A Briefer History of Time

by Stephen Hawking

  When a star runs out of fuel, it starts to cool off and gravity takes over, causing it to contract. This contraction squeezes the atoms together and causes the star to become hotter again. As the star heats up further, it would start to convert helium into heavier elements such as carbon or oxygen. This, however, would not release much more energy, so a crisis would occur. What happens next is not completely clear, but it seems likely that the central regions of the star would collapse to a very dense state, such as a black hole. The term “black hole” is of very recent origin. It was coined in 1969 by the American scientist John Wheeler as a graphic description of an idea that goes back at least two hundred years, to a time when there were two theories about light: one, which Newton favored, was that it was composed of particles, and the other was that it was made of waves. We now know that actually, both theories are correct. As we will see in Chapter 9, by the wave/particle duality of quantum mechanics, light can be regarded as both a wave and a particle. The descriptors wave and particle are concepts humans created, not necessarily concepts that nature is obliged to respect by making all phenomena fall into one category or the other!

  Under the theory that light is made up of waves, it was not clear how it would respond to gravity. But if we think of light as being composed of particles, we might expect those particles to be affected by gravity in the same way that cannonballs, rockets, and planets are. In particular, if you shoot a cannonball upward from the surface of the earth—or a star—like the rocket on page 58, it will eventually stop and then fall back unless the speed with which it starts upward exceeds a certain value. This minimum speed is called the escape velocity. The escape velocity of a star depends on the strength of its gravitational pull. The more massive the star, the greater its escape velocity. At first people thought that particles of light traveled infinitely fast, so gravity would not have been able to slow them down, but the discovery by Roemer that light travels at a finite speed meant that gravity might have an important effect: if the star is massive enough, the speed of light will be less than the star’s escape velocity, and all light emitted by the star will fall back into it. On this assumption, in 1783 a Cambridge don, John Michell, published a paper in the Philosophical Transactions of the Royal Society of London in which he pointed out that a star that was sufficiently massive and compact would have such a strong gravitational field that light could not escape: any light emitted from the surface of the star would be dragged back by the star’s gravitational attraction before it could get very far. Such objects are what we now call black holes, because that is what they are: black voids in space.

  Cannonballs Above and Below Escape Velocity

  What goes up need not come down-if it is shot upward faster than the escape velocity

  A similar suggestion was made a few years later by a French scientist, the Marquis de Laplace, apparently independent of Michell. Interestingly, Laplace included it only in the first and second editions of his book The System of the World, leaving it out of later editions. Perhaps he decided it was a crazy idea—the particle theory of light went out of favor during the nineteenth century because it seemed that everything could be explained using the wave theory. In fact, it is not really consistent to treat light like cannonballs in Newton’s theory of gravity because the speed of light is fixed. A cannonball fired upward from the earth will be slowed down by gravity and will eventually stop and fall back; a photon, however, must continue upward at a constant speed. A consistent theory of how gravity affects light did not come along until Einstein proposed general relativity in 1915, and the problem of understanding what would happen to a massive star, according to general relativity, was first solved by a young American, Robert Oppenheimer, in 1939.

  The picture that we now have from Oppenheimer’s work is as follows. The gravitational field of the star changes the paths of passing light rays in space-time from what they would have been had the star not been present. This is the effect that is seen in the bending of light from distant stars observed during an eclipse of the sun. The paths followed in space and time by light are bent slightly inward near the surface of the star. As the star contracts, it becomes denser, so the gravitational field at its surface gets stronger. (You can think of the gravitational field as emanating from a point at the center of the star; as the star shrinks, points on its surface get closer to the center, so they feel a stronger field.) The stronger field makes light paths near the surface bend inward more. Eventually, when the star has shrunk to a certain critical radius, the gravitational field at the surface becomes so strong that the light paths are bent inward to the point that light can no longer escape.

  According to the theory of relativity, nothing can travel faster than light. Thus if light cannot escape, neither can anything else; everything is dragged back by the gravitational field. The collapsed star has formed a region of space-time around it from which it is not possible to escape to reach a distant observer. This region is the black hole. The outer boundary of a black hole is called the event horizon. Today, thanks to the Hubble Space Telescope and other telescopes that focus on X-rays and gamma rays rather than visible light, we know that black holes are common phenomena—much more common than people first thought. One satellite discovered fifteen hundred black holes in just one small area of sky. We have also discovered a black hole in the center of our galaxy, with a mass more than one million times that of our sun. That supermassive black hole has a star orbiting it at about 2 percent the speed of light, faster than the average speed of an electron orbiting the nucleus in an atom!

  In order to understand what you would see if you were watching a massive star collapse to form a black hole, it is necessary to remember that in the theory of relativity there is no absolute time. In other words, each observer has his own measure of time. The passage of time for someone on a star’s surface will be different from that for someone at a distance, because the gravitational field is stronger on the star’s surface.

