Of Time and Space and Other Things

by Isaac Asimov

  And so it is. It is now believed to be over 2,000,000 light-years from us and to contain at least 200,000,000, 000 stars. Still other galaxies were discovered at vastly greater distances. Indeed, we now suspect that within the observable universe there are at least 100,000,000,000 galaxies, and the distance of some of them has been esti mated as high as 6,000,000,000 light-years.

  Let us take Olbers' three assumptions then and substi tute the word "galaxies" for "stars" and see how they sound.

  Assumption 1, that the universe is infinite, sounds good.

  At least there is no sign of an end even out to distances of billions of light-years.

  Assumption 2, that galaxies (not stars) are infinite in number and evenly spread throughout the universe, sounds good, too. At least they are evenly distributed for as far out as we can see, and we can see pretty far.

  Assumption 3, that galaxies (not stars) are of uniform average brightness throughout space, is harder to handle.

  However, we have no reason to suspect,-6at distant galaxies are consistently larger or smaller than nearby ones, and if the galaxies come to some uniform average size and star-content, then it certainly seems reasonable to suppose they are uniformly bright as well.

  Well, then, why is the night sky black? We're back to that.

  Let's try another tack. Astronomers can determine whether a distant luminous object is approaching us- or receding from us by studying its spectrum (that is, its lijzht as spread out in a rainbow of wavelengths from short wavelength violet to long-wavelength red).

  The spectrum is crossed by dark lines which are in a fixed position if the object is motionless with respect to us. If the object is approaching us, the lines shift toward the violet. If the object is receding from us, the lines shift toward the red. From the size of the shift astronomers can determine the velocity of approach or recession.

  In the 1910s and 1920s the spectra of some galaxies (or bodies later understood to be galaxies) were studied, and except for one or two of the very nearest, all are re ceding from us. In fact, it soon became apparent that the farther galaxies are receding more rapidly than the nearer ones. Hubble was able to formulate what is now called "Hubble's Law" in 1929. This states that the velocity of recession of a galaxy is proportional to its distance from us. If Galaxy A is twice as far as Ga laxy D, it is receding at twice the velocity. The farthest observed galaxy, 6,000, 000,000 light-years from us, is receding at a velocity half that of light.

  The reason for Hubble's Law is taken to lie in the ex pansion of the universe itseff-an expansion which can be made to follow from the equations set up by Einstein's General Theory of Relativity (which, I hereby state firmly, I will not go into).

  Given the expansion of the universe, now, how are Olbers' assumptions affected?

  If, at a distance of 6,000,000,000 light-years a galaxy recedes at half the speed of light, then at a distance of 12,000,000,000 light-years a galaxy ought to be receding at the speed of light (if Hubble's Law holds). Surely, further distances are meaningless, for we cannot halve velocities greater than that of light. Even if that were pos sible, no light, or any other "message" could reach us from such a more-distant galaxy and it would not, in effect, be in our universe. Consequently, we can imagine the universe to be finite after all, with a "Hubble radius" of some 12,000,000,000 light-years.

  But that doesn't wipe out Olbers' paradox. Under the requirements of Einstein's theories, as galaxies move faster and faster relative to an observer, they become shorter and shorter in the line of travel and take up less and less space, so that there is room for larger and larger numbers of galaxies. In fact, even in a finite universe, with a radius of 12,000,000,000 light-years, there might still be an in finite number of galaxies; almost all of them (paper-thin) existing in the outermost few miles of the Universe-sphere.

  So Assumption 2 stands even if Assumption I does not; and Assumption 2, by itself, can be enough to insure a star-bright sky.

  But what about the red shift?

  Astronomers measure the red shift by the change in position of the spectral lines, but those lines move only because the entire spectrum moves. A shift to the red is a shift in the direction of lesser energy. A receding galaxy delivers less radiant energy to the Earth than the same galaxy would deliver if it were standing still relative to us - just because of the red shift. The faster a galaxy recedes the less radiant energy it delivers. A galaxy receding at the speed of light delivers no radiant energy at all no matter how bright it might be.

