A Brief History of Time

by Stephen Hawking

I shall take the simpleminded view that a theory is just a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make.

The lack of an absolute standard of rest meant that one could not determine whether two events that took place at different times occurred in the same position in space.

Newton was very worried by this lack of absolute position, or absolute space, as it was called, because it did not accord with his idea of an absolute God. In fact, he refused to accept lack of absolute space, even though it was implied by his laws.

Maxwell’s theory predicted that radio or light waves should travel at a certain fixed speed. But Newton’s theory had got rid of the idea of absolute rest, so if light was supposed to travel at a fixed speed, one would have to say what that fixed speed was to be measured relative to.

The fundamental postulate of the theory of relativity, as it was called, was that the laws of science should be the same for all freely moving observers, no matter what their speed.

An equally remarkable consequence of relativity is the way it has revolutionized our ideas of space and time. In Newton’s theory, if a pulse of light is sent from one place to another, different observers would agree on the time that the journey took (since time is absolute), but will not always agree on how far the light traveled (since space is not absolute). Since the speed of the light is just the distance it has traveled divided by the time it has taken, different observers would measure different speeds for the light. In relativity, on the other hand, all observers must agree on how fast light travels. They still, however, do not agree on the distance the light has traveled, so they must therefore now also disagree over the time it has taken. (The time taken is the distance the light has traveled—which the observers do not agree on—divided by the light’s speed—which they do agree on.) In other words, the theory of relativity put an end to the idea of absolute time!

No particular observer’s measurements are any more correct than any other observer’s, but all the measurements are related. Any observer can work out precisely what time and position any other observer will assign to an event, provided he knows the other observer’s relative velocity.

Nowadays we use just this method to measure distances precisely, because we can measure time more accurately than length. In effect, the meter is defined to be the distance traveled by light in 0.000000003335640952 second, as measured by a cesium clock.

In general relativity, bodies always follow straight lines in four-dimensional space-time, but they nevertheless appear to us to move along curved paths in our three-dimensional space. (This is rather like watching an airplane flying over hilly ground. Although it follows a straight line in three-dimensional space, its shadow follows a curved path on the two-dimensional ground.)

even if there were events before the big bang, one could not use them to determine what would happen afterward, because predictability would break down at the big bang.

Correspondingly, if, as is the case, we know only what has happened since the big bang, we could not determine what happened beforehand. As far as we are concerned, events before the big bang can have no consequences, so they should not form part of a scientific model of the universe. We should therefore cut them out of the model and say that time had a beginning at the big bang.

Einstein pointed out that what was called Brownian motion—the irregular, random motion of small particles of dust suspended in a liquid—could be explained as the effect of atoms of the liquid colliding with the dust particles.

But a machine that was powerful enough to accelerate particles to the grand unification energy would have to be as big as the Solar System—and would be unlikely to be funded in the present economic climate.

One could well say of the event horizon what the poet Dante said of the entrance to Hell: “All hope abandon, ye who enter here.” Anything or anyone who falls through the event horizon will soon reach the region of infinite density and the end of time.

Black holes are one of only a fairly small number of cases in the history of science in which a theory was developed in great detail as a mathematical model before there was any evidence from observations that it was correct.

A neutron star has a radius of about ten miles, only a few times the critical radius at which a star becomes a black hole. If a star could collapse to such a small size, it is not unreasonable to expect that other stars could collapse to even smaller size and become black holes.

The number of black holes may well be greater even than the number of visible stars, which totals about a hundred thousand million in our galaxy alone.

We also have some evidence that there is a much larger black hole, with a mass of about a hundred thousand times that of the sun, at the center of our galaxy.

It is thought that similar but even larger black holes, with masses of about a hundred million times the mass of the sun, occur at the centers of quasars.

Normally, the energy of the particle is still positive, but the gravitational field inside a black hole is so strong that even a real particle can have negative energy there. It is therefore possible, if a black hole is present, for the virtual particle with negative energy to fall into the black hole and become a real particle or antiparticle. In this case it no longer has to annihilate with its partner. Its forsaken partner may fall into the black hole as well. Or, having positive energy, it might also escape from the vicinity of the black hole as a real particle or antiparticle

suppose that only in the smooth regions were galaxies and stars formed and were conditions right for the development of complicated self-replicating organisms like ourselves who were capable of asking the question: why is the universe so smooth? This is an example of the application of what is known as the anthropic principle, which can be paraphrased as “We see the universe the way it is because we exist.”

