Part 3
Or consider this simple illustration: Cut a strip of motion picture film into its separate scenes and pile them up in order till it is as high as it is broad. You have then a cubical event. Two dimensions of the cube are spatial; the third dimension is essentially temporal, although in a spatial form. If one of the films from the middle of the pack represents the present then the films below represent the past and those above the future. The people on the picture you picked out know only of the scene there depicted though they may have a fading memory of the past and a dim anticipation of the future. But to you who are outside of the film pack all the scenes are equally visible. They are all present to you. This is the way most Christians have conceived of God, as one to whom past and future form one eternal present, so he sees simultaneously all things that have been, are or will be.
If our pile of film were made up of snapshots taken one a day throughout a man’s life we should see at one glance his growth from babyhood to boyhood, to maturity and old age. We could turn the leaves of his life backward or forward as we will. Some day perhaps we shall have stereo-movies, scenes in three dimensions with time as the fourth.
This idea of time as a fourth dimension is not a new one. In 1754 d’Alembert, defining “dimension” in the Encyclopedia, wrote: “A brilliant man of my acquaintance believes that one may regard duration as a fourth dimension.” In 1903 Minkowski worked out the idea in mathematical form. H. G. Wells, always quick to catch up a new scientific theory to use as a plot for a story, wrote in 1895 of “The Time Machine,” a vehicle by which a man could travel back and forth in time as he can travel east and west in a motor car. In this he visits the future and finds mankind split into two species, a subterranean working class living on--literally--a pleasure-loving leisure class.
In “The Plattner Case” Wells tells of a chemical professor who was by an explosion knocked into--not the middle of next week as we commonly say--but into the fourth dimension of space. Ten days later he was knocked back again into our world but the only evidence of the truth of his story was that his heart beat on the right side and he was left handed and otherwise reversed in a way that would be impossible in a space of three dimensions.
[Illustration: In space of three dimensions we cannot make a right hand glove and a left hand glove look the same no matter how we turn them around. But if we turn one glove inside out it will match the other except that the lining now appears on the outside.]
[Illustration: Our two hands cannot be turned inside out so as to look the same in three dimensions, though they might in four dimensions.]
We can turn a glove inside out in three dimensions and so make it just like its mate of the other hand, but we cannot turn a solid inside out except in four-dimensional space.
In another of his “Thirty Strange Stories” Wells tells “The Story of Davidson’s Eyes.” While Davidson was working in his London laboratory a lightning shock so affected his eyesight that he could not see the familiar objects about him which he could feel but looked instead at a South Sea island on the opposite side of the globe. This might be possible in a curved space of four dimensions although Wells professes to pooh-pooh such an absurd suggestion while he ingeniously insinuates it. George Macdonald in his fantastic romance “Lilith” also introduces the fourth dimension.
Points that are far apart if measured in three dimensions may be close together in the fourth. We can readily understand this if time is the fourth dimension, for events can happen at the same instant though thousands of miles apart. But it is not impossible to conceive of the fourth dimension as spatial instead of temporal if we approach the problem from a simpler standpoint. Let us think of ourselves as living in a “Flatland” of two dimensions with no thought of a third. There yet survive in enlightened America individuals who believe that “the sun do move” and who deny that the earth is “round like a ball.” That is, they do not recognize the curvature of the earth in the third dimension. But if such an individual were to travel in a “straight” line westward over the “level” land and water he would, much to his surprise, come back to his starting point which he had left 25,000 miles behind him.
[Illustration: By movement in one dimension we cannot make the lines _AB_ and _B′A′_ coincide for if we drag _B′A′_ straight on to _AB_ the ends will not match. But if we swing _B′A′_ around through the second dimension we bring it on _AB_ so the letters correspond.]
[Illustration: In space of two dimensions, such as a table top, we cannot bring these two triangles into the same position. If we drag one straight over on to the other (movement in one dimension) they will not fit together. If we swing one triangle around (movement in two dimensions) they still do not fit. But if we take one triangle off the table and turn it over (movement in the third dimension) we can then lay it by the side of the other and they will match perfectly.]
