The Theory Of Everything: The Origin and Fate of the Universe

by Stephen Hawking

Even those who realized that Newton’s theory of gravity showed that the universe could not be static did not think to suggest that it might be expanding. Instead, they attempted to modify the theory by making the gravitational force repulsive at very large distances.

However, we now believe such an equilibrium would be unstable. If the stars in some region got only slightly near each other, the attractive forces between them would become stronger and would dominate over the repulsive forces. This would mean that the stars would continue to fall toward each other. On the other hand, if the stars got a bit farther away from each other, the repulsive forces would dominate and drive them farther apart.

Another objection to an infinite static universe is normally ascribed to the German philosopher Heinrich Olbers.

The difficulty is that in an infinite static universe nearly every line or side would end on the surface of a star. Thus one would expect that the whole sky would be as bright as the sun, even at night. Olbers’s counterargument was that the light from distant stars would be dimmed by absorption by intervening matter. However, if that happened, the intervening matter would eventually heat up until it glowed as brightly as the stars.

The only way of avoiding the conclusion that the whole of the night sky should be as bright as the surface of the sun would be if the stars had not been shining forever, but had turned on at some finite time in the past. In that case, the absorbing matter might not have heated up yet, or the light from distant stars might not yet have reached us.

St. Augustine accepted a date of about 5000 B.C. for the creation of the universe according to the book of Genesis. It is interesting that this is not so far from the end of the last Ice Age, about 10,000 B.C., which is when civilization really began.

But in 1929, Edwin Hubble made the landmark observation that wherever you look, distant stars are moving rapidly away from us. In other words, the universe is expanding. This means that at earlier times objects would have been closer together.

An expanding universe does not preclude a creator, but it does place limits on when He might have carried out his job.

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.

On this assumption, a Cambridge don, John Michell, wrote a paper in 1783 in the Philosophical Transactions of the Royal Society of London. In it, he pointed out that a star that was sufficiently massive and compact would have such a strong gravitational field that light could not escape.

In fact, it is not really consistent to treat light like cannon-balls in Newton’s theory of gravity because the speed of light is fixed. A can-nonball 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. How, then, can Newtonian gravity affect light? A consistent theory of how gravity affects light did not come until Einstein proposed general relativity in 1915; and even then it was a long time before the implications of the theory for massive stars were worked out.

In 1928 an Indian graduate student named Subrahmanyan Chandrasekhar set sail for England to study at Cambridge with the British astronomer Sir Arthur Eddington.

This meant that when the star got sufficiently dense, the repulsion caused by the exclusion principle would be less than the attraction of gravity. Chandrasekhar calculated that a cold star of more than about one and a half times the mass of the sun would not be able to support itself against its own gravity. This mass is now known as the Chandrasekhar limit.

If a star’s mass is less than the Chandrasekhar limit, it can eventually stop contracting and settle down to a possible final state as a white dwarf with a radius of a few thousand miles and a density of hundreds of tons per cubic inch. A white dwarf is supported by the exclusion principle repulsion between the electrons in its matter. We observe a large number of these white dwarf stars. One of the first to be discovered is the star that is orbiting around Sirius, the brightest star in the night sky.

there was another possible final state for a star also with a limiting mass of about one or two times the mass of the sun, but much smaller than even the white dwarf. These stars would be supported by the exclusion principle repulsion between the neutrons and protons, rather than between the electrons. They were therefore called neutron stars. They would have had a radius of only ten miles or so and a density of hundreds of millions of tons per

Stars with masses above the Chandrasekhar limit, on the other hand, have a big problem when they come to the end of their fuel. In some cases they may explode or manage to throw off enough matter to reduce their mass below the limit, but it was difficult to believe that this always happened, no matter how big the star. How would it know that it had to lose weight? And even if every star managed to lose enough mass, what would happen if you added more mass to a white dwarf or neutron star to take it over the limit? Would it collapse to infinite density?

The light cones, which indicate the paths followed in space and time by flashes of light emitted from their tips, are bent slightly inward near the surface of the star. This can be seen in the bending of light from distant stars that is observed during an eclipse of the sun. As the star contracts, the gravitational field at its surface gets stronger and the light cones get bent inward more. This makes it more difficult for light from the star to escape, and the light appears dimmer and redder to an observer at a distance. Eventually, when the star has shrunk to a certain critical radius, the gravitational field at the surface becomes so strong that the light cones are bent inward so much that the 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.

The work that Roger Penrose and I did between 1965 and 1970 showed that, according to general relativity, there must be a singularity of infinite density within the black hole. This is rather like the big bang at the beginning of time, only it would be an end of time for the collapsing body and the astronaut. At the singularity, the laws of science and our ability to predict the future would break down. However, any observer who remained outside the black hole would not be affected by this failure of predictability, because neither light nor any other signal can reach them from the singularity.

In other words, the singularities produced by gravitational collapse occur only in places like black holes, where they are decently hidden from outside view by an event horizon.

