Chapter III: Part 3

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.

You now try observing horizontal rays of light but they seem to bend; that is, a beam of sunshine entering a pinhole on one side of your _camera obscura_ will not strike the wall at a spot exactly opposite but a little below it, if you have instruments sufficiently delicate to show this. You try vertical rays of light in this fashion: You examine with the spectroscope rays of light coming from two sources below (behind) your instrument, one at a distance and the other nearer. Now since you are moving away with increasing speed, the light from the farther source will have to take longer strides to catch up. Or in other words, its frequency will be reduced and it will be shoved toward the red end of the spectrum where the longer waves are. You will have noticed that when a whistling train rushes past the train you are on, the whistle as it comes toward you is raised in pitch (decreased wave-length) and as it recedes from you is lowered in pitch (increased wave-length).

Now, says Einstein to himself, if my Principle of Equivalence is correct and there is no difference between (1) weight and (2) the accelerated upward movement of an observer, then all the optical effects that I have thought out in the second case must apply to the first, that is, to gravitation. It must follow that a ray of light passing through a gravitational field will be bent out of its course as though it were attracted by the heavy body. This prediction has been verified. It must further follow that light proceeding from a heavy body like the sun or a star will be held back or slowed up by the attraction of gravitation, and the spectral lines will be displaced toward the left as compared with the same lines in the spectrum of an earthly light. Now such displacement has been observed in stellar spectra but it does not seem to be of the right value to satisfy Einstein’s equation and it has not been observed in sunlight.

The remarkable thing about it is that Einstein, by following a line of reasoning somewhat like that which I have crudely outlined, not merely supplied an explanation for phenomena that had been observed but could not be explained (such as the discrepancy in the orbit of Mercury) but he provided in advance the explanation for phenomena that had never been observed until he directed attention to it (such as the deflection of starlight by the sun). Sir Oliver Lodge says of this:[5]

Before Einstein’s prediction nothing of the kind had been seen, nothing of the kind had been looked for, nor, so far as it is known, had such an amount of deflection been suspected.

Whatever may ultimately be thought of the validity of Einstein’s views as a whole it is evident that he has worked out a mathematical method of unprecedented power and wide usefulness.

Professor Bumstead of Yale says:

Einstein’s theory is important in that it exemplifies a method which is in many respects new in theoretical physics and which may prove to be a very powerful method for advancing scientific knowledge. There was no idea that the prediction of the bending of light would fix up Mercury’s perihelion and incidentally explain a two-century old astronomical difficulty. That came straight out of a blue sky.

MECHANICAL VERSUS MATHEMATICAL MINDS

We sometimes hear it said that “Einstein has overthrown Newton’s theory of gravitation.” That is impossible because Newton did not have any theory of gravitation. He merely laid down the law of gravitation. He told how bodies behaved toward their neighbors; he did not tell why. Newton was not content with the idea of action at a distance through empty space and he tried to explain gravitation by the pressure of the ether on material bodies but he was not satisfied with the results and did not publish them. In the 234 years since many men have tried their hands at devising some sort of machinery that will “explain” gravitation. For human beings are like Toddie of “Helen’s Babies” and want to have the watch opened so they can “see the wheels go wound.” At least Anglo-Saxons have that desire. Poincaré, the French physicist, said this is the distinction between the Anglo-Saxon and Latin minds; the former are uneasy until they can imagine a mechanical model to represent natural phenomena, the latter are satisfied with a mathematical formula expressing the action. The ether, which was invented to explain light, also required “explanation.” Lord Kelvin imagined it to consist of spinning tops which have a sort of mobile stability. Sir Oliver Lodge has filled it with a complicated structure of interlocking geared wheels to account for electro-magnetic action. These are typical Anglo-Saxon modes of thinking. On the other hand, Einstein, who, in spite of his Hebrew blood and German training, has preëminently what Poincaré claims as the Latin temperament, does not have any use for the ether and does not care at all whether he can “picture” the fourth dimensions on paper or not.

