The World on a String

1.

In the golden years of the Liberal Party in England, before the First World War, Herbert Asquith was the patrician prime minister and Winston Churchill was an obstreperous young politician. At question time in the House of Commons, Churchill frequently challenged Asquith with provocative statements and awkward questions. After one of these Churchillian assaults, Asquith lamented, “I wish I knew as much about anything as that young man knows about everything.” Reading this eloquent book in which Brian Greene lays out before us his vision of the cosmos, I feel some sympathy for Asquith. Asquith expresses my reaction to the book precisely.

I recommend Greene’s book to any nonexpert reader who wants an up-to-date account of theoretical physics, written in colloquial language that anyone can understand. For the nonex-pert reader, my doubts and hesitations are unimportant. It is not important whether Greene’s picture of the universe will turn out to be technically accurate. The important thing is that his picture is coherent and intelligible and consistent with recent observations. Even if many of the details later turn out to be wrong, the picture is a big step toward understanding. Progress in science is often built on wrong theories that are later corrected. It is better to be wrong than to be vague. Greene’s book explains to the nonexpert reader two essential themes of modern science. First it describes the historical path of observation and theory that led from Newton and Galileo in the seventeenth century to Einstein and Stephen Hawking in the twentieth. Then it shows us the style of thinking that led beyond Einstein and Hawking to the fashionable theories of today. The history and the style of thinking are authentic, whether or not the fashionable theories are here to stay.

In his book The Elegant Universe, published in 1999, Greene gave us a more detailed and technical account of string theory, the theory to which his professional life as a physicist has been devoted. The earlier book was remarkably successful in translating the abstruse and abstract ideas of string theory into readable prose. Early in his new book he gives a brief summary of string theory as he expounded it in The Elegant Universe:

…Superstring theory starts off by proposing a new answer to an old question: what are the smallest, indivisible constituents of matter? For many decades, the conventional answer has been that matter is composed of particles—electrons and quarks—that can be modeled as dots that are indivisible and that have no size and no internal structure. Conventional theory claims, and experiments confirm, that these particles combine in various ways to produce protons, neutrons, and the wide variety of atoms and molecules making up everything we’ve ever encountered.

Superstring theory tells a different story. It does not deny the key role played by electrons, quarks, and the other particle species revealed by experiment, but it does claim that these particles are not dots. Instead, according to superstring theory, every particle is composed of a tiny filament of energy, some hundred billion billion times smaller than a single atomic nucleus (much smaller than we can currently probe), which is shaped like a little string. And just as a violin string can vibrate in different patterns, each of which produces a different musical tone, the filaments of superstring theory can also vibrate in different patterns. But these vibrations don’t produce different musical notes; remarkably, the theory claims that they produce different particle properties. A tiny string vibrating in one pattern would have the mass and the electric charge of an electron; according to the theory, such a vibrating string would be what we have traditionally called an electron. A tiny string vibrating in a different pattern would have the requisite properties to identify it as a quark, a neutrino, or any other kind of particle. All species of particles are unified in superstring theory since each arises from a different vibrational pattern executed by the same underlying entity.

This is a fine beginning for a theory of the universe, and maybe it is true. To be useful, a scientific theory does not need to be true, but it needs to be testable. My doubts about string theory arise from the fact that it is not at present testable. Greene discusses in his Chapters 13 and 14 the prospects for experimental tests of the theory. The experiments that he describes will certainly open new doors to the understanding of nature, even if they do not answer the question whether string theory is true.

The Fabric of the Cosmos covers a wider field than The Elegant Universe and paints it with a broader brush. There is not much overlap between the two books. Only Chapter 12 of the new book, which summarizes the earlier book and gives us the gist of string theory without the details, overlaps strongly. Greene himself suggests that readers who have read The Elegant Universe should skim through Chapter 12. Except for this chapter, the two books cover different subjects and can be read independently. Neither is a prerequisite for reading the other. The new book is easier, and should preferably be read first. Readers who got stuck halfway through The Elegant Universe may find the new book more digestible.

