the left is shorter and seems broader because it is reflected from a cylindrical surface set horizontally. But if the man and his image are measured by scales in the real world and the mirror world they come out the same. So, too, it would be impossible for us to find out if everything in the world were expanded or contracted in all directions. In other words, all measurements are relative. According to Einstein any body in movement is shortened in the direction of the line of motion while the transverse dimension remains the same. If, then, a man is being carried headlong through space with a velocity approaching the speed of light he would be shortened like the man on the left. If he were moving sideways he would be like the man on the right.

The man’s image in a plane mirror seems to him symmetrical but reversed. His right hand has somehow got over on his left side and vice versa. Such a transformation as the mirror seems to effect cannot be actually accomplished in ordinary space, but would conceivably be possible in a space of four dimensions.]

Now you are sure he is cheating--must have some sort of telescoping rod that contracts and expands according to the way he holds it. You point out to him that his measure is unreliable, but to your surprise his gestures seem intended to convince you that you instead are using the elastic rule. You shake your fist in his face--to which he responds with equal indignation--and then you turn to the squatty chap in the other mirror, hoping he will be amenable to reason. But he also measures himself as 72 inches high and 18 inches wide by his own rule. If you try the still queerer-looking fellow in the concavo-convex mirror who is distorted in all sorts of ways you will find that his rule lengthens and shortens and bends just enough to make him as symmetrical a man as yourself. And how can he be otherwise since he is the image of yourself?

You are therefore driven to doubt the invariableness of your own yardsticks. Suppose when you wake up tomorrow everything, including all means of measuring, is twice as big as it is today. Could you tell the difference? Would it make any difference? Would there be any difference? Is there any such thing as absolute distance? Are not all measurements relative?

Such questions had from the earliest times occupied the attention of speculative philosophers, but they passed from the realm of metaphysics to the realm of physics in 1886 when Michelson and Morley made their famous experiment on the speed of light in various directions. Their object was to find out if the ether, the hypothetical medium carrying the light waves, was stationary and drifted back through the earth as the earth moved onward. They devised an instrument of such delicacy that the stamp of a foot a hundred yards off would be noticeable. A ray of light was divided into two parts; one half was sent forward and back in the direction toward which that part of the earth where the experiment was made was moving at the time; the other half was sent back and forth across the line of this motion. But the two rays of light following different routes came back at the same instant and matched up exactly. In order to correct for any inequality in the instrument, Michelson and Morley turned it around so the arm that formerly pointed across the line of motion now pointed in the direction of that motion and the other arm pointed across, but that made no difference. The light traveled with the same velocity regardless of the motion of the earth.

This negative result was just as astonishing as if you should stand at a certain spot on the bank of a river half a mile wide and should send out two boats, one to go up the river half a mile against the current and then back with the current and the other boat to go across the river and back. If both boats should return at the same moment you would be puzzled to account for it. One way of accounting for it would be that your measurement of the half-mile course upstream had been a little short. This was the explanation of the Michelson-Morley experiment given by the Dutch physicist, Lorentz. He suggested that the arm of the instrument shortened a trifle as it was turned from across the line of the earth’s motion to the direction of that motion. The amount of shrinkage necessary to compensate for the ether drift would be exceedingly small. Besides how could you measure the change in the length of the arm if the rule you laid alongside of it altered in the same proportion? Lorentz’s explanation could not be disproved, yet it was so upsetting to our ordinary ideas of the stability of matter that it was hard to accept.

Einstein took Lorentz’s idea and made it one of the fundamental principles of his new theory of the universe and then deduced from this theory sundry very startling conclusions, some of which could be--and have been--confirmed by experiment. According to Einstein the size and shape of any body depends upon the rate and direction of its movement. For ordinary speeds the alteration is very slight, but it becomes considerable at rates approaching the speed of light, 186,000 miles a second. If, for instance, you could shoot an arrow from a bow with a velocity of 160,000 miles a second, it would shrink to about half its length, as measured by a man remaining still on earth. A man traveling along with the arrow could discover no change. No force could bring the arrow or even the smallest particle of matter to a motion greater than the speed of light, and the nearer it comes to this limit the greater the force required to move it faster. This means that the mass of a body, instead of being absolute and unalterable as we have supposed, increases with the speed of its movement. Newton’s laws of dynamics are therefore valid only for matter in motion at such moderate speeds as we have to deal with in our experiments on earth and in our observations of the heavenly bodies. When we come to consider velocities approximating that of light the ordinary laws of physics are subject to an increasing correction.

If a person calculates that he is attaining a speed faster than light he will seem to another observer to be moving the other way. That is, any motion above the speed of light is negative motion. Just as a tourist traveling more than 12,000 miles away from home in any direction will really be getting nearer home the farther he goes.

Such speculations would not have bothered anybody twenty years ago, for then the physicist did not have to handle any cases of such high speeds. But when radium was discovered it was found that this metal was continuously throwing off particles of negative electricity with approximately the speed of light. Now if these electrons are not matter they are at any rate the material of which matter is made. They can be detected and counted and tracked and deflected and speeded and weighed. They are very real things, perhaps the ultimate reality of all things, yet their extreme velocity carries them out of Newton’s world and into Einstein’s.

INTRODUCING THE FOURTH DIMENSION

Now Einstein’s world, as I said before, differs from the world in which we are accustomed to live in many particulars. It has four dimensions instead of three. One of these dimensions may be time. Time, too, must be relative, not absolute. This is even harder to imagine than the relativity of space.

As some schoolboy said: “If there were no matter in the universe the law of gravitation would fall to the ground.” Quite so.

WHAT IS MEANT BY DIMENSIONS

No dimensions:

A mathematical point. Has position but no size. Represented by a dot. Like this .

One dimension:

Has length but no breadth. Made by moving a point along straight in any direction. Represented by a line. Like this ----

Two dimensions:

A plane surface like this page.