  Suppose an intrepid astronaut is on the surface of a collapsing star and stays on the surface as it collapses inward. At some time on his watch—say, 11:00—the star would shrink below the critical radius at which the gravitational field becomes so strong that nothing can escape. Now suppose his instructions are to send a signal every second, according to his watch, to a spaceship above, which orbits at some fixed distance from the center of the star. He begins transmitting at 10:59:58, that is, two seconds before 11:00. What will his companions on the spaceship record?

  We learned from our earlier thought experiment aboard the rocket ship that gravity slows time, and the stronger the gravity, the greater the effect. The astronaut on the star is in a stronger gravitational field than his companions in orbit, so what to him is one second will be more than one second on their clocks. And as he rides the star’s collapse inward, the field he experiences will grow stronger and stronger, so the interval between his signals will appear successively longer to those on the spaceship. This stretching of time would be very small before 10:59:59, so the orbiting astronauts would have to wait only very slightly more than a second between the astronaut’s 10:59:58 signal and the one that he sent when his watch read 10:59:59. But they would have to wait forever for the 11:00 signal.

  Everything that happens on the surface of the star between 10:59:59 and 11:00 (by the astronaut’s watch) would be spread out over an infinite period of time, as seen from the spaceship. As 11:00 approached, the time interval between the arrival of successive crests and troughs of any light from the star would get successively longer, just as the interval between signals from the astronaut does. Since the frequency of light is a measure of the number of its crests and troughs per second, to those on the spaceship the frequency of the light from the star will get successively lower. Thus its light would appear redder and redder (and fainter and fainter). Eventually, the star would be so dim that it could no longer be seen from the spaceship: all that would be left would be a black hole in space. It would, however, continue to exert the
same gravitational force on the spaceship, which would continue to orbit.

  This scenario is not entirely realistic, however, because of the following problem. Gravity gets weaker the farther you are from the star, so the gravitational force on our intrepid astronaut’s feet would always be greater than the force on his head. This difference in the forces would stretch him out like spaghetti or tear him apart before the star had contracted to the critical radius at which the event horizon formed! However, we believe that there are much larger objects in the universe, such as the central regions of galaxies, which can also undergo gravitational collapse to produce black holes, like the supermassive black hole at the center of our galaxy. An astronaut on one of these would not be torn apart before the black hole formed. He would not, in fact, feel anything special as he reached the critical radius, and he could pass the point of no return without noticing it— though to those on the outside, his signals would again become further and further apart, and eventually stop. And within just a few hours (as measured by the astronaut), as the region continued to collapse, the difference in the gravitational forces on his head and his feet would become so strong that again it would tear him apart.

  Tidal Forces

  Since gravity weakens with distance, the earth pulls on your head with less force than it pulls on your feet, which are a meter or two closer to the earth’s center The difference is so tiny we cannot feel it, but an astronaut near the surface of a black hole would be literally torn apart.

  Sometimes, when a very massive star collapses, the outer regions of the star may get blown off in a tremendous explosion called a supernova. A supernova explosion is so huge that it can give off more light than all the other stars in its galaxy combined. One example of this is the supernova whose remnants we see as the Crab Nebula. The Chinese recorded it in 1054. Though the star that exploded was five thousand light-years away, it was visible to the naked eye for months and shone so brightly that you could see it even during the day and read by it at night. A supernova five hundred light-years away— one-tenth as far—would be one hundred times brighter and could literally turn night into day. To understand the violence of such an explosion, just consider that its light would rival that of the sun, even though it is tens of millions of times farther away. (Recall that our sun resides at the neighborly distance of eight light-minutes.) If a supernova were to occur close enough, it could leave the earth intact but still emit enough radiation to kill all living things. In fact, it was recently proposed that a die-off of marine creatures that occurred at the interface of the Pleistocene and Pliocene epochs about two million years ago was caused by cosmic ray radiation from a supernova in a nearby cluster of stars called the Scorpius-Centaurus association. Some scientists believe that advanced life is likely to evolve only in regions of galaxies in which there are not too many stars—“zones of life”— because in denser regions phenomena such as supernovas would be common enough to regularly snuff out any evolutionary beginnings. On the average, hundreds of thousands of supernovas explode somewhere in the universe each day. A supernova happens in any particular galaxy about once a century. But that’s just the average. Unfortunately—for astronomers at least—the last supernova recorded in the Milky Way occurred in 1604, before the invention of the telescope.