In the history of science there is always a tension between revolutionaries and conservatives, between those who build grand castles in the air and those who prefer to lay one brick at a time on solid ground. The normal state of tension is between young revolutionaries and old conservatives. This is the way it is now, and the way it was eighty years ago when the quantum revolution happened. I am a typical old conservative, out of touch with the new ideas and surrounded by young string theorists whose conversation I do not pretend to understand. In the 1920s, the golden age of quantum theory, the young revolutionaries were Werner Heisenberg and Paul Dirac, making their great discoveries at the age of twenty-five, and the old conservative was Ernest Rutherford, dismissing them with his famous statement, “They play games with their symbols but we turn out the real facts of Nature.” Rutherford was a great scientist, left behind by the revolution that he had helped to bring about. That is the normal state of affairs.

Fifty years ago, when I was considerably younger than Greene is now, things were different. The normal state of affairs was inverted. At that time, in the late 1940s and early 1950s, the revolutionaries were old and the conservatives were young. The old revolutionaries were Albert Einstein, Dirac, Heisenberg, Max Born, and Erwin Schrödinger. Every one of them had a crazy theory that he thought would be the key to understanding everything. Einstein had his unified field theory, Heisenberg had his fundamental length theory, Born had a new version of quantum theory that he called reciprocity, Schrödinger had a new version of Einstein’s unified field theory that he called the Final Affine Field Laws, and Dirac had a weird version of quantum theory in which every state had probability either plus two or minus two. Probability, as com-mon sense defines it, is a number between zero and one expressing our degree of confidence that an event will happen. Probability one means that the event always happens; probability zero means that it never happens. In Dirac’s Alice-in-Wonderland world, every state happens either more often than always or less often than never. Each of the five old men believed that physics needed another revolution as profound as the quantum revolution that they had led twenty-five years earlier. Each of them believed that his pet idea was the crucial first step along a road that would lead to the next big breakthrough.

Young people like me saw all these famous old men making fools of themselves, and so we became conservatives. The chief young players then were Julian Schwinger and Richard Feynman in America and Sin-Itiro Tomonaga in Japan. Anyone who knew Feynman might be surprised to hear him labeled a conservative, but the label is accurate. Feynman’s style was ebullient and wonderfully original, but the substance of his science was conservative. He and Schwinger and Tomonaga understood that the physics they had inherited from the quantum revolution was pretty good. The physical ideas were basically correct. They did not need to start another revolution. They only needed to take the existing physical theories and clean up the details. I helped them with the later stages of the cleanup. The result of our efforts was the modern theory of quantum electrodynamics, the theory that accurately describes the way atoms and radiation behave.

This theory was a triumph of conservatism. We took the theories that Dirac and Heisenberg had invented in the 1920s, and changed as little as possible to make the theories self-consistent and user-friendly. Nature smiled on our efforts. When new experiments were done to test the theory, the results agreed with the theory to eleven decimal places. But the old revolutionaries were still not convinced. After the results of the first experiments had been announced, I brashly accosted Dirac and asked him whether he was happy with the big success of the theory that he had created twenty-five years earlier.

Dirac, as usual, stayed silent for a while before replying. “I might have thought that the new ideas were correct,” he said, “if they had not been so ugly.” That was the end of the conversation. Einstein too was unimpressed by our success. During the time that the young physicists at the Institute for Advanced Study in Princeton were deeply engaged in developing the new electrodynamics, Einstein was working in the same building and walking every day past our windows on his way to and from the Institute. He never came to our seminars and never asked us about our work. To the end of his life, he remained faithful to his unified field theory.

Looking back on this history, I feel no shame in being a conservative today. I belong to a generation that saw conservatism triumph, and I remain faithful to our ideals just as Einstein remained faithful to his. But now my generation is passing from the scene, and I am wondering what the next cycle of history will bring. After the revolutionaries of string theory have grown old, what will the next generation think of them? Will there be another generation of young revolutionaries? Or shall we again have an inversion of the normal state of things, with a new generation of young conservatives in rebellion against the elderly pioneers of string theory? My generation will not be around to see these questions answered.

2.

One of the main themes in Greene’s book is the disconnect between Einstein’s theory of general relativity and quantum mechanics, the two discoveries that revolutionized physics at the beginning of the twentieth century. Einstein’s theory is primarily a theory of gravity, describing the gravitational field as a curvature of space-time, and describing the fall of an apple as the response of the apple to the curvature of space-time induced by the mass of the earth. Einstein’s theory treats the apple and the earth as classical objects with precisely defined positions and velocities, paying no attention to the uncertainties introduced by quantum mechanics. The apple and the earth are large enough so that the quantum uncertainties are negligible.

