Cosmos - Carl Sagan (1980)

Chapter 8. TRAVELS IN SPACE AND TIME

We have loved the stars too fondly to be fearful of the night.

—Tombstone epitaph of two amateur astronomers

The rising and falling of the surf is produced in part by tides. The Moon and the Sun are far away. But their gravitational influence is very real and noticeable back here on Earth. The beach reminds us of space. Fine sand grains, all more or less uniform in size, have been produced from larger rocks through ages of jostling and rubbing, abrasion and erosion, again driven through waves and weather by the distant Moon and Sun. The beach also reminds us of time. The world is much older than the human species.

A handful of sand contains about 10,000 grains, more than the number of stars we can see with the naked eye on a clear night. But the number of stars we can see is only the tiniest fraction of the number of stars that are. What we see at night is the merest smattering of the nearest stars. Meanwhile the Cosmos is rich beyond measure: the total number of stars in the universe is greater than all the grains of sand on all the beaches of the planet Earth.

Despite the efforts of ancient astronomers and astrologers to put pictures in the skies, a constellation is nothing more than an arbitrary grouping of stars, composed of intrinsically dim stars that seem to us bright because they are nearby, and intrinsically brighter stars that are somewhat more distant. All places on Earth are, to high precision, the same distance from any star. This is why the star patterns in a given constellation do not change as we go from, say, Soviet Central Asia to the American Midwest. Astronomically, the U.S.S.R. and the United States are the same place. The stars in any constellation are all so far away that we cannot recognize them as a three-dimensional configuration as long as we are tied to Earth. The average distance between the stars is a few light-years, a light-year being, we remember, about ten trillion kilometers. For the patterns of the constellations to change, we must travel over distances comparable to those that separate the stars; we must venture across the light-years. Then some nearby stars will seem to move out of the constellation, others will enter it, and its configuration will alter dramatically.

Our technology is, so far, utterly incapable of such grand interstellar voyages, at least in reasonable transit times. But our computers can be taught the three-dimensional positions of all the nearby stars, and we can ask to be taken on a little trip—a circumnavigation of the collection of bright stars that constitute the Big Dipper, say—and watch the constellations change. We connect the stars in typical constellations, in the usual celestial follow-the-dots drawings. As we change our perspective, we see their apparent shapes distort severely. The inhabitants of the planets of distant stars witness quite different constellations in their night skies than we do in ours—other Rorschach tests for other minds. Perhaps sometime in the next few centuries a spaceship from Earth will actually travel such distances at some remarkable speed and see new constellations that no human has ever viewed before—except with such a computer.

The Big Dipper, as seen from the Earth (top left), from the back (top right) and from the side (right). The last two views would be seen if we were able to travel to the proper vantage points, about 150 light-years away.

The appearance of the constellations changes not only in space but also in time; not only if we alter our position but also if we merely wait sufficiently long. Sometimes stars move together in a group or cluster; other times a single star may move very rapidly with respect to its fellows. Eventually such stars leave an old constellation and enter a new one. Occasionally, one member of a double-star system explodes, breaking the gravitational shackles that bound its companion, which then leaps into space at its former orbital velocity, a slingshot in the sky. In addition, stars are born, stars evolve, and stars die. If we wait long enough, new stars appear and old stars vanish. The patterns in the sky slowly melt and alter.

Even over the lifetime of the human species—a few million years—constellations have been changing. Consider the present configuration of the Big Dipper, or Great Bear. Our computer can carry us in time as well as in space. As we run the Big Dipper backwards into the past, allowing for the motion of its stars, we find quite a different appearance a million years ago. The Big Dipper then looked quite a bit like a spear. If a time machine dropped you precipitously in some unknown age in the distant past, you could in principle determine the epoch by the configuration of the stars: If the Big Dipper is a spear, this must be the Middle Pleistocene.

Computer-generated images of the Big Dipper as it would have been seen on Earth one million years ago and half a million years ago. Its present appearance is shown at bottom.

