Three Roads to Quantum Gravity (10 page)

So, our world is incredibly big, slow and cold compared with the fundamental world. Our job is to remove the prejudices and blinkers imposed by our parochial perspective and imagine space and time in their own terms, on their natural scale. We do have a very powerful toolkit that enables us to do this, consisting of the theories we have so far developed. We must take the theories that we trust the most, and tune them as best we can to give us a picture of the Planck scale. The story I am telling in this book is based on what we have learned by doing this.

In the earlier chapters I argued that our world cannot be understood as a collection of independent entities living in a fixed, static background of space and time. Instead, it is a network of relationships the properties of every part of which are determined by its relationships to the other parts. In this chapter we have learned that the relations that make up the world are causal relations. This means that the world is not
made of stuff, but of processes by which things happen. Elementary particles are not static objects just sitting there, but processes carrying little bits of information between events at which they interact, giving rise to new processes. They are much more like the elementary operations in a computer than the traditional picture of an eternal atom.

We are very used to imagining that we see a three-dimensional world when we look around ourselves. But is this really true? If we keep in mind that what we see is the result of photons impinging on our eyes, it is possible to imagine our view of the world in a quite different way. Look around and imagine that you see each object as a consequence of photons having just travelled from it to you. Each object you see is the result of a process by which information travelled to you in the shape of a collection of photons. The farther away the object is, the longer it took the photons to travel to you. So when you look around you do not see space - instead, you are looking back through the history of the universe. What you are seeing is a slice through the history of the world. Everything you see is a bit of information brought to you by a process which is a small part of that history.

The whole history of the world is then nothing but the story of huge numbers of these processes, whose relationships are continually evolving. We cannot understand the world we see around us as something static. We must see it as something created, and under continual recreation, by an enormous number of processes acting together. The world we see around us is the collective result of all those processes. I hope this doesn’t seem too mystical. If I have written this book well then, by the end of it, you may see that the analogy between the history of the universe and the flow of information in a computer is the most rational, scientific analogy I could make. What is mystical is the picture of the world as existing in an eternal three-dimensional space, extending in all directions as far as the mind can imagine. The idea of space going on and on for ever has nothing to do with what we see. When we look out, we are looking back in time through the history of the universe, and after not too long we come to
the big bang. Before that there may be nothing to see - or, at the very least, if there is something it will most likely look nothing like a world suspended in a static three-dimensional space. When we imagine we are seeing into an infinite three-dimensional space, we are falling for a fallacy in which we substitute what we actually see for an intellectual construct. This is not only a mystical vision, it is wrong.

I
n the cultural iconography of our time, black holes have become mythic objects. In science fiction novels and films they often evoke images of death and transcendence, recalling the irreversibility of certain passages and the promise of our eventual emergence into a new universe. I am not a very good actor, but I was once asked by a friend, the director Madeline Schwartzman, to act in one of her films. Luckily I got to play a physics professor giving a lecture on black holes. In the film, called Soma Sema, the myth of Orpheus is merged with two major scientific and technological themes of our time: total nuclear war and black holes. Orpheus, my student, seeks through her music to be an exception to all three versions of the irreversible.

Among those of us who think about space and time professionally, black holes play a central role. A whole subculture of astronomers is devoted to understanding how they form and how to find them. By now, dozens of candidate black holes have been observed. But what is most exciting is that there are probably vast numbers of them out there. Many if not most galaxies, including our own, seem to have an enormous black hole at their centre, with a mass millions of times that of our Sun. And there is evidence, both observational and theoretical, that a small fraction of stars end their lives as black holes. A typical galaxy such as ours could well contain tens or even hundreds of millions of these stellar black holes. So black holes are out there, and interstellar
travellers of the far future will have to be careful to avoid them. But beyond the fascination they hold for astronomers, black holes are important to science for other reasons. They are a central object of study for those of us who work on quantum gravity. In a sense, black holes are microscopes of infinite power which make it possible for us to see the physics that operates on the Planck scale.

Because they feature prominently in popular culture, almost everyone knows roughly what a black hole is. It is a place where gravity is so strong that the velocity required to escape from it is greater than the speed of light. So no light can emerge from it, and neither can anything else. We can understand this in terms of the notion of causal structure we introduced in the last chapter. A black hole contains a great concentration of mass that causes the light cones to tip over so far that the light moving away from the black hole actually gets no farther from it (
Figure 13
). So the surface of a black hole is like a one-way mirror: light moving towards it can pass into it, but no light can escape from it. For this reason the surface of a black hole is called the horizon. It is the limit of what observers outside the black hole can see.