Now some of us are excessively Anglo-Saxon in our attitude toward mathematics. It is with a fellow-feeling for such folks that I have filled this little volume with such crude and absurd analogies as trains and elevators and projectiles flying through space and Coney Island mirrors. To the mathematically minded such illustrations are not simplifications but complications, not representations but caricatures. Mathematics is the proper language of physics as the five-barred staff is the proper language of music. Ask a musician to explain a symphony in plain everyday English and he cannot do it, though he carry the Oxford Dictionary in his head. He can have the music played for us or he can show us the printed score but he could never convey it in ordinary language however long he might be willing to talk or we to listen. But we must not do the musician or the mathematician the injustice to suspect that his notions are hazy or absurd because he cannot explain (_i.e._ translate) them to us.

Nor should we assume that the new ideas, because they are more difficult for us to grasp, are necessarily more complicated or extravagant than the old. A friend of mine who is familiar with both tells me that Einstein’s papers are easier reading than Newton’s “Principia.”

The aim of science is simplification through generalization and this is the widest generalization yet attempted. It promises to bring gravitation into relationship with other forces. One great generalization, the law of the conservation of energy worked out by Joule and others in the forties, brought heat and work and chemical power all into one simple system. Clerk Maxwell in the seventies brought together in one beautiful formulation all the diverse phenomena of light, electricity and magnetism.

But gravitation has always stood out against any such league of natural forces. It refused to come into the combine. It remained unique, independent, irreducible, unalterable and inexplicable. Everything else is correlated and interactive. Heat destroys magnetism, magnetism produces electricity; electricity dissolves chemical combination; chemical combination produces heat; heat causes motion; motion makes magnetism; magnetism produces heat; and so on in endless round, each affecting all the others. Different substances behave very differently; one is more easily heated than another; some are readily magnetized or electrified, others are not so susceptible; certain elements rush into each others’ arms, others cannot be forced into combination.

But gravitation seemed indifferent to all these things; it showed no prejudices or preferences. It attracted with equal force all sorts of substances, no matter whether they were hot or cold, shiny or black, moving or still, electrified or magnetized or neither. Other forces and effects too required time for action at a distance. Sound travels at the rate of 1,100 feet a second in ordinary air. Light travels at the rate of 186,337 miles a second in a vacuum. But the force of gravity seemed not to require any time but to be everywhere, acting all the while, and nothing could shield it off or shut it out or in any way interfere with it. The substance or mass of a body as measured by its weight (the gravitational pull of the earth) was always identical with its mass as measured by its inertia (its resistance to being set in motion). All the energies are interchangeable. All other forces could be reduced or increased, annulled or brought into effect at will. Not so gravitation. Any bodies of a certain mass placed at a certain distance apart are always drawn by the same attraction. That is, gravitation is affected by nothing except geometrical relationships.

This naturally leads us to suspect that gravitation is nothing but a geometrical relationship, that it is somehow a peculiarity of space itself. If so, our demand of the physicist that he show us gravitation,--drag out this mysterious force from its hiding-place and let us see it--is altogether irrational. It is like a blind man hunting in a dark cellar at midnight for a black cat that isn’t there. The geometrician tells us that the internal angles of any triangle are equal to two right angles. Shall we ask him, what is the force that makes it so? Shall we refuse to ride on a trolley car until the electrician can answer our persistent question; “but what _is_ electricity?” When we ask such a question we are really asking him to tell us what electricity _is not_. To show us what electricity is he can keep his mouth shut and simply point to the dynamo that produces it, the wire that conveys it and the motor that consumes it. But what we secretly mean is that he show us a mechanical model that imperfectly imitates some of the actions of electricity or a mathematical formula that will calculate its effects.

Now Einstein seems in the way of making gravitation the foundation of a new system of geometry. Instead of “explaining” gravitation in terms of something else he will explain other things in terms of gravitation, or rather of his space-time manifold of which gravitation is one of the properties.

Einstein’s _law_ of gravitation proves to be more accurate than Newton’s law, but the correction is trifling except in rare cases. But Einstein’s _theory_ of gravitation is fundamental and far-reaching and if it is substantiated it will revolutionize physics and radically affect our ordinary conceptions of the universe. The verification of a prediction does not necessarily prove the truth of the hypothesis that led to the prediction. Many a scientific discovery has come out of a false assumption. Just as a miner may reopen an abandoned gold mine or work over his dump heap to get more out of it, so scientists often return to an old theory which they had abandoned for a more fruitful hypothesis.