We can also ask the computer to run a constellation forward into time. Consider Leo the Lion. The zodiac is a band of twelve constellations seemingly wrapped around the sky in the apparent annual path of the Sun through the heavens. The root of the word is that for zoo, because the zodiacal constellations, like Leo, are mainly fancied to be animals. A million years from now, Leo will look still less like a lion than it does today. Perhaps our remote descendants will call it the constellation of the radio telescope—although I suspect a million years from now the radio telescope will have become more obsolete than the stone spear is now.

The (nonzodiacal) constellation of Orion, the hunter, is outlined by four bright stars and bisected by a diagonal line of three stars, which represent the belt of the hunter. Three dimmer stars hanging from the belt are, according to the conventional astronomical projective test, Orion’s sword. The middle star in the sword is not actually a star but a great cloud of gas called the Orion Nebula, in which stars are being born. Many of the stars in Orion are hot and young, evolving rapidly and ending their lives in colossal cosmic explosions called supernovae. They are born and die in periods of tens of millions of years. If, on our computer, we were to run Orion rapidly into the far future, we would see a startling effect, the births and spectacular deaths of many of its stars, flashing on and winking off like fireflies in the night.

The solar neighborhood, the immediate environs of the Sun in space, includes the nearest star system, Alpha Centauri. It is really a triple system, two stars revolving around each other, and a third, Proxima Centauri, orbiting the pair at a discreet distance. At some positions in its orbit, Proxima is the closest known star to the Sun—hence its name. Most stars in the sky are members of double or multiple star systems. Our solitary Sun is something of an anomaly.

The second brightest star in the constellation Andromeda, called Beta Andromedae, is seventy-five light-years away. The light by which we see it now has spent seventy-five years traversing the dark of interstellar space on its long journey to Earth. In the unlikely event that Beta Andromedae blew itself up last Tuesday, we would not know it for another seventy-five years, as this interesting information, traveling at the speed of light, would require seventy-five years to cross the enormous interstellar distances. When the light by which we now see this star set out on its long voyage, the young Albert Einstein, working as a Swiss patent clerk, had just published his epochal special theory of relativity here on Earth.

Space and time are interwoven. We cannot look out into space without looking back into time. Light travels very fast. But space is very empty, and the stars are far apart. Distances of seventy-five light-years or less are very small compared to other distances in astronomy. From the Sun to the center of the Milky Way Galaxy is 30,000 light-years. From our galaxy to the nearest spiral galaxy, M31, also in the constellation Andromeda, is 2,000,000 light-years. When the light we see today from M31 left for Earth, there were no humans on our planet, although our ancestors were evolving rapidly to our present form. The distance from the Earth to the most remote quasars is eight or ten billion light-years. We see them today as they were before the Earth accumulated, before the Milky Way was formed.

This is not a situation restricted to astronomical objects, but only astronomical objects are so far away that the finite speed of light becomes important. If you are looking at a friend three meters (ten feet) away, at the other end of the room, you are not seeing her as she is “now”; but rather as she “was” a hundred millionth of a second ago. [(3 m) / (3 × 108 m/sec) = 1/(108 / sec) = 10–8 sec, or a hundredth of a microsecond. In this calculation we have merely divided the distance by the speed to get the travel time.] But the difference between your friend “now” and now minus a hundred-millionth of a second is too small to notice. On the other hand, when we look at a quasar eight billion light-years away, the fact that we are seeing it as it was eight billion years ago may be very important. (For example, there are those who think that quasars are explosive events likely to happen only in the early history of galaxies. In that case, the more distant the galaxy, the earlier in its history we are observing it, and the more likely it is that we should see it as a quasar. Indeed, the number of quasars increases as we look to distances of more than about five billion light-years).

The two Voyager interstellar spacecraft, the fastest machines ever launched from Earth, are now traveling at one ten-thousandth the speed of light. They would need 40,000 years to go the distance to the nearest star. Do we have any hope of leaving Earth and traversing the immense distances even to Proxima Centauri in convenient periods of time? Can we do something to approach the speed of light? What is magic about the speed of light? Might we someday be able to go faster than that?

If you had walked through the pleasant Tuscan countryside in the 1890’s, you might have come upon a somewhat long-haired teenage high school dropout on the road to Pavia. His teachers in Germany had told him that he would never amount to anything, that his questions destroyed classroom discipline, that he would be better off out of school. So he left and wandered, delighting in the freedom of Northern Italy, where he could ruminate on matters remote from the subjects he had been force-fed in his highly disciplined Prussian schoolroom. His name was Albert Einstein, and his ruminations changed the world.