  The leading candidate for the next supernova explosion in our galaxy is a star called Rho Cassiopeiae. Fortunately, it is a safe and comfortable ten thousand light-years from us. It is in a class of stars known as yellow hypergiants, one of only seven known yellow hypergiants in the Milky Way. An international team of astronomers began to study this star in 1993. In the next few years they observed it undergoing periodic temperature fluctuations of a few hundred degrees. Then in the summer of 2000, its temperature suddenly plummeted from around 7,000 degrees to 4,000 degrees Celsius. During that time, they also detected titanium oxide in the star’s atmosphere, which they believe is part of an outer layer thrown off from the star by a massive shock wave.

  In a supernova, some of the heavier elements produced near the end of the star’s life are flung back into the galaxy and provide some of the raw material for the next generation of stars. Our own sun contains about 2 percent of these heavier elements. It is a second-or third-generation star, formed some five billion years ago out of a cloud of rotating gas containing the debris of earlier supernovas. Most of the gas in that cloud went to form the sun or got blasted away, but small amounts of the heavier elements collected together to form the bodies that now orbit the sun as planets like the earth. The gold in our jewelry and the uranium in our nuclear reactors are both remnants of the supernovas that occurred before our solar system was born!

  When the earth was newly condensed, it was very hot and without an atmosphere. In the course of time, it cooled and acquired an atmosphere from the emission of gases from the rocks. This early atmosphere was not one in which we could have survived. It contained no oxygen, but it did contain a lot of other gases that are poisonous to us, such as hydrogen sulfide (the gas that gives rotten eggs their smell). There are, however, other primitive forms of life that can flourish under such conditions. It is thought that they developed in the oceans, possibly as a result of chance combinations of atoms into large structures, called macromolecules, that were capable of assembling other atoms in the ocean into similar structures. They would thus have reproduced themselves and multiplied. In some cases there would be errors in the reproduction. Mostly these errors would have been such that the new macromolecule could not reproduce itself and eventually would have been destroyed. However, a few of the errors would have produced new macromolecules that were even better at reproducing themselves. They would have therefore had an advantage and would have tended to replace the original macromolecules. In this way a process of evolution was started that led to the development of more and more complicated, self-reproducing organisms. The first primitive forms of life consumed various materials, including hydrogen sulfide, and released oxygen. This gradually changed the atmosphere to the composition that it has today, and allowed the development of higher forms of life such as fish, reptiles, mammals, and ultimately the human race.

  The twentieth century saw man’s view of the universe transformed: we realized the insignificance of our own planet in the vastness of the universe, and we discovered that time and space were curved and inseparable, that the universe was expanding, and that it had a beginning in time.

  The picture of a universe that started off very hot and cooled as it expanded was based on Einstein’s theory of gravity, general relativity. That it is in agreement with all the observational evidence that we have today is a great triumph for that theory. Yet because mathematics cannot really handle infinite numbers, by predicting that the universe began with the big bang, a time when the density of the universe and the curvature of space-time would have been infinite, the theory of general relativity predicts that there is a point in the universe where the theory itself breaks down, or fails. Such a point is an example of what mathematicians call a singularity. When a theory predicts singularities such as infinite density and curvature, it is a sign that the theory must somehow be modified. General relativity is an incomplete theory because it cannot tell us how the universe started off.

  In addition to general relativity, the twentieth century also spawned another great partial theory of nature, quantum mechanics. That theory deals with phenomena that occur on very small scales. Our picture of the big bang tells us that there must have been a time in the very early universe when the universe was so small that, even when studying its large-scale structure, it was no longer possible to ignore the small-scale effects of quantum mechanics. We will see in the next chapter that our greatest hope for obtaining a complete understanding of the universe from beginning to end arises from combining these two partial theories into a single quantum theory of gravity, a theory in which the ordinary laws of science hold everywhere, including at the beginning of time, without the need for there to be any singularities.

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  QUANTUM GRAVITY

  THE SUCCESS OF SCIENTIFIC THEORIES, particularly Newton’s theory of gravity, led the Marquis de Laplace at the beginning of the nineteenth century to argue that the universe was completely deterministic. Laplace believed that there should be a set of scientific laws that would allow us—at least in principle—to predict everything that would happen in the universe. The only input these laws would need is the complete state of the universe at any one time. This is called an initial condition or a boundary condition. (A boundary can mean a boundary in space or time; a boundary condition in space is the state of the universe at its outer boundary—if it has one.) Based on a complete set of laws and the appropriate initial or boundary condition, Laplace believed, we should be able to calculate the complete state of the universe at any time.

  The requirement of initial conditions is probably intuitively obvious: different states of being at present will obviously lead to different future states. The need for boundary conditions in space is a little more subtle, but the principle is the same. The equations on which physical theories are based can generally have very different solutions, and you must rely on the initial or boundary conditions to decide which solutions apply. It’s a little like saying that your bank account has large amounts going in and out of it. Whether you end up bankrupt or rich depends not only on the sums paid in and out but also on the boundary or initial condition of how much was in the account to start with.