Part 8

RADIAL DISPLACEMENT OF STARS IN SECONDS OF ANGLE

As observed by the British astronomers: .20 .32 .56 .54 .84 .97 1.02

As predicted by Einstein: .32 .33 .40 .53 .75 .85 .88

This is regarded by the astronomers of the British Eclipse Expedition as sufficiently close to confirm Einstein’s law but those who hesitate to accept so far-reaching and subversive a theory on the basis of these few minute measurements may hold their judgment in suspense until 1922 when the next solar eclipse, visible in Australia, takes place. Or possibly some means may be found to take star photographs close to the sun while shining. Our California mountain observatories may be of service in this since they are perched above much of the dust and mist and denser air that cause a strong light to irradiate and fog the photographic plate. Doubtless, too, the old photographs of earlier eclipses will now be got out to see if they contain any stars suitable for measuring.

Some of the opponents of Einstein suggest that the observed deflection of the starlight may be due to a solar atmosphere that refracts the rays like our earthly air. But it is hardly probable that an enveloping atmosphere sufficiently dense and so far-extending as to produce such an effect would have remained unobserved and it is highly improbable that the density of such an atmosphere should have just the density and decrease with the distance at just the rate to produce the deflection predicted by Einstein’s calculation.

The discovery is rather disconcerting to astronomers, for all their calculations for the last three hundred years have been based upon the assumption that light travels in straight lines at even speed through empty space or, what is the same thing, through the ether. If now light is pulled aside by gravitation as it goes by a solid body the rays from a distant star having to pass through the tangled throng of the Milky Way might travel a very devious route and the star would appear to us to be located in a different place from where it really is. In fact it is possible that a star which we see double may actually be single but that rays starting out from it in different directions may be so deflected by passing near other stars that when they reach us they appear to come from different points of space and so appear to us as twin stars. There may, too, be dead or dark stars on the way whose existence we cannot discern and allow for.

Now those of us who are not astronomers are not much concerned over a discrepancy of a few hundredths of a second in the measurement of an angle by the telescope. We do not care much where Mercury will be five centuries hence, for we do not know quite where it is now. If astronomers made the laws of Nature instead of merely discovering them we might be afraid that at their next congress they might repeal Newton’s law of gravitation and send us all flying off into space. But fortunately they have no such power and even though they should all become adherents of Einstein’s most revolutionary theories, Newton’s laws of mechanics and Euclid’s laws of geometry would remain as true as they ever were, not perhaps absolutely and universally true, as we have assumed, but sufficiently accurate for all practical purposes. Deviations from them can only become detectable when we come to consider movements as swift as light waves or electrons.

How a heavy object can alter space relations may be seen from this simple illustration: Stretch a sheet of rubber over a hoop like a drumhead. It is now level and flat and if parallel lines are drawn across it in two directions so as to divide it up into squares like a checkerboard all these lines are straight and equidistant and all the squares are of equal size.

A row of worms, starting in an even rank and crawling along the parallel lines across the drumhead, would keep even all the way. Now lay a bullet on the center of the drumhead. The rubber sags down and stretches, most in the middle, least at the edges. The “parallel” lines are no longer equidistant. The squares are no longer equal. The lines are no longer of the same length. If now we repeat our worm race we shall find that those worms following lines close to the weight have to go down hill and up again and so travel a greater distance to traverse the same number of squares than those following lines nearer the edge which lie comparatively flat and are nearly as short as before. Consequently the worms will be slowed up in proportion to their nearness to the center and the row of their heads will be swung around at an angle to their former frontage.

We might “explain” this by assuming that the worms on seeing the bullet to one side were drawn by their curiosity a little toward it, those nearest of course being drawn the most. Or if we had got beyond this crude animistic method of explanation we might assume that the bullet was attached to the head of each worm by an invisible lariat which being pulled by the bullet drew the worms more or less to one side, the shorter the lariat the stronger the pull. Or if we had outgrown this crude mechanical method of explanation we might assume the existence of a “force” in the lead which in some mysterious manner attracts the heads of the worms inversely as the square of their distance. But instead of inventing a wormhead psychology or an invisible cord or an incomprehensible force is it not simpler to consider the space between and to suppose that the lines to be traversed are lengthened in the neighborhood of the weight?