  Thus, Assumption 3 falls! It would hold true if the uni verse were static, but not if it is expanding. Each succeed ing shell in an expanding universe delivers less light than the one within because its content of galaxies is succes sively farther from us; is subjected to a successively greater red shift; and falls short, more and more, of the expected radiant energy it might deliver.

  And because Assumption 3 fails, we receive only a finite amount of energy from the universe and the night sky is black.

  According to the most popular models of the universe, this expansion will always continue. It may continue with out the production of new galaxies so that, eventually, billions of years hence, our Galaxy (plus a few of its neighbors, which together make up the "local cluster" of galaxies) will seem alone in the universe. AU the other galaxies will have receded too far to detect. Or new galaxies may continuously form so that, the universe will always seem full of galaxies, despite its expansion. Either way, however, expansion will continue and the night sky will remain black.

  There is another suggestion, however, that the universe oscillates; that -the expansion will gradually slow down until the universe comes to a moment of static pause, then begins to contract again, faster and faster, till it tightens at last into a small sphere that explodes and brings about a new expansion.

  If so, then as the expansion slows the diinming effect of the red shift will diminish and the night sky will slowly brighten. By the time the universe is static the sky will be uniformly star-brigbt as Olbers' paradox required. Then, once the universe starts contracting, there will be a "violet shift" and the energy delivered will increase so that the sky will become far brighter and still brighter.

  This will be true not only for the Earth (if it still existed in the far future of a contracting universe) but for any body of any sort in the universe. In a static or, worse still, a contracting universe there could, by Olbers' paradox, be no cold bodies, no solid bodies. There would be uniform high temperatures everywhere-in the millions of degrees, I suspect-and life simply could not exist.

  So I get back to my earlier statement. The reason there is life on Earth, or anywhere in the universe, is simply that the'distant galaxies are moving away from us.

  In fact, now that we know the ins and outs of Olbers' paradox, might we, do you suppose, be able to work out the recession of the distant galaxies as a necessary conse quence of the blackness of the night sky? Maybe we could amend the famous statement of the French philosopher Rene Descartes.

  He said, "I think, therefore I am!"

  And we could add: "I am, therefore the universe ex pandsl"

  10. A Galaxy At A Time

  Four or five'vears ago there was a small fire at a school two blocks from my house. It wasn't much of a fire, really, producing smoke and damaging some rooms in the base ment, but nothing more. What's more, it was outside school hours so that no lives were in danger.

  Nevertheless, as soon as the first piece of fire apparatus was on the scene the audience had begun to gather. Every idiot in town and half the idiots from the various con tiguous towns came racing down to see the fire. They came by auto and by oxcart, on bicycle and on foot. They came with girl friends on their arms, with aged parents on their shoulders, and with infants at the breast.

  They parked all the streets solid for miles around and after the first fire engine had come on the scene nothing more could have been added to it except by helicopter.

  Apparently this happens every time. At every di
saster, big or small, the two-legged ghouls gather and line up shoulder to shoulder and chest to back. They do this, it seems, for two purposes: a) to stare goggle-eyed and slack-jawed at destruction and misery, and b) to prevent the approach of the proper authorities who are attempting to safeguard life and property.

  Naturally, I wasn't one of those who rushed to see the fire and I felt very self-righteously noble about it. How ever (since we are all friends), I will confess that this is not necessarily because I am free of the destructive in stinct. It's just that a messy little fire in a basement isn't my idea of destruction; or a good, roaring blaze at the munitions dump, either.

  If a star were to blow up, then we might have some thing.

  Come to think of it, my instinct for destruction must be well developed after all, or I wouldn't find myself so fascinated by the subject of supernovas, those colossal stellar explosions.