The weak anthropic principle states that in a universe that is large or infinite in space and/or time, the conditions necessary for the development of intelligent life will be met only in certain regions that are limited in space and time.

Some, however, go much further and propose a strong version of the principle. According to this theory, there are either many different universes or many different regions of a single universe, each with its own initial configuration and, perhaps, with its own set of laws of science.

Like any other scientific theory, it may initially be put forward for aesthetic or metaphysical reasons, but the real test is whether it makes predictions that agree with observation.

the no boundary condition for the universe, together with the weak anthropic principle, can explain why all three arrows point in the same direction—and moreover, why a well-defined arrow of time should exist at all.

the psychological arrow is determined by the thermodynamic arrow, and that these two arrows necessarily always point in the same direction. If one assumes the no boundary condition for the universe, we shall see that there must be well-defined thermodynamic and cosmological arrows of time, but they will not point in the same direction for the whole history of the universe. However, I shall argue that it is only when they do point in the same direction that conditions are suitable for the development of intelligent beings who can ask the question: why does disorder increase in the same direction of time as that in which the universe expands?

Suppose, however, that God decided that the universe should finish up in a state of high order but that it didn’t matter what state it started in. At early times the universe would probably be in a disordered state. This would mean that disorder would decrease with time. You would see broken cups gathering themselves together and jumping back onto the table. However, any human beings who were observing the cups would be living in a universe in which disorder decreased with time. I shall argue that such beings would have a psychological arrow of time that was backward. That is, they would remember events in the future, and not remember events in their past. When the cup was broken, they would remember it being on the table, but when it was on the table, they would not remember it being on the floor.

If you remember every word in this book, your memory will have recorded about two million pieces of information: the order in your brain will have increased by about two million units. However, while you have been reading the book, you will have converted at least a thousand calories of ordered energy, in the form of food, into disordered energy, in the form of heat that you lose to the air around you by convection and sweat. This will increase the disorder of the universe by about twenty million million million million units—or about ten million million million times the increase in order in your brain—and that’s if you remember everything in this book.

As their name suggests, cosmic strings are objects that are like string in that they have length but a tiny cross section. Actually, they are more like rubber bands because they are under enormous tension, something like a million million million million tons.

We thus have experimental evidence both that space-time can be warped (from the bending of light during eclipses) and that it can be curved in the way necessary to allow time travel (from the Casimir effect).

The reason we say that humans have free will is because we can’t predict what they will do. However, if the human then goes off in a rocket ship and comes back before he or she set off, we will be able to predict what he or she will do because it will be part of recorded history. Thus, in that situation, the time traveler would have no free will.

As has been discussed in this chapter and Chapter 7, “empty” space is filled with pairs of virtual particles and antiparticles that appear together, move apart, and then come back together and annihilate each other. So, one can regard the pair of particles as a single particle moving on a closed loop in space-time. When the pair is moving forward in time (from the event at which it appears to that at which it annihilates), it is called a particle. But when the particle is traveling back in time (from the event at which the pair annihilates to that at which it appears), it is said to be an antiparticle traveling forward in time.

The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing? Is the unified theory so compelling that it brings about its own existence? Or does it need a creator, and, if so, does he have any other effect on the universe? And who created him?

In 1986, the Russian-American physicist Andrei Linde calculated that if inflation starts at a sufficiently high energy, there will always be someplace where the fluctuations win: the energy remains high, and inflation continues eternally. But there will be other places where the fluctuations lose and the expected trend of decreasing energy takes hold. These patches become entire individual universes such as our own. If we could zoom out far enough, we would see countless other universes, separated by Linde’s regions of the multiverse that are continuing to inflate.

Eternal inflation and the no boundary proposal together predict that our universe is not unique. Instead, from the quantum fuzz at the big bang many different universes emerge, possibly with different local laws of physics and chemistry.