The Bounds of Space and Time

by DONALD H. MENZEL

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MOST of us have pondered the significance of infinity. Pondered and wondered! Here we are, at an instant of time. We look backward down the long corridors of history and forward into the dim and uncertain corridors of the future. Have those corridors a beginning or an end? Or do they stretch on indefinitely, in both directions? Although this question is extremely important, the limitations of the human mind make impossible the comprehension of infinity. And we cannot comprehend a limited universe either.

Suppose that I possess advance information to the effect that the world will end tomorrow. The sun and stars and planets will vanish from the sky. The earth will dissolve at the final tick of the celestial clock. Even then our minds still want to bridge the gap and say, “Well, what about the day after tomorrow?” I have heard people say that they would go insane if they had to worry about such questions day after day.

We encounter similar limitations in our concept of space. Here a trained mathematician has some advantage over the layman. Although he recognizes his inability to visualize what he may term “warped or curved spaces,” he can study their mathematical properties and see how it is that space can be finite even though the universe may be unbounded.

I think it was Einstein who first popularized this concept. Certainly it was he who put time on a par with space in the equations that describe the properties of the universe. The world of relativity is not one of geometry, with spheres, triangles, cubes, and other geometrical figures. No! The world of relativity is one full of action, a universe of events. And if we use the word “geometry” at all, we are trying to describe the world of events, the world of reality.

A beginning for the earth or solar system does not involve psychological or philosophical problems, so Let us see if we can find any clues that will help us date so remote a happening as the earth’s beginning. We find the information we seek in the rocks themselves — or, rather, in the atoms that compose the rocks. We recognize the existence of some ninety-six chemical elements. Some are abundant, like aluminum, magnesium, iron, or hydrogen. Others are rare, like gold, platinum, radium, or uranium. A few we have built only recently in that remarkable modern laboratory, the atomic pile.

Certain varieties of these atoms are unstable; radium and uranium arc perhaps the most familiar examples of radioactive substances. Here I do not refer to tlie special instability that makes the atom bomb possible. I refer to the ordinary, gardenvariety instability we have recognized for more than half a century: radioactivity. The nucleus of an ordinary uranium atom can explode a number of times, forming different atoms in the process, finally ending up as lead. These atoms are not now being formed; so they must be the remnants of radioactive matter left over when the universe was made.

There are two kinds of uranium. The heavier one, which weighs 238 on the atomic scale, ends up as lead 206. Uranium 235 (the lighter one used for atom bombs) finally forms lead 207. By measuring the amounts of lead in a rock, we can infer the age of the sample. The older the rock the greater the proportion of the lighter lead. And when we study the oldest samples of all, including the meteorites, we find an age of about four and a half billion years.

The theory behind this calculation is something like estimating the age of a community from the quantity of trash accumulated on the city dump — or from the number of headstones in the local cemeteries. We conclude, therefore, that the solar system, including the earth and meteorites, began some four and a half billion years ago.

Telescope measures show that the universe is expanding or exploding at an enormous rate. The great clusters of stars we call galaxies are speeding away from us. The most distant ones are receding more rapidly than the nearer ones. These observations pose a peculiar problem for us. Why should we be at the center of the explosion? Why should all galaxies apparently shun us, as if we were a plague spot of the universe?

We might conclude that we merely have a favorable location somewhere near the center of the explosion, and that the most distant objects got to be most distant because they moved most rapidly. However, with millions of galaxies, it does seem a little unlikely that our position should be so unique — exactly in the center.

Einstein’s theory of relativity offers an alternative possibility. It states, in effect, that no matter what galaxy we might happen to call our own, we should find the same thing happening: all the nebulae would tend to recede from it. Hence, if just any galaxy could be the center of the universe, we conclude that there must be no unique center.

This thought is a little difficult for our earthconfined minds to grasp. And yet we discover a simple analogy on the earth itself. Except for the poles of rotation, there are no unique points on the surface of the earth. Birmingham could readily compete with Boston for the title of the “Hub” city. Indeed, choose any spot in the world as an arbitrary starting point, for the surface of a sphere has no center.