A WORM’S-EYE VIEW OF THE WORLD
[Illustration]
Suppose yourself a worm--the Bible says you are anyway--and crawling around on a sheet of paper. With your vermicular mind you doubtless would take a superficial view of the universe and find it as impossible to imagine a third dimension as man does a fourth. If in the course of your crawling you came across a triangle you might--if you were a measuring worm--pace it off and find that the distance from _A_ to _B_ was 8 inches, from _B_ to _C_ was 6 inches and from this data, if you knew the law of the hypothenuse, you might calculate that the distance from _A_ to _C_ was 10 inches. On measuring it you would find your prediction verified and so gain perfect confidence in your plane geometry. But unbeknownst to you, poor worm with your eyes fixed on the paper, some man may have picked up the sheet and crumpled it up or rolled it over so that _A_ and _C_ are only one inch apart--in the third dimension. The worm is right when he thinks the distance between these points is 10 inches: so is the man right when he says it is one inch. It depends on the point of view.
Now in Einstein’s view something of this sort happens to our three-dimensional space when matter gets into it. We know for instance that if you divide the circumference of any circle by the diameter the ratio figures out as 3.1415+. It has been calculated to 707 decimal places but we can dispense with the rest of them and call the whole thing Pi for short. Write it in Greek as π and it looks more learned. Now if you place a heavy particle, say a lead bullet, in the center of a circle the ratio of the diameter to the circumference, according to Einstein, becomes a little less than Pi, for the circle has been warped, so to speak, into the fourth dimension by the strain of gravitation. The difference in such a case is too small to be measurable by any known means, but it is supposed to be an actual, not an imaginary, deviation from the geometrical law.
Now the sun being a big heavy body must extend its gravitational strain for a considerable distance around and a ray of light passing through this crumpled up space would not be able to pursue a straight course. And, according to the eclipse observations, it does not. Light like everything else follows “the easiest way” and this is not always the straight and narrow path. A river takes the easiest, not the shortest, way to the sea and this leads it through many meanderings. Most of us, I suppose, have a mental image of Newton’s gravitation as a sort of rope by which the sun pulls the earth into its orbit when it is disposed to fly off on a tangent. But from Einstein’s viewpoint we should rather think of the earth as picking its way as best it can through a space-and-time combination that has been strained and distorted by the power of the sun. I visualize Einstein’s solar system as a spider web with the sun in the middle like the spider and the planets like flies trying to get around through the tangled strands. But it is more complicated than that for each planet has its own lesser web of radiating influence to drag about with it wherever it goes.
Newton’s idea is simpler, but unfortunately light at least seems to follow Einstein’s law, not Newton’s. That is why Einstein is such a troublesome fellow. If he would confine himself to metaphysical speculation nobody need bother about these strange notions of his. But when he points how they can be proved and then British astronomers and American physicists find things according to his deductions he cannot be ignored. The man does not seem to have that decent respect for the opinions of mankind that leads most of us to limit our logic to the sphere of common sense. When he gets an idea in his head he follows it wherever it leads him even though he bumps up against Euclid and Newton and the rest of us. For instance, if you admit the second of his two fundamental postulates, that the speed of light is constant, regardless of the velocity of its source, you are irresistibly led--unless you let go of his hand somewhere on the way--to the conclusion that time is a local affair; that there is no way of telling by light signals whether two clocks at a distance are keeping the same time, or whether two events at different places occur simultaneously. You could not tell this even if you could shoot a watch from one place to the other with the speed of light, for no matter how many seconds--or years--the watch might be on its way it would register the same time. If instead of a watch a man could travel at that speed he would not grow old on the way. According to Einstein no man, watch or any other material thing can travel with the speed of light, for it would require an infinite force to give the smallest particle such a velocity. But let us suppose that a hollow projectile holding a man, such as Jules Verne and Wells used on their voyages to the moon, should be sent off into space with a velocity one twenty-thousandth less than light. If at the end of a year the projectile should be caught like a comet by the gravitation of some star and be swung around and sent back to the earth, the man on stepping out of his shell would be two years older but he would find the world two hundred years older. This would be, as Professor Langevin suggests in _Scientia_, 1911, an interesting way to study history, but it would be risky, not to say impossible. Still French scientists, like Napoleon, have no place in their dictionaries for so stupid a word as “impossible” and M. Esnault-Pelterie has figured out that a thousand pounds of radium would be sufficient to carry a man to Venus in 35 hours if a hollow projectile could be fitted up like a rocket with the radium in the rear sending out a rapid fire of electrons.
