“In the beginning God created the heaven and the earth…. And God made two great lights; the greater light to rule the day, and the lesser light to rule the night; He made the stars also…. Thus the heavens and the earth were finished, and all the host of them. And on the seventh day God ended His work which He had made; and He rested on the seventh day from all His work which He had made.”
If there is some dispute over this Biblical version of how the universe began, there is little dispute that the universe did, indeed, begin somehow. But in contemplating the topic, some of life’s great unanswered questions arise: How did all of this—we, this earth, this universe—happen? These are also known as the eternal questions, the ones that have always had a claim on mankind’s sense of wonder.
What makes this month’s interview subject remarkable, among other things, is that he may be one of the few humans to have answers to these questions. In a field where genius is commonplace, physicist Stephen W. Hawking is described by his peers as “the intellectual successor to Einstein.”
But his intellectual prowess is only one of the things that set Hawking apart from most people. For the past 27 years, he has been slowly dying of a motor neuron disease, amyotrophic lateral sclerosis, commonly called Lou Gehrig’s disease. As the disease has progressed, he has been confined to a wheelchair, virtually unable to move, and has, within the past four years, been unable to speak. The disease has not affected his mind, however, and in the view of some of his peers, his intellectual power may have been enhanced since the onset of the disease.
With extraordinary will power, Hawking has continued his research, his writing and his mission to inform the public of work in his field. He does this with the help of a sophisticated computer. A screen connected to the device is mounted on the front of his electric-powered wheelchair, and he is able to compose sentences by selecting words from dictionary lists summoned onto the screen. With the few fingers on either hand he is still capable of moving, he directs a cursor to the correct word or phrase. The computer can then synthesize the sentences he composes into a flat-sounding, HAL-like voice. It can also transform specific words Hawking selects directly into mathematical equations.
Hawking also feels an obligation, even with the short time he has left, to reach a wider public. He wrote an immensely popular book, “A Brief History of Time,” which, so far, has been on the New York Times bestseller list for 91 weeks. Although it attempts to reduce the esoteric subject of cosmology to an understandable level, it is a difficult read for most people who have not taken college-level physics. In this interview, which caused the physicist considerable fatigue and strain, Hawking tries to spread the word even further.
In 1970, Hawking and a fellow mathematician and physicist, Roger Penrose, submitted a joint paper supporting the theory that the universe began with what is commonly referred to as the Big Bang. That is, at one point in time, all the matter in the universe was compressed into an infinitely dense state defined as a “singularity.” Through some force (not excluding a Supreme Creator), this energy was released to create all the matter in the universe. Hawking had developed new mathematical techniques to prove Penrose’s earlier 1965 theory that a star collapsing under its own gravity can ultimately shrink to zero size and zero volume, creating what is known as a black hole. They postulated that if that can occur, then the reverse is possible: A black hole can, at some point, be caused to release its energy to form matter once again—as, for example, at the creation.
The Hawking-Penrose theory is now the generally accepted theory of the beginning of the universe. But in keeping with Hawking’s personality and relentless intellect, he now disputes his own findings, demanding a more clearly articulated theory. He contends that quantum effects (the behavior of particles at atomic and subatomic levels) should also be taken into account. Hawking and Jim Hartle, of the University of California, have further proposed a new hypothesis (“no boundary condition”) that, if applied with other concepts of physics, may explain the beginning of our universe.
That, in turn, could lead to the development of a “unified” theory—how all matter, from the galactic to the subatomic, interacts. It is to this quest—the Holy Grail of physics—that Hawking has devoted his past several years of work. It is the same quest that eluded Einstein for half a century.
Hawking holds the post of Lucasian Professor of Mathematics at Cambridge University, a chair once held by the father of modern physics, Isaac Newton. Hawking’s world is, of course, largely a life of the mind. In that world, there are mathematical constructs of space and time, elementary particles of matter never seen, black holes, neutron stars, white dwarfs and wormholes in space where time travel is theoretically possible. For Hawking, it is a limitless place where the imagination is unconstrained.
To interview Hawking, Playboy dispatched free-lance journalist Morgan Strong to England’s venerable Cambridge University, on the banks of the River Cam. Here is his report:
“In the late summer, Cambridge is a raucous little town. It is filled not with Cambridge students but with hordes of Italian, French and American students. For a fairly hefty fee, they come each summer to inhabit the ancient chambers and to walk the meticulously groomed gardens of Old Cambridge quads.
"Amid this campus frenzy, I first saw Stephen Hawking making his way up the cobblestone street to his office in his motorized wheelchair. I was standing by the door. Our appointment was for later in the afternoon, and I had just left his secretary to confirm that it was still on. Hawking had been ill the past several days and had not been in. That, and a schedule of recent honors—he had just been made a Companion of Honour by the Queen and had lunched at Buckingham Palace—had made our schedule rather fluid.