THE WEIGHT OF LIGHT

It is interesting to see that our modern physicists show a disposition to adopt a corpuscular or emission theory of light not unlike the conception which Newton steadfastly and vainly defended against the undulatory theory. Professor Thomson, of Cambridge, reminds us that the crucial experiment between the two theories was the test made by Bennet in 1792 to determine if light exerted any pressure on a body when it struck it as it would if light consisted of minute particles driven straight forward with great velocity. Bennet found no such pressure and the corpuscular theory was regarded as disproved. But it was later found that the undulatory theory also involved such a pressure, and recent experimenters have proved and measured it. As Professor Thomson says:

It is perhaps fortunate that Bennet had not at his command more delicate apparatus. Had he discovered the pressure of light, it would have shaken confidence in the undulatory theory and checked that magnificent work at the beginning of the last century which so greatly increased out knowledge of optics.

Of course any modern form of the emission theory of light must account, as Newton’s did not, for such phenomena as interference and polarization, which are so satisfactorily handled by the undulatory theory. That is, it must combine the best features of both. Professor Thomson shows that only an exceedingly small fraction of the ether is concerned in the forward movement of light, in other words, “the wave front must be more analogous to bright specks on a dark ground than to a uniformly illuminated surface.” He does not, however, go so far as Planck in regarding it as proved that radiant energy of all kinds has a unit or atomic structure, the color of the light depending on the size of these particles.

The discovery of the pressure of a beam of light has led to some startling conclusions. For example, what shall be done with Newton’s law that action and reaction are equal? When a gun is fired the kick of the gun is balanced by the momentum of the projectile. When a reflector throws a beam of light into space, the kick of it is there all right but where is the projectile, if light is merely the undulation of an imponderable fluid? We may suppose that the light strikes some dark body out in space, transmits its impulse to that and Newton’s laws is satisfied, but it may be a long time before such a body is encountered and it may never be: at any rate a law that remains in a state of innocuous desuetude for several thousand years is not good for much. We must then assume that light has mass since it has inertia and momentum. But if light has mass it must have weight; that is, it must be attracted by gravitation. The eclipse observations confirmed this deduction. Newton would have expected something of this, for he says in his _Opticks_:[6]

Query 1.--Do not Bodies act upon Light at a distance, and by their action bend its Rays, and is not this action (_caeteris paribus_) strongest at the least distance?

The observed deflection of light due to the sun’s gravitation is greater than Newton would have anticipated but it would have been still more disconcerting to the nineteenth-century physicists, for in giving up Newton’s emission theory they had come to regard light as merely a form of motion in a weightless medium, the ether. Disembodied energy, like heat and light in ethereal space, was regarded as having no mass or weight. Twentieth-century physicists are coming to the opposite view, that the mass of a body is the measure of its internal energy. If so, mass is not constant but changes with composition, temperature, structure, electrification and motion.

As Einstein himself expresses it:

It is evident that it is not possible to attribute an absolute sense to the notion of acceleration, no more than to the notion of velocity. It is only possible to speak of the acceleration of a material point in connection with a body taken as the body of reference. It follows from this that there is no sense in attributing to a body a “resistance to acceleration” in the absolute sense, like the resistance of inertia in the classical mechanics. Further, this resistance of inertia ought to be so much the greater when there is, in the neighborhood of the body, more inert masses not in accelerated movement. On the other hand, this resistance ought to disappear when these masses participate in the acceleration of the body.

Now it is altogether remarkable that the equations of the gravitational field contain these different aspects of the resistance of inertia, which one might call the _relativity of inertia_.

The progress of science is continually toward a dematerialization of matter. Physical analysis resolves the crude, heavy, solid stuff that our senses show us into finer and finer particles farther and farther apart until these practically disappear into mere points of irradiating influence. First the mass is divided into the molecule and this again into the atom, assumed, at the time it was invented, to be the ultimate unit of matter. But recently the atom has been shown to be a sort of solar system, but more complex, composed of hundreds of electrons, corpuscles of electricity, whose radius is calculated to be 1/10,000,000,000,000 of a centimeter (a centimeter is so ---- long). “But the size of the centers of disturbance, which in Einstein’s theory are associated with matter, bears to the size of the electron about the same proportion as the size of the smallest particle visible under the most powerful microscope to that of the earth itself.”[7]

The old axiom was, “matter cannot act where it is not.” The new version might rather read: “matter cannot act except where it is not.” That is to say, attention is now directed to the space surrounding a material body or electrical corpuscle.