TURNING TIME BACKWARD
To loosen up our conventional ideas of the fixity of time and space we may accept the aid of the scientific romancers. Camille Flammarion, the famous French astronomer, wrote a fantastic little book called “Lumen” which tells of a man who died in 1864. His soul flew straight to its heaven which was one of the planets of Capella, the largest star in the constellation Auriga. Here he found the benevolent inhabitants of that sphere, who were endowed with superhuman powers of sight, watching with great distress the bloody scenes of the French revolution of 1793, and wondering how it would come out. To the visitor from the earth this was an old story, to the people of Alpha Aurigae it was a present spectacle, for the distance of the star was such that it took light 72 years to travel from the earth, so they were 72 years belated in their observation of current events on our planet.
The spirit of the defunct Parisian, having the power of flying through empty space at any speed he chose, found that he had thereby also acquired control of time and could hasten, retard, stop or reverse the course of events at will by simply varying his speed. If he remained stationary, scenes on the earth would unfold at their normal rate and in regular order. If he traveled away from the earth with the speed of light everything seemed to stand still. If he traveled faster than light he overtook the rays that had left the earth farther and farther back in the past so he saw through them events in the reverse order. For instance when he looked down on Waterloo he saw the battlefield strewn with corpses and Napoleon walking toward Waterloo backward pushing his horse by the bridle. This is how the battle looked to the interspatial observer:
When my sight was sufficiently habituated to the scene, I perceived some soldiers coming to life out of the eternal night, and by a single effort standing up. The dead horses revived like the dead cavaliers, and the latter remounted them. As soon as two or three thousand men had returned to life, I saw them form unconsciously in line of battle. The two armies took their places fronting one another, and began to fight desperately with a fury that one might have taken for despair. As the combat deepened on both sides, the soldiers came to life more rapidly....
At each gap made by the cannon in the serried ranks a group of resuscitated dead filled up the gaps immediately. When the belligerents had spent the whole day in tearing one another to pieces with grape-shot, with cannons and bullets, with bayonets, sabers and swords--when the great battle was over, there was not a single person killed, no one was even wounded; even uniforms that before it were torn and in disorder were in good condition, the men were safe and sound, and the ranks in correct form. The two armies slowly withdrew from one another, as if the heat of the battle and all its fury had no other object than the restoration to life, amid the smoke of the combat, of the two hundred thousand corpses which had lain on the field a few hours before. What an exemplary and desirable battle it was!
Another literary curiosity on the same theme is “Ignis” by Comte Didier de Chousy. This tells of certain engineers who attempted to utilize the internal heat of the earth by running the waters of a lake into a deep boring. The result was an explosion that blew off a piece of the planet. But the passengers on this artificial asteroid on looking down through their well at the earth they had left could see the lake and city undisturbed and watch themselves at work as they were before the place blew up. The explanation was that this fragment of the earth was projected into space more rapidly than the speed of light and so was catching up with the rays that had gone out before the explosion; these rays, of course, carried the picture of earlier scenes. But Einstein would say that this story--as we might ourselves have suspected--must be fiction for according to his theory the speed of light is the absolute limit of motion, the infinity of velocity, which no material body may excel or attain. He does not, however, say anything about the possible speed of a disembodied spirit such as Flammarion employed in his imaginary exploration of space.
THE METAPHYSICS OF THE MOVIES
But from such fantasies we can see that the order in which we view events depends upon how fast and in what direction we are moving and that past and future may be reversed to our vision. This is easily made apparent by means of motion pictures. If the film is reeled off in the wrong direction the action is reversed. So we see divers rising gracefully out of the water and landing on the spring board. Newly hatched chickens, dismayed at the sight of this unfriendly world, calmly tuck themselves back into their broken shells which close in upon them. When we have come to the close of a perfect Thanksgiving Day the obliging operator may give us an encore of the dinner reversed by running his machine backward. Then we see pieces of turkey politely picked out of the mouths of the diners with their forks and replaced upon the plates. When these are passed back to the carver he puts the slices neatly in their places and the fowl is then sent back to the oven to be unroasted. The cook then sticks on the feathers. The hired man carries the turkey out to the chopping block where with one swift stroke he restores the head and the fowl runs off backwards. This is just as correct as the ordinary order. The sequence of events is the same. Cause and effect are linked together as firmly as before, only they have exchanged places. A scientist knowing nothing of our world except from watching such reversed motion pictures might deduce from them the same consistent and logical system of natural laws that we now have although some of them, for instance, the second law of thermo-dynamics, would be reversed in form.
