Category: Science


Along with Andrew Wiles and Linus Pauling, Stephen Hawking is one of the very few modern scientists whose name is a household word.

Hawking, the Lucasian Professor of Mathematics (Isaac Newton’s chair) at Cambridge University, has an insight and an imagination that soar across the cosmos, devising dreams and schemes of how the universe works. The legend of Hawking is of course immensely augmented by the fact that he is afflicted with motor neurone disease (commonly known in the U.S. as “Lou Gehrig’s Disease”). In fact he has known that he had the disease since the age of twenty-one (Hawking is now sixty). He did not expect to live to the age of twenty-five and was tempted to despair. Instead, by his own telling, the knowledge of having this deadly illness gave him courage and hope and a will to live. It took his aimless and futile life (which Hawking himself has described elsewhere in painful and shamefaced detail) and gave it direction and purpose. And he has applied that newfound Gestalt to the development of ideas in theoretical physics.

To read any of Hawking’s many books, one would never realize just how devastating Hawking’s illness is. He speaks of it only rarely and as if it were just a minor in- convenience. However, his friend Roger Penrose has told me quite frankly that it requires an army of people just to keep Hawking going: He cannot speak, he can- not walk, he cannot pick up a pen, and he cannot even breathe on his own.

Hawking’s popular writing is redolent of joy and good humor and great high spirits. One cannot but think that the world would be a better place if we all had the good and optimistic frame of mind of Stephen Hawking. His is truly a profile in courage.

Stephen Hawking’s A Brief History of Time [HAW] has been a publishing phenomenon. Penned in 1988, it spent more than four years on the bestseller lists and sold more than ten million copies in forty languages. As Hawking’s postdoc Nathan Myhrvold (of Microsoft fame) has said, Hawking has sold more books on physics than Madonna has on sex. Part of the appeal of Time is the Hawking mystique, but a considerable part of its charm is the breezy and friendly style in which the book is written. Like mathematics, physics is stark and rigorous and forbidding, enshrouded by technical lingo and recondite ideas. Although “relativity”, “the uncertainly principle”, “the speed of light”, and “black holes” hold great charm and fascination for the layman, most writings on these topics are either facile and incorrect or onerous and obscure. Hawking forges a brilliant path between these two extremes. Obviously everything he says is author- itative and accurate; in those instances where he must blow smoke, he is quite honest about it and still gives the reader a sense of what is going on. Hawking uses analogy and humor and example and metaphor to depict his ideas in an attractive and compelling manner.

So if A Brief History of Time is the be-all and end- all of the popular conception of cosmology, then why is there any need for another book? Well, pub- lishers like to sell books; and Stephen Hawking is a best-selling author. But let us be more charitable. By Hawking’s own telling, Time is a tough go for the untrained reader. As I was reading the book’s description of the forward and backward light cones, I was struck by how simple and obvious these ideas are to a trained scientist (like myself), and how utterly obscure they must be to a tyro. The rather more expensive “illustrated edition” of Time has many attractive graphics, but the original and widely disseminated first edition has only a few sim- ple line drawings. As a result, and in spite of its immense popularity, the book comes off as a bit dry and uninviting. The common wisdom is that millions bought the book, but few have gotten past the first twenty pages.

Enter The Universe in a Nutshell. In his preface, Hawking acknowledges the difficulties noted in the preceding paragraph and touts the importance of good pictures. This new book, he claims, will be much more accessible to the lay reader. He points out, wisely I think, that Time is written in a linear order—just like a mathematical monograph. Chapter n + 1 in Time depends strictly on Chapters 1 to n. Of course the mathematical scientist is accustomed to this type of vertical development. The average reader is not. In a much-read article [THU] on mathematics education, William Thurston points out that mathematics is a “tall subject.” The student painstakingly climbs up the pole to the point where he loses his grip, and then he falls down (never to rise again). Thurston argues for the value of making mathematics a “wider subject” with a broad-based infrastructure. Hawking has got this message. In his new book, his organization pattern is a tree: After the introductory material, the book branches out in several different directions. The reader may dip into the succeeding chapters at will and jump around as interest and inclination dictate. Perhaps more important is that Nutshell has marvelous figures, many of them in full color. These are pictures (very elementary ones) of sci- entific ideas, or of equations, or of the scientists themselves. There are sidebars on Kurt Gödel and Kip Thorne and Richard Feynman and John Wheeler and Star Trek and any number of other familiar people and topics. The book is just plain fun. Even when the casual reader gets lost, and he certainly will, he will be encouraged and carried along by the graphics and by the verbal byplay that accompanies the more serious text proper. An added feature is that the book has a concise and useful glossary. Many a reader will have difficulty keeping track of terms and ideas, and this tool will certainly keep many an aficionado going.