Although we laymen are not concerned with the niceties of astronomical measurements there is an aspect of this conflict of theories that does interest us. The theory of Newton or, to go back further, of Galileo, that the earth moves around the sun, altered profoundly the philosophical and religious beliefs of the world, and the theory of Einstein is much more far-reaching and revolutionary in its metaphysical implications than the former. Professor Planck, who has just received the Nobel Prize for his discoveries in physics, said of Einstein’s first paper:

It surpasses in boldness everything previously suggested in speculative natural philosophy and even in the philosophical theories of knowledge. Non-Euclidean geometry is child’s play in comparison.... 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 Copernican system of the universe.

MUTABLE THEORIES AND STABLE FACTS

There is a feeling very prevalent among the general public interested in such things that the foundations of modern science are being swept away by the recent discoveries. The layman has been led to believe that such laws as gravitation, the conservation of matter and the immutability of the elements are the most certain and absolute truths of science. But now he hears reputable men of science talk calmly about the decay of matter and the transformation of one element into another, and gravely consider a theory which makes invalid Newton’s three laws of motion. It surprises, even shocks, him, as much as it would to have a convention of bishops discuss the question of whether there is a God, or the Supreme Court agree to set aside the Constitution of the United States, or a congress of physicians resolve that all medicine does more harm than good. He knows that the mere broaching of such heretical views in these assemblies would be met with a storm of indignation and that all the weapons of contempt, ridicule and even personal spite would be directed against the rash innovator. Therefore he is astonished and puzzled to see that in the scientific world these revolutionary theories are received with interest and even pleasure, and in the criticism to which they are subjected there is scarcely a trace of animosity. And he does not see why men of science who have accepted doctrines apparently contradictory to their former teachings do not appear shamefaced and apologetic before the public, like augurs whose tricks had been exposed.

The difficulty of the layman arises from his not understanding how a scientist looks at his science; not realizing how firmly he holds to its facts and how loosely he holds to its theories. The scientist never bothers his head with the question whether a particular theory is true or false. He considers it simply as more or less useful, more or less adequate, succinct and comprehensive. A theory is merely a tool, and he drops one theory and picks up another at will and without a thought of inconsistency, just as a carpenter drops his saw and picks up his chisel. He will say that the earth moves around the sun one moment, and the next will revert to the theory of Chaldean astronomers, because it is more convenient, and say “the sun rises.”

Really, the new discoveries are not so upsetting to science as they appear to the general public. Unexpected and revolutionary as they are, no page of millions that record the experiments and observations of science is invalidated. No man’s work is proved wrong. Revolutions in science do not destroy; they extend.

In the reaction of public opinion toward any novel and revolutionary idea there are three stages observable.

1. That it is not true.

2. That it is not new even if it is true.

3. That it does not make any difference anyhow.

The first is merely the natural and instinctive reaction against any disturbing intellectual innovation. It is a flat denial inspired by that unconscious neophobia or xenophobia that possesses all of us more or less. The second stage is the effort at compromise in which usually both the advocates and opponents of the new idea coöperate by endeavoring to prove that it is not so novel and unprecedented as was at first assumed but fits in very fairly with our accepted notions, in fact may be regarded as a supplement or even a natural development of them. The third stage, like the second, is designed as an attempt to disarm opposition by allaying alarm in the conservative mind.

The second line of argument has a good deal of validity, for even the most startling and original idea will be found on closer examination to have its roots deep in the ground of the past and to have been approximately anticipated many times before. The third line of argument also contains some truth for we find everyday life does go on in much the same way, although it may seem that the foundations have been knocked from under our mental, moral or social universe by some new notion. Yet as the popular mind gradually accepts and adapts itself to the novel conception we generally find that its influence is even more far-reaching than was at first anticipated.

