Kitty Ferguson first became acquainted with Stephen Hawking and his family when she and her husband and children lived in Cambridge in the late 1980s. Around that time she retired from her career as a professional singer and conductor and began writing and lecturing about science and scientists for readers and audiences with little or no scientific background. Her eight books have appeared to critical acclaim all over the world, in twenty-seven languages. In 2000 she worked with Hawking, helping edit his book The Universe in a Nutshell.
Kitty grew up in San Antonio, Texas, moved to New York City at the age of nineteen to study at the Juilliard School of Music, and lived for forty-eight years in New York City and Chester, New Jersey. She and her husband now divide their time between Cambridge and South Carolina. They have three grown children and two grandchildren.
Visit Kitty’s website at www.kitty-ferguson.com
TRANSWORLD PUBLISHERS
61–63 Uxbridge Road, London W5 5SA
www.penguin.co.uk
Transworld is part of the Penguin Random House group of companies whose addresses can be found at global.penguinrandomhouse.com
Originally published in Great Britain in 1992 by Bantam Books,
by arrangement with Franklin Watts, Inc.
This edition first published in Great Britain in 2011 by Bantam Press
an imprint of Transworld Publishers
Bantam edition published 2012
Bantam edition reissued 2016
Copyright © Kitty Ferguson 1991, 2001, 2011, 2016
Cover photography © Getty Images
Illustrations here, here, here, here, here, here, here, here, here, here, here, here, here, here, here, here by Patrick Mulrey
Kitty Ferguson has asserted her right under the Copyright, Designs and Patents Act 1988 to be identified as the author of this work.
Every effort has been made to obtain the necessary permissions with reference to copyright material, both illustrative and quoted. We apologize for any omissions in this respect and will be pleased to make the appropriate acknowledgements in any future edition.
A CIP catalogue record for this book is available from the British Library.
Version 1.0 Epub ISBN 9781448110476
ISBN 9780857503671
This ebook is copyright material and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased or as strictly permitted by applicable copyright law. Any unauthorized distribution or use of this text may be a direct infringement of the author’s and publisher’s rights and those responsible may be liable in law accordingly.
1 3 5 7 9 10 8 6 4 2
To my granddaughters Grace and Alice
I WISH TO thank Stephen Hawking for his time and patience in helping me understand his theories, and for putting up with some terribly naïve questions from me.
I am grateful to my agents, Brie Burkeman and Rita Rosenkranz, and my editors, Sally Gaminara at Transworld Publishers and Luba Ostashevsky at Palgrave Macmillan.
I am also grateful to the following for their assistance in many ways, including reading and checking over portions of this book and conversing with me about the subjects discussed in it. Some of the people listed below have had no direct involvement. Some are no longer alive. But the extent to which they have helped me, through the years, understand Stephen Hawking and his work and the cience related to it, means it would be unconscionable not to thank them here.
Sidney Coleman, Judith Croasdell, Paul Davies, Bryce DeWitt, Yale Ferguson, Matthew Fremont, Joan Godwin, Andrei Linde, Sue Masey, Don Page, Malcolm Perry, Brian Pippard, Joanna Sanferrare, Leonard Susskind, Neil Turok, Herman and Tina Vetter, John A. Wheeler and Anna Zytkow.
Nonetheless, any shortcomings in this book are my full responsibility.
Kitty Ferguson
BLACK HOLES IN SPACETIME
THE FIRE IN THE EQUATIONS: SCIENCE, RELIGION & THE SEARCH FOR GOD
PRISONS OF LIGHT: BLACK HOLES
MEASURING THE UNIVERSE: THE HISTORICAL QUEST TO QUANTIFY SPACE
STEPHEN HAWKING: QUEST FOR A THEORY OF EVERYTHING (1991 and 2001)
TYCHO AND KEPLER – THE UNLIKELY PARTNERSHIP THAT FOREVER CHANGED OUR UNDERSTANDING OF THE HEAVENS
THE MUSIC OF PYTHAGORAS (2008)
LOST SCIENCE: ASTONISHING TALES OF FORGOTTEN GENIUS (APRIL 2017)
IN THE CENTRE of Cambridge, England, there are a handful of narrow lanes that seem hardly touched by the twentieth or twenty-first centuries. The houses and buildings represent a mixture of eras, but a step around the corner from the wider thoroughfares into any of these little byways is a step back in time, into a passage leading between old college walls or a village street with a medieval church and churchyard or a malt house. Traffic noises from equally old but busier roads nearby are barely audible. There is near silence, birdsong, voices, footsteps. Scholars and townspeople have walked here for centuries.