There are perhaps those who will criticize Nut- shell for not being sufficiently serious. Popular singer/songwriter Neil Sedaka says that people fault him for having too much fun with his music. Certainly Hawking has tremendous fun with his physics. A few sample passages suggest the over- all tone:

 

Newton occupied the Lucasian chair at Cambridge that I now hold, though it wasn’t electrically operated in his time.
This [time dilation as explained by relativity theory] might suggest that if one wanted to live longer, one should keep flying to the east so that the plane’s speed is added to the earth’s rotation. However, the tiny fraction of a second one would gain would be more than canceled by eating airline meals.
…I estimate the probability that Kip Thorne could go back and kill his grand- father [using time travel] as less than one in ten with a trillion trillion trillion trillion trillion zeroes after it. That’s a pretty small probability, but if you look closely at the picture of Kip, you may see a slight fuzziness around the edges. That corresponds to the faint possibility that some bastard from the future came back and killed his grandfather, so he’s not really there.

 

The reader of this review can surely see that I am a great admirer of Stephen Hawking. His strength and his courage and his exuberance are both infectious and inspiring. But I also appreciate the tremendous intellectual effort that it takes to explain a subject as technical and deep as cosmology to the lay public. It takes real gifts, and tremendous determination, to pull this off. It requires a certain amount of chutzpah even to try it. The likelihood of failure is considerable, and the likelihood of embarrassment before one’s colleagues is huge. Yet we in the mathematical sciences have suffered in the public eye, have suffered in the derby for funding, and have suffered among the sciences because we have not been willing to take these risks. I can only hope that we will all see Stephen Hawking as a role model and that we will therefore try—even in a small way, perhaps by consenting to an interview with the campus newspaper—to communicate as Hawking has. There is much to be gained, and the risks are well worth it. Now that Hawking has forged the path, it is much easier for the rest of us to follow.

Hawking confesses that when he wrote A Brief History of Time he felt that physicists were on the verge of a great overarching theory that would, in particular, reconcile general relativity with quan- tum mechanics. Part of the purpose of the present book is to bring the reader up to date with progress on this unified theory in the past thirteen years. Hawking addresses this goal by way of describing various avenues of research that he, himself, has pursued. This of course makes perfect sense, and he does a splendid job of giving the reader a feel for p-branes, string theory, Feynman’s multiple histories, black holes, and many other cutting edge ideas. I am not at all sure that, having labored through the book, the reader will have a clear idea of where we are now as compared to where we were in 1988. One is tempted at this point to compare Hawking’s new book with Brian Greene’s The Ele- gant Universe [GRE]. Greene states point blank in his preface that “… physicists believe that they have finally found a framework for stitching these insights together into a seamless whole—a single theory that, in principle, is capable of describing all physical phenomena.” He then proceeds to spend 387 pages telling us (by way of superstring theory and the like) how the physicists have achieved this end. Greene is less interested in en- tertaining us than in telling a very serious story. As a result, his book is rather more cerebral and ponderous than Hawking’s. It has nevertheless been well received and has certainly acquainted a broad cross-section of the populace with some important scientific developments. But the book is perhaps more austere than even A Brief History of Time. It contains much more solid information than, and will reach a much more limited audi- ence than, The Universe in a Nutshell. This is a trade-off with which both authors should be comfortable.

