STEPHEN W HAWKING THE THEORY OF EVERYTHING
Download Full Book PDF Here CONTENTS
ideas about the universe . . . . . . . . . . . . . . . . . . . . . . .1
the expanding universe . . . . . . . . . . . . . . . . . . . . . . . .13
black holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
black holes ain’t so black . . . . . . . . . . . . . . . . . . . . .57
the origin and fate of the universe . . . . . . . . . . . . .77
the direction of time . . . . . . . . . . . . . . . . . . . . . . . . .103
the theory of everything . . . . . . . . . . . . . . . . . . . . .119
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .137
In this series of lectures, I shall try to give an outline of what we think is the history of the universe from the big bang to black holes. In the first lecture I shall briefly review past ideas about the universe and how we got to our present picture. One might call this the history of the universe.
In the second lecture I shall describe how both Newton’s and Einstein’s theories of gravity led to the conclusion that the universe could not be static; it had to be either expanding or contracting. This, in turn, implied that there must have been a time between ten and twenty billion years ago when the density of the universe was infinite. This is called the big bang. It would have been the beginning of the universe.
In the third lecture I shall talk about black holes. These are formed when a massive star or an even larger body collapses in on itself under its own gravitational pull. According to Einstein’s general theory of relativity, anyone foolish enough to fall into a black hole will be lost forever. They will not be able to come out of the black hole again. Instead, history, as far as they are concerned, will come to a sticky end at a singularity. However, general
relativity is a classical theory—that is, it doesn’t take into account the uncertainty principle of quantum mechanics.
In the fourth lecture, I shall describe how quantum mechanics allows energy to leak out of black holes. Black holes aren’t as black as they are painted.
In the fifth lecture, I shall apply quantum mechanical ideas to the big bang and the origin of the universe. This leads to the idea that space-time may be finite in extent but without boundary or edge. It would be like the surface of the Earth but with two more dimensions.
In the sixth lecture, I shall show how this new boundary proposal could explain why the past is so different from the future, even though the laws of physics are time-symmetric.
Finally, in the seventh lecture, I shall describe how we are trying to find a unified theory that will include quantum mechanics, gravity, and all the other interactions of physics. If we achieve this, we shall really understand the universe and our position in it.
IDEAS ABOUT THE UNIVERSE
As long ago as 340 B.C. Aristotle, in his book On the Heavens, was able to put forward two good arguments for believing that the Earth was a round ball rather than a flat plate. First, he realized that eclipses of the moon were caused by the Earth coming between the sun and the moon. The Earth’s shadow on the moon was always round, which would be true only if the Earth was spherical. If the Earth had been a flat disk, the shadow would have been elongated and elliptical, unless the eclipse always occurred at a time when the sun
was directly above the center of the disk.
Second, the Greeks knew from their travels that the Pole Star appeared lower in the sky when viewed in the south than it did in more northerly regions. From the difference in the apparent position of the Pole Star in Egypt and Greece, Aristotle even quoted an estimate that the distance around the Earth was four hundred thousand stadia. It is not known exactly what length a stadium was, but it may have been about two hundred yards. This would make Aristotle’s estimate about twice the currently accepted figure.
The Greeks even had a third argument that the Earth must be round, for why else does one first see the sails of a ship coming over the horizon and only later see the hull? Aristotle thought that the Earth was stationary and that the sun, the moon, the planets, and the stars moved in circular orbits about the Earth. He believed this because he felt, for mystical reasons, that the Earth was the center of the universe and that circular motion was the most perfect.
This idea was elaborated by Ptolemy in the first century A.D. into a complete cosmological model. The Earth stood at the center, surrounded by eight spheres, which carried the moon, the sun, the stars, and the five planets known at the time: Mercury, Venus, Mars, Jupiter, and Saturn. The planets themselves moved on smaller circles attached to their respective spheres in order to account for their rather complicated observed paths in the sky. The outermost sphere carried the so-called fixed stars, which always stay in the same positions relative to each other but which rotate together across the sky. What lay beyond the last sphere was never made very clear, but it certainly was not part of mankind’s observable universe.
Ptolemy’s model provided a reasonably accurate system for predicting the positions of heavenly bodies in the sky. But in order to predict these positions correctly, Ptolemy had to make an assumption that the moon followed a path that sometimes brought it twice as close to the Earth as at other times. And that meant that the moon had sometimes to appear twice as big as it usually does. Ptolemy was aware of this flaw but nevertheless his model was generally, although not universally, accepted. It was adopted by the Christian church as the picture of the universe that was in accordance with Scripture. It had the
great advantage that it left lots of room outside the sphere of fixed stars for heaven and hell.