"I thought it appropriate to walk over and introduce myself. Hawking was slumped in his wheelchair, his head turned away to his right, his eyes open and staring down. He did not move when I said hello. He was gravely ill, more so, certainly, than I had understood. He looked terribly frail and small; he could not have weighed more than 100 pounds. I repeated my name and explained that I was there for the ‘Playboy Interview.’ This time, Hawking smiled but moved nothing else.
"He began to clasp a small control in his right hand, and a computer screen mounted on his wheelchair lit up. Laboriously selecting words from lists that appeared on the top of the screen, he created a sentence. Hello, I will meet with you at 2:30, the screen read. Then a disembodied voice sounded from somewhere in the stack of equipment, wires and batteries on the back of his wheelchair, repeating the words on the screen.
"He smiled again and with some effort, moved his left hand to the arm of the wheelchair. He pressed a switch and the wheelchair lurched through the arch to the courtyard of his office building, his nurse following.
"For the next several days, and for several hours each day, I would be in Hawking’s company—in his home, at his office and, for one evening, as his guest, accompanying him and his mother to dinner at the faculty dining room of Gonville and Caius College.
"He utterly seems to dismiss the disease that has literally ravaged him. He simply barrels ahead, doing his best to ignore it. But no one who sees him or spends any time with him can do the same. I have conducted interviews in wartime and in terrorist zones that were endurance contests. But the many hours Hawking and I spent on this interview were more painful than any of those in the past. In fact, I think they may have been more of a mental agony for me than for Hawking. He always managed to inject humor and wit into the conversation, even when it was clear that he was uncomfortable.
"If Hawking has any physical limitations, they seem unknown to him. On the evening we had dinner together, after we left the college, his mother and I walked cautiously along a badly lit dirt path through a small wooded area toward his house. Hawking was ahead in his wheelchair, accompanied by his nurse. Suddenly, he put it to the floor. This frail, small man, completely vulnerable, raced off through the night, leaving his nurse—who was forced to run desperately, trying to catch up—far behind. He drove erratically, weaving wildly from side to side, the River Cam only a few feet from the path.
"He did not stop until he had reached the main street bordering the park 50 yards or so away, and then only for a few seconds. He careened out into the street to a crosswalk, abruptly stopping traffic. (Luckily, British drivers will stop if a pedestrian enters the crosswalk. It occurred to me that had it been New York, the world surely would have been less one physicist.)
"Hawking raced across the intersection and out into the middle of the street and roared out of sight toward his home several blocks away. As the nurse tottered after him, his mother calmly explained to me, 'Stephen must be tired; he’s always in a hurry to get home when he’s tired.’
"So was I.”
Hello, Professor Hawking.
Hawking: Hello, how are you? Please forgive my American accent. [Smiles]
Your computer does sound like a Midwesterner. Can you tell us a little about your early life, before the secrets of the universe caught your interest?
Yes. I was born on January eighth, 1942, three hundred years to the day after the death of Galileo. I was born in Oxford—even though my parents’ home was in London—because Oxford was a good place to be during the war.
Galileo was tried and imprisoned for heresy by the Catholic Church for his theories of the universe. Did he have something in common with you?
Yes. However, I estimate that about two hundred thousand other babies were also born on that date. [Smiles] And I don’t know if any of them were later interested in astronomy.
You have had a little trouble with the current Pope. Didn’t he caution you against going too far in your work?
Yes. There are two views of the universe. One is that it is ruled by mysterious spirituality—forces that are never properly understood. The other is that it is governed by rational laws that can be formulated in mathematical theorems. It is clear which view I hold.
Yes. Your quest is to gain understanding, based on scientific discovery, of how the universe began. But Church leaders believe they already have that understanding, don’t they?
The history of human civilization has been one of gradual discovery of more and more and more scientific laws that govern a bigger and bigger and bigger part of our experience. I see no reason why it should not continue until we have a complete unified theory for everything in the universe. I don’t hold with mysticism. I think it is a soft option for those not willing to make the effort to understand the rational laws that govern the universe. I think that from the time of Galileo, Church leaders have learned better than to pronounce on cosmology.
Understanding cosmology will not help feed anyone. It won’t even wash clothes any brighter. But man or woman does not live by bread alone.
Getting back to your personal history, you had a rather conventional childhood. There were no awkward displays of adolescent brilliance during your school days.
Yes. I went to a public school—what Americans call a private school—Saint Albans. My father had wanted me to go to Westminster School, one of the main private schools. He had gone to a minor public school himself and felt that this had always held him back. But at Saint Albans, I received as good an education as or better than I would have at Westminster. I was never more than halfway up the class at school.