Einstein had been fascinated by Bernstein’s People’s Book of Natural Science, a popularization of science that described on its very first page the astonishing speed of electricity through wires and light through space. He wondered what the world would look like if you could travel on a wave of light. To travel at the speed of light? What an engaging and magical thought for a boy on the road in a countryside dappled and rippling in sunlight. You could not tell you were on a light wave if you traveled with it. If you started on a wave crest, you would stay on the crest and lose all notion of it being a wave. Something strange happens at the speed of light. The more Einstein thought about such questions, the more troubling they became. Paradoxes seemed to emerge everywhere if you could travel at the speed of light. Certain ideas had been accepted as true without sufficiently careful thought. Einstein posed simple questions that could have been asked centuries earlier. For example, what do we mean when we say that two events are simultaneous?

Imagine that I am riding a bicycle toward you. As I approach an intersection I nearly collide, so it seems to me, with a horse-drawn cart. I swerve and barely avoid being run over. Now think of the event again, and imagine that the cart and the bicycle are both traveling close to the speed of light. If you are standing down the road, the cart is traveling at right angles to your line of sight. You see me, by reflected sunlight, traveling toward you. Would not my speed be added to the speed of light, so that my image would get to you considerably before the image of the cart? Should you not see me swerve before you see the cart arrive? Can the cart and I approach the intersection simultaneously from my point of view, but not from yours? Could I experience a near collision with the cart while you perhaps see me swerve around nothing and pedal cheerfully on toward the town of Vinci? These are curious and subtle questions. They challenge the obvious. There is a reason that no one thought of them before Einstein. From such elementary questions, Einstein produced a fundamental rethinking of the world, a revolution in physics.

If the world is to be understood, if we are to avoid such logical paradoxes when traveling at high speeds, there are some rules, commandments of Nature, that must be obeyed. Einstein codified these rules in the special theory of relativity. Light (reflected or emitted) from an object travels at the same velocity whether the object is moving or stationary: Thou shalt not add thy speed to the speed of light. Also, no material object may move faster than light: Thou shalt not travel at or beyond the speed of light. Nothing in physics prevents you from traveling as close to the speed of light as you like; 99.9 percent of the speed of light would be just fine. But no matter how hard you try, you can never gain that last decimal point. For the world to be logically consistent, there must be a cosmic speed limit. Otherwise, you could get to any speed you wanted by adding velocities on a moving platform.

Europeans around the turn of the century generally believed in privileged frames of reference: that German, or French, or British culture and political organization were better than those of other countries; that Europeans were superior to other peoples who were fortunate enough to be colonized. The social and political application of the ideas of Aristarchus and Copernicus was rejected or ignored. The young Einstein rebelled against the notion of privileged frames of reference in physics as much as he did in politics. In a universe filled with stars rushing helter-skelter in all directions, there was no place that was “at rest,” no framework from which to view the universe that was superior to any other framework. This is what the word relativity means. The idea is very simple, despite its magical trappings: in viewing the universe, every place is as good as every other place. The laws of Nature must be identical no matter who is describing them. If this is to be true—and it would be stunning if there were something special about our insigificant location in the Cosmos—then it follows that no one may travel faster than light.

We hear the crack of a bullwhip because its tip is moving faster than the speed of sound, creating a shock wave, a small sonic boom. A thunderclap has a similar origin. It was once thought that airplanes could not travel faster than sound. Today supersonic flight is commonplace. But the light barrier is different from the sound barrier. It is not merely an engineering problem like the one the supersonic airplane solves. It is a fundamental law of Nature, as basic as gravity. And there are no phenomena in our experience—like the crack of the bullwhip or the clap of thunder for sound—to suggest the possibility of traveling in a vacuum faster than light. On the contrary, there is an extremely wide range of experience—with nuclear accelerators and atomic clocks, for example—in precise quantitative agreement with special relativity.