I should emphasize that the horizon is not the surface of the object that formed the black hole. Rather it is the boundary of the region that is capable of sending light out into the universe. Light emitted by any body inside the horizon is trapped and cannot get any farther than the horizon. The object that formed the black hole is rapidly compressed, and according to general relativity it quickly reaches infinite density.

Behind the horizon of a black hole is a part of the universe made up of causal processes that go on, in spite of the fact that we receive no information from them. Such a region is called a hidden region. There are at least a billion billion black holes in the universe, so there are quite a lot of hidden regions that are invisible to us, or to any other observer. Whether a region is hidden or not depends in part on the observer. An observer who falls into a black hole will see things that her friends who stay outside will never see. In Chapter 2 we found that different observers may see different parts of the universe in
their past. The existence of black holes means that this is not just a question of waiting long enough for light from a distant region to reach us. We could be right next to a black hole, yet never be able to see what observers inside it can see, however long we waited.

Light cones in the vicinity of a black hole. The solid black line is the singularity where the gravitational field is infinitely strong. The dotted lines are the horizons, consisting of light rays that stay the same distance from the singularity. Light cones just at the horizon are tilted to show that a light ray trying to move away from the black hole just stays at the same distance and travels along the horizon. A light cone inside the horizon is tilted so far that any motion into the future brings one closer to the singularity.

All observers have their own hidden region. The hidden region of each observer consists of all those events that they will not be able to receive information from, no matter how long they wait. Each hidden region will include the interiors
of all the black holes in the universe, but there may be other regions hidden as well. For example, if the rate at which the universe expands increases with time, there will be regions of the universe from which we shall never receive light signals, no matter how long we wait. A photon from such a region may be travelling in our direction at the speed of light, but because of the increase in the rate of the expansion of the universe it will always have more distance to travel towards us than it has travelled so far. As long as the expansion continues to accelerate, the photon will never reach us. Unlike black holes, the hidden regions produced by the acceleration of the expansion of the universe depend on the history of each observer. For each observer there is a hidden region, but they are different for different observers.

This raises an interesting philosophical point, because objectivity is usually assumed to be connected with observer independence. It is commonly assumed that anything that is observer dependent is subjective, meaning that it is not quite real. But the belief that observer dependence rules out objectivity is a residue of an older philosophy, usually associated with the name of Plato, according to which truth resides not in our world but in an imaginary world consisting of all ideas which are eternally true. According to this philosophy, anybody could have access to any truth about the world, because the process of finding truth was held to be akin to a process of remembering, rather than observing. This philosophy is hard to square with Einstein’s general theory of relativity because, in a universe defined by that theory, something may be both objectively true and at the same time knowable only by some observers and not others. So ‘objectivity’ is not the same as ‘knowable by all’. A weaker, less stringent interpretation is required: that all those observers who are in a position to ascertain the truth or falsity of some observation should agree with one another.

The hidden region of any observer has a boundary that divides the part of the universe they can see from the part they cannot. As with a black hole, this boundary is called the horizon. Like the invisible regions, horizons are observer dependent concepts. For any observer who remains outside
it, a black hole has a horizon - the surface that divides the region from which light cannot escape from the rest of the universe. Light leaving a point just inside the horizon of the black hole will be pulled inexorably into the interior; light just outside the horizon will be able to escape (
Figures 13
and
14
). Although the horizon of a black hole is an observer dependent concept, there are a large number of observers who share that horizon: all those who are outside that black hole. So the horizon of a black hole is an objective property. But it is not a horizon for all observers, because any observer who falls through it will be able to see inside. And an observer who crosses the horizon of a black hole will become invisible to observers who remain outside.

The paths of three light rays that move away from the singularity. They start just inside, outside and just at the horizon.

It helps to know that horizons are themselves surfaces of light. They are made up of those light rays that just fail to reach the observer (
Figure 14
). The horizon of a black hole is a surface of light that has begun to move outwards from the black hole but, because of the black hole’s gravitational field, fails to get any farther from its centre. Think of the horizon as a curtain made of photons. Photons leaving from any point just inside the horizon are drawn inwards, even if they were initially moving away from the centre of the black hole.

On the other hand, a photon that starts just outside the horizon of a black hole will reach us, but it will be delayed because light cones near the horizon are tilted almost so far that no light can escape. The closer to the horizon the photon starts, the longer will be the delay. The horizon is the point where the delay becomes infinite - a photon released there never reaches us.