There’s hope for us all. You really were just an average student?
[Smiles] When I was twelve, one of my friends bet another friend a bag of sweets that I would never amount to anything. I don’t know if the bet was ever settled and, if so, which way it was decided.
After Saint Albans, you went on to university to study physics.
Well, my father was a doctor and wanted me to study medicine at his old college, University College, Oxford. I wanted to study mathematics, more mathematics and physics. But my father thought there would not be any jobs in mathematics, apart from teaching. He therefore made me do chemistry, physics and only a small amount of mathematics. I duly went to University College in 1959 to do physics, which was the subject that interested me, since physics governs the laws of the universe.
Then you had made up your mind early on what you wanted to do?
Yes. From the age of twelve, I had wanted to be a scientist. And cosmology seemed the most fundamental science.
During your time at Oxford, we understand that you were, again, an indifferent student.
Most of the other students at Oxford in my year had done military service and were a lot older. I felt rather lonely during my first year and part of the second. It was only in my third year that I really felt happy at Oxford. The prevailing attitude there at that time was very casual, very antiwork.
At Oxford, you were supposed to be brilliant without effort or to accept your limitations and get a fourth-class degree. To work hard to get a better class of degree was regarded as the mark of a gray man, the worst epithet in the Oxford vocabulary.
That epithet today may be nerd.
Well, anyway, the physics course at Oxford was arranged in a way that made it particularly easy to avoid work. I did one exam before I went up, and then had three years at Oxford, with just the final exams at the end. I once calculated that I’d done about a thousand hours’ work in those three years, an average of an hour a day. I’m not proud of that; I’m just describing the attitude at the time, which I shared with my fellow students—an attitude of complete boredom and feeling that nothing was worth making an effort for.
In your last year at Oxford, you were diagnosed as having ALS, or amyotrophic lateral sclerosis, also known as Lou Gehrig’s disease, which is supposed to be fatal within a very short time. It must have transformed you.
Yes. When you are faced with the possibility of an early death, it makes you realize that life is worth living and that there are lots of things you want to do.
According to newspaper interviews, and a recent 20/20 segment by Hugh Downs on ABC-TV when you got your diagnosis, you simply gave up and went on a drinking binge for a few years.
It’s a good story, but it’s not true.
What did happen?
The realization that I had an incurable disease that was likely to kill me in a few years was a bit of a shock. Why should it happen to me? Why should I be cut off like this? But while I was in the hospital, I saw a boy die of leukemia in the bed opposite me. It was not a pretty sight. Clearly, there were people worse off than I. Whenever I feel inclined to be sorry for myself, I remember that boy.
And you didn’t go off on the long binge, as reported?
I took to listening to Wagner, but the reports that I drank heavily are an exaggeration. The trouble is, once one article said it, others copied it, because it made a good story. Anything that has appeared in print so many times has to be true.
Still, it’s astonishing that you had so mild a reaction. Most people might have given up—or gone on that binge.
My dreams were disturbed for a while. Before my condition was diagnosed, I had been very bored with life. There had not seemed to be anything worth doing. But shortly after I came out of the hospital. I dreamed that I was going to be executed. I suddenly realized that if I were reprieved, there were a lot of worthwhile things I could do. Another dream I had several times was that I would sacrifice my life to save others. After all, if I were going to die anyway, it might do some good.
Doesn’t this terrible disease make you angry?
Yes. I’m a normal human being with normal needs and emotions.
You got married and started a family shortly after you were diagnosed.
Yes, I got engaged to Jane Wilde, whom I had met just about the time my condition was diagnosed. That engagement changed my life. It gave me something to live for. But it also meant I had to get a job if we were to be married.
Did your lazy stroll through Oxford hurt you in finding a job?
Yes. Eventually, I applied for a research fellowship in theoretical physics at Caius College, Cambridge. And, to my great surprise, I got a fellowship and we were married a few months later.
How did your disease affect your lifestyle?
When we were married, Jane was still an undergraduate at Westfield College in London, so she had to go up to London during the week. This meant that we had to find a place that was central, where I could manage on my own, because by then, I could not walk far. I asked the college for help, but I was told that it was not college policy to help fellows with housing.
But you managed.
Yes. After several years, we were given the ground-floor flat in this house, which is owned by the college. This suits me very well, because it has large rooms and wide doors. It is sufficiently central so that I can get to my university department, or the college, in my electric wheelchair. It is also nice for our children, because it is surrounded by garden, which is looked after by the college gardeners.
Wasn’t it extremely difficult raising your three children?
Yes. Up to 1974, I was able to feed myself and get in and out of bed. Jane managed to help me, and to bring up two of our children, without outside help. But things were getting more difficult, so we took to having one of my research students live with us to help. In 1980, we changed to a system of community and private nurses, who would come in for an hour or two in the morning and the evening.