The problems of simultaneity do not apply to sound as they do to light because sound is propagated through some material medium, usually air. The sound wave that reaches you when a friend is talking is the motion of molecules in the air. Light, however, travels in a vacuum. There are restrictions on how molecules of air can move which do not apply to a vacuum. Light from the Sun reaches us across the intervening empty space, but no matter how carefully we listen, we do not hear the crackle of sunspots or the thunder of the solar flares. It was once thought, in the days before relativity, that light did propagate through a special medium that permeated all of space, called “the luminiferous aether.” But the famous Michelson-Morley experiment demonstrated that such an aether does not exist.

We sometimes hear of things that can travel faster than light. Something called “the speed of thought” is occasionally proffered. This is an exceptionally silly notion—especially since the speed of impulses through the neurons in our brains is about the same as the speed of a donkey cart. That human beings have been clever enough to devise relativity shows that we think well, but I do not think we can boast about thinking fast. The electrical impulses in modern computers do, however, travel nearly at the speed of light.

Special relativity, fully worked out by Einstein in his middle twenties, is supported by every experiment performed to check it. Perhaps tomorrow someone will invent a theory consistent with everything else we know that circumvents paradoxes on such matters as simultaneity, avoids privileged reference frames and still permits travel faster than light. But I doubt it very much. Einstein’s prohibition against traveling faster than light may clash with our common sense. But on this question, why should we trust common sense? Why should our experience at 10 kilometers an hour constrain the laws of nature at 300,000 kilometers per second? Relativity does set limits on what humans can ultimately do. But the universe is not required to be in perfect harmony with human ambition. Special relativity removes from our grasp one way of reaching the stars, the ship that can go faster than light. Tantalizingly, it suggests another and quite unexpected method.

Following George Gamow, let us imagine a place where the speed of light is not its true value of 300,000 kilometers per second, but something very modest: 40 kilometers per hour, say—and strictly enforced. (There are no penalties for breaking laws of Nature, because there are no crimes: Nature is self-regulating and merely arranges things so that its prohibitions are impossible to transgress.) Imagine that you are approaching the speed of light on a motor scooter. (Relativity is rich in sentences beginning “Imagine …” Einstein called such an exercise a Gedankenexperiment, a thought experiment.) As your speed increases, you begin to see around the corners of passing objects. While you are rigidly facing forward, things that are behind you appear within your forward field of vision. Close to the speed of light, from your point of view, the world looks very odd—ultimately everything is squeezed into a tiny circular window, which stays just ahead of you. From the standpoint of a stationary observer, light reflected off you is reddened as you depart and blued as you return. If you travel toward the observer at almost the speed of light, you will become enveloped in an eerie chromatic radiance: your usually invisible infrared emission will be shifted to the shorter visible wavelengths. You become compressed in the direction of motion, your mass increases, and time, as you experience it, slows down, a breathtaking consequence of traveling close to the speed of light called time dilation. But from the standpoint of an observer moving with you—perhaps the scooter has a second seat—none of these effects occur.

These peculiar and at first perplexing predictions of special relativity are true in the deepest sense that anything in science is true. They depend on your relative motion. But they are real, not optical illusions. They can be demonstrated by simple mathematics, mainly first-year algebra and therefore understandable to any educated person. They are also consistent with many experiments. Very accurate clocks carried in airplanes slow down a little compared to stationary clocks. Nuclear accelerators are designed to allow for the increase of mass with increasing speed; if they were not designed in this way, accelerated particles would all smash into the walls of the apparatus, and there would be little to do in experimental nuclear physics. A speed is a distance divided by a time. Since near the velocity of light we cannot simply add speeds, as we are used to doing in the workaday world, the familiar notions of absolute space and absolute time—independent of your relative motion—must give way. That is why you shrink. That is the reason for time dilation.

Traveling close to the speed of light you would hardly age at all, but your friends and your relatives back home would be aging at the usual rate. When you returned from your relativistic journey, what a difference there would be between your friends and you, they having aged decades, say, and you having aged hardly at all! Traveling close to the speed of light is a kind of elixir of life. Because time slows down close to the speed of light, special relativity provides us with a means of going to the stars. But is it possible, in terms of practical engineering, to travel close to the speed of light? Is a starship feasible?