In the case of the Copernican theory it took about two centuries for the controversy to pass through the three stages and the mind of the public to become readjusted to the new conception of the earth’s revolution. In the case of the Darwinian theory of evolution the process was accomplished in about fifty years. The Einstein theory is more subversive of ordinary ideas than either of the others so it would naturally take longer to soak in. But the modern mind seems to be subject to acceleration and we see in the two months since the notion has been sprung upon the public that all three of the lines of argument are appearing at once and so the controversial period may run its course in five years though it will be longer before its indirect influence upon our fundamental philosophy and habits of thought are fully felt.

SCIENTIFIC VERSUS LEGAL LAWS

In all such discussions we must bear in mind that “law” in the scientific sense of the word means, not a commandment or a rule, but merely a way of working. It is a concise description of how things behave. There are no laws _in_ Nature; there are only laws _of_ Nature; that is to say, laws drawn out of Nature (or, if you prefer Latin to Anglo-Saxon, laws deduced from Nature) by man for his own convenience in thinking. Physical laws are therefore essentially psychological; mere memory schemes, calculating machines. The law of gravitation is no more gravity than the funny wriggles that my stenographer is making in her notebook are the sounds I am uttering. To change geometries does not require any such effort as to change cars. It means merely changing our minds. But this is harder for some of us than it ought to be. Here is where the theory of relativity will be of use to us. Poincaré, the French mathematician, cousin of the late President, said: “These two propositions, ‘the earth turns round’ and ‘it is more convenient to suppose the earth turns round’ have the same meaning. There is nothing more in the one than in the other.” If Galileo and his inquisitors had understood the Principle of Relativity it might have saved them both trouble; the former temporary imprisonment and the latter everlasting disgrace. A revolution in science is simply a change in mental attitude. Maybe a political revolution is no more.

It is disconcerting to the layman to be told, first, that matter consists of solid round atoms in empty space; next, that it is made of mere particles of electricity and negative at that; then that it is constituted out of strains in the ether; again, that the atoms are bubbles in the ether; and finally, that there is not any ether. But these various hypotheses are like the crayon strokes that an artist makes about a figure he is trying to draw. They are all attempts at preliminary sketches for mental pictures of natural phenomena. We do not call the geographers inconsistent and contradictory because one colors Massachusetts red on the map and another colors it green. All scientific hypotheses are put to the pragmatic test of which works the best in unlocking the secrets of Nature. Is “wheat” or “sesame” the magic word? Whether we call a dog “Fido” or “Towser” depends not on which name is shorter or sounds better but on which the dog answers to. If gravitation comes to heel better when we say “Einstein” than when we say “Newton,” all right, we’ll change. I trust that these frivolous illustrations will not lead my readers to accuse me of treating gravity with levity.

The layman--and with him must be included all those who have merely learned science but not used it--talks a great deal about “the laws of Nature,” which he regards as abstract, immutable, universal and eternal edicts, part of which are transcribed into the textbooks. To the working scientist they are only more or less convenient formulas; in the ultimate analysis only mnemonic symbols for stringing together facts to make them easier to handle, like _vibgyor_, for the spectrum colors. He knows that most of them are limited in their scope and only approximate in their accuracy. His chief delight is in discovering these limitations and irregularities. He regards these “laws” with no awe or reverence. He has no attachment for any of them--unless it happens to be one that he has formulated himself. If he finds a new hypothesis that works better he throws the old one aside as he does his old model dynamo, or keeps it around as handy still for doing some of the common work of the laboratory. It is, to recur to our example, just as “true,” using the word in its ordinary sense, to say that the sun goes around the earth as to say that the earth goes around the sun, for all motion is relative, and we can regard either body as the stationary one or both as moving, as we choose. When we say that the statement that the earth moves around the sun is the “true” one, we merely mean that it is the more convenient form of expression, for on this hypothesis the paths of the earth and the other planets become circles (or more accurately speaking, irregular and eccentric spirals) while on the other and older hypothesis their paths are very complicated and difficult to handle mathematically. The theory that the earth moves is not only simpler than that of a stationary earth, but it is wider in its scope. It explains more, that is, it connects up with other knowledge, such as the flattening at the poles. Copernicus, then, did not discover a new fact about the solar system. He only invented a lazier way of thinking about it.