You have twenty-four-hour nursing care now.
Yes. I caught pneumonia in 1985. I had to have a tracheotomy. After that, I had to have twenty-four-hour nursing care.
There are two views of the universe. One is that it is ruled by mysterious spirituality. The other is that it is governed by rational laws.
Is it the operation that prevents you from speaking?
Yes. Before the operation, my speech was slurred, so that only a few people who knew me well could understand me. But at least I could communicate. I wrote scientific letters by dictating to a secretary, and I gave lectures through an interpreter, who repeated my words more clearly.
But after the operation, I could communicate only by spelling words out letter by letter, raising my eyebrows when someone pointed to the correct letter on a card. It is very difficult to carry on a conversation like that, let alone write a scientific paper.
And now you have the computer.
Walt Woltosz, a software expert in California, heard of my plight. He sent me a computer program he had written called Equalizer. This allowed me to select words from a series of menus on the screen by pressing a switch in my hand. When I have built up what I want to say, I can send it to a speech synthesizer.
Why did you choose theoretical physics for your research?
Because of my disease. I chose my field because I knew I had ALS. Cosmology, unlike many other disciplines, does not require lecturing. It was a fortunate choice, because it was one of the few areas in which my speech disability was not a serious handicap. I was also fortunate that when I started my research, in 1962, general relativity and cosmology were underdeveloped fields, with little competition, so my disease would not be a serious impediment. There were lots of exciting discoveries to be made, and not many people to make them. Nowadays, there is much more competition. [Smiles]
Did you experience difficulty at the beginning?
I was not making much progress with my research, because I didn’t have much mathematical background. But gradually, I began to understand what I was doing.
Let’s see if we can understand some of it. To begin with, you use only one fundamental equation in your book, A Brief History of Time, which forms the basis of your work. Can you define it for us?
That equation, E = mc2, expresses the fact that energy and mass are really the same thing. E is for energy and m is for mass. The speed of light, c, is in the equation just to make the units the same on both sides. However, you can use units in which c equals one. This equation is important because it shows that matter can be transformed into energy and vice versa. In fact, it seems that in the early stages of the universe, all matter was made out of energy.
Energy that was then transformed to mass—or the solid bodies that make up the universe.
Yes. The energy was borrowed from the gravitational force of the universe, which had compressed everything to infinite density before it was released in the Big Bang. The total net energy of the universe is zero. Thus, the whole universe is for nothing. Who says there is no such thing as a free lunch? [Smiles]
How does the total energy of the universe equal zero?
It takes energy to create matter. But the matter in the universe is attracting all other matter in the universe. This attraction gives the matter a negative energy that is exactly equal to the energy required to create the matter. Thus, the total energy of the universe is zero.
So once matter is created, the energy exists in the matter, which is spread out across the universe. Where did the energy that was needed for the Big Bang to occur come from?
The energy needed to create the Big Bang came from the universe it created.
In the equation, time is also important. Why?
Before Einstein, time was thought of as completely separate from space. People believed that there was what was called absolute time. That is, each event could be given a unique value of time. However, experiments showed that this could not be the case. And Einstein showed that the experiments could be explained if one said that time was not separate from space but was combined with it in something called space time.
According to Einstein, that means the time of an observed event in space is dependent on the position of the observer. So it becomes another measurement, like width and height.
Yes. Later, Einstein was able to show that gravity could be explained if space time were not flat but curved. This idea of space time has completely transformed the way we look at the universe.
A black hole is also critical to your theory. Could you explain?
A black hole is a region in which the gravitational field is so strong nothing can escape. Within a black hole, there will be a singularity, where space time comes to an end. This singularity, an infinitely dense point of matter, is rather like the singularity that occurred in the Big Bang and is the beginning of space time and the whole of the universe.
Why is it called a black hole?
The gravitational field of the singularity would be so strong that light itself could not escape from a region around it but would be dragged back by the gravitational field. The region from which it is not possible to escape is called a black hole. Its boundary is called the event horizon.
If a black hole is not observable, how do you find one?
From 1970 to 1974, I worked mainly on black holes. In 1974, I made perhaps my most surprising discovery: Black holes are not completely black! When one takes small-scale behavior into account, particles and radiation can leak out of a black hole. The black hole emits radiation as if it were a hot body.
If your theories are correct, then a black hole will eventually explode in a way similar to how the universe began?
Why does that happen?
Because of the uncertainty principle of quantum mechanics, particles and energy will slowly leak out of the black hole. This will make it grow smaller and smaller and leak energy more rapidly. Eventually, the black hole will disappear in a tremendous explosion.
Quantum mechanics is the study of the behavior of systems at small scales.