Tuscany was not only the caldron of some of the thinking of the young Albert Einstein; it was also the home of another great genius who lived 400 years earlier, Leonardo da Vinci, who delighted in climbing the Tuscan hills and viewing the ground from a great height, as if he were soaring like a bird. He drew the first aerial perspectives of landscapes, towns and fortifications. Among Leonardo’s many interests and accomplishments—in painting, sculpture, anatomy, geology, natural history, military and civil engineering—he had a great passion: to devise and fabricate a machine that could fly. He drew pictures, constructed models, built full-size prototypes—and not one of them worked. No sufficiently powerful and lightweight engine then existed. The designs, however, were brilliant and encouraged the engineers of future times. Leonardo himself was depressed by these failures. But it was hardly his fault. He was trapped in the fifteenth century.

A similar case occurred in 1939 when a group of engineers calling themselves the British Interplanetary Society designed a ship to take people to the Moon—using 1939 technology. It was by no means identical to the design of the Apollo spacecraft, which accomplished exactly this mission three decades later, but it suggested that a mission to the Moon might one day be a practical engineering possibility.

Today we have preliminary designs for ships to take people to the stars. None of these spacecraft is imagined to leave the Earth directly. Rather, they are constructed in Earth orbit from where they are launched on their long interstellar journeys. One of them was called Project Orion after the constellation, a reminder that the ship’s ultimate objective was the stars. Orion was designed to utilize explosions of hydrogen bombs, nuclear weapons, against an inertial plate, each explosion providing a kind of “putt-putt,” a vast nuclear motorboat in space. Orion seems entirely practical from an engineering point of view. By its very nature it would have produced vast quantities of radioactive debris, but for conscientious mission profiles only in the emptiness of interplanetary or interstellar space. Orion was under serious development in the United States until the signing of the international treaty that forbids the detonation of nuclear weapons in space. This seems to me a great pity. The Orion starship is the best use of nuclear weapons I can think of.

Project Daedalus is a recent design of the British Interplanetary Society. It assumes the existence of a nuclear fusion reactor—something much safer as well as more efficient than existing fission power plants. We do not have fusion reactors yet, but they are confidently expected in the new few decades. Orion and Daedalus might travel at 10 percent the speed of light. A trip to Alpha Centauri, 4.3 light-years away, would then take forty-three years, less than a human lifetime. Such ships could not travel close enough to the speed of light for special relativistic time dilation to become important. Even with optimistic projections on the development of our technology, it does not seem likely that Orion, Daedalus or their ilk will be built before the middle of the twenty-first century, although if we wished we could build Orion now.

For voyages beyond the nearest stars, something else must be done. Perhaps Orion and Daedalus could be used as multigeneration ships, so those arriving at a planet of another star would be the remote descendants of those who had set out some centuries before. Or perhaps a safe means of hibernation for humans will be found, so that the space travelers could be frozen and then reawakened centuries later. These nonrelativistic starships, enormously expensive as they would be, look relatively easy to design and build and use compared to starships that travel close to the speed of light. Other star systems are accessible to the human species, but only after great effort.

Fast interstellar spaceflight—with the ship velocity approaching the speed of light—is an objective not for a hundred years but for a thousand or ten thousand. But it is in principle possible. A kind of interstellar ramjet has been proposed by R. W. Bussard which scoops up the diffuse matter, mostly hydrogen atoms, that floats between the stars, accelerates it into a fusion engine and ejects it out the back. The hydrogen would be used both as fuel and as reaction mass. But in deep space there is only about one atom in every ten cubic centimeters, a volume the size of a grape. For the ramjet to work, it needs a frontal scoop hundreds of kilometers across. When the ship reaches relativistic velocities, the hydrogen atoms will be moving with respect to the spaceship at close to the speed of light. If adequate precautions are not taken, the spaceship and its passengers will be fried by these induced cosmic rays. One proposed solution uses a laser to strip the electrons off the interstellar atoms and make them electrically charged while they are still some distance away, and an extremely strong magnetic field to deflect the charged atoms into the scoop and away from the rest of the spacecraft. This is engineering on a scale so far unprecedented on Earth. We are talking of engines the size of small worlds.

