Relativity and the Absurdities of Alice

This sounded pleasant enough, but, of course, odd too, which was due to the fact that Alice lived before 1908. Since that time, and especially since 1913, a number of gentlemen wearing glasses and looking wondrous wise, and no doubt as wise as they look, have proved to us that it can always be tea-time if we care to figure it out properly and get away from a commonplace three-dimensional existence.

To-day any budding physicist can tell you without cracking a smile that ‘a conception of the physical world in its objective four-dimensional scheme would merely be an abridged statement of the correspondence of the subjective time-space experiences in the realm of the various senses, and nothing more.’ Remember, it is not the Hatter speaking now, but the average serious-minded young man or woman at college, who has been taking notes of the lectures on Relativity given by the Professor of Mathematical Physics. The words used above happen to be those of an Oxford Don, but the professors at almost any other University can put the case just as succinctly. Perhaps at the University on the Cam they discuss gravitation, space, and time more than elsewhere, which is natural when we recall that Sir Isaac Newton himself and Lewis Carroll were once undergrads there and, later, professors. The Cambridge Professor of Astronomy is easily a leader in demonstrating the new Einsteinian theory of gravitation. Sir Isaac never had a theory of gravitation, only a law; but Einstein has both theory and law.

Our professor says that if we would only let him ‘interpose some kind of dispersive medium, so that light of some wave-length could be found traveling with every velocity and following every track in space-time, then, if we were looking at a solid which suddenly went out of existence, we should receive at the same moment light-impressions from every particle in its interior, supposing them self-luminous. We actually should see the inside of it.’ Now, this would surely have satisfied Alice, for she did so want to know what the flame of a candle looked like after it was blown out. But even Alice did not yearn to see the insides of things-in-themselves; and besides, if it is to be always tea-time, as these professors can easily bring about, it will perhaps be more pleasant not to see more than the insides of the tea-cups.

Alice’s friend the March Hare had a watch which he looked at gloomily. He had used butter on it, the best, too; but, as the Hatter said, ‘Some crumbs must have gotten in as well.’ But that is a trifling matter compared with the six clocks that our professor has on his mantel, all good time-keepers and set right. Yet he can make you view them in such a way that the clock on the extreme left indicates noon, the clock next to it points to eleven, the third clock to ten, and so on. If the mantelpiece were long enough and he had clocks enough, he could turn to-day into yesterday; and we could all say together, ‘How queer everything is to-day, and yesterday things went on just as usual.’

On this side of the Atlantic, a professor at Columbia tells us in a snappy little volume that, if we could only look far enough straight before us, we would in time see our back hair, if we had any. Or if a man goes to the top of a high mountain and aims a gun in any direction and shoots, provided the bullet goes fast enough, it will whiz round the world and on its return hit him behind the ears. Which goes to prove that it may be dangerous to stand back of some marksmen.

Or, again, let a man start for Arcturus. By terrestrial chronology, it will take one hundred years, traveling at the rate of one hundred and eighty-six thousand miles each second. When he arrives at Arcturus, some professor of mathematical physics at the leading University will say, ‘How do you do? I timed your start. Of course you have not had breakfast yet?’ The explanation is that, traveling with the speed of light, the yard-stick or light year shortened almost to zero in the line of travel. Now here we have one way of getting eternal youth.

Alice longed to be able ‘to shut up like a telescope’; and she thought she could if she only knew how to begin. That’s just it. One must know how to make the right beginning. And the modern theory of general relativity does seem to prove that we have never started right on earth. We thought we were standing still, while all the time we were hurrying so fast that it makes one’s hair stand up on end just to think of it. Why, since you began this article, say five minutes ago, you have flown through space thirty-eight hundred miles.

And that is not all. For no one can be sure of his shape now; because size depends upon speed. All motion is relative. If Alice had moved fast enough, she could have diminished her weight. All students of physics to-day know that mass and energy are essentially same thing.