Now these four successive methods of explanation have been used to account for gravitation. First it was assumed by the ancient Babylonians and Hebrews that the sun and stars were living beings, gods or angels, moving of their own volition around the earth, or at least that each was guided in its orbit by its particular god or angel. The later Greeks of Ptolemy’s time supposed the heavenly bodies to be set in concentric crystal spheres and so revolved; I presume by somebody turning a crank behind the scenes. Then came Newton and said: “Let’s discard the Ptolemaic spheres and all mechanical connection and assume a force of gravitation attracting all bodies in proportion to their masses and inversely proportional to the squares of the distances separating them.” Now comes Einstein and says: “Let’s discard this hypothetical force and simply assume that the field of time and space traversed by a moving body is altered if there is another body in the vicinity.” In Einstein’s view gravitation is not a force; it is a distortion of space and time in the presence of matter. A comet sweeping past the sun cannot pursue a straight course, as it could in interstellar space, but follows a curved path about the sun which is for the comet the shortest way it can go under the circumstances.

So, too, a row of light waves coming from a distant star keeps an even front as they pass through empty space but as they come close to the sun they find their paths impeded, or, we may say, stretched. Those going nearest the sun are slowed up the most; those farthest off the least. Consequently the wavefront is slued around a bit and the direction of the ray is slightly altered.

If now light waves have difficulty getting past the sun we should expect that they would experience like difficulty getting away from the sun. They would be slowed up a bit by its gravitational pullback. The frequency would be reduced; the interval of time between wave-crests lengthened. This means, in the case of sound, lowering the pitch. Touch your finger to the turntable of your phonograph and you flat the tone. In the case of light, it means change of color toward the red. This effect, according to Einstein, should be, but has not been, observed.

“If Einstein’s third prediction is verified,” says Sir Oliver Lodge, “Einstein’s theory will dominate all higher physics and the next generation of mathematical physicists will have a terrible time of it. For university courses and for all practical purposes we shall have the Galilean and Newtonian dynamics but they will reign as a limited monarchy and sooner or later the Einstein physics cannot fail to influence every intelligent man. If these complications are to come into science we must leave them to the younger men. I hope that gravitation, now that it has begun to interact with light, will begin to give up its secrets, but in my time I must be content to get secrets out dynamically and leave transcendental methods to others.”

One English scientist, Thomas Case, writes to The Times to protest that it would have been in much better taste for the Royal Society to have adjourned its discussion “before bringing into question the reputation of Newton, who was President of the Royal Society for the last twenty-five years of his life and raised the society to the acme of its fame.”

WHO IS EINSTEIN?

Albert Einstein was born in Germany in 1874. He early showed the bent of his genius and at the age of twelve, when his fellow pupils were plodding along with their daily tasks, he was plunging through works of higher mathematics borrowed from his teacher. He was only eighteen when he conceived the outlines of his theory and ten years later it was ready to give to the world. He left Germany for Switzerland at the age of sixteen and became naturalized as a Swiss citizen. His first academic position was the Professorship of Mathematical Physics at the Zürich Polytechnic. Then the founding of the Kaiser Wilhelm Academy for Research at Berlin gave him opportunity to work out his theories undisturbed by other duties. Shortly before the war he was called to Berlin to succeed the famous Dutch physicist, Professor van’t Hoff in the Academy. The object of this institution was the same as Carnegie had when he founded his institution for scientific research at Washington, which was to seek out the exceptional man wherever he may be found and set him at his peculiar tasks. At Berlin Einstein receives a salary of $4,500 and has nothing to do but sit and think. This he continued to do all through the five years of war and revolution as quietly and persistently as Kant at Königsberg during the wars and revolutions of a century before. Or as Archimedes at the siege of Syracuse who was absorbed in drawing geometrical figures in the sand--his blackboard--when a Roman soldier ran him through with a spear. On two occasions he took part in the world-struggle going on about his study, both actions greatly to his credit. In the beginning he refused to sign the manifesto of the German men of science denying all the charges against Germany, and at the time of the armistice he signed an appeal in favor of the revolution. He is an ardent Zionist and has promised to aid the Hebrew university which is to be founded at Jerusalem.

According to tradition, Isaac Newton was led to his theory of gravitation by observing an apple falling from a tree in his garden. The newspaper correspondents start a similar tradition by reporting that Einstein got his theory of gravitation by observing a man falling from the roof of a building in Berlin. Now a man has the advantage of an apple in that he is able to tell his sensations. When Dr. Einstein, who had seen the accident from his library window in the top story of a neighboring apartment house, reached the spot he found the man had hit upon a pile of soft rubbish and had escaped almost without injury. Asked how it felt to fall he told Dr. Einstein that he had no sensation of downward pull at all. This led Dr. Einstein to consider whether the relativity theory, which he had applied only to the case of uniform motion in a straight line, could not be extended to difform or accelerated motion by gravitation. So the special relativity theory which he had enunciated in 1905 developed ten years later into a generalized relativity theory (Verallgemeinerten Relativitätstheorie).