The Universe in a Nutshell has many features going for it. Like A Brief History of Time, it has a delightfully wry and enticing title. It draws the reader in quickly and painlessly and sustains him with wit and popular touchstones and fun. The reader of Nutshell will know, because Hawking has told him quite explicitly, that we have not yet reached our goal of a unified theory and that we probably never will. To Hawking’s mind, and to mine as well, this is all to the good because the journey is much more enthralling than the finish. The reader of Nutshell will have been left with many opened doors and unanswered questions, and this is clearly how Hawking wants it. Readers of his next book will have all the necessary prerequisites.

Buy the book

Do Aliens Exist?

THE aliens are out there and Earth had better watch out, at least according to Stephen Hawking. He has suggested that extraterrestrials are almost certain to exist — but that instead of seeking them out, humanity should be doing all it that can to avoid any contact.

The suggestions come in a new documentary series in which Hawking, one of the world’s leading scientists, will set out his latest thinking on some of the universe’s greatest mysteries.

Alien life, he will suggest, is almost certain to exist in many other parts of the universe: not just in planets, but perhaps in the centre of stars or even floating in interplanetary space.

Hawking’s logic on aliens is, for him, unusually simple. The universe, he points out, has 100 billion galaxies, each containing hundreds of millions of stars. In such a big place, Earth is unlikely to be the only planet where life has evolved.

“To my mathematical brain, the numbers alone make thinking about aliens perfectly rational,” he said. “The real challenge is to work out what aliens might actually be like.”

Stephen Hawking: ALIENS – Part 1 of 4

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He suggests that aliens might simply raid Earth for its resources and then move on:

“We only have to look at ourselves to see how intelligent life might develop into something we wouldn’t want to meet. I imagine they might exist in massive ships, having used up all the resources from their home planet. Such advanced aliens would perhaps become nomads, looking to conquer and colonise whatever planets they can reach.”

Stephen Hawking: ALIENS – Part 2 of 4

Hawking has suggested the possibility of alien life before but his views have been clarified by a series of scientific breakthroughs, such as the discovery, since 1995, of more than 450 planets orbiting distant stars, showing that planets are a common phenomenon.

So far, all the new planets found have been far larger than Earth, but only because the telescopes used to detect them are not sensitive enough to detect Earth-sized bodies at such distances.

Stephen Hawking: ALIENS – Part 3 of 4

Another breakthrough is the discovery that life on Earth has proven able to colonise its most extreme environments. If life can survive and evolve there, scientists reason, then perhaps nowhere is out of bounds.

Hawking’s belief in aliens places him in good scientific company. In his recent Wonders of the Solar System BBC series, Professor Brian Cox backed the idea, too, suggesting Mars, Europa and Titan, a moon of Saturn, as likely places to look.

Stephen Hawking: ALIENS – Part 4 of 4

Similarly, Lord Rees, the astronomer royal, warned in a lecture earlier this year that aliens might prove to be beyond human understanding.

“I suspect there could be life and intelligence out there in forms we can’t conceive,” he said. “Just as a chimpanzee can’t understand quantum theory, it could be there are aspects of reality that are beyond the capacity of our brains.”

Click here for the full DVD of Stephen Hawking’s Universe

The problem of the origin of the universe, is a bit like the old question: Which came first, the chicken, or the egg. In other words, what agency created the universe. And what created that agency. Or perhaps, the universe, or the agency that created it, existed forever, and didn’t need to be created. Up to recently, scientists have tended to shy away from such questions, feeling that they belonged to metaphysics or religion, rather than to science. However, in the last few years, it has emerged that the Laws of Science may hold even at the beginning of the universe. In that case, the universe could be self contained, and determined completely by the Laws of Science.

The debate about whether, and how, the universe began, has been going on throughout recorded history. Basically, there were two schools of thought. Many early traditions, and the Jewish, Christian and Islamic religions, held that the universe was created in the fairly recent past. For instance, Bishop Usher calculated a date of four thousand and four BC, for the creation of the universe, by adding up the ages of people in the Old Testament. One fact that was used to support the idea of a recent origin, was that the Human race is obviously evolving in culture and technology. We remember who first performed that deed, or developed this technique. Thus, the arguement runs, we can not have been around all that long. Otherwise, we would have already progressed more than we have. In fact, the biblical date for the creation, is not that far off the date of the end of the last Ice Age, which is when modern humans seem first to have appeared.