But let us spend a moment thinking about such a ship. The Earth gravitationally attracts us with a certain force, which if we are falling we experience as an acceleration. Were we to fall out of a tree—and many of our proto-human ancestors must have done so—we would plummet faster and faster, increasing our fall speed by ten meters (or thirty-two feet) per second, every second. This acceleration, which characterizes the force of gravity holding us to the Earth’s surface, is called 1 g, g for Earth gravity. We are comfortable with accelerations of 1 g; we have grown up with 1 g. If we lived in an interstellar spacecraft that could accelerate at 1 g, we would find ourselves in a perfectly natural environment. In fact, the equivalence between gravitational forces and the forces we would feel in an accelerating spaceship is a major feature of Einstein’s later general theory of relativity. With a continuous 1 g acceleration, after one year in space we would be traveling very close to the speed of light [(0.01 km/sec2) × (3 × 107 sec) = 3 × 105 km/sec].

Suppose that such a spacecraft accelerates at 1 g, approaching more and more closely to the speed of light until the midpoint of the journey; and then is turned around and decelerates at 1 g until arriving at its destination. For most of the trip the velocity would be very close to the speed of light and time would slow down enormously. A nearby mission objective, a sun that may have planets, is Barnard’s Star, about six light-years away. It could be reached in about eight years as measured by clocks aboard the ship; the center of the Milky Way, in twenty-one years; M31, the Andromeda galaxy, in twenty-eight years. Of course, people left behind on Earth would see things differently. Instead of twenty-one years to the center of the Galaxy, they would measure an elapsed time of 30,000 years. When we got home, few of our friends would be left to greet us. In principle, such a journey, mounting the decimal points ever closer to the speed of light, would even permit us to circumnavigate the known universe in some fifty-six years ship time. We would return tens of billions of years in our future—to find the Earth a charred cinder and the Sun dead. Relativistic spaceflight makes the universe accessible to advanced civilizations, but only to those who go on the journey. There seems to be no way for information to travel back to those left behind any faster than the speed of light.

The designs for Orion, Daedalus and the Bussard Ramjet are probably farther from the actual interstellar spacecraft we will one day build than Leonardo’s models are from today’s supersonic transports. But if we do not destroy ourselves, I believe that we will one day venture to the stars. When our solar system is all explored, the planets of other stars will beckon.

Space travel and time travel are connected. We can travel fast into space only by traveling fast into the future. But what of the past? Could we return to the past and change it? Could we make events turn out differently from what the history books assert? We travel slowly into the future all the time, at the rate of one day every day. With relativistic spaceflight we could travel fast into the future. But many physicists believe that a voyage into the past is impossible. Even if you had a device that could travel backwards in time, they say, you would be unable to do anything that would make any difference. If you journeyed into the past and prevented your parents from meeting, then you would never have been born—which is something of a contradiction, since you clearly exist. Like the proof of the irrationality of √2, like the discussion of simultaneity in special relativity, this is an argument in which the premise is challenged because the conclusion seems absurd.

But other physicists propose that two alternative histories, two equally valid realities, could exist side by side—the one you know and the one in which you were never born. Perhaps time itself has many potential dimensions, despite the fact that we are condemned to experience only one of them. Suppose you could go back into the past and change it—by persuading Queen Isabella not to support Christopher Columbus, for example. Then, it is argued, you would have set into motion a different sequence of historical events, which those you left behind in our time line would never know about. If that kind of time travel were possible, then every imaginable alternative history might in some sense really exist.

History consists for the most part of a complex bundle of deeply interwoven threads, social, cultural and economic forces that are not easily unraveled. The countless small, unpredictable and random events that flow on continually often have no long-range consequences. But some, those occurring at critical junctures or branch points, may change the pattern of history. There may be cases where profound changes can be made by relatively trivial adjustments. The farther in the past such an event is, the more powerful may be its influence—because the longer the lever arm of time becomes.