On the other hand, quantum mechanics describes the behavior of atoms and elementary particles, for which the quantum uncertainties have a dominating influence, and pays no attention to gravity. The atoms and particles are small enough so that any gravitational fields that they induce are negligible. The two theories divide the universe of physics between them without overlapping, general relativity taking care of large objects from apples to galaxies, and quantum mechanics taking care of small objects from molecules to light-quanta. General relativity is important for astronomy and cosmology, while quantum mechanics is important for atomic physics and chemistry. This division of the universe works well for all practical purposes. It works well because the gravitational effects of single atoms or particles are unobservably small.

Greene takes it for granted, and here the great majority of physicists agree with him, that the division of physics into separate theories for large and small objects is unacceptable. General relativity is based on the idea that space-time is a flexible structure pulled and pushed by material objects. Quantum mechanics is based on the idea that space-time is a rigid framework within which observations are made. The two theories are mathematically incompatible. Greene believes that there is an urgent need to find a theory of quantum gravity that applies to large and small objects alike. Quantum gravity means a unified theory that works like general relativity for large objects and like quantum mechanics for small objects. In spite of heroic efforts by many people, no consistent theory of quantum gravity was found until string theory came along. The first and greatest triumph of string theory was its success in unifying general relativity with quantum mechanics. That success gave its discoverers some justification for claiming that it could be a “theory of everything.” String theory is still incomplete and far from ready for practical application, but it does in principle provide us with a theory of quantum gravity.

As a conservative, I do not agree that a division of physics into separate theories for large and small is unacceptable. I am happy with the situation in which we have lived for the last eighty years, with separate theories for the classical world of stars and planets and the quantum world of atoms and electrons. Instead of insisting dogmatically on unification, I prefer to ask the question whether a unified theory would have any real physical meaning. The essence of any theory of quantum gravity is that there exists a particle called the graviton which is a quantum of gravity, just like the photon which is a quantum of light. Such a particle is necessary in quantum gravity, because energy is carried in discrete little packets called quanta, and a quantum of gravitational energy would behave like a particle.

The question that I am asking is whether there is any conceivable way in which we could detect the existence of individual gravitons. It is easy to detect individual photons, as Einstein showed, by observing the behavior of electrons kicked out of metal surfaces by light incident on the metal. The difference between photons and gravitons is that gravitational interactions are enormously weaker than electromagnetic interactions. If you try to detect individual gravitons by observing electrons kicked out of a metal surface by incident gravitational waves, you find that you have to wait longer than the age of the universe before you are likely to see a graviton. I looked at various possible ways of detecting gravitons and did not find a single one that worked. Because of the extreme weakness of the gravitational interaction, any putative detector of gravitons has to be extravagantly massive. If the detector has normal density, most of it is too far from the source of gravitons to be effective, and if it is compressed to a high density around the source it collapses into a black hole. There seems to be a conspiracy of nature to prevent the detector from working.

I propose as a hypothesis to be tested that it is impossible in principle to observe the existence of individual gravitons. I do not claim that this hypothesis is true, only that I can find no evidence against it. If it is true, quantum gravity is physically meaningless. If individual gravitons cannot be observed in any conceivable experiment, then they have no physical reality and we might as well consider them non-existent. They are like the ether, the elastic solid medium which nineteenth-century physicists imagined filling space. Electric and magnetic fields were supposed to be tensions in the ether, and light was supposed to be a vibration of the ether. Einstein built his theory of relativity without the ether, and showed that the ether would be unobservable if it existed. He was happy to get rid of the ether, and I feel the same way about gravitons.

According to my hypothesis, the gravitational field described by Einstein’s theory of general relativity is a purely classical field without any quantum behavior. Gravitational waves exist and can be detected, but they are classical waves and not collections of gravitons. If this hypothesis is true, we have two separate worlds, the classical world of gravitation and the quantum world of atoms, described by separate theories. The two theories are mathematically different and cannot be applied simultaneously. But no inconsistency can arise from using both theories, because any differences between their predictions are physically undetectable.