When I wrote my first book about Stephen Hawking in 1990, I began the story in one of those little streets, Free School Lane. It runs off Bene’t Street, beside the church of St Bene’t’s with its eleventh-century bell tower. Around the corner, in the lane, flowers and branches still droop through the iron palings of the churchyard, as they did twenty years ago. Bicycles tethered there belie the antique feel of the place, but a little way along on the right is a wall of black, rough stones with narrow slit windows belonging to the fourteenth-century Old Court of Corpus Christi College, the oldest court in Cambridge. Turn your back to that wall and you will see, high up beside a gothic-style gateway, a plaque that reads, THE CAVENDISH LABORATORY. This gateway and the passage beyond are a portal to a more recent era, oddly tucked away in the medieval street.
There is no hint of the friary that stood on this site in the twelfth century or the gardens that were later planted on its ruins. Instead, bleak, factory-like buildings, almost oppressive enough to be a prison, tower over grey asphalt pavement. The situation improves further into the complex, and in the two decades since I first wrote about it some newer buildings have gone up, but the glass walls of these well-designed modern structures are still condemned to reflect little besides the grimness of their older neighbours.
For a century, until the University of Cambridge built the ‘New’ Cavendish Labs in 1974, this complex housed one of the most important centres of physics research in the world. Here, ‘J. J.’ Thomson discovered the electron, Ernest Rutherford probed the structure of the atom – and the list goes on and on. When I attended lectures here in the 1990s (for not everything moved to the New Cavendish in 1974), enormous chalk-boards were still in use, hauled noisily up and down with crank-driven chain-pulley systems to make room for the endless strings of equations in a physics lecture.
The Cockcroft Lecture Room, part of this same site, is a much more up-to-date lecture room. Here, on 29 April 1980, scientists, guests and university dignitaries gathered in steep tiers of seats, facing a two-storey wall of chalkboard and slide screen – still well before the advent of PowerPoint. The occasion was the inaugural lecture of a new Lucasian Professor of Mathematics, 38-year-old mathematician and physicist Stephen William Hawking. He had been named to this illustrious chair the previous autumn.
The title announced for his lecture was a question: ‘Is the End in Sight for Theoretical Physics?’ Hawking startled his listeners by announcing that he thought it was. He invited them to join him in a sensational escape through time and space on a quest to find the Holy Grail of science: the theory that explains the universe and everything that happens in it – what some were calling the Theory of Everything.
Watching Stephen Hawking, silent in a wheelchair while one of his students read his lecture for the audience, no one unacquainted with him would have thought he was a promising choice to lead such an adventure. Theoretical physics was for him the great escape from a prison more grim than any suggested by the Old Cavendish Labs. Beginning when he was a graduate student in his early twenties, he had lived with encroaching disability and the promise of an early death. Hawking has amyotrophic lateral sclerosis, known in America as Lou Gehrig’s disease after the New York Yankees’ first baseman, who died of it.fn1 The progress of the disease in Hawking’s case had been slow, but by the time he became Lucasian Professor he could no longer walk, write, feed himself, or raise his head if it tipped forward. His speech was slurred and almost unintelligible except to those who knew him best. For the Lucasian lecture, he had pains-takingly dictated his text earlier, so that it could be read by the student. But Hawking certainly was and is no invalid. He is an active mathematician and physicist, whom some were even then calling the most brilliant since Einstein. The Lucasian Professorship is an extremely prestigious position in the University of Cambridge, dating from 1663. The second holder of the chair was Sir Isaac Newton.
It was typical of Hawking’s iconoclasm to begin this distinguished professorship by predicting the end of his own field. He said he thought there was a good chance the so-called Theory of Everything would be found before the close of the twentieth century, leaving little for theoretical physicists like himself to do.