Yes. Atoms or elementary particles. In any case, a black hole cannot just suddenly pop out of nothing and explode, because there has to be something there to provide energy.
The matter that has been compressed by a star collapsing upon itself?
Yes. Mass or energy is always conserved. That means empty space, with no matter or energy in it, will stay empty. A black hole cannot simply appear in previously empty space. It has to be made from matter or energy, such as a star that collapses in on itself because of its own gravity.
Even though you’ve made black holes a central part of your life’s work, you concede that one has yet to be discovered. In fact, you mention in your book that you have a bet with a colleague that one will not be discovered. Is that true?
Yes. I had a wager with Kip Thorne at Cal Tech that Cygnus X-l was not a black hole. It was an insurance policy, really. I had done a lot of work on black holes, and it all would have been wasted if it had turned out that they didn’t exist. But then, at least I would have had the satisfaction of winning my bet. [Smiles]
Well, now I consider the evidence for black holes so good, thanks to Cygnus X-l, that I have conceded the bet. Cygnus X-l is a system consisting of a normal star orbiting around an unseen companion. It seems that matter is being blown off the normal star and falling on the companion. As it falls toward the companion, it develops a spiral motion, like water running out of a bath. It will get very hot and will give off X rays that are observed. We can show that the mass of the companion is at least six times that of the sun. That’s too much to be a white dwarf or a neutron star, so it must be a black hole.
We feel privileged to hear the news. Can you go beyond deduction and establish what a black hole is, physically?
We want a volunteer who will jump into the black hole and find out what happens inside. Unfortunately, he won’t be able to signal back to us to let us know.
Because of something called a light cone. A light cone of an event, A, is the set of events that can be reached from the event by signals traveling at the speed of light. Now, according to the theory of relativity, nothing can travel faster than light. Thus an event, B, outside the permitted light cone of A, cannot be affected by what happens at A. And the signal can’t get out because it’s traveling at less than the speed of light
We think we follow you. In your book, you say that in such an event, a person—or any object—would be torn apart by gravitational forces. And the intense gravity would prevent even radio signals from escaping.
Yes. A volunteer astronaut would have a sticky end at a singularity. His particles would survive, but that, I suppose, is small comfort. [Smiles]
But isn’t there a possibility that he or she might escape through what is called a wormhole?
Yes. Particles that fall into a black hole may pass through a thin tube, or wormhole, and come out somewhere else in the universe. But wormholes occur only in imaginary time. The history of the particles, and of an astronaut in real time, will come to a bad end at a singularity.
There are no real wormholes?
The wormholes I mention in the book occurred in real time. And no, it seems that that kind of wormhole will not occur. However, since the book was written, I and other people have been working on a different kind of wormhole that occurs in imaginary time.
What is imaginary time?
Imaginary time is another direction of time, one that is at right angles to ordinary, real time. It seems that there will be large numbers of imaginary-time wormholes branching off, and joining on, everywhere. We do not notice them directly, but they affect everything we observe directly. It is an exciting area of research.
In the past fifteen years, we have realized that it may be possible to use quantum theory to fully unify time with space. This would mean we could get away from this one-dimensional, linelike behavior of time.
And you use imaginary time, and wormholes, to speculate about objects traveling through time, don’t you?
[Smiles] Objects will pass through a thin tube, or wormhole, in imaginary time, and out into another universe, or another part of our universe. In ordinary time, one could pass through a black hole and come out of a white hole.
A white hole?
Yes. The laws of physics are symmetrical and if there are objects called black holes, which things can fall into but not out of, there ought to be objects that things can fall out of but not into. One can call these white holes.
In ordinary time. But you said that was impossible.
A white hole is the time reverse of a black hole. The white hole may be in another universe, or another part of our universe. We could use this method for space travel. Otherwise, the distances are so vast it would take millions of years to go to the next galaxy and return. But if you could go through a black hole and out a white hole, you could be back in time for tea.
And if it were possible, in theory at least, you could travel back in time?
Yes. The trouble is, there would be nothing to stop you from getting back before you set out. [Smiles]
Or you could get back and find yourself dead. Or your world dead.
Fortunately, for our survival, it seems that space times in which one can travel back to the past are unstable. The least disturbance, such as a spaceship going through, will cause the passage between a black hole and a white hole to pinch off. The history of the spaceship would come to an end, torn apart and crushed out of existence.
The earth’s surface is finite in area, but it doesn’t have any boundary. I like to say that in all my travels, I have never managed to fall off.
But getting back to reality, so to speak, are wormholes in imaginary time different?
Wormholes in imaginary time don’t have singularities and can occur in any situation. They will change the apparent interactions of particles in ways that still have to be calculated properly. But it does seem that one important interaction is affected in a very significant way. This is the so-called cosmological constant, which gives space time an inbuilt tendency to expand or contract.