  Yet in thinking of them, I have, it turns out, been a piker. Here I've been assuming for years that a supernova was the grandest spectacle the universe had to offer (pro vided you were standing several dozen light-years away) but, thanks to certain 1963 findings, it turns out that a supemova taken by itself is not much more than a two inch firecracker.

  This realization arose out of radio astronomy. Since World War 11, astronomers have been picking up micro wave (very short radio-wave) radiation from various parts of the sky, and have found that some of it comes from our own neighborhood. The Sun itself is a radio source and so are Jupiter and Venus.

  The radio sources of the Solar System, however, are virtually insignificant. We would never spot them if we weren't right here with them. To pick up radio waves across the vastness of stellar distances we need something better. For instance, one radio source from beyond the Solar System is the Crab Nebula. Even after its radio waves have been diluted by spreading out for five thousand light-years before reaching us, we can still pick up what remams and impinges upon our instruments. But then the Crab Nebula represents the remains of a supernova that blew itself to kingdom come-the first light of the explo sion reaching the Earth about 900 years ago.

  But a great number of radio sources lie outside our Galaxy altogether and are millions and even billions of light-years distant. Still their radio-wave emanations can be detected and so they must represent energy sources that shrink mere supemovas to virtually nothing.

  For instance, one particularly strong source turned out, on investigation, to arise from a galaxy 200,000,000 light years away. Once the large telescopes zeroed in on that galaxy it turned out to be distorted in shape. After closer study it became quite clear that it was not a galaxy at all, but two galaxies in the process of collision.

  When two galaxies collide like that, there is little likeli hood of actual collisions between stars (which are too small and too widely spaced). However, if the galaxies possess clouds of dust (and many galaxies, including our own, do), these clouds will collide and the turbulence of the collision will set up radio-wave emission, as does the turbulence (in order of decreasing intensity) of the gases of the Crab Nebula, of our Sun, of the atmosphere of Jupiter, and of the atmosphere of Venus.

  But as more and more radio sources were detected and pinpointed, the number found among the far-distant',ga laxies seemed impossibly high. There might be occasional collisions among galaxies but it seemed most unlikely that there could be enough collisions to account for all those radio sources.

  Was there any other possible explanation? What was needed was some cataclysm just as vast and intense as that represented by a pair of colliding galaxies, but one that involved a single gallaxy. Once freed from the neces sity of supposing collisions we can explain any number of radio sources.

  But what can a single galaxy do alone, without the help of a sister galaxy?

  Well, it can explode.

  But how? A galaxy isn't really a single object. It is simply a loose aggregate of up to a couple of hundred billion stars. These stars can explode individually, but how can we have an explosion of a whole galaxy at a time?

  To answer that, let's begin by understanding that a galaxy isn't really as loose an aggregation as we might tend to think. A galaxy like our own may stretch out 100,000 light-years in its longest diameter, but most of that consists of nothing more than a thin powdering of stars-thin enough to be ignored. We happen to live in this thinly starred outskirt of our own Galaxy so we accept that as the norm, but it isn't.

  The nub of a galaxy is its nucleus, a dense packet of stars roughly spherical in shape and with a diameter of, say, 10,000 light-years. Its volume is then 525,000,000,000 cubic light-years, and if it contains 100,000,000,000 stars, that means there is I star per 5.25 cubic light-years.

  With stars massed together like that, the average dis tance between stars in the galactic nucleus is 1.7 light-years - but that's the average over the entire volume. The den sity of star numbers in such a nucleus increases as one moves toward the center, and I think it is entirely fair to expect that toward the center of the nucleus, stars are not separated by more than half a light-year.

  Even half a light-year is something like 3,000,000,000, 000 miles or 400 times the extreme width of Pluto's orbit, so that the stars aren't actually crowded, they're not likely to be colliding with each other, and yet…

  Now suppose that, somewhere in a galaxy, a supernova lets go.

  What happens?