A polio virus is a tiny microorganism. We encounter many of them every day. But only rarely, fortunately, does one of them infect one of us and cause this dread disease. Franklin D. Roosevelt, the thirty-second President of the United States, had polio. Because the disease was crippling, it may have provided Roosevelt with a greater compassion for the underdog; or perhaps it improved his striving for success. If Roosevelt’s personality had been different, or if he had never had the ambition to be President of the United States, the great depression of the 1930’s, World War II and the development of nuclear weapons might just possibly have turned out differently. The future of the world might have been altered. But a virus is an insignificant thing, only a millionth of a centimeter across. It is hardly anything at all.

On the other hand, suppose our time traveler had persuaded Queen Isabella that Columbus’ geography was faulty, that from Eratosthenes’ estimate of the circumference of the Earth, Columbus could never reach Asia. Almost certainly some other European would have come along within a few decades and sailed west to the New World. Improvements in navigation, the lure of the spice trade and competition among rival European powers made the discovery of America around 1500 more or less inevitable. Of course, there would today be no nation of Colombia, or District of Columbia or Columbus, Ohio, or Columbia University in the Americas. But the overall course of history might have turned out more or less the same. In order to affect the future profoundly, a time traveler would probably have to intervene in a number of carefully chosen events, to change the weave of history.

It is a lovely fantasy, to explore those worlds that never were. By visiting them we could truly understand how history works; history could become an experimental science. If an apparently pivotal person had never lived—Plato, say, or Paul, or Peter the Great—how different would the world be? What if the scientific tradition of the ancient Ionian Greeks had survived and flourished? That would have required many of the social forces of the time to have been different—including the prevailing belief that slavery was natural and right. But what if that light that dawned in the eastern Mediterranean 2,500 years ago had not flickered out? What if science and the experimental method and the dignity of crafts and mechanical arts had been vigorously pursued 2,000 years before the Industrial Revolution? What if the power of this new mode of thought had been more generally appreciated? I sometimes think we might then have saved ten or twenty centuries. Perhaps the contributions of Leonardo would have been made a thousand years ago and those of Albert Einstein five hundred years ago. In such an alternate Earth, Leonardo and Einstein would, of course, never have been born. Too many things would have been different. In every ejaculation there are hundreds of millions of sperm cells, only one of which can fertilize an egg and produce a member of the next generation of human beings. But which sperm succeeds in fertilizing an egg must depend on the most minor and insignificant of factors, both internal and external. If even a little thing had gone differently 2,500 years ago, none of us would be here today. There would be billions of others living in our place.

If the Ionian spirit had won, I think we—a different “we,” of course—might by now be venturing to the stars. Our first survey ships to Alpha Centauri and Barnard’s Star, Sirius and Tau Ceti would have returned long ago. Great fleets of interstellar transports would be under construction in Earth orbit—unmanned survey ships, liners for immigrants, immense trading ships to plow the seas of space. On ail these ships there would be symbols and writing. If we looked closely, we might see that the language was Greek. And perhaps the symbol on the bow of one of the first starships would be a dodecahedron, with the inscription “Starship Theodorus of the Planet Earth.”

In the time line of our world, things have gone somewhat more slowly. We are not yet ready for the stars. But perhaps in another century or two, when the solar system is all explored, we will also have put our planet in order. We will have the will and the resources and the technical knowledge to go to the stars. We will have examined from great distances the diversity of other planetary systems, some very much like our own and some extremely different. We will know which stars to visit. Our machines and our descendants will then skim the light years, the children of Thales and Aristarchus, Leonardo and Einstein.

We are not yet certain how many planetary systems there are, but there seem to be a great abundance. In our immediate vicinity, there is not just one, but in a sense four: Jupiter, Saturn and Uranus each has a satellite system that, in the relative sizes and spacings of the moons, resembles closely the planets about the Sun. Extrapolation of the statistics of double stars which are greatly disparate in mass suggests that almost all single stars like the Sun should have planetary companions.