Where will these particles then go?
Baby universes. According to some recent work of mine, the particles will go off into a baby universe of their own. This baby universe may join on again to our region of space time. If it does, it would appear to us to be another black hole that formed and then evaporated. Particles that fell into one black hole would appear as particles emitted by the other black hole, and vice versa.
All of that is abstruse mathematical theory, isn’t it? It seems difficult to imagine actually observing any of it.
Mathematical models of the universe that use the concept of imaginary time can give us explanations of why the universe began in the way it did. If you like, you can say that the use of imaginary time is just a mathematical trick that doesn’t tell us anything about reality, or about the nature of time.
But if you take a positivist position, as I do, questions about reality don’t have any meaning. All one can ask is whether imaginary time is useful in formulating mathematical models that describe what we observe. This it certainly is. One can take an extreme position and say that imaginary time is really the fundamental concept in which the mathematical model should be formulated. Ordinary time would be a derived concept we invent for psychological reasons. We invent ordinary time so that we can describe the universe as a succession of events in time, rather than as a static picture, like a surface map of the earth.
Playboy: What effect does the cosmological constant have?
By observing the motion of distant galaxies, we can determine that this constant is either zero or very small. This is very surprising, because quantum theory would lead us to expect a value for the cosmological constant that is very much larger than what we observe.
How much larger is “very much larger”?
I mean at least a billion billion billion billion billion times larger. Until recently, there has been no explanation for the cosmological constant. But if one includes [the late physicist] Richard Feynman’s idea of a sum over histories containing wormholes, one finds that the apparent value of the cosmological constant is exactly zero. Mathematical models of the universe that use the concept of imaginary time can give an explanation of why the universe began in the way it did, and why the cosmological constant is zero.
Quantum theory, however, is unable to predict specific events. How accurate can these mathematical models be?
In general, quantum mechanics does not predict a single definite result for an observation. Instead, it predicts a number of possible outcomes and tells us how likely each of them is.
You’ve suggested, however, that a unified theory of the universe is possible with the inclusion of quantum theory. But how can quantum theory and relativity be combined?
Quantum theory depends on the use of a new kind of number—complex numbers. A complex number can be regarded as a shorthand way of writing a pair of ordinary numbers. It can be represented as a point on a plane, with the two numbers corresponding to the positions of the point in the horizontal and vertical directions.
For example: The complex number that is a shorthand for the pair of numbers one and two would be represented by a point one unit to the right of the center and two units up. Or 1 + 2i. Here it is a so-called imaginary number; i is the square root of minus one.
Look here: If one uses imaginary rather than real time, space time becomes Euclidean. That is, time is just like another direction in space. You can multiply, divide, add and subtract complex numbers as you can ordinary numbers.
And that allows for mathematical constructs in space time?
And what, exactly, is the relation of imaginary time to real time?
By using imaginary numbers, one adds up all the probabilities for all the histories of particles with certain properties—such as passing through certain points at certain times. One then has to extrapolate the result back to real space time, in which time is different depending on directions in space. This is not the most familiar approach to quantum theory, but it gives the same results as other methods.
Doesn’t that randomness make it difficult—even chaotic—to apply to the laws of science?
Yes. Einstein objected strongly to this randomness with the famous statement that God does not play dice with the universe! But all evidence points to the proposition that God is, indeed, an inveterate gambler. [Smiles] He throws the dice to determine the outcome of every observation.
This uncertainty is best defined by Feynman’s theory, which states that a particle does not have a single, well-defined path or history. Instead, it can be regarded as moving through space time on all possible paths. Each path or history has a probability that depends on its shape. For this idea to work, one has to consider histories that take place in imaginary time rather than the real time in which we live our lives. In the case of quantum gravity, Feynman’s idea of a sum over histories would involve summing over different possible histories for the universe. That is, different Euclidean curved space times.
So the answer to your question is that adding up the complex numbers associated with each path doesn’t give a well-defined sum. But one can get a well-defined answer if one supposes that the time label of an event is not just an ordinary number, as we normally think, but a complex number.
Not an easy concept. What immediate use is there in understanding imaginary time and wormholes?
Well, we were talking about whether anything ever could escape a black hole. Imaginary time can provide a means of escape for objects that fall into a black hole. The ordinary history of an object in real time will come to an end, crushed out of existence, inside the black hole. But if one considers the history of the object in imaginary time, that history cannot come to an end, if the no-boundary proposal of the universe is correct.
Can you explain—briefly—the no-boundary concept?
