Part 6
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.”