The man of science invents an hypothesis whenever he needs one in his business. It is to him merely a new tool, a _novum organum_. If there is not an ether it would be necessary to create one. So he did it. He had to have a noun for the verb “undulate.” When he had created it he saw it was not good. The properties with which he endowed it were self-contradictory, and it refused either to move with the earth or to pass through it. But these theoretical inconsistencies do not bother the physicist much. In spite of them the ether is a handy thing to have about the laboratory. The scientist does not abandon a theory because it has inconsistencies any more than he divorces his wife because she has inconsistencies. Certainly the physicist did not consider himself presumptuous in thus inventing ether for his own convenience. He knew that the ordinary man had in the same way invented “matter” long ago for his own convenience. It is a crude, inadequate and impossible idea, this naïve conception of matter as something solid, heavy, hard, inert, indestructible, impenetrable, colored and surfaced; but it is good enough for part of the people all of the time and for all of the people part of the time. The physicist himself uses it for everyday. Only in his rigorous moments does he come down to bed-rock and say, with Poincaré, “Mass is a co-efficient which it is convenient to introduce into calculations.”

But when the physicist thus reduces matter to a small italic _m_ some people are sure to say that he is denying the existence of matter. What would they say about Riemann who considers matter to be holes in the ether? A definition is a different thing from a denial. There are people among us who deny the existence of matter and they call themselves “Scientists,” too, but they are not the ones who are devoting their days and nights to the study of the workings of matter in order to make it the servant of man.

A professor of chemistry would not think of asking his students if the atomic theory is true any more than he would ask them if the atomic theory is blue. He does not care whether they believe the atomic theory or not. He only wants them to be able to use the atomic theory for getting certain valuable results. Consequently, he watches with interest and without apprehension the progress of discovery in radio-activity which is undermining the old conception of the atom. He would be glad to get rid of the atomic theory if he could find something better because after all it is a clumsy thing and will not hold half the facts he wants to put into it. He would have no more hesitation about dropping it than he has in setting down one beaker to pick up a larger one when what he has in the first is frothing over. He does not want to spill anything, but he does not care what vessel it is in. Revolutions in science never go backward and they differ from political revolutions in that nothing worth saving is lost in transition. The new theory must always include all that the old one does and more. In their struggle for existence, formulas fight like snakes; the one that can swallow the other beats. Now a four-dimensional universe can take in a three-dimensional universe and have space to spare for whatever the narrower conception could not include so it seems likely to prevail.

We now know how to sympathize with those poor frightened people who lived in the times of Copernicus and Galileo when they were told that the solid earth on which they stood was not supported by anything, but whirling about and rushing around through empty space and that half the time they hung with their heads down over immeasurable space with nothing to hold on to. But they got used to it in time and lived happily ever after. So may we.

For the benefit of those who want to get their information at first hand I append an article by Dr. Einstein himself which appeared in the London _Times_ of December 13, 1919, and in _Science_ of January 6, 1920:

TIME, SPACE, AND GRAVITATION

_By Dr. Albert Einstein_

I respond with pleasure to your Correspondent’s request that I should write something for the _Times_ on the Theory of Relativity.

After the lamentable breach in the former international relations existing among men of science, it is with joy and gratefulness that I accept this opportunity of communication with English astronomers and physicists. It was in accordance with the high and proud tradition of English science that English scientific men should have given their time and labor, and that English institutions should have provided the material means, to test a theory that had been completed and published in the country of their enemies in the midst of war. Although investigation of the influence of the solar gravitational field on rays of light is a purely objective matter, I am none the less very glad to express my personal thanks to my English colleagues in this branch of science; for without their aid I should not have obtained proof of the most vital deduction from my theory.

There are several kinds of theory in Physics. Most of them are constructive. These attempt to build a picture of complex phenomena out of some relatively simple proposition. The kinetic theory of gases, for instance, attempts to refer to molecular movement the mechanical, thermal, and diffusional properties of gases. When we say that we understand a group of natural phenomena, we mean that we have found a constructive theory which embraces them.