On the other hand, some people, such as the Greek philosopher, Aristotle, did not like the idea that the universe had a beginning. They felt that would imply Divine intervention. They prefered to believe that the universe, had existed, and would exist, forever. Something that was eternal, was more perfect than something that had to be created. They had an answer to the argument about human progress, that I described. It was, that there had been periodic floods, or other natural disasters, which repeatedly set the human race right back to the beginning.

Both schools of thought held that the universe was essentially unchanging in time. Either it had been created in its present form, or it had existed forever, like it is today. This was a natural belief in those times, because human life, and, indeed the whole of recorded history, are so short that the universe has not changed significantly during them. In a static, unchanging universe, the question of whether the universe has existed forever, or whether it was created at a finite time in the past, is really a matter for metaphysics or religion: either theory could account for such a universe. Indeed, in 1781, the philosopher, Immanuel Kant, wrote a monumental, and very obscure work, The Critique of Pure Reason. In it, he concluded that there were equally valid arguements, both for believing that the universe had a beginning, and for believing that it did not. As his title suggests, his conclusions were based simply on reason. In other words, they did not take any account of observations about the universe. After all, in an unchanging universe, what was there to observe?

In the 19th century, however, evidence began to accumulate that the earth, and the rest of the universe, were in fact changing with time. On the one hand, geologists realized that the formation of the rocks, and the fossils in them, would have taken hundreds or thousands of millions of years. This was far longer than the age of the Earth, according to the Creationists. On the other hand, the German physicist, Boltzmann, discovered the so-called Second Law of Thermodynamics. It states that the total amount of disorder in the universe (which is measured by a quantity called entropy), always increases with time. This, like the argument about human progress, suggests that the universe can have been going only for a finite time. Otherwise, the universe would by now have degenerated into a state of complete disorder, in which everything would be at the same temperature.

Another difficulty with the idea of a static universe, was that according to Newton’s Law of Gravity, each star in the universe ought to be attracted towards every other star. So how could they stay at a constant distance from each other. Wouldn’t they all fall together. Newton was aware of this problem about the stars attracting each other. In a letter to Richard Bentley, a leading philosopher of the time, he agreed that a finite collection of stars could not remain motionless: they would all fall together, to some central point. However, he argued that an infinite collection of stars, would not fall together: for there would not be any central point for them to fall to. This argument is an example of the pitfalls that one can encounter when one talks about infinite systems. By using different ways to add up the forces on each star, from the infinite number of other stars in the universe, one can get different answers to the question: can they remain at constant distance from each other. We now know that the correct proceedure, is to consider the case of a finite region of stars. One then adds more stars, distributed roughly uniformly outside the region. A finite collection of stars will fall together. According to Newton’s Law of Gravity, adding more stars outside the region, will not stop the collapse. Thus, an infinite collection of stars, can not remain in a motionless state. If they are not moving relative to each other at one time, the attraction between them, will cause them to start falling towards each other. Alternatively, they can be moving away from each other, with gravity slowing down the velocity of recession.

Despite these difficulties with the idea of a static and unchanging universe, no one in the seventeenth, eighteenth, nineteenth or early twentieth centuries, suggested that the universe might be evolving with time. Newton and Einstein, both missed the chance of predicting, that the universe should be either contracting, or expanding. One can not really hold it against Newton, because he was two hundred and fifty years before the observational discovery of the expansion of the universe. But Einstein should have known better. Yet when he formulated the General Theory of Relativity to reconcile Newton’s theory with his own Special Theory of Relativity, he added a so-called, “cosmological constant”. This had a repulsive gravitational effect, which could balance the attractive effect of the matter in the universe. In this way, it was possible to have a static model of the universe.

Einstein later said: The cosmological constant was the greatest mistake of my life. That was after observations of distant galaxies, by Edwin Hubble in the 1920’s, had shown that they were moving away from us, with velocities that were roughly proportional to their distance from us. In other words, the universe is not static, as had been previously thought: it is expanding. The distance between galaxies is increasing with time.