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LET us follow this analogy a trifle further. Suppose that the earth is expanding — like a balloon being blown up from inside. Then, if you are located, let us say, in Birmingham, you will find that the cities of the world are moving away from you. New York will recede more rapidly than Atlanta because New York is farther away, and Boston is moving away more rapidly than New York. But this property is not peculiar to Birmingham. If you should be at Boston, instead, the cities of the world would appear to be receding from that spot.

The world of stars is not a two-dimensional space like the surface of a balloon. It is three-dimensional. But mathematicians can reason by analogy that if this three-dimensional world could expand something like a balloon, we should find a universe similar to the one we encounter today.

We can project ourselves backward in time, turning the expansion into contraction, and recall those fragments from the distant realms of space. With some surprise, we find that these fragments, about four and a half billion years ago, were back near the starting point. The expansion or the explosion must have started just about that time.

Here are two independent pieces of evidence which lead us to conclude that something exceptional happened just under five billion years ago. And we might just as well call this event the beginning of the universe, though perhaps the word “beginning” carries with it a significance different from “creation.” The most distant objects in the universe of which we now are cognizant require from three to four billion years for their light to reach us. We are almost seeing them before they are born. We try to bridge the gap in time and see what the world was like before the cosmic explosion set the clouds of nebulae skyrocketing into space.

One theory — perhaps the one most widely held today — holds great promise. The Abbé Lemaître, a Belgian prelate, suggested that all the matter in the universe once was concentrated in what we might call a giant egg. I really mean concentrated. The individual atoms were so closely packed together that the matter may have been a million times denser than steel. A single pinhead made of this primitive matter would have weighed about a hundred pounds. Some estimates have set the density even greater, so that that primeval pinhead would tip the scales at a thousand or even ten thousand tons!

We do not know the exact size of this egg. In fact, size is almost meaningless in such a body, because size implies the presence of a gauge or independent measuring rod. However, according to present-day standards the egg probably had a diameter somewhere between a hundred and a thousand times greater than that of the orbit of the earth.

Our imaginations tempt us to visualize this cosmic egg as a sort of rock surrounded by a vast sea of nothing. But, from the standpoint of the egg, there was no possible way to penetrate the shell and explore this supposedly empty realm beyond. A rocket ship that might try to take off from the edge and leave the egg behind would be doomed to failure. No power source could possibly enable the ship to break away.

Our egg, presumably, is extremely hot. But if we are on the outside looking in, we are doomed to disappointment. Any ray of light that tries to escape falls back leadenly to the surface of the egg. None escapes to render the egg visible to a person on the outside.

What I am saying is this: that there may be two worlds — one inside and one outside the egg. But they are completely independent and it is impossible for us ever to pass from one to the other. I do not mean to imply that a being in the outside world would be completely unaware of the existence of the egg. The same law that forbids radiation to escape from the egg also forbids it to enter. Hence, if light from the sun or star were to fall upon the egg, the radiation would be reflected. In this sense we could “see” the egg as we see a rock or any other opaque body. But we cannot expect to break it open.

For countless eons (or for only an instant, according to whatever system you deem appropriate to tell time in so static a universe) this cosmic egg lay incubating. Suddenly, about five billion years ago, the egg hatched, if a violent explosion equivalent to the blast of a super atomic bomb may be termed “hatching.”

What made this egg hatch? Here is a question that seems beyond our present ability to answer, though we may eventually understand how the explosion started. In any event, we see that mutual gravitational pull tended to hold the mass together. There may have been small oscillations; the “shell" was flexible (like that of a reptile’s egg). It may have moved spasmodically, like a cat in a gunny sack. I strongly suspect that electric currents, inherent in the initial mass, may have exerted explosive forces similar to those of solar prominences.

Anyway, the mass broke up and the universe was on its way: an enormous, expanding cloud of gas and radiation. Some force, perhaps gravitation, caused the cloud to break into pieces, like a cake cut with a knife. These were the masses that formed the supergalaxies, the largest cosmic units we recognize. At some slightly later stage, these units further broke up into crumbs, shall we say, just to continue the cake analogy. These crumbs — individually so large that light takes about a hundred thousand years to move across one of them — represent the galaxies or Milky Way systems of stars.