In 1983, Jim Hartle and I proposed that both time and space are finite in extent but don’t have any boundary or edge. They would be like the surface of the earth, but with two more dimensions. The earth’s surface is finite in area, but it doesn’t have any boundary. I like to say that in all my travels, I have never managed to fall off. [Smiles]
Our proposal says that the state of the universe should be given by a sum over histories, where the histories were only closed Euclidean spaces of finite size and without boundary or edge. This proposal can be paraphrased as, The boundary condition of the universe is that it has no boundary. It is only if the universe is in this no-boundary state that the laws of science, on their own, determine how the universe should behave. If the universe is in any other state, the class of Euclidean curved spaces in the sum over histories will include spaces with singularities.
In order to determine the probabilities of such singular histories, one would have to invoke some principle other than the known laws of science. This principle would be something external to our universe; we could not deduce it from within the universe. On the other hand, if the universe is in the no-boundary state, we could, in principle, determine completely how the universe should behave, up to the limits of the uncertainty principle.
Ah, a familiar term. That would be Heisenberg’s uncertainty principle. Can you briefly explain that?
Werner Heisenberg, a German scientist, formulated his famous uncertainty principle in 1926. In order to predict the future position and velocity of a particle, one has to be able to measure its present position and velocity accurately. The obvious way to do this is to shine a light on the particle. Some of the waves of light will be scattered by the particle and indicate its position. However, one will not be able to determine the position of the particle more accurately than the distance between the wave crests of light, so one needs to use light of a short wave length in order to measure the position of the particle precisely.
Now, by Planck’s quantum principle, one cannot use an arbitrarily small amount of light; one has to use at least one quantum [the indivisible unit in which waves may be emitted or absorbed]. This quantum will disturb the particle and change its velocity in a way that cannot be predicted. Moreover, the more accurately one measures the position, the shorter the wave length of the light that one needs, hence the higher the energy of a single quantum. So the velocity of the particle will be disturbed by a larger amount. In other words, the more accurately you try to measure the position of the particle, the less accurately you can measure its speed and vice versa.
Getting back to the no-boundary state: If your proposal were proved, it would be of some importance to science, wouldn’t it?
It would be clearly nice for science if the universe were in the no-boundary state, but how can you tell whether it is? The answer is that the no-boundary proposal makes definite predictions for how the universe should behave.
If the proposal were correct, there would be no singularities, and the laws of science would hold everywhere, including at the beginning of the universe. How the universe began would be determined by the laws of science. I would have succeeded in my ambition to know how the universe began. But I still wouldn’t know why.
But didn’t you say there would be no singularities in the no-boundary state? And hasn’t your work always stressed the need for singularities?
It has been interesting to watch the change in the climate of opinion on singularities. When I was a graduate student, almost no one took them seriously. Now, as a result of the singularity theorems, nearly everyone believes that the universe began with a singularity.
In the meantime, however, I have changed my mind. I still believe that the universe had a beginning, but that it was not a singularity.
How did you arrive at that conclusion?
The general theory of relativity is what is called a classical theory. That is, it does not take into account the fact that particles do not have precisely defined positions and velocities but are smeared out over a small region by the uncertainty principle of quantum mechanics. This does not matter in normal situations, because the radius of curvature of space time is very large compared with the uncertainty in the position of a particle. However, the singularity theorems indicate that space time will be highly distorted with a small radius of curvature at the beginning of the present expansion phase of the universe. In this situation, the uncertainty will be very important. Thus, general relativity brings about its own downfall by predicting singularities. In order to discuss the beginning of the universe, we need a theory that combines general relativity with quantum mechanics.
The elusive unified theory, or the T.O.E. [theory of everything]?
We do not yet know the exact form of the correct theory of quantum gravity. The best candidate we have for the moment is the theory of superstrings, but there are still a number of unresolved difficulties. However, there are certain features that we expect to be present in any viable theory.
One is Einstein’s idea that the effects of gravity can be represented by a space time that is curved or distorted by the matter and energy in it. Objects try to follow the nearest thing to a straight line in this curved space. However, because it is curved, their paths appear to be bent, as if by a gravitational field.
You’ve also included Feynman’s sum over histories.
Yes, we expect Richard Feynman’s proposal that quantum theory can be formulated as a sum over histories to be present in the ultimate theory. Remember, that was the idea that a particle has every possible path or history in space time, depending on its shape. The probabilities of such spaces would not be determined by the theory. Instead, they would have to be assigned in some arbitrary way.
“Some arbitrary way"—randomness again?
What this means is that science could not predict the probabilities of such singular histories for space time and, hence, could not predict how the universe should behave. However, it may well be that the universe is in the state defined by a sum over nonsingular Euclidean curved spaces only. In this case, the theory would determine the universe completely; one would not have to appeal to some agency external to the universe to determine how it began.