Another major theme of Greene’s book is the interpretation of quantum mechanics and the weird phenomena of quantum entanglement. He devotes two long chapters, “Entangling Space” and “Time and the Quantum,” to this theme. He makes a valiant attempt to clarify a notoriously foggy subject. But he makes his task more difficult by insisting that quantum mechanics must include everything. He rejects without any serious discussion the dualistic interpretation of quantum mechanics, the idea that there are two separate worlds, the classical world and the quantum world, each following its own rules. The dualistic view, limiting the scope of quantum mechanics to well-defined experimental situations, makes the problems of interpretation much simpler.

The dualistic interpretation of quantum mechanics says that the classical world is a world of facts while the quantum world is a world of probabilities. Quantum mechanics predicts what is likely to happen while classical mechanics records what did happen. This division of the world was invented by Niels Bohr, the great contemporary of Einstein who presided over the birth of quantum mechanics. Lawrence Bragg, another great contemporary, expressed Bohr’s idea more simply: “Everything in the future is a wave, everything in the past is a particle.” Since the greater part of our knowledge is knowledge of the past, Bohr’s division limits the scope of quantum mechanics to a small part of science. I like Bohr’s division, because it allows the possibility that gravitons may not exist. If the scope of quantum theory is limited, gravity may legitimately be excluded from it. But Greene will not accept any such limitation. After briefly describing Bohr’s point of view, he says:

For decades, this perspective held sway. However, its calmative effect on the mind struggling with quantum theory notwithstanding, one can’t help feeling that the fantastic predictive power of quantum mechanics means that it is tapping into a hidden reality that underlies the workings of the universe.

I prefer the calmative effect of Bohr’s perspective on the mind, while Greene prefers the hidden reality. In his first chapter, Greene shows us what he means by hidden reality:

Superstring theory combines general relativity and quantum mechanics into a single, consistent theory…. And as if that weren’t enough, superstring theory has revealed the breadth necessary to stitch all of nature’s forces and all of matter into the same theoretical tapestry. In short, superstring theory is a prime candidate for Einstein’s unified theory.

These are grand claims, and, if correct, represent a monumental step forward. But the most stunning feature of superstring theory, one that I have little doubt would have set Einstein’s heart aflutter, is its profound impact on our understanding of the fabric of the cosmos…. Instead of the three spatial dimensions and one time dimension of common experience, superstring theory requires nine spatial dimensions and one time dimension…. As we don’t see these extra dimensions, superstring theory is telling us that we’ve so far glimpsed but a meager slice of reality.

The last-but-one chapter, “Teleporters and Time Machines,” is a pleasant interlude, describing some possible engineering applications of quantum entanglement and general relativity. The teleporter is a device that can scan an object at one place and reproduce a precise copy of it at another place far away, using quantum entanglement to ensure that the reproduction is exact. The good news is that such a device is in principle possible. The bad news is that it inevitably destroys the object that it copies. The time machine is a tunnel through hyperspace connecting two portals that exist at different places and times in our universe. If you can find the portal that is later in time, you can walk through the tunnel to emerge in your own past. The good news is that such a tunnel is a possible solution of the equations of general relativity. The bad news is that a tunnel large enough to walk through would require more than the total energy output of the sun to hold it open. Neither the teleporter nor the time machine is likely to contribute much to the welfare of our descendants. Greene describes these fantasies with a proper mixture of scientific accuracy and irony.

3.

Three years ago, in January 2001, I was invited to the World Economic Forum in Davos, Switzerland. Brian Greene was also invited, and we were asked to hold a public debate on the question “When will we know it all?” In other words, when will the last big problems of science be solved? The audience consisted mainly of industrial and political tycoons. Our debate was intended to entertain the tycoons, not to give them a serious scientific education. To make it more amusing, Greene was asked to take an extreme position saying “Soon,” and I was asked to take an extreme position saying “Never.”