One of the most significant and still mysterious characteristics of these galaxies is the tendency that many of them have to form spiral structures. A few are amorphous masses, but we can arrange them in a sequence that strongly suggests an evolutionary pattern, as indicated by the late Dr. Edwin P. Hubble of Mount Wilson Observatory.

Rotation is probably responsible for the dominant form of these galaxies, which are flat, diskshaped structures. Each galaxy of the millions accessible for telescopic study has peculiar characteristics that make it as much of an individual as you or I. But the dominance of spiral structure, ranging all the way from a delicate wave to tight loops, shows the basic importance of this formation. We have generally supposed that rotation is responsible for it, but we are not entirely sure. Some of them display a layer of dust in them.

1 should not be surprised to find that cosmic electric currents similar to those we find in solar prominences play a part. In space we find many clouds of gas whose filamentary structure calls to mind the similar nature of prominences. Why such clouds do not evaporate into space is puzzling — unless there are weak electric currents flowing through the interstellar medium.

The stars and stellar families did not form immediately. Nor did they form all at once. In fact we see some stars in the sky that could not possibly have existed since the beginning. They shine too brightly. They are using up their energy at so great a rate that their lives will be short — short, that is, in terms of the cosmic scale.

According to the dictionary, evolution is the natural force that tends to grow complex things out of simple ones. We see that gravitation and electromagnetism must play an important part in the evolution of the universe. The forces between atoms and the ability of atomic nuclei to release vast amounts of energy are also important.

As a result of this atomic interplay, the chemical nature of the universe changed rapidly during the first few minutes of its existence. An experienced cook can judge, from the color and tenderness, just how long and at what temperature the meat was roasted. Similarly, from the chemical composition of the universe, an atomic scientist can calculate what happened during the early stages of the universe. Within minutes after the initial explosion occurred, the temperature dropped below the critical value for cooking up new atoms, and the present chemical composition of the universe was fixed — fixed, that is, except for the atom-building processes going on within the stars. Our knowledge of this early phase of atomic cookery is due largely to George Gamow, atomic scientist of George Washington Iniversity.

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ARE there any other major forces contributing to change in the universe? If gravitation and related forces are building complex structures, we see one natural law that operates in reverse — a conflict between what the biologist might term anabolism and catabolism. This important force, which tends to tear down, is built on the laws of chance. We call it the second law of thermodynamics.

The first law of thermodynamics is simple. It merely states that the total energy content of the universe is constant. We must include all kinds of energy—motion, gravitation, electricity, and atomic. The second law relates to the way in which energy flows in the universe. It guarantees — or practically guarantees — that a bucket of water put on a hot stove will boil rather than freeze. A hot object placed near a cold one will grow cooler.

How does the law of chance enter into this phenomenon?

Atoms and radiation are undergoing constant shuffling throughout the universe. We may aptly compare the world to a huge pack of cards. The arrangement at any moment, with honest and meticulous shuffling, is purely a matter of chance. If bridge were played with millions of cards instead of the customary fifty-two, the chances of really good hands would be very small. The game would be colorless. Successive hands would be very like the ones preceding. But the game that nature is playing with atoms is far from colorless. Nor are successive deals the same. Each one shows a progressive change in the direction of uniformity.

Wherein does our analogy fail? The answer, and apparently the only answer, is that the “cards” were stacked originally. We are far from the ultimate completely shuffled state indicative of a rundown universe. Energy struggles to escape from stellar prisons. The universe is rushing toward a condition with matter strewn in cosmic ash heaps and with radiation flung to the ends of space. To start the world over again we should have to collect the escaped radiation and force it, against its will — that is, against the laws of nature—back into the cores of stellar cinders. When cards have been thoroughly shuffled, what process will rearrange them in their original state? To revive the cosmos from this final depression will require more than a new deal. He who wishes to revivify the universe must be able to restack the deck.