The discovery of the expansion of the universe, completely changed the discussion about its origin. If you take the present motion of the galaxies, and run it back in time, it seems that they should all have been on top of each other, at some moment, between ten and twenty thousand million years ago. At this time, which is called the Big Bang, the density of the universe, and the curvature of spacetime, would have been infinite. Under such conditions, all the known laws of science would break down. This is a disaster for science. It would mean that science alone, could not predict how the universe began. All that science could say is that: The universe is as it is now, because it was as it was then. But Science could not explain why it was, as it was, just after the Big Bang.

Not surprisingly, many scientists were unhappy with this conclusion. There were thus several attempts to avoid the Big Bang. One was the so-called Steady State theory. The idea was that, as the galaxies moved apart from each other, new galaxies would form in the spaces inbetween, from matter that was continually being created. The universe would have existed, and would continue to exist, forever, in more or less the same state as it is today.

The Steady State model required a modification of general relativity, in order that the universe should continue to expand, and new matter be created. The rate of creation needed was very low: about one particle per cubic kilometre per year. Thus, this would not be in conflict with observation. The theory also predicted that the average density of galaxies, and similar objects, should be constant, both in space and time. However, a survey of extra-galactic sources of radio waves, was carried out by Martin Ryle and his group at Cambridge. This showed that there were many more faint sources, than strong ones. On average, one would expect that the faint sources were the more distant ones. There were thus two possibilities: Either, we were in a region of the universe, in which strong sources were less frequent than the average. Or, the density of sources was higher in the past, when the light left the more distant sources. Neither of these possibilities was compatible with the prediction of the Steady State theory, that the density of radio sources should be constant in space and time. The final blow to the Steady State theory was the discovery, in 1965, of a background of microwaves. These had the characteristic spectrum of radiation emited by a hot body, though, in this case, the term, hot, is hardly appropriate, since the temperature was only 2.7 degrees above Absolute Zero. The universe is a cold, dark place! There was no reasonable mechanism, in the Steady State theory, to generate microwaves with such a spectrum. The theory therefore had to be abandoned.

Another idea to avoid a singularity, was suggested by two Russians, Lifshitz and Khalatnikov. They said, that maybe a state of infinite density, would occur only if the galaxies were moving directly towards, or away from, each other. Only then, would the galaxies all have met up at a single point in the past. However, one might expect that the galaxies would have had some small sideways velocities, as well as their velocity towards or away from each other. This might have made it possible for there to have been an earlier contracting phase, in which the galaxies somehow managed to avoid hitting each other. The universe might then have re-expanded, without going through a state of infinite density.

When Lifshitz and Khalatnikov made their suggestion, I was a research student, looking for a problem with which to complete my PhD thesis. Two years earlier, I had been diagnosed as having ALS, or motor neuron disease. I had been given to understand that I had only two or three years to live. In this situation, it didn’t seem worth working on my PhD, because I didn’t expect to finish it. However, two years had gone by, and I was not much worse. Moreover, I had become engaged to be married. In order to get married, I had to get a job. And in order to get a job, I needed to finish my thesis.

I was interested in the question of whether there had been a Big Bang singularity, because that was crucial to an understanding of the origin of the universe. Together with Roger Penrose, I developed a new set of mathematical techniques, for dealing with this and similar problems. We showed that if General Relativity was correct, any reasonable model of the universe must start with a singularity. This would mean that science could predict that the universe must have had a beginning, but that it could not predict how the universe should begin: for that one would have to appeal to God.

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 singularities 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.

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 spacetime, is very large compared to the uncertainty in the position of a particle. However, the singularity theorems indicate that spacetime 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 principle 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 which combines General Relativity with quantum mechanics.

We do not yet know the exact form of the correct theory of quantum gravity. The best candidate we have at 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 spacetime, 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.

