Part 6

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.