Since that lecture, many people have come to think of Stephen Hawking as the standard-bearer of the quest for that theory. However, the candidate he named for Theory of Everything was not one of his own theories but ‘N=8 supergravity’, a theory which many physicists at that time hoped might unify all the particles and the forces of nature. Hawking is quick to point out that his work is only one part of a much larger picture, involving physicists all over the world, and also part of a very old quest. The longing to understand the universe must surely be as ancient as human consciousness. Ever since human beings first began to look at the night skies as well as at the enormous variety of nature around them, and considered their own existence, they’ve been trying to explain all this with myths, religion, and, later, mathematics and science. We may not be much nearer to understanding the complete picture than our remotest ancestors, but most of us like to think, as does Stephen Hawking, that we are.
Hawking’s life story and his science continue to be full of paradoxes. Things are often not what they seem. Pieces that should fit together refuse to do so. Beginnings may be endings; cruel circumstances can lead to happiness, although fame and success may not; two brilliant and highly successful scientific theories taken together yield nonsense; empty space isn’t empty; black holes aren’t black; the effort to unite everything in a simple explanation reveals, instead, a fragmented picture; and a man whose appearance inspires shock and pity takes us joyfully to where the boundaries of time and space ought to be – but are not.
Anywhere we look in our universe, we find that reality is astoundingly complex and elusive, sometimes alien, not always easy to take, and often impossible to predict. Beyond our universe there may be an infinite number of others. The close of the twentieth century has come and gone, and no one has discovered the Theory of Everything. Where does that leave Stephen Hawking’s prediction? Can any scientific theory truly explain it all?
THE IDEA THAT all the amazing intricacy and variety we experience in the world and the cosmos may come down to something remarkably simple is not new or far-fetched. The sage Pythagoras and his followers in southern Italy in the sixth century BC studied the relationships between lengths of strings on a lyre and the musical pitches these produced, and realized that hidden behind the confusion and complexity of nature there is pattern, order, rationality. In the two and a half millennia since, our forebears have continued to find – often, like the Pythagoreans, to their surprise and awe – that nature is less complicated than it first appears.
Imagine, if you can, that you are a super-intelligent alien who has absolutely no experience of our universe: is there a set of rules so complete that by studying them you could discover exactly what our universe is like? Suppose someone handed you that rule book. Could it possibly be a short book?
For decades, many physicists believed that the rule book is not lengthy and contains a set of fairly simple principles, perhaps even just one principle that lies behind everything that has happened, is happening, and ever will happen in our universe. In 1980, Stephen Hawking made the brash claim that we would hold the rule book in our hands by the end of the twentieth century.
My family used to own a museum facsimile of an ancient board game. Archaeologists digging in the ruins of the city of Ur in Mesopotamia had unearthed an exquisite inlaid board with a few small carved pieces. It was obviously an elaborate game, but no one knew its rules. The makers of the facsimile had tried to deduce them from the design of the board and pieces, but those like ourselves who bought the game were encouraged to make our own decisions and discoveries about how to play it.
You can think of the universe as something like that: a magnificent, elegant, mysterious game. Certainly there are rules, but the rule book didn’t come with the game. The universe is no beautiful relic like the game found at Ur. Yes, it is old, but the game continues. We and everything we know about (and much we do not) are in the thick of the play. If there is a Theory of Everything, we and everything in the universe must be obeying its principles, even while we try to discover what they are.
You would expect the complete, unabridged rules for the universe to fill a vast library or supercomputer. There would be rules for how galaxies form and move, for how human bodies work and fail to work, for how humans relate to one another, for how subatomic particles interact, how water freezes, how plants grow, how dogs bark – intricate rules within rules within rules. How could anyone think this could be reduced to a few principles?
Richard Feynman, the American physicist and Nobel laureate, gave an excellent example of the way the reduction process happens. There was a time, he pointed out, when we had something we called motion and something else called heat and something else again called sound. ‘But it was soon discovered,’ wrote Feynman:
after Sir Isaac Newton explained the laws of motion, that some of these apparently different things were aspects of the same thing. For example, the phenomena of sound could be completely understood as the motion of atoms in the air. So sound was no longer considered something in addition to motion. It was also discovered that heat phenomena are easily understandable from the laws of motion. In this way, great globs of physics theory were synthesized into a simplified theory.’1
All matter as we normally think of it in the universe – you and I, air, ice, stars, gases, microbes, this book – is made up of minuscule building blocks called atoms. Atoms in turn are made up of smaller objects, called particles, and a lot of empty space.
