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

by Stephen Hawking

This said that each body in the universe was attracted toward every other body by a force which was stronger the more massive the bodies and the closer they were to each other.

In an infinite universe, every point can be regarded as the center because every point has an infinite number of stars on each side of it.

We now know it is impossible to have an infinite static model of the universe in which gravity is always attractive.

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.

Even when Einstein formulated the general theory of relativity in 1915, he was sure that the universe had to be static. He therefore modified his theory to make this possible, introducing a so-called cosmological constant into his equations.

The situation is rather like steadily blowing up a balloon which has a number of spots painted on it. As the balloon expands, the distance between any two spots increases, but there is no spot that can be said to be the center of the expansion.

the universe is expanding so sufficiently slowly that the gravitational attraction between the different galaxies causes the expansion to slow down and eventually to stop.

there is a third kind of solution, in which the universe is expanding only just fast enough to avoid recollapse. In this case the separation also starts at zero, and increases forever. However, the speed at which the galaxies are moving apart gets smaller and smaller, although it never quite reaches zero.

we need to know the present rate of expansion of the universe and its present average density. If the density is less than a certain critical value, determined by the rate of expansion, the gravitational attraction will be too weak to halt the expansion. If the density is greater than the critical

value, gravity will stop the expansion at some time in the future and cause the universe to recollapse.

So all we know is that the universe is expanding by between 5 percent and 10 percent every thousand million years.

If we add up the masses of all the stars that we can see in our galaxy and other galaxies, the total is less than one-hundredth of the amount required to halt the expansion of the universe, even in the lowest estimate of the rate of expansion.

And paradoxically, the more fuel a star starts off with, the sooner it runs out. This is because the more massive the star is, the hotter it needs to be to balance its gravitational attraction.

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.

His companions watching from the spaceship would find the intervals between successive signals from the astronaut getting longer and longer as eleven o’clock approached. However, the effect would be very small before 10:59:59. They 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 eleven o’clock signal. The light waves emitted from the surface of the star between 10:59:59 and eleven o’clock, by the astronaut’s watch, would be spread out over an infinite period of time, as seen from the spaceship.

cosmic censorship hypothesis

The physicist John Wheeler once calculated that if one took all the heavy water in all the oceans of the world, one could build a hydrogen bomb that would compress matter at the center so much that a black hole would be created. Unfortunately, however, there would be no one left to observe it.

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.

But they tell us that, on average, there cannot be more than three hundred little black holes in every cubic light-year in the universe. This limit means that primordial black holes could make up at most one millionth of the average mass density in the universe.

Our own sun contains about 2 percent of these heavier elements because it is a second– or third–generation star.

Third, why did the universe start out with so nearly the critical rate of expansion to just avoid recollapse? 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.

Fourth, despite the fact that the universe is so uniform and homogenous on a large scale, it contains local lumps such as stars and galaxies. These are thought to have developed from small differences in the density of the early universe from one region to another. What was the origin of these density fluctuations?

Why is the universe so uniform, and expanding at just the critical rate to avoid recollapse?

The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart. This is because you have to expend energy to separate them. You have to pull against the gravitational force attracting them together. Thus, in a sense, the gravitational field has negative energy. In the case of the whole universe, one can show that this negative gravitational energy exactly cancels the positive energy of the matter. So the total energy of the universe is zero.

“The boundary condition of the universe is that it has no boundary.”

This might suggest that the so–called imaginary time is really the fundamental time, and that what we call real time is something we create just in our minds.

In real time, the universe has a beginning and an end at singularities that form a boundary to space-time and at which the laws of science break down. But in imaginary time, there are no singularities or boundaries. So maybe what we call imaginary time is really more basic, and what we call real time is just an idea that we invent to help us describe what we think the universe is like. But according to the approach I described in the first lecture, a scientific theory is just a mathematical model we make to describe our observations. It exists only in our minds. So it does not have any meaning to ask: Which is real, “real” or “imaginary” time? It is simply a matter of which is a more useful description.

The increase of disorder or entropy with time is one example of what is called an arrow of time, something that gives a direction to time and distinguishes the past from the future.