We cannot yet directly see the planets of other stars, tiny points of light swamped in the brilliance of their local suns. But we are becoming able to detect the gravitational influence of an unseen planet on an observed star. Imagine such a star with a large “proper motion,” moving over decades against the backdrop of more distant constellations; and with a large planet, the mass of Jupiter, say, whose orbital plane is by chance aligned at right angles to our line of sight. When the dark planet is, from our perspective, to the right of the star, the star will be pulled a little to the right, and conversely when the planet is to the left. Consequently, the path of the star will be altered, or perturbed, from a straight line to a wavy one. The nearest star for which this gravitational perturbation method can be applied is Barnard’s Star, the nearest single star. The complex interactions of the three stars in the Alpha Centauri system would make the search for a low-mass companion there very difficult. Even for Barnard’s Star, the investigation must be painstaking, a search for microscopic displacements of position on photographic plates exposed at the telescope over a period of decades. Two such quests have been performed for planets around Barnard’s Star, and both have been by some criteria successful, implying the presence of two or three planets of Jovian mass moving in an orbit (calculated by Kepler’s third law) somewhat closer to their star than Jupiter and Saturn are to the Sun. But unfortunately the two sets of observations seem mutually incompatible. A planetary system around Barnard’s Star may well have been discovered, but an unambiguous demonstration awaits further study.

Other methods of detecting planets around the stars are under development, including one where the obscuring light from the star is artificially occulted—with a disk in front of a space telescope, or by using the dark edge of the Moon as such a disk—and the reflected light from the planet, no longer hidden by the brightness of the nearby star, emerges. In the next few decades we should have definite answers to which of the hundred nearest stars have large planetary companions.

In recent years, infrared observations have revealed a number of likely preplanetary disk-shaped clouds of gas and dust around some of the nearby stars. Meanwhile, some provocative theoretical studies have suggested that planetary systems are a galactic commonplace. A set of computer investigations has examined the evolution of a flat, condensing disk of gas and dust of the sort that is thought to lead to stars and planets. Small lumps of matter—the first condensations in the disk—are injected at random times into the cloud. The lumps accrete dust particles as they move. When they become sizable, they also gravitationally attract gas, mainly hydrogen, in the cloud. When two moving lumps collide, the computer program makes them stick. The process continues until all the gas and dust has been in this way used up. The results depend on the initial conditions, particularly on the distribution of gas and dust density with distance from the center of the cloud. But for a range of plausible initial conditions, planetary systems—about ten planets, terrestrials close to the star, Jovians on the exterior—recognizably like ours are generated. Under other circumstances, there are no planets—just a smattering of asteroids; or there may be Jovian planets near the star; or a Jovian planet may accrete so much gas and dust as to become a star, the origin of a binary star system. It is still too early to be sure, but it seems that a splendid variety of planetary systems is to be found throughout the Galaxy, and with high frequency—all stars must come, we think, from such clouds of gas and dust. There may be a hundred billion planetary systems in the Galaxy awaiting exploration.

Not one of those worlds will be identical to Earth. A few will be hospitable; most will appear hostile. Many will be achingly beautiful. In some worlds there will be many suns in the daytime sky, many moons in the heavens at night, or great particle ring systems soaring from horizon to horizon. Some moons will be so close that their planet will loom high in the heavens, covering half the sky. And some worlds will look out onto a vast gaseous nebula, the remains of an ordinary star that once was and is no longer. In all those skies, rich in distant and exotic constellations, there will be a faint yellow star—perhaps barely seen by the naked eye, perhaps visible only through the telescope—the home star of the fleet of interstellar transports exploring this tiny region of the great Milky Way Galaxy.

The themes of space and time are, as we have seen, intertwined. Worlds and stars, like people, are born, live and die. The lifetime of a human being is measured in decades; the lifetime of the Sun is a hundred million times longer. Compared to a star, we are like mayflies, fleeting ephemeral creatures who live out their whole lives in the course of a single day. From the point of view of a mayfly, human beings are stolid, boring, almost entirely immovable, offering hardly a hint that they ever do anything. From the point of view of a star, a human being is a tiny flash, one of billions of brief lives flickering tenuously on the surface of a strangely cold, anomalously solid, exotically remote sphere of silicate and iron.

In all those other worlds in space there are events in progress, occurrences that will determine their futures. And on our small planet, this moment in history is a historical branch point as profound as the confrontation of the Ionian scientists with the mystics 2,500 years ago. What we do with our world in this time will propagate down through the centuries and powerfully determine the destiny of our descendants and their fate, if any, among the stars.