One of the four fundamental forces of nature is gravity. One way of thinking about the gravitational force holding us to the Earth is as ‘messages’ carried by bosons called gravitons between the particles of the atoms in your body and the particles of the atoms in the Earth, influencing these particles to draw closer to one another. Gravity is the weakest of the forces, but, as we’ll see later, it is a very long-range force and acts on everything in the universe. When it adds up, it can dominate all the other forces.
A second force, the electromagnetic force, is messages carried by bosons called photons among the protons in the nucleus of an atom, between the protons and the electrons nearby, and among electrons. The electromagnetic force causes electrons to orbit the nucleus. On the level of everyday experience, photons show up as light, heat, radio waves, microwaves and other waves, all known as electromagnetic radiation. The electromagnetic force is also long-range and much stronger than gravity, but it acts only on particles with an electric charge.
A third message service, the strong nuclear force, causes the nucleus of the atom to hold together.
A fourth, the weak nuclear force, causes radioactivity and plays a necessary role, in stars and in the early universe, in the formation of the elements.
The gravitational force, the electromagnetic force, the strong nuclear force, and the weak nuclear force … the activities of those four forces are responsible for all messages among all fermions in the universe and for all interactions among them. Without the four forces, every fermion (every particle of matter) would exist, if it existed at all, in isolation, with no means of contacting or influencing any other, oblivious to every other. To put it bluntly, whatever doesn’t happen by means of one of the four forces doesn’t happen. If that is true, a complete understanding of the forces would give us an understanding of the principles underlying everything that happens in the universe. Already we have a remarkably condensed rule book.
Much of the work of physicists in the twentieth century was aimed at learning more about how the four forces of nature operate and how they are related. In our human message system, we might discover that telephone, fax and e-mail are not really so separate after all, but can be thought of as the same thing showing up in three different ways. That discovery would ‘unify’ the three message services. In a similar way, physicists have sought, with some success, to unify the forces. They hope ultimately to find a theory which explains all four forces as one showing up in different ways – a theory that may even unite both fermions and bosons in a single family. They speak of such a theory as a unified theory.
A theory explaining the universe, the Theory of Everything, must go several steps further. Of particular interest to Stephen Hawking, it must answer the question, what was the universe like at the instant of beginning, before any time whatsoever had passed? Physicists phrase that question: what are the ‘initial conditions’ or the ‘boundary conditions at the beginning of the universe’? Because this issue of boundary conditions has been and continues to be at the heart of Hawking’s work, it behooves us to spend a little time with it.
The Boundary Challenge
Suppose you put together a layout for a model railway, then position several trains on the tracks and set the switches and throttles controlling the train speeds as you want them, all before turning on the power. You have set up boundary conditions. For this session with your train set, reality is going to begin with things in precisely this state and not in any other. Where each train will be five minutes after you turn on the power, whether any train will crash with another, depends heavily on these boundary conditions.
Imagine that when you have allowed the trains to run for ten minutes, without any interference, a friend enters the room. You switch off the power. Now you have a second set of boundary conditions: the precise position of everything in the layout at the second you switched it off. Suppose you challenge your friend to try to work out exactly where all the trains started out ten minutes earlier. There would be a host of questions besides the simple matter of where the trains are standing and how the throttles and switches are set. How quickly does each of the trains accelerate and slow down? Do certain parts of the tracks offer more resistance than others? How steep are the gradients? Is the power supply constant? Is it certain there has been nothing to interfere with the running of the train set – something no longer evident? The whole exercise would indeed be daunting. Your friend would be in something like the position of a modern physicist trying to work out how the universe began – what were the boundary conditions at the beginning of time.
Boundary conditions in science do not apply only to the history of the universe. They simply mean the lie of the land at a particular point in time, for instance the start of an experiment in a laboratory. However, unlike the situation with the train set or a lab experiment, when considering the universe, one is often not allowed to set up boundary conditions. One of Hawking’s favourite questions is how many ways the universe could have begun and still ended up the way we observe it today, assuming that we have correct knowledge and understanding of the laws of physics and they have not changed. He is using ‘the way we observe the universe today’ as a boundary condition and also, in a more subtle sense, using the laws of physics and the assumption that they have not changed as boundary conditions. The answer he is after is the reply to the question, what were the boundary conditions at the beginning of the universe, or the ‘initial conditions of the universe’ – the exact layout at the word go, including the minimal laws that had to be in place at that moment in order to produce at a certain time in the future the universe as we know it today? It is in considering this question that he has produced some of his most interesting work and surprising answers.
A unified description of the particles and forces, and knowledge of the boundary conditions for the origin of the universe, would be a stupendous scientific achievement, but it would not be a Theory of Everything. In addition, such a theory must account for values that are ‘arbitrary elements’ in all present theories.