A new pack of cards has the four suits arranged in sequence. After a single shuffle the order is disarranged, and statistics tell us the original order would thereafter recur naturally only once on the average in a million trillion trillion trillion trillion trillion shuffles. The chance against the “perfect” bridge hand of thirteen trumps is 160 billion to one. If every man, woman, and child in the United States were to play ten hands of bridge a day, the ideal hand would be expected to occur about once a year.

If time were truly infinite, every arrangement of all the particles might be expected to recur again and again. Is the universe perpetuated in this manner? We must not forget that the deck has been stacked at least once.

We see, however, one major fallacy in the argument. By this reasoning I, or rather an assemblage of matter that unfortunately resembled me, must have long ago been writing exactly the same words that you are now reading. This immediately calls to mind a drawn chess game wherein the same position has occurred several times over.

Is the universe like such a chess game? Repetition would seem to be a sort of inane activity. Indeed, Sir Arthur Eddington, well-known British astronomer-philosopher, discarded the possibility chiefly because he felt that il would be rather tiresome to keep doing the same things over and over, He says, “I am an evolutionist, not a multiplicationist.”

However, I specifically point out that repetition cannot possibly occur in a universe that is expanding.

The second law of thermodynamics makes the universe “run down.” Stars use up their sources of atomic energy, grow cold, and die. We have seen that the force of gravitation is reversible. There is nothing in the motions of the planets to indicate in which direction time is going. From the standpoint of celestial mechanics, a motion picture of the solar system looks just as reasonable backward as forward. The exception is our own earth, where the friction of the lunar tides is radiated into space as heat.

But where is the world going? And how long will it last? We have explored the beginning. Let us now talk about the end.

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FORECASTING the end of the world is a favorite pastime of astrological or numerological devotees. Nowadays such predictions seldom rate more than a few lines in the newspapers and are treated with contempt or amusement. But it was not always so. When the Scriptures were taken more literally — as well as more seriously — the fear of imminent catastrophe was general, Men regarded every bright comet that appeared as a warning from heaven that the cataclysm was at hand. Every volcanic eruption and every earth tremor caused the devout to pray for postponement of the dreaded event.

Predictions of the end of the world fall, generally, into three classes: I) supernatural cataclysms engineered by a deity shocked at the wickedness of ancient Gomorrah or modern Hollywood, 2) destruction from natural causes, and 3) death from mere old age. Science cannot deny the possibility of a catastrophe of the first sort, though most scientists profess disbelief in miraculous phenomena. In any event, the miraculous does not readily lend itself to mathematical analysis. We can, however, invoke the law s of mathematics, chemistry, physics, and astronomy in an attempt to pierce the veil of the future, a billion years, a trillion years. Will the sun still be shining? Will our earth still be here? What will it be like? Will it still be populated by our descendants?

By now we cosmogonists are ready to admit that our earth is an insignificant part of the universe. Even so, some of us would regard the destruction of the earth as serious, despite the fact that its loss, from the cosmic viewpoint, would be inconsequential.

What calamities can befall our own planet or affect its habitability? First of all, there is the danger from collision. Men have ever been fearful lest the earth or sun smash into some cosmic body. The dark-star menace has been the theme of many a thrilling bit of science fiction. The prototype of such stories was written about fifty years ago by the famous astronomer, Simon Newcomb, who pictured the effect of a giant meteor’s falling into the sun. The solar activity resulting from the crash heated the oceans to the boiling point, covered the earth with a sea of slime and mud, and destroyed all traces of life. Such a collision is always a possibility and it might, work real havoc provided the dark body were large enough.

Space, however, appears to be fairly free from bodies of planetary size, though the earth is being continually bombarded on all sides by small bits of iron and rock. Most of these, which are about the size of sand grains and small pebbles, are kindled by friction of the upper atmosphere and are burned out long before they reach the ground. These are meteors or “shooting stars,”of which many millions daily strike the earth. Occasionally larger ones, not entirely consumed, reach the ground. Though several meteors have caused considerable damage, there is no definite record of one’s having caused the death of any man.