The motion-picture man has also the power to alter the speed of the passage of time as he will by turning the crank faster or slower. Sometimes he is quite too careless in the way he employs this prerogative. If he is behind time on his schedule he will rush through a lazy siesta scene in a Mexican plaza with all the fury of a Mack Sennett farce. But this telescoping of time can be used to advantage as when he shows us the growth of a plant, the unfolding of its flower and the ripening of its fruit, all in fifteen minutes. On the other hand motion may be slowed up by taking twice as many pictures a minute as usual and projecting them at the ordinary rate. For instance, if it is a dog jumping up to grab a piece of meat from his master’s hand, we see the dog rise slowly from the ground and, while poised in mid-air, eye the meat carefully to select the best point of attack, then deliberately take it between his jaws and gradually descend. Now notice that this is just as true a picture of the dog’s jump as any other. The movie man has simply expanded time measurements as he expands space measurements when he shows us a close-up. A close-up with a face covering a sixteen-foot screen is just as true as a smaller picture. It is what we should always see if the lens of our eyes were a bit more convex. We look through the small end of an opera-glass and objects seem magnified. We look through the large end and objects seem minified. This is not an illusion. The opera-glass _does_ actually enlarge or reduce _what we see_.
So, too, time intervals can be lengthened or shortened. Take a dose of hashish--no, don’t--I should say, if you did take a dose you would find that your perception of duration was prolonged. If while under the influence of the drug you drop a book it will seem an hour getting to the ground. De Quincey describes such experiences in his “Confessions of an Opium Eater.” But without entering into such abnormal states we all know by everyday experience how time flies or lags according to the number of our sensations. Bergson’s philosophy is built upon the distinction between the idea of duration as experienced by all of us and the idea of time as established by the physicists for comparative measurements.
We live in deeds not years; in thoughts not breaths; In feelings not in figures on a dial. --_Festus._
For all we know an ephemeral insect that dies in a day may live a longer life than a Galapagos turtle that exists for two centuries.
What Mark Twain said about classical music applies also to science; “It is not so bad as it sounds.” The thing that the chemist calls “sodium chloride” other folks call “salt”--and so does he when he is off duty. Don’t let the scientist bluff you by his polysyllabic propensity. Just try to see what he means by such language. Now what these new-fashioned non-Euclidean geometricians call “the four-dimensional space-time continuum” is essentially the same system of reference as you have used ever since you could toddle. Minkowski did not invent it. Everybody thinks that way unless he is an idiot. Each one of us has had to build up his own philosophy of the universe long before we went to school, mostly before we could talk. We had to study geometry while we were in our cradles--worse than that we had to work out a practical system of geometry for ourselves without the help of Euclid or anyone else. We had to excogitate a system of relationship between the sights and sounds and touches that came to us before we could get along in the world. Probably we all solve this riddle of the universe in about the same way although since there is no way of directly comparing notes we cannot be sure about that.
THE EGOCENTRIC THEORY OF THE UNIVERSE
But the framework that we construct to hold everything outside of ourselves is essentially of the following form:
You are the center of your universe. Everything and every event that you are considering is related to you here and now. Starting from this, your point of place and time, you imagine eight straight lines stretching out toward infinity in eight directions as divergent as possible. These lines--call them destinations or directions or dimensions or coördinates as you please--consist of four opposing pairs, right and left, up and down, forward and back, future and past. Somewhere along or between these four dimensional lines that cross in your brain you can find a place for anything that you need; your pencil, the discovery of America, the sun and next Friday. You can connect up all these things by lines which may represent changes, that is the tracks of movements in space and time. To connect the pencil in your hand with the discovery of America you would have to count back 428 years on the time line and measure off on the east-west and north-south lines whatever distance you may be from San Salvador--not to consider the motion of the earth.