Another element that we expect to be present in the ultimate theory, is Richard Feynman’s proposal that quantum theory can be formulated, as a Sum Over Histories. In it simplest form, the idea is that a particle has every possible path, or history, in space time. 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 perceive ourselves as living. Imaginary time may sound like something out of science fiction, but it is a well defined mathematical concept. It can be thought of as a direction of time that is at right angles to real time, in some sense. One adds up the probabilities for all the particle histories with certain properties, such as passing through certain points at certain times. One then has to extrapolate the result, back to the real space time in which we live. This is not the most familiar approach to quantum theory, but it gives the same results as other methods.

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 curved space times. One has to specify what class of possible curved spaces should be included in the Sum over Histories. The choice of this class of spaces, determines what state the universe is in. If the class of curved spaces that defines the state of the universe, included spaces with singularities, the probabilities of such spaces would not be determined by the theory. Instead, they would have to be assigned in some arbitrary way. What this means, is that science could not predict the probabilities of such singular histories for spacetime. Thus, it could not predict how the universe should behave. However, it is possible that the universe is in a state defined by a sum that includes only non singular curved spaces. In this case, the laws of science 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 non singular histories only, is like the drunk looking for his key under the lamp post: it may not be where he lost it, but it is the only place in which he might find it. Similarly, the universe may not be in the state defined by a sum over non singular histories, but it is the only state in which science could predict how the universe should be.

In 1983, Jim Hartle and I, proposed that the state of the universe should be given by a Sum over a certain class of Histories. This class consisted of curved spaces, without singularities, and which were of finite size, but which did not have boundaries or edges. They would be like the surface of the Earth, but with two more dimensions. The surface of the Earth has a finite area, but it doesn’t have any singularities, boundaries or edges. I have tested this by experiment. I went round the world, and I didn’t fall off.

The proposal that Hartle and I made, 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 the probabilities of each possible history. Thus, it is only in this case that the known laws would determine how the universe should behave. If the universe is in any other state, the class of 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 set by the Uncertainty Principle.

It would clearly be nice for science if the universe were in the “no boundary” state, but how can we tell whether it is? The answer is, that the no boundary proposal makes definite predictions, for how the universe should behave. If these predictions were not to agree with observation, we could conclude that the universe is not in the “no boundary” state. Thus, the “no boundary” proposal is a good scientific theory, in the sense defined by the philosopher, Karl Popper: it can be falsified by observation.

If the observations do not agree with the predictions, we will know that there must be singularities in the class of possible histories. However, that is about all we would know. We would not be able to calculate the probabilities of the singular histories. Thus, we would 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, that was ten or twenty billion years ago. But if predictability broke down in the very strong gravitational fields in 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.

Of course, one could say that one didn’t care about a breakdown in predictability, that occurred in a distant star. However, in quantum theory, anything that is not actually forbidden, can and ~will happen. Thus, if the class of possible histories includes spaces with singularities, these singularities could occur anywhere, not just at the Big Bang and in collapsing stars. This would mean that we couldn’t predict anything. Conversely, the fact that we are able to predict events, is experimental evidence against singularities, and for the “no boundary” proposal.

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 takes degrees of latitude on the surface of the Earth to be the anallogue 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 spacetime, much like any other, the laws of science would hold at the beginning, as elsewhere.

From the analogy with the surface of the Earth, one might expect that the end of the universe would be similar to the beginning, just as the North Pole is much like the South Pole. However, the North and South Poles correspond to the beginning and end of the history of the universe, in imaginary time, not the real time that we experience. If one extrapolates the results of the “Sum over Histories” from imaginary time to real time, one finds that the beginning of the universe in real time can be very different from its end. It is difficult to work out the details, of what the no boundary proposal predicts for the beginning and end of the universe, for two reasons. First, we don’t yet know the exact laws that govern gravity according to the Uncertainty Principle of quantum mechanics. Though we know the general form and many of the properties that they should have. Second, even if we knew the precise laws, we could not use them to make exact predictions. It would be far too difficult, to solve the equations exactly. Nevertheless, it does seem possible to get an approximate idea, of what the no boundary condition would imply. Jonathan Halliwell and I, have made such an approximate calculation. We treated the universe as a perfectly smooth and uniform background, on which there were small perturbations of density. In real time, the universe would appear to begin its expansion at a minimum radius. At first, the expansion would be what is called inflationary. That is, the universe would double in size every tiny fraction of a second, just as prices double every year in certain countries. The world record for economic inflation, was probably Germany after the First World War. The price of a loaf of bread, went from under a mark, to millions of marks in a few months. But that is nothing compared to the inflation that seems to have occurred in the early universe: an increase in size by a factor of at least a million million million million million times, in a tiny fraction of a second. Of course, that was before the present government.