  In most cases, nothing (except that one star is smashed to flinders). If the supernova were in a galactic suburb in our own neighborhood, for instance-the stars would be so thinly spread out that none of them would be near enough to pick up much in the way of radiation. The in credible quantities of energy poured out into space by such a supemova would simply spread and thin out and come to nothing.

  In the center of a galactic nucleus, the supernova is not quite as easy to dismiss. A good supernova at its height is releasing energy at nearly 10,000,000,000 times the rate of our Sun. An object five light-years away would pick up a tenth as much energy per second as the Earth picks up from the Sun. At half a light-year from the supernova it would pick up ten times as much energy per second as Earth picks up from the Sun.

  This isn't good. If a supernova let go five light-years from us we would have a year of bad heat problems. If it were half a light-year away I suspect there would be little left of earthly life. However, don't worry. There is only one star-system within five light-years of us and it is not the kind that can go supemova.

  But what about the effects on the stars themselves? If our Sun were in the neighborhood of a supernova it would be subjected to a batb of energy and its own temperature would have to go up. After the supernova is done, the Sun would seek its own equilibrium again and be as good as before (though life on its planets may not be). However, in the process, it would have increased its fuel consump tion in proportion to the fourth power of its absolute tem perature. Even a small rise in temperature might lead to a surprisingly large consumption of fuel.

  It is by fuel consumption that one measures a star's age.

  When the fuel supply shrinks low enough, the star expands into a red giant or explodes into a supernova. A distant supenova by war@ng the Sun slightly for a year might cause it to move a century, or ten centuries closer to such a crisis. Fortunately, our Sun has a long lifetime ahead of it (several billion years), and a few centuries or even a million years would mean little.

  Some stars, however, cannot afford to age even slightly.

  They are already close to that state of fuel consumption which will lead to drastic changes, perhaps even supernova -hood. Let's call such stars, which are on the brink, pre supernovas. How many of them would there be per galaxy?

  It has been estimated that there are an average of 3 supemovas per century in the average galaxy. That means that in 33,000,000 years there are about a million super novas in the average galaxy. Considering that a galactic life span may easily be a hundred billion years, any star that's only a few million years removed from supemova hood may reason
ably well be said to be on the brink. if, out of the hundred billion stars in an average galac tic nucleus, a million stars are on the brink, then 1 star out of 100,000 is a pre-supern6va. This means that pre supemovas within galactic nuclei are separated by average distances of 80 light-years. Toward the center of the nu cleus, the average distance of separation might be as low as 25 light-years.

  But iven-at 25 light-years, the light from a supemova would be only 1/2:-,o that which the Earth receives from the

  Sun, and its effect would be trifling. And, as a matter of fact, we frequently see supemovas light up one galaxy or another and nothing happens. At least, the supemova slowly dies out and the galaxy is then as it was before.

  However, if the average galaxy has I pre-supemova in every 100,000 stars, particular galaxies may be poorer than that in supernovas richer. An occasional galaxy may be particularly rich and I star out of every 1000 may be a pre-supernova.

  In such a galaxy, the nucleus would contain 100,000, 000 pre-supemovas, separated by an average distance of 17 light-years. Toward the center, the average separation might be no more than 5 light-years. If a supemova lights up a pre-supernova only 5 light-years away it will shorten its life significantly, and if that supernova had been a thousand years from explosion before, it might be only two months from explosion afterward.

  Then, when it lets go, a more distant pre-supemova which has had its lifetime shortened, but not so drastically, by the first, may have its lifetime shortened again by the second and closer supernova, and after a few months it blasts.

  On and on like a bunch of tumbling dominoes this would go, until we end up with a galaty in which not a single supernova lets bang, but several million,perhaps, one after the other.

  There is the galactic explosion. Surely such a tumbling of dominoes would be sufficient to give birth to a corusca tion of radio waves that would still be easily detectable even after it had spread out for a billion light-years.