The most familiar matter particles are the electrons that orbit the nuclei of atoms and the protons and neutrons that are clustered in the nuclei. Protons and neutrons are made up of even tinier particles of matter called ‘quarks’. All matter particles belong to a class of particles called ‘fermions’, named for the great Italian physicist Enrico Fermi. They have a system of messages that pass among them, causing them to act and change in various ways. A group of humans might have a message system consisting of four different services: telephone, fax, e-mail and ‘snail mail’. Not all the humans would send and receive messages and influence one another by means of all four message services. You can think of the message system among the fermions as four such message services, called forces. There is another class of particles that carry these messages among the fermions, and sometimes among themselves as well: ‘messenger’ particles, more properly called ‘bosons’. Apparently every particle in the universe is either a fermion or a boson.
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.
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.
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.
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 millennium –
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.
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.
Explaining gravity as an exchange of messenger particles presents problems. When you think of the force holding you to the Earth as the exchange of gravitons (messenger particles of gravity) between the matter particles in your body and the matter particles that make up the Earth, you are describing the gravitational force in a quantum-mechanical way. But because all these gravitons are also exchanging gravitons among themselves, mathematically this is a messy business. We get infinities, mathematical nonsense.
Physical theories cannot really handle infinities. When they have appeared in other theories, theorists have resorted to something known as ‘renormalization’. Richard Feynman used renormalization when he developed a theory to explain the electromagnetic force, but he was far from pleased about it. ‘No matter how clever the word,’ he wrote, ‘it is what I would call a dippy process!’7 It involves putting in other infinities and letting the infinities cancel each other out. It does sound dubious, but in many cases it seems to work in practice. The resulting theories agree with observation remarkably well.
Renormalization works in the case of electromagnetism, but it fails in the case of gravity. The infinities in the gravitational force are of a much nastier breed than those in the electromagnetic force. They refuse to go away. Supergravity, the theory Hawking spoke about in his Lucasian lecture, and superstring theory, in which the basic objects in the universe are not pointlike particles but tiny strings or loops of string, began to make promising inroads in the twentieth century; and later in this book we shall be looking at even more promising recent developments. But the problem is not completely solved.
On the other hand, what if we allow quantum mechanics to invade the study of the very large, the realm where gravity seems to reign supreme? What happens when we rethink what general relativity tells us about gravity in the light of what we know about the uncertainty principle, the principle that you can’t measure accurately the position and the momentum of a particle at the same time? Hawking’s work along these lines has had bizarre results: black holes aren’t black, and the boundary conditions may be that there are no boundaries.
While we are listing paradoxes, here’s another: empty space isn’t empty. Later in this book we’ll discuss how we arrive at that conclusion. For now be content to know that the uncertainty principle means that so-called empty space teems with particles and antiparticles. (The matter– antimatter used in science fiction is a familiar example.)
General relativity tells us that the presence of matter or energy makes spacetime curve, or warp. We’ve already mentioned one result of that curvature: the bending of light beams from distant stars as they pass a massive body like the sun.
Keep those two points in mind: (1) ‘Empty’ space is filled with particles and antiparticles, adding up to an enormous amount of energy. (2) The presence of this energy causes curvature of spacetime.
If both are true the entire universe ought to be curled up into a small ball. This hasn’t happened. When general relativity and quantum mechanics work together, what they predict seems to be dead wrong. Both general relativity and quantum mechanics are exceptionally good theories, two of the outstanding intellectual achievements of the twentieth century. They serve us magnificently not only for theoretical purposes but in many practical ways. Nevertheless, put together they yield infinities and nonsense. The Theory of Everything must somehow resolve that nonsense.
Once again imagine that you are an alien who has never seen our universe. With the Theory of Everything you ought nevertheless to be able to predict everything about it … right? It’s possible you can predict suns and planets and galaxies and black holes and quasars – but can you predict next year’s Derby winner? How specific can you be? Not very.
The calculations necessary to study all the data in the universe are ludicrously far beyond the capacity of any imaginable computer. Hawking points out that although we can solve the equations for the movement of two bodies in Newton’s theory of gravity, we can’t solve them exactly for three bodies, not because Newton’s theory doesn’t work for three bodies but because the maths is too complicated. The real universe, needless to say, has more than three bodies in it.