Language Lesson
Arbitrary elements include such ‘constants of nature’ as the mass and charge of the electron and the velocity of light. We observe what these are, but no theory explains or predicts them. Another example: physicists know the strength of the electromagnetic force and the weak nuclear force. The electroweak theory is a theory that unifies the two, but it cannot tell us how to calculate the difference in strength between the two forces. The difference in strength is an ‘arbitrary element’, not predicted by the theory. We know what it is from observation, and so we put it into a theory ‘by hand’. This is considered a weakness in a theory.
When scientists use the word predict, they do not mean telling the future. The question ‘Does this theory predict the speed of light?’ isn’t asking whether the theory tells us what that speed will be next Tuesday. It means, would this theory make it possible for us to work out the speed of light if it were impossible to observe what that speed is? As it happens, no present theory does predict the speed of light. It is an arbitrary element in all theories.
One of Hawking’s concerns when he wrote A Brief History of Time was that there be a clear understanding of what is meant by a theory. A theory is not Truth with a capital T, not a rule, not fact, not the final word. You might think of a theory as a toy boat. To find out whether it floats, you set it on the water. You test it. When it flounders, you pull it out of the water and make some changes, or you start again and build a different boat, benefiting from what you’ve learned from the failure.
Some theories are good boats. They float a long time. We may know there are a few leaks, but for all practical purposes they serve us well. Some serve us so well, and are so solidly supported by experiment and testing, that we begin to regard them as truth. Scientists, keeping in mind how complex and surprising our universe is, are extremely wary about calling them that. Although some theories do have a lot of experimental success to back them up and others
are hardly more than a glimmer in a theorist’s eyes – brilliantly designed boats that have never been tried on the water – it is risky to assume that any of them is absolute, fundamental scientific ‘truth’.
It is important, however, not to dither around for ever, continuing to call into question well-established theories without having a good reason for doing so. For science to move ahead, it is necessary to decide whether some theories are dependable enough, and match observation sufficiently well, to allow us to use them as building blocks and proceed from there. Of course, some new thought or discovery might come along and threaten to sink the boat. We’ll see an example of that later in this book.
In A Brief History of Time Stephen Hawking wrote that a scientific 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. It exists only in our minds and does not have any other reality (whatever that may mean).’2 The easiest way to understand this definition is to look at some examples.
There is a film clip showing Hawking teaching a class of graduate students, probably in the early 1980s, with the help of his graduate assistant. By this time Hawking’s ability to speak had deteriorated so seriously that it was impossible for anyone who did not know him well to understand him. In the clip, his graduate assistant interprets Hawking’s garbled speech to say, ‘Now it just so happens that we have a model of the universe here’, and places a large cardboard cylinder upright on the seminar table. Hawking frowns and mutters something that only the assistant can understand. The assistant apologetically picks up the cylinder and turns it over to stand on its other end. Hawking nods approval, to general laughter.
A ‘model’, of course, does not have to be something like a cardboard cylinder or a drawing that we can see and touch. It can be a mental picture or even a story. Mathematical equations or creation myths can be models.
Getting back to the cardboard cylinder, how does it resemble the universe? To make a full-fledged theory out of it, Hawking would have to explain how the model is related to what we actually see around us, to ‘observations’, or to what we might observe if we had better technology. However, just because someone sets a piece of cardboard on the table and tells how it is related to the actual universe does not mean anyone should accept this as the model of the universe. We are to consider it, not swallow it hook, line and sinker. It is an idea, existing ‘only in our minds’. The cardboard cylinder may turn out to be a useful model. On the other hand, some evidence may turn up to prove that it is not. We shall have found that we are part of a slightly different game from the one the model suggested we were playing. Would that mean the theory was ‘bad’? No, it may have been a very good theory, and everyone may have learned a great deal from considering it, testing it, and having to change it or discard it. The effort to shoot it down may have required innovative thinking and experiments that will lead to something more successful or pay off in other ways.
What is it then that makes a theory a good theory? Quoting Hawking again, it must ‘accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations’.3
For example, Isaac Newton’s theory of gravity describes a very large class of observations. It predicts the behaviour of objects dropped or thrown on Earth, as well as planetary orbits.
It’s important to remember, however, that a good theory does not have to arise entirely from observation. A good theory can be a wild theory, a great leap of imagination. ‘The ability to make these intuitive leaps is really what characterizes a good theoretical physicist,’ says Hawking.4 However, a good theory should not be at odds with things already observed, unless it gives convincing reasons for seeming to be at odds. Superstring theory, one of the most exciting current theories, predicts more than three dimensions of space, a prediction that certainly seems inconsistent with observation. Theorists explain the discrepancy by suggesting the extra dimensions are curled up so small we are unable to recognize them.