This inflation was a good thing, in that it produced a universe that was smooth and uniform on a large scale, and was expanding at just the critical rate to avoid recollapse. The inflation was also a good thing in that it produced all the contents of the universe, quite literally out of nothing. When the universe was a single point, like the North Pole, it contained nothing. Yet there are now at least 10 to the 80 particles in the part of the universe that we can observe. Where did all these particles come from? The answer is, that Relativity and quantum mechanics, allow matter to be created out of energy, in the form of particle anti particle pairs. So, where did the energy come from, to create the matter? The answer is, that it was borrowed, from the gravitational energy of the universe. The universe has an enormous debt of negative gravitational energy, which exactly balances the positive energy of the matter. During the inflationary period, the universe borrowed heavily from its gravitational energy, to finance the creation of more matter. The result was a triumph for Reagan economics: a vigorous and expanding universe, filled with material objects. The debt of gravitational energy, will not have to be repaid until the end of the universe.

The early universe could not have been exactly homogeneous and uniform, because that would violate the Uncertainty Principle of quantum mechanics. Instead, there must have been departures from uniform density. The no boundary proposal, implies that these differences in density, would start off in their ground state. That is, they would be as small as possible, consistent with the Uncertainty Principle. However, during the inflationary expansion, they would be amplified. After the period of inflationary expansion was over, one would be left with a universe that was expanding slightly faster in some places, than in others. In regions of slower expansion, the gravitational attraction of the matter, would slow down the expansion still further. Eventually, the region would stop expanding, and would contract to form galaxies and stars. Thus, the no boundary proposal, can account for all the complicated structure that we see around us. However, it does not make just a single prediction for the universe. Instead, it predicts a whole family of possible histories, each with its own probability. There might be a possible history in which Walter Mondale won the last presidential election, though maybe the probability is low.

The no boundary proposal, has profound implications for the role of God in the affairs of the universe. It is now generally accepted, that the universe evolves according to well defined laws. These laws may have been ordained by God, but it seems that He does not intervene in the universe, to break the laws. However, until recently, it was thought that these laws did not apply to the beginning of the universe. It would be up to God to wind up the clockwork, and set the universe going, in any way He wanted. Thus, the present state of the universe, would be the result of God’s choice of the initial conditions. The situation would be very different, however, if something like the no boundary proposal were correct. In that case, the laws of physics would hold, even at the beginning of the universe. So God would not have the freedom to choose the initial conditions. Of course, God would still be free to choose the laws that the universe obeyed. However, this may not be much of a choice. There may only be a small number of laws, which are self consistent, and which lead to complicated beings, like ourselves, who can ask the question: What is the nature of God? Even if there is only one, unique set of possible laws, it is only a set of equations. What is it that breathes fire into the equations, and makes a universe for them to govern. Is the ultimate unified theory so compelling, that it brings about its own existence. Although Science may solve the problem of ~how the universe began, it can not answer the question: why does the universe bother to exist? Maybe only God can answer that.

The time has come to face up to the truth,
whatever the consequences, those are the rules.
Nothing happens by luck or by chance,
the timing is perfect and your world is enhanced.

You’re reading this message because of a light,
that has guided you inward, to see toward what’s right.

Some of the travelers who get on this ride,
are not ready to see it, to think or decide.

They just need a push, a shove or a guide,
the great illusion is inward, and not just outside.
It’s the secret of life that flows in us all,
but why understand it and why climb this wall?

Nothing is simple as we hide under our beds,
all is a paradox and it’s all in our heads.

Fantasy is lucid on this trip through the dream,
the path travels inward ~ building high self esteem.

Overcoming all images of fear and of strife.
thought creates reality  …that’s the Mystery of Life!