Einstein’s law is practically this: ‘The gravitational mass of a body is equal to its inertial mass.’ If, when we were reading Alice long ago, we had in a moment of forgetfulness written the above on our final examination papers in mechanics, it is a certainty that it would have cost us our degree. What distress of mind it would have caused our old instructor if we had said things — that is, assuming that professors really feel keenly such errors! And to-day the point of view has changed. If a conscientious old instructor in mathematics insists that a straight line is the shortest distance between two points, he will soon be enlightened. Or if someone quotes Herbert Spencer’s dictum that the proposition concerning parallel lines not meeting at infinity is undemonstrable, because no one could go there, mathematical proof is forthcoming to show that the lines may meet because of a warp in space which makes them geodesics. Up to now we have lived in a three-dimensional world, but the coming generations will be satisfied only with a fourth.

Now the greater part of the mass is due to concealed energy. What will happen when we come into knowledge of the control of sub-atomic energy? for these small fry move with terrific velocities. Shall we soon be able to release this energy, and later to harness it? Some marvelous discoveries are being made. Alice in dreamland underwent remarkable transformations; but the physicists are changing substances and analyzing the structure of atoms in a way that makes Lewis Carroll’s wildest flight of fancy seem humdrum. Even the grin of the Cheshire cat, which remained after Pussy faded out, is simplicity itself compared with a hydrogen atom losing its electrons and becoming a different gas. The chemists construct all nuclei out of hydrogen nuclei, which means that the ninety-two elements, some not yet found on earth, can be traced back to a common ancestor — the hydrogen or helium nucleus.

And here, strangely, Einstein’s work has a direct application. It seems that the mass of a helium nucleus is not just the sum of its four alpha particles plus two electrons, but an extra mass due to the energy of formation. (It is C. G. Darwin speaking, reviewing the work of Aston and others with positive rays.)

Surely we are near the transformation of the elements. We can now knock off a few hydrogen particles from nitrogen and oxygen. A new mechanics — the mechanics of the atom — is here; and the old laws of classical dynamics must yield, for they fail to meet requirements. Nearly every month a new chapter is written in this story of the structure of matter. We have moved — we no longer live in Flatland. We do not have to measure our angles according to Euclid: he has had his day. Even that greatest generalization of the human mind, Newton’s law of attraction, proportional to the masses and inversely as the square of the distance, gets a jolt. For light seems to have pressure and weight. Sunshine actually punches the earth with a fist that weighs one hundred and sixty tons. A ray of light from a star grazing the edge of the sun is bent, not because of refraction, but is pulled in by gravitation as if it were a stream of bullets. The bending has been measured. At the last total solar eclipse, two parties sent out to Brazil and Africa by the Royal Astronomical Society secured about a dozen photographs in the twelve minutes the eclipse lasted. The positions of certain stars (about seven), are displaced. The shift is not just the amount which a gravitational pull on the light would produce, according to the old law of gravitation, — and Sir Isaac himself hinted that such a thing might occur, — but twice the amount, which fits in nicely with the new law of gravitation, and is very close to what Einstein had said in advance it would be.

May we not say with Alice, ‘Curioser and curiouser! Now, I am opening it’? Gravitation fades out of the scene as a force, and becomes a distortion of space in the presence of matter. It makes one think of the Cheshire cat and its grin.

The new law also accounts for the discrepancy in Mercury’s perihelion, which has bothered astronomers for some years. It may, however, be said that most of us did not worry much over this erratic swinging of the long axis of the planet’s orbit.

But to return to Alice: Rule 42 read that ‘all persons more than a mile high should leave the Court.’ Now we know how to get around this rule. On the trip to Arcturus, we saw that change of mass with speed is the same as the time-length change. Hence, if a person moved so fast that his mass was doubled, his size would be reduced one half.

Shades of Augustus De Morgan, return from the mists beyond the Styx! They say, but do not yet prove, that the ratio of the circumference to the diameter is altered when we introduce matter at the centre. Let us suppose that they succeed in squaring the circle — then what becomes of the Budget of Paradoxes?

A resounding chorus smites the air. Minkowski, Lorentz, Larmor, Planck, Silberstein, Eddington, Cottingham, Crommelein, Davidson, Schlick, Slosson, Weyl, and all the rest sing in a hearty bass, Space and Time are deprived of the last vestige of physical objectivity.’ Einstein's tenor rings clear above the rest: ‘Let those who are unfamiliar with physics no longer feel like the wanderer who was unable to see the forest for the trees.’