But in addition to this most weighty group of theories, there is another group consisting of what I call theories of principle. These employ the analytic, not the synthetic method. Their starting-point and foundation are not hypothetical constituents, but empirically observed general properties of phenomena, principles from which mathematical formulæ are deduced of such a kind that they apply to every case which presents itself. Thermodynamics, for instance, starting from the fact that perpetual motion never occurs in ordinary experience, attempts to deduce from this, by analytic processes, a theory which will apply in every case. The merit of constructive theories is their comprehensiveness, adaptability, and clarity, that of the theories of principle, their logical perfection, and the security of their foundation.

The theory of relativity is a theory of principle. To understand it, the principles on which it rests must be grasped. But before stating these it is necessary to point out that the theory of relativity is like a house with two separate stories, the special relativity theory and the general theory of relativity.

Since the time of the ancient Greeks it has been well known that in describing the motion of a body we must refer to another body. The motion of a railway train is described with reference to the ground, of a planet with reference to the total assemblage of visible fixed stars. In physics the bodies to which motions are spatially referred are termed systems of coördinates. The laws of mechanics of Galileo and Newton can be formulated only by using a system of coördinates.

The state of motion of a system of coördinates cannot be chosen arbitrarily if the laws of mechanics are to hold good (it must be free from twisting and from acceleration). The system of coördinates employed in mechanics is called an inertia-system. The state of motion of an inertia-system, so far as mechanics are concerned, is not restricted by nature to one condition. The condition in the following proposition suffices: a system of coördinates moving in the same direction and at the same rate as a system of inertia is itself a system of inertia. The special relativity theory is therefore the application of the following proposition to any natural process:--“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.”

The second principle on which the special relativity theory rests is that of the constancy of the velocity of light in a vacuum. Light in a vacuum has a definite and constant velocity, independent of the velocity of its source. Physicists owe their confidence in this proposition to the Maxwell-Lorentz theory of electro-dynamics.

The two principles which I have mentioned have received strong experimental confirmation, but do not seem to be logically compatible. The special relativity theory achieved their logical reconciliation by making a change in kinematics, that is to say, in the doctrine of the physical laws of space and time. It became evident that a statement of the coincidence of two events could have a meaning only in connection with a system of coördinates, that the mass of bodies and the rate of movement of clocks must depend on their state of motion with regard to the coördinates.

But the older physics, including the laws of motion of Galileo and Newton, clashed with the relativistic kinematics that I have indicated. The latter gave origin to certain generalized mathematical conditions with which the laws of nature would have to conform if the two fundamental principles were compatible. Physics had to be modified. The most notable change was a new law of motion for (very rapidly) moving mass-points, and this soon came to be verified in the case of electrically-laden particles. The most important result of the special relativity system concerned the inert mass of a material system. It became evident that the inertia of such a system must depend on its energy-content, so that we were driven to the conception that inert mass was nothing else than latent energy. The doctrine of the conservation of mass lost its independence and became merged in the doctrine of conservation of energy.

The special relativity theory, which was simply a systematic extension of the electro-dynamics of Maxwell and Lorentz, had consequences which reached beyond itself. Must the independence of physical laws with regard to a system of coördinates be limited to systems of coördinates in uniform movement of translation with regard to one another? What has nature to do with the coördinate systems that we propose and with their motions? Although it may be necessary for our descriptions of nature to employ systems of coördinates that we have selected arbitrarily, the choice should not be limited in any way so far as their state of motion is concerned. (General theory of relativity.) The application of this general theory of relativity was found to be in conflict with a well-known experiment, according to which it appeared that the weight and the inertia of a body depended on the same constants (identity of inert and heavy masses). Consider the case of a system of coördinates which is conceived as being in stable rotation relative to a system of inertia in the Newtonian sense. The forces which, relatively to this system, are centrifugal must, in the Newtonian sense, be attributed to inertia. But these centrifugal forces are, like gravitation, proportional to the mass of the bodies. Is it not, then, possible to regard the system of coördinates as at rest, and the centrifugal forces as gravitational? The interpretation seemed obvious, but classical mechanics forbade it.

This slight sketch indicates how a generalized theory of relativity must include the laws of gravitation, and actual pursuit of the conception has justified the hope. But the way was harder than was expected, because it contradicted Euclidean geometry. In other words, the laws according to which material bodies are arranged in space do not exactly agree with the laws of space prescribed by the Euclidean geometry of solids. This is what is meant by the phrase “a warp in space.” The fundamental concepts “straight,” “plane,” etc., accordingly lose their exact meaning in physics.