There are some solutions of the equations of general relativity in which it is possible for our astronaut to see a naked singularity. He may be able to avoid hitting the singularity and instead fall through a “worm hole” and come out in another region of the universe. This would offer great possibilities for travel in space and time, but unfortunately it seems that the solutions may all be highly unstable. The least disturbance, such as the presence of an astronaut, may change them so that the astronaut cannot see the singularity until he hits it and his time comes to an end. In other words, the singularity always lies in his future and never in his past.

The strong version of the cosmic censorship hypothesis states that in a realistic solution, the singularities always lie either entirely in the future, like the singularities of gravitational collapse, or entirely in the past, like the big bang.

I had already discussed with Roger Penrose the idea of defining a black hole as the set of events from which it was not possible to escape to a large distance. This is now the generally accepted definition. It means that the boundary of the black hole, the event horizon, is formed by rays of light that just fail to get away from the black hole. Instead, they stay forever, hovering on the edge of the black hole. It is like running away from the police and managing to keep one step ahead but not being able to get clear away.

The second law of thermodynamics has a rather different status than that of other laws of science. Other laws, such as Newton’s law of gravity, for example, are absolute law—that is, they always hold. On the other hand, the second law is a statistical law—that is, it does not hold always, just in the vast majority of cases.

a research student at Princeton named Jacob Bekenstein suggested that the area of the event horizon was a measure of the entropy of the black hole. As matter carrying entropy fell into the black hole, the area of the event horizon would go up, so that the sum of the entropy of matter outside black holes and the area of the horizons would never go down.

black hole has entropy, then it ought also to have a temperature. But a body with a nonzero temperature must emit radiation at a certain rate. It is a matter of common experience that if one heats up a poker in the fire, it glows red hot and emits radiation.

The positive energy of the outgoing radiation would be balanced by a flow of negative energy particles into the black hole. By Einstein’s famous equation E = mc2, energy is equivalent to mass. A flow of negative energy into the black hole therefore reduces its mass. As the black hole loses mass, the area of its event horizon gets smaller, but this decrease in the entropy of the black hole is more than compensated for by the entropy of the emitted radiation, so the second law is never violated.

If the rate of expansion one second after the big bang had been smaller by even one part in a hundred thousand million million, the universe would have recollapsed before it ever reached its present size. On the other hand, if the expansion rate at one second had been larger by the same amount, the universe would have expanded so much that it would be effectively empty now.

Guth suggested that the universe might behave in a similar way: The temperature might drop below the critical value without the symmetry between the forces being broken. If this happened, the universe would be in an unstable state, with more energy than if the symmetry had been broken. This special extra energy can be shown to have an antigravitational effect. It would act just like a cosmological constant.

When the universe doubles in size, the positive matter energy and the negative gravitational energy both double, so the total energy remains zero. During the inflationary phase, the universe increases its size by a very large amount. Thus, the total amount of energy available to make particles becomes very large. As Guth has remarked, “It is said that there is no such thing as a free lunch. But the universe is the ultimate free lunch.”

The inflationary model showed that the present state of the universe could have arisen from quite a large number of different initial configurations. It cannot be the case, however, that every initial configuration would have led to a universe like the one we observe. So even the inflationary model does not tell us why the initial configuration was such as to produce what we observe.

Using the no boundary condition, one finds that the universe must have started off with just the minimum possible nonuniformity allowed by the uncertainty principle. The universe would have then undergone a period of rapid expansion, like in the inflationary models. During this period, the initial nonuniformities would have been amplified until they could have been big enough to explain the origin of galaxies. Thus, all the complicated structures that we see in the universe might be explained by the no boundary condition for the universe and the uncertainty principle of quantum mechanics.

So long as the universe had a beginning that was a singularity, one could suppose that it was created by an outside agency. But if the universe is really completely self-contained, having no boundary or edge, it would be neither created nor destroyed. It would simply be. What place, then, for a creator?

Disorder increases with time because we measure time in the direction in which disorder increases. You can’t have a safer bet than that.

But what would happen if and when the universe stopped expanding and began to contract again? Would the thermodynamic arrow reverse and disorder begin to decrease with time? This would lead to all sorts of science–fiction–like possibilities for people who survived from the expanding to the contracting phase. Would they see broken cups gathering themselves together off the floor and jumping back on the table?

The collapse of a star to form a black hole is rather like the later stages of the collapse of the whole universe. Thus, if disorder were to decrease in the contracting phase of the universe, one might also expect it to decrease inside a black hole.

On the other hand, the other partial theories depend on quantum mechanics in an essential way. A necessary first step, therefore, is to combine general relativity with the uncertainty principle. As we have seen, this can produce some remarkable consequences, such as black holes not being black, and the universe being completely self–contained and without boundary. The trouble is, the uncertainty principle means that even empty space is filled with pairs of virtual particles and antiparticles. These pairs would have an infinite amount of energy. This means that their gravitational attraction would curve up the universe to an infinitely small size.

One possible answer is the anthropic principle. Two space dimensions do not seem to be enough to allow for the development of complicated beings like us.

It seems clear that life, at least as we know it, can exist only in regions of space-time in which three space and one time dimension are not curled up small.