HOW TO LOSE WEIGHT

A man falling out of an airplane is obeying a natural impulse, namely, the force of gravitation. So long as he does not resist he is free as air, light as a feather, and altogether comfortable. He can look down with complacency and contempt on the poor mortals below him who are trying to stand up against this natural impulse and laboriously dragging one foot after another as they crawl about the earth when they might be flying through space without effort as he is. It is only when he tries to stop his free fall by bumping against the ground that he gets into trouble on account of gravitation. It was in this way that the Calvinists, who were a sort of mathematical theologians, conceived of the fall of man. The sinner is simply obeying the force of natural depravity, namely, moral gravity, and so long as he is conscienceless and does not consider his inevitable end he has no knowledge of the moral law and is quite happy in his downfall.

A person falling freely loses all his weight. His hat does not press down on his head. His feet do not press down on his shoes. If he lets go of his walking-stick it does not “fall down” at his feet. It stands upright and simply travels along with him. For, as Galileo showed when he dropped his big and little cannon ball off the Leaning Tower of Pisa, all bodies fall with the same speed.

If he were in a falling elevator with an opaque door he would not know he were falling unless he surmised it from the absence of gravitation as evidenced by his own feeling of lost weight and the queer behavior of the objects in the car. He might fall all his life and never find it out. The law of gravitation is like criminal law; you don’t feel it till you come into conflict with it.

Or if our illustration requires too tall a skyscraper, let us imagine that a comet as it flies by knocks a chip off the earth with a group of people on it. This terrestrial fragment, cast loose in space, gets caught by the attractive force of some gigantic and distant star and falls toward it with ever-increasing velocity for thousands of years. The inhabitants of this errant orb would never know it from their own feelings or any observations they could make on their own little world. Does that seem incredible to you? Then tell me how do you know but this our world is such a planet and together with the solar system has been falling for thousands of years toward some center of attraction? Astronomers, indeed, say that we are moving at tremendous speed toward Canis Major, in other words that the world is going to the dogs.

All this means that uniformly accelerated motion, such as gravitation imparts to a freely falling body, is, like uniform translatory motion, a question of relativity and cannot be discovered by an observer carried along by such movement.

The idea that uniform translation, like the moving train we have considered, is merely relative motion, is an old idea and not hard to understand or accept. But when we try to extend the principle of relativity to acceleration, that is, to a rate of motion that is continuously increased or retarded, we get a new and revolutionary conception of the universe and are drawn into some very startling conclusions. Einstein took this step five years ago and that is what has caused the present excitement. For Einstein when he once gets hold of an idea follows it wherever it leads him with the undaunted determination of a Nantucket sailor towed by a harpooned whale. It was a whale of an idea that he harpooned in 1915 and it carried him into strange waters. It led directly to a contradiction or correction of one of the two fundamental postulates which he had laid down as the foundation of his theory of the universe in 1905, namely, that the velocity of light in space is a constant. But he promptly abandoned this idea with cheerful nonchalance in favor of the new notion that the velocity of light is affected by gravitation.

A SUBSTITUTE FOR GRAVITY

Let us then follow Einstein and apply his Principle of Equivalence to accelerated motion and see what it leads to. Imagine yourself shut up inside a closed chamber, like an elevator car, somewhere out in space away from the gravitational forces of the earth or sun. Suppose this chamber to be rising with a constantly increasing velocity. We can, if we want to be definite about it, assume that the chamber is a big shell pulled up by a cable coiling around a conical windlass that hauls it up faster all the time. Or we can assume that it is propelled from behind by the continuous backfire of explosives, like the rocket which Professor Goddard proposes to send to the moon. All we need is some force, not gravitation, capable of giving the chamber every second an additional velocity of thirty-two feet a second. Now the point is that if you were in such an upward-moving chamber you would not know but what you were resting on the earth. Everything would behave exactly the same. If you now weigh one hundred and fifty pounds on the scales, that is, if your shoe soles press down with that force, the floor of the rising chamber would press upward with that same force and you would not know the difference. If you let loose a ball from your hand the floor would rise up to meet it and it would appear to fall. If you threw the ball upward with a velocity greater than the velocity of the chamber at the moment, the ball would rise, but since the velocity of the chamber was constantly increasing the floor would gain on the ball and catch up with it. This would look to you just the same as when on earth you threw a ball into the air and it fell back to the ground, drawn, as you are accustomed to think, by “the force of gravitation.” But here we have no “force,” but merely a mode of motion.

Under such circumstances it would seem that all Nature conspired to keep you in the dark. You appeal to the ether, that supposedly stable and stationary medium that fills all space, but that also fails you. You try the Michelson-Morley experiment to see if you are moving through the ether or at rest on the earth but your apparatus expands or contracts just enough to deceive you.