In the generalized theory of relativity, the doctrine of space and time, kinematics, is no longer one of the absolute foundations of general physics. The geometrical states of bodies and the rates of clocks depend in the first place on their gravitational fields, which again are produced by the material systems concerned.

Thus the new theory of gravitation diverges widely from that of Newton with respect to its basal principle. But in practical application the two agree so closely that it has been difficult to find cases in which the actual differences could be subjected to observation. As yet only the following have been suggested:--

1. The distortion of the oval orbits of planets round the sun (confirmed in the case of the planet Mercury).

2. The deviation of light-rays in a gravitational field (confirmed by the English Solar Eclipse expedition).

3. The shifting of spectral lines toward the red end of the spectrum in the case of light coming to us from stars of appreciable mass (not yet confirmed).

The great attraction of the theory is its logical consistency. If any deduction from it should prove untenable, it must be given up. A modification of it seems impossible without destruction of the whole.

No one must think that Newton’s great creation can be overthrown in any real sense by this or by any other theory. His clear and wide ideas will forever retain their significance as the foundation on which our modern conceptions of physics have been built.

A final comment. The description of me and my circumstances in _The Times_ shows an amusing feat of imagination on the part of the writer. By an application of the theory of relativity to the taste of readers, today in Germany I am called a German man of science, and in England I am represented as a Swiss Jew. If I come to be regarded as a _bête noire_, the descriptions will be reversed, and I shall become a Swiss Jew for the Germans and a German man of science for the English!

FOOTNOTES:

[Footnote 1: Bergson: “Time and Free Will,” p. 221.]

[Footnote 2: Bergson in his “Laughter” traces all humor back to this fundamental absurdity of making a man act mechanically.]

[Footnote 3: “We can thus say that all these paradoxical phenomena (or rather negations of phenomena) which have been enumerated above can only happen after the end or before the beginning of eternity” (De Sitter).]

[Footnote 4: If you insist upon seeing just what is the difference between Einstein’s and Newton’s laws of gravitation here it is as given in _The Scientific Monthly_ of January, 1920:

Any particle or light pulse moves so that the integral of _ds_ between the two points of its path (in four dimensions) is stationary where

(according to Einstein)
_ds^{2}_ = -(1 - 2_m_/_r_)^{-1}_dr^{2}_-_r^{2}_ _d θ^{2}_ + (1 - 2_m_/_r_)_dt_

or (according to Newton)
_ds^{2}_ = _dr^{2}_ - _r^{2}_ _d θ^{2}_ + (1 - 2_m_/_r_)_dt_

These expressions are in polar coördinates for a particle of gravitational mass _m_.

The new factor introduced by Einstein is, as shown above,

1/{1-(2_m_/_r_)} ]

[Footnote 5: _Nineteenth Century_, December, 1919.]

[Footnote 6: Quoted by Eddington in _Contemporary Review_, December, 1919.]

[Footnote 7: Sir Joseph Thomson in _Nature_, December 4, 1919.]

And finally

IF YOU WANT TO READ MORE ABOUT THE EINSTEIN THEORIES

_For the non-mathematical reader_:

ABBOTT, EDWIN.

Flatland, by A Square. Boston, 1891.

An amusing way of leading up to the fourth dimension.

CAMPBELL, NORMAN.

The Commonsense of Relativity. _Philosophical Magazine_,
April, 1911.

CARR, WILDON.

The Metaphysical Implications of the Theory of Relativity.
_Philosophical Review_, Jan., 1915.

CARUS, PAUL.

The Principle of Relativity. Chicago: Open Court Publishing
Co., 1913.

COMSTOCK, D. F.

The Principle of Relativity. _Science_, May 20, 1910,
vol. 31, p. 767.

CUNNINGHAM, E.

Einstein’s Relativity Theory of Gravitation. _Nature_,
Dec. 4, 11, and 18, 1919.

An interesting non-mathematical discussion of the latest
phases of the theory.

EDDINGTON, A. S.

Einstein’s Theory of Space and Time. _Contemporary_
_Review_, Dec, 1919.

Good popular article.

EDDINGTON, A. S.