A much simpler model, however, was proposed in 1514 by a Polish priest, Nicholas Copernicus. At first, for fear of being accused of heresy, Copernicus published his model anonymously. His idea was that the sun was stationary at the center and that the Earth and the planets moved in circular orbits around the sun. Sadly for Copernicus, nearly a century passed before this idea was to be taken seriously. Then two astronomers—the German, Johannes Kepler, and the Italian, Galileo Galilei—started publicly to support the Copernican theory, despite the fact that the orbits it predicted did not quite match the ones observed. The death of the Aristotelian–Ptolemaic theory came in 1609. In that year Galileo started observing the night sky with a telescope, which had just been invented. When he looked at the planet Jupiter, Galileo found that it was accompanied by several small satellites, or moons, which orbited around it. This implied that everything did not have to orbit directly around the Earth as Aristotle and Ptolemy had thought. It was, of course, still possible to believe that the Earth was stationary at the center of the universe, but that the moons of Jupiter moved on extremely complicated paths around the Earth, giving the appearance that they orbited Jupiter. However, Copernicus’s theory was much simpler.
At the same time, Kepler had modified Copernicus’s theory, suggesting that the planets moved not in circles, but in ellipses. The predictions now finally matched the observations. As far as Kepler was concerned, elliptical orbits were merely an ad hoc hypothesis—and a rather repugnant one at that because ellipses were clearly less perfect than circles. Having discovered, almost by accident, that elliptical orbits fitted the observations well, he could not reconcile with his idea that the planets were made to orbit the sun by magnetic forces.
An explanation was provided only much later, in 1687, when Newton published his Principia Mathematica Naturalis Causae. This was probably the most important single work ever published in the physical sciences. In it, Newton not only put forward a theory of how bodies moved in space and time, but he also developed the mathematics needed to analyze those motions. In addition, Newton postulated a law of universal gravitation. This said that each body in the universe was attracted to every other body by a force that was
stronger the more massive the bodies and the closer they were to each other. It was the same force that caused objects to fall to the ground. The story that Newton was hit on the head by an apple is almost certainly apocryphal. All Newton himself ever said was that the idea of gravity came to him as he sat in a contemplative mood, and was occasioned by the fall of an apple.
Newton went on to show that, according to his law, gravity causes the moon to move in an elliptical orbit around the Earth and causes the Earth and the planets to follow elliptical paths around the sun. The Copernican model got rid of Ptolemy’s celestial spheres and with them the idea that the universe had a natural boundary. The fixed stars did not appear to change their relative positions as the Earth went around the sun. It, therefore, became natural to suppose that the fixed stars were objects like our sun but much farther away. This raised a problem. Newton realized that, according to his theory of gravity, the stars
should attract each other; so, it seemed they could not remain essentially motionless. Would they not all fall together at some point?
In a letter in 1691 to Richard Bentley, another leading thinker of his day, Newton argued that this would indeed happen if there were only a finite number of stars. But he reasoned that if, on the other hand, there were an infinite number of stars distributed more or less uniformly over infinite space, this would not happen because there would not be any central point for them to fall to. This argument is an instance of the pitfalls that one can encounter when one talks about infinity.
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. The correct approach, it was realized only much later, is to consider the finite situation in which the stars all fall in on each other. One then asks how things change if one adds more stars roughly uniformly distributed outside this region. According to Newton’s law, the extra stars would make no difference at all to the original ones, and so the stars would fall in just as fast. We can add as many stars as we like, but they will still always collapse in on themselves. We now know it is impossible to have an infinite static model of the universe in which gravity is always attractive.
It is an interesting reflection on the general climate of thought before the twentieth century that no one had suggested that the universe was expanding or contracting. It was generally accepted that either the universe had existed forever in an unchanging state or that it had been created at a finite time in the past, more or less as we observe it today. In part, this may have been due to people’s tendency to believe in eternal truths as well as the comfort they found in the thought that even though they may grow old and die, the universe is unchanging.
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. This did not significantly affect their predictions of the motions of the planets. But it would allow an infinite distribution of stars to remain in equilibrium, with the attractive forces between nearby stars being balanced by the repulsive forces from those that were farther away.
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. In fact, various contemporaries of Newton had raised the problem, and the Olbers article of 1823 was not even the first to contain plausible arguments on this subject. It was, however, the first to be widely noted. 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. And that brings us to the question of what could have caused the stars to have turned on in the first place.