We’ve already seen what Hawking means by his second requirement, that a theory contain only a few arbitrary elements.
The final requirement, according to Hawking, is that it must suggest what to expect from future observations. It must challenge us to test it. It must tell us what we will observe if the theory is correct. It should also tell us what observations would prove that it is not correct. For example, Albert Einstein’s theory of general relativity predicts that beams of light from distant stars bend a certain amount as they pass massive bodies like the sun. This prediction is testable. Tests have shown Einstein was correct.
Some theories, including most of Stephen Hawking’s, are impossible to test with our present technology, perhaps even with any conceivable future technology. They are tested with mathematics. They must be mathematically consistent with what we do know and observe. But we cannot observe the universe in its earliest stages to find out directly whether his ‘no-boundary proposal’ (to be discussed later) is correct. Although some tests were proposed for proving or disproving ‘wormholes’, Hawking does not think they would succeed. But he has told us what he thinks we will find if we ever do have the technology, and he is convinced that his theories are consistent with what we have observed so far. In some cases he has risked making some very specific predictions about the results of experiments and observations that push at the boundaries of our present capabilities.
If nature is perfectly unified, then the boundary conditions at the beginning of the universe, the most fundamental particles and the forces that govern them, and the constants of nature, are interrelated in a unique and completely compatible way, which we might be able to recognize as inevitable, absolute and self-explanatory. To reach that level of understanding would indeed be to discover the Theory of Everything … of Absolutely Everything … even the answer, perhaps, to the question of why does the universe fit this description … to ‘know the Mind of God’, as Hawking termed it in A Brief History of Time, or ‘the Grand Design’, as he would phrase it less dramatically in a more recent book by that name.
Laying Down the Gauntlet
We are ready to list the challenges that faced any ‘Theory of Everything’ candidate when Hawking delivered his Lucasian Lecture in 1980. You’ll learn in due course how some requirements in this list have changed subtly since then.
It must give us a model that unifies the forces and particles.
It must answer the question, what were the ‘boundary conditions’ of the universe, the conditions at the very instant of beginning, before any time whatsoever passed?
It must be ‘restrictive’, allowing few options. It should, for instance, predict precisely how many types of particles there are. If it leaves options, it must somehow account for the fact that we have the universe we have and not a slightly different one.
It should contain few arbitrary elements. We would rather not have to peek too often at the actual universe for answers. Paradoxically, the Theory of Everything itself may be an arbitrary element. Few scientists expect it to explain why there should exist either a theory or anything at all for it to describe. It is not likely to answer Stephen Hawking’s question: ‘Why does the universe [or, for that matter, the Theory of Everything] go to all the bother of existing?’5
It must predict a universe like the universe we observe or else explain convincingly why there are discrepancies. If it predicts that the speed of light is ten miles per hour, or disallows penguins or pulsars, we have a problem. A Theory of Everything must find a way to survive comparison with what we observe.
It should be simple, although it must allow for enormous complexity. The physicist John Archibald Wheeler of Princeton wrote:
Behind it all
is surely an idea so simple,
so beautiful,
so compelling that when –
in a decade, a century,
or a mill
ennium –
we grasp it,
we will all say to each other,
how could it have been otherwise?
How could we have been so stupid
for so long?6
The most profound theories, such as Newton’s theory of gravity and Einstein’s relativity theories, are simple in the way Wheeler described.
It must solve the enigma of combining Einstein’s theory of general relativity (a theory that explains gravity) with quantum mechanics (the theory we use successfully when talking about the other three forces). This is a challenge that Stephen Hawking has taken up. We introduce the problem here. You will understand it better after reading about the uncertainty principle of quantum mechanics in this chapter and about general relativity later.
Theory Meets Theory
Einstein’s theory of general relativity is the theory of the large and the very large – stars, planets, galaxies, for instance. It does an excellent job of explaining how gravity works on that level.
Quantum mechanics is the theory of the very small. It describes the forces of nature as messages among fermions (matter particles). Quantum mechanics also contains something extremely frustrating, the uncertainty principle: we can never know precisely both the position of a particle and its momentum (how it is moving) at the same time. In spite of this problem, quantum mechanics does an excellent job of explaining things on the level of the very small.
One way to combine these two great twentieth-century theories into one unified theory would be to explain gravity, more successfully than has been possible so far, as an exchange of messenger particles, as we do with the other three forces. Another avenue is to rethink general relativity in the light of the uncertainty principle.
Stephen Hawking, His Life and Work Page 2