Nor can we predict our health, although we understand the principles that underlie medicine, the principles of chemistry and biology, extremely well. The problem again is that there are too many billions upon billions of details in a real-life system, even when that system is just one human body.
With the Theory of Everything in our hands we’d still be a staggeringly long way from predicting everything. Even if the underlying principles are simple and well understood, the way they work out is enormously complicated. ‘A minute to learn, the lifetime of the universe to master’, to paraphrase an advertising slogan. ‘Lifetime of the universe to master’ is a gross understatement.fn1
Where does that leave us? What horse will win the Grand National next year is predictable with the Theory of Everything, but no computer can hold all the data or do the maths to make the prediction. Is that correct?
There’s a further problem. We must look again at the uncertainty principle of quantum mechanics.
At the level of the very small, the quantum level of the universe, the uncertainty principle also limits our ability to predict.
Think of all those odd, busy inhabitants of the quantum world, both fermions and bosons. They’re an impressive zoo of particles. Among the fermions there are electrons, protons and neutrons. Each proton or neutron is, in turn, made up of three quarks, which are also fermions. Then we have the bosons: photons (messengers of the electromagnetic force), gravitons (the gravitational force), gluons (the strong force), and Ws and Zs (the weak force). It would be helpful to know where all these and many others are, where they are going, and how quickly they are getting there. Is it possible to find out?
The diagram of an atom in Figure 2.1 is the model proposed by Ernest Rutherford at the Cavendish Labs in Cambridge early in the twentieth century. It shows electrons orbiting the nucleus of the atom as planets orbit the sun. We now know that things never really look like this on the quantum level. The orbits of electrons cannot be plotted as though electrons were planets. We do better to picture them swarming in a cloud around the nucleus. Why the blur?
The uncertainty principle makes life at the quantum level a fuzzy, imprecise affair, not only for electrons but for all the particles. Regardless of how we go about trying to observe what happens, it is impossible to find out precisely both the momentum and the position of a particle at the same time. The more accurately we measure how the particle is moving, the less accurately we know its position, and vice versa. It works like a seesaw: when the accuracy of one measurement goes up, the accuracy of the other must go down. We pin down one measurement only by allowing the other to become more uncertain.
The best way to describe the activity of a particle is to study all the possible ways it might be moving and then calculate how likely one way is as opposed to another. It becomes a matter of probabilities. A particle has this probability to be moving – that way – or it has that probability to be – here. Those probabilities are nevertheless very useful information.
It’s a little like predicting the outcome of elections. Election poll experts work with probabilities. When they deal with large enough numbers of voters, they come up with statistics that allow them to predict who will win the election and by what margin, without having to know how each individual will vote. When quantum physicists study a large number of possible paths that particles might follow, the probabilities of their moving thus and so or of being in one place rather than another become concrete information.
Pollsters admit that interviewing an individual can influence a vote by causing the voter to become more aware of issues. Physicists have a similar dilemma. Probing the quantum level influences the answers they find.
Thus far the comparison between predicting elections and studying the quantum level seems a good one. Now it breaks down: on election day, each voter does cast a definite vote one way or another, secret perhaps but not uncertain. If pollsters placed hidden cameras in voting booths – and were not arrested – they could find out how each individual voted. It is not like that in quantum physics. Physicists have devised ingenious ways of sneaking up on particles, all to no avail. The world of elementary particles does not just seem uncertain because we haven’t been clever enough to find a successful way to observe it. It really is uncertain. No wonder Hawking, in his Lucasian lecture, called quantum mechanics ‘a theory of what we do not know and cannot predict’.8
Taking this limitation into account, physicists have redefined the goal of science: the Theory of Everything will be a set of laws that make it possible to predict events up to the limit set by the uncertainty principle, and that means in many cases satisfying ourselves with statistical probabilities, not specifics.
Hawking sums up our problem. In answer to the question of whether everything is predetermined either by the Theory of Everything or by God, he says yes, he thinks it is. ‘But it might as well not be, because we can never know what is determined. If the theory has determined that we shall die by hanging, then we shall not drown. But you would have to be awfully sure that you were destined for the gallows to put to sea in a small boat during a storm.’9 He regards the idea of free will as ‘a very good approximate theory of human behaviour’.10