A cosmic projectile that fell in Arizona many thousands of years ago made a dent almost a mile across and six hundred feet deep. Numerous such meteor craters are known. As recently as 1908, a meteorite struck in northern Siberia, exterminating a large herd of reindeer, uprooting trees over an area of some five thousand square miles. The seismic shock and atmospheric blast were recorded halfway around the globe. If such a bolide were to fall in the center of a densely populated area like New York City, it would undoubtedly cause tremendous damage and much loss of life. Even so, such a catastrophe would fall far short of being the end of the world.

The menace of comets was widely advertised about 1910, when the earth barely missed the head and actually passed through the tail of Halley’s comet. Here the danger, as heralded in the newspapers, was twofold: from solid matter in the nucleus and from poisonous gases, cyanogen and carbon monoxide, which the spectroscope revealed to be present. The latter danger, in particular, was played up in the more lurid newspapers. The word picture of the morning after, painted by some journalist with an eye for the sensational, sticks in my memory to this day; a view of the sun’s rising on a world utterly lifeless — and soundless “save for the ghastly popping of swollen bodies.”

Pure sensationalism! The gases mentioned are lethal, to be sure. But the tail of a comet is almost a vacuum and would add only the minutest amount of gas to the relatively dense earth’s atmosphere. Motorcar exhausts put far more carbon monoxide into the air of a city street than would be found in an equal volume of a comet. Head-on collision might produce some damage. The nucleus of every comet contains solid matter, meteorites held together with frozen gases. Certain well-defined crater-like depressions, the savannas of the South Atlantic states, may well have resulted from cometary impact. The moon’s pock-marked surface is ordinarily accounted for in terms of meteoric collision.

Collisions with stars or gaseous nebulae are also possible. As far as potential damage is concerned, we can immediately drop the nebulae from the picture. Like comets’ tails, they are too tenuous to offer appreciable resistance to the passage of bodies through them. A star, on the other hand, would spread devastation. Several thousand million years ago, possibly when the universe was less expanded than at present, the chance of such an encounter may have been much greater than it is now. We have already noted the low cost of insurance against cosmic accident of this type. The possibility of a collision happening within the entire life of the sun is negligible.

But if a collision did occur, or if the sun happened to explode naturally, to form a nova, the earth would Hare up momentarily. Oceans would boil and evaporate in a vast explosion of steam. The mountains would burn with a red heat and our rivers would run with molten metal. In a matter of hours, the earth — including the ashes of all of its former inhabitants — would have evaporated into space.

What future has the moon? It is now receding into space — slowing down the earth by tidal friction in the meanwhile. This recession will continue for a long time — for billions of years—until finally the earth and moon rotate like partners in a dance, facing one another, while the day of twenty-four hours lengthens to nearly two months!

But this is not the end. The tides slowly make the earth reverse. Eventually the sun will rise in the west and set in the east. And now the moon draws in toward the earth. Enormous tides rise until, finally, the earth’s pull on the near side of the moon so exceeds that on the far side that the moon breaks into millions of pieces. These distribute themselves around the earth in the form of a ring, like that of the planet Saturn. A ring of rocks surrounding the earth!

I ask you to make allowance for the uncertainties in my picture of the future. I warn you that I have gone far beyond our existing knowledge. In thus extending our recently discovered “laws" of physics over millions or billions of years, we are like the fabled race of ephemerids who lived in the tube of a thermometer. Ephemerids are a sort of intelligent bacteria. Their span of life was a tiny fraction of a second, but of this handicap they were unconscious. They had their astronomers who determined the height of the thermometer tube, and their physicists who made laboratory experiments. Of all their natural laws, one was very firmly established by observation over hundreds of generations: the mercury was rising at the rate of a thousandth of a millimeter a second. By simple arithmetic they could calculate the end of their contracting universe, when the mercury would reach the top of the tube and crush them against the wall of glass. Imagine the turmoil that resulted when some later generation of scientists discovered that the mercury had reversed itself.

This fable is pure fancy, of course. And yet I know of no law of physics today as firmly established as that of the ephemerids. The law of gravitation? A mere infant, discovered so they say by Sir Isaac Newton in 1665 although it was in effect long before Newton’s day.