In a way, the proposal that the state of the universe is determined by a sum over nonsingular histories only is like a drunk looking for his key under the lamppost: It may not be where he lost it, but it is the only place with enough light to find it. Similarly, the universe may not be in the state defined by a sum over nonsingular histories, but it is the only state in which science could predict how the universe should be.
Knowledge is not knowledge unless you share it with someone.
We hate to suggest this, but what if the no-boundary proposal is wrong?
[Smiles] If the observations do not agree with predictions, we will know that there must be singularities in the class of possible histories. However, that is all we will know. We will not be able to calculate the possibilities of singular histories. Thus, we will not be able to predict how the universe should behave.
One might think that this unpredictability wouldn’t matter too much if it occurred only at the Big Bang. After all, if a week is a long time in politics, ten thousand million years is pretty close to eternity. But if predictability broke down in the very strong gravitational fields of the Big Bang, it could also break down whenever a star collapsed. This could happen several times a week in our galaxy alone! Thus, our power of prediction would be poor, even by the standards of weather forecasts.
So what does the no-boundary proposal predict for the universe? The first point to make is that because all the possible histories for the universe are finite in extent, any quantity that one uses as a measure of time will have a greatest and a least value. So the universe will have a beginning and an end. However, the beginning will not be a singularity. Instead, it will be a bit like the North Pole of the earth. If one took degrees of latitude on the surface of the earth to be the analogue of time, one could say that the surface of the earth began at the North Pole. Yet the North Pole is a perfectly ordinary point on the earth. There’s nothing special about it, and the same laws hold at the North Pole as at other places on the earth. Similarly, the event that we might choose to label as "the beginning of the universe” would be an ordinary point of space time, much like any other, and the laws of science would hold at the beginning, as elsewhere!
As much—or as little—as we can understand of your work, it again strikes us that most of your ideas depend on obscure mathematical concepts, far removed from ordinary, observable life.
Imaginary time may sound like science fiction, but it is a well-defined mathematical concept.
Yes, to mathematicians and physicists, but to most of us, it’s beyond immediate understanding.
Then what can the general public gain from trying to understand these concepts? Most of us would say we had more immediate problems to deal with.
This is why I have spent some of my time attempting to explain what we do. I think knowledge of the general ideas of the recent discoveries in cosmology are useful to the public.
True, understanding cosmology will not help feed anyone. It won’t even wash clothes any brighter. But man or woman does not live by bread alone. We all feel the need to come to terms with the universe in which we find ourselves, and to understand how we got here.
And that’s why you wrote A Brief History of Time?
There are several reasons why I wrote the book. One was to pay my daughter’s school fees. I didn’t succeed in that, because by the time the book came out, she was in her last year of high school. But I still have to pay for her college.
That’s an excellent reason. Are there others?
The main reason was that I had written several popular articles and given a number of popular lectures. They had been well received, and I had enjoyed doing them, but I wanted to try something bigger. I felt that we had made tremendous progress in the past twenty-five years in understanding the universe, and I wanted to share this with the general public. I think it is important that the public take some interest in science and have some general understanding of it.
Science has changed our lives a great deal and will change them even more in the future. If we are to decide in a democratic way what direction society should take, it is necessary that the public has some understanding of science.Then you’re doing something political—knowledge as the great leveler, not confined to a few who understand the language.
Knowledge and understanding of how the universe works, and of how it began, had become the preserve of a few specialists. But we all share the human condition, and we all want to know where we came from. My book is an attempt to share with the general public the knowledge that the specialists have found. Knowledge is not knowledge unless you share it with someone. Normally, specialists communicate only with other specialists; I feel they should communicate with the general public, as well.
You say that you may succeed in knowing how the universe began, but you will not know why. You do not—as Einstein did not—dismiss the notion of a Supreme Creator.
I think I’m careful in my book. I leave open the question of whether God exists and what His nature would be. One can never prove that God doesn’t exist. What I did was show that it was not necessary to appeal to God to decide how the universe began, because that is determined by the laws of science. However, one could say that the laws of science were God’s choice for how the universe behaves.
Apart from now being able to pay your daughter’s college fees, has the book made any difference in your life?
It has not made that much difference. Even before the book, a certain number of people, mainly Americans [smiles], would come up to me in the street, but it has made that sort of encounter more frequent. And other things like interviews and public lectures have taken up the limited time I have to do research. However, I’m now cutting down on such things and getting back to research.
We assume that every scientist hopes for recognition for his efforts. You have received a number of honors but not yet the Nobel Prize. Do you think you may someday receive the Nobel?
Most of my work has been generally accepted. I have received a lot of recognition recently. But I don’t know if I will ever get the Nobel Prize, because that is given only for theoretical work that has been confirmed by observation. It is very, very difficult to observe the things I have worked on. [Smiles]