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ASSUMPTIONS ! Postulates! Axioms! Theories! Physical laws! Is there any reasonable way to overcome the handicap imposed by the finiteness of human life? The difficulty lies in the fact that socalled physical laws are not “laws” at all, in the precise meaning of the word. They are not rules to be explicitly obeyed; like the ephemerids’ law, they are descriptions of the behavior of nature as perceived by man. The correctness of this viewpoint is borne out by the alacrity with which physicists amend them when they discover exceptions. The law of gravitation has already undergone substantial revisions in terms of Einstein’s theory of relativity.

Stars, particularly Polaris, have ever been the poet’s symbol of constancy. Science reveals, beneath this disguise of drab monotony, a dynamic and changing universe. The words that Shakespeare put to Caesar’s lips—

have the opposite significance in terms of the polestar’s true behavior: its small but perceptible daily motion, its gradual drift across the heavens, and its fluctuations in brightness and velocity.

The whole universe seems to be evolving, slow as some of the changes may appear to finite man. Every sun is pouring out vast quantities of energy in the form of light and heat. Every second brings the world a second nearer to extinction since, as far as we have been able to ascertain, no replenishment occurs. The sun picks up a few meteors; feeble starlight and so-called cosmic radiation fall on its surface, but these additions are negligible. They can have no more effect on the life of a star than an extra bucketful of water thrown into Lake Erie would have on the life of Niagara Falls.

It is, of course, conceivable that the stars may have a source of energy of a nature still unrecognized by earth-bound scientists. Fred Hoyle and Hermann Bondi, well-known British astronomers, have recently suggested that stars, moving through the universe, attract to themselves enough hydrogen to replenish the loss of energy by radiation. They have further supposed that, as space expands, new atoms of hydrogen form to till that space. But this process of continuous creation of matter is completely speculative, and no observational evidence exists to support the idea.

I cannot bring myself to believe that the universe is a perpetual-motion machine, effectively manufacturing energy from nothing. Without such a miracle, the present state of the cosmos appears to be temporary. Someday the cosmic fuel will give out and the sun will grow cold along with the other stars. If this view discourages you, take heart from the fact that you probably will be able to find a few stellar embers still glowing on the cosmic hearth a hundred billion years from now.

But, if changelessness is an ideal, we shall eventually find it — the stagnation of a Buddhist Nirvana, the quiescence of death. In this distant future we find space strewn with the cold bodies of stars. Perhaps the earth, then a frozen fragment, still swings around the burned-out cinder that used to be our sun. Radiation, the soul of stellar life, has leaked out of the stars and dispersed itself uniformly through space. The universe is a mere graveyard, haunted by the ghosts of the dead.

The phoenix, fabled Arabian bird, was supposed to end its long life by flying into the fire, only to rise with renewed youth and live through another cycle. Has our world an existence similar to that of the phoenix? Will a new universe arise from the ashes of the old? When two dead stars happen to collide there will be a momentary Hash. Some persons seem to believe that the stars could thus be rekindled. But the fires lit in this fashion would sputter feebly and then die away.

Some scientists have visualized an inverse process occurring out in the depths of space, the building up of atoms from wandering stellar energy. In cosmic radiation they see the birth cries of infant atoms—atoms that may subsequently condense into stars to replace those of our present system when they are worn out. Every known law of science, especially the law of chance, argues against such a possibility.

Will the galaxies ever cease their expansion and fall back to their starting point, like a spent skyrocket? If not, it appears that the universe, like the century plant, is fated to bloom but once and die. However, we cannot be sure that expansion will continue indefinitely. If the expansion can reverse into contraction, we visualize the possibility that the universe may eventually rebuild the egg from which it was born, setting the stage for another performance of the cosmic drama. There are difficulties, probably insuperable, with this truly phoenix-like view of creation, appealing though it may be to those who find perpetual extinction philosophically unattractive. I am inclined to favor the opposite view: indefinite expansion, the flashing of fireworks, a glorious blaze, followed by oblivion!