Here is my version of Greene’s opening statement, reconstructed from my unreliable memory after we came back from Switzerland. He said, this generation of scientists is amazingly lucky. Within a few years or decades, we will discover the fundamental laws of nature. The fundamental laws will be a finite set of equations, like Maxwell’s equations of electrodynamics or Einstein’s equations of gravitation. Everything else will then follow from these equations. Once we have the fundamental equations, we are done. There will be no fundamental problems left. When we know the fundamental equations of physics, everything else, chemistry, biology, neurology, psychology, and so on, can be reduced to physics and explained by using the equations. All that will be left for scientists to do will be applied science, tidying up details and using the equations to solve practical problems. If we are not smart enough to find the equations, then we will leave it to our grandchildren to finish the job. Either way, the end of fundamental science is near.

Greene said his confidence in our ability to find the fundamental laws is based on the marvelous fact that the laws of nature are simple and beautiful. The history of physics shows that this is true of all the laws that we have discovered in the past. We did not need to do unending experiments to discover the laws. We guessed the laws by looking for equations which had the greatest mathematical simplicity and beauty. Then only a few experiments were needed to test the equations and find out whether we guessed right. This happened over and over again, first with Newton’s laws of motion and gravitation, then with Maxwell’s equations of electromagnetism, then with Einstein’s equations of special and general relativity, then with Schrödinger’s and Dirac’s equations of quantum mechanics. Now with string theory the game is almost over. The mathematical beauty of this theory is so compelling that it has to be right, and if it is right it explains everything from particle physics to cosmology.

Since I am reconstructing Greene’s argument from memory, it is possible that I am exaggerating the claims that he was making for theoretical physics. One thing that I remember clearly is the phrase “We are done,” meaning that once we physicists have found the fundamental equations the era of basic scientific inquiry is over. I still hear him saying, “We are done,” in a tone of triumphant finality.

I began my reply by saying that nobody denies the amazing success of theoretical physics in the last four hundred years. Nobody denies the truth of Einstein’s triumphant words: “The creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.” It is true that the fundamental equations of physics are simple and beautiful, and that we have good reason to expect that the equations still to be discovered will be even more simple and beautiful. But the reduction of other sciences to physics does not work. Chemistry has its own concepts, not reducible to physics. Biology and neurology have their own concepts not reducible to physics or to chemistry. The way to understand a living cell or a living brain is not to consider it as a collection of atoms. Chemistry and biology and neurology will continue to advance and to make new fundamental discoveries, no matter what happens to physics. The territory of new sciences, outside the narrow domain of theoretical physics, will continue to expand.

Theoretical science may be divided roughly into two parts, analytic and synthetic. Analytic science reduces complicated phenomena to their simpler component parts. Synthetic science builds up complicated structures from their simpler parts. Analytic science works downward to find the fundamental equations. Synthetic science works upward to find new and unexpected solutions. To understand the spectrum of an atom, you needed analytic science to give you Schrödinger’s equation. To understand a protein molecule or a brain, you need synthetic science to build a structure out of atoms or neurons. Greene was saying, only analytic science is worthy of the name of science. For him, synthetic science is nothing but practical problem solving. I said, on the contrary, good science requires a balance between analytic and synthetic tools, and synthetic science becomes more and more creative as our knowledge increases.

Another reason why I believe science to be inexhaustible is Gödel’s theorem. The mathematician Kurt Gödel discovered and proved the theorem in 1931. The theorem says that given any finite set of rules for doing mathematics, there are undecidable statements, mathematical statements that cannot either be proved or disproved by using these rules. Gödel gave examples of undecidable statements that cannot be proved true or false using the normal rules of logic and arithmetic. His theorem implies that pure mathematics is inexhaustible. No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. Now I claim that because of Gödel’s theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel’s theorem applies to them. The theorem implies that even within the domain of the basic equations of physics, our knowledge will always be incomplete.

I ended by saying that I rejoiced in the fact that science is inexhaustible, and I hoped the nonscientists in the audience would rejoice too. Science has three advancing frontiers that will always remain open. There is the mathematical frontier, which will always remain open thanks to Gödel. There is the complexity frontier, which will always remain open because we are investigating objects of ever-increasing complexity, molecules, cells, animals, brains, human beings, societies. And there is the geographical frontier, which will always remain open because our unexplored universe is expanding in space and time. My hope and my belief is that there will never come a time when we shall say, “We are done.”

After Greene’s opening statement and my reply, the debate in Davos continued with additional remarks from us and questions from the audience. His new book and my review are a further continuation of the same debate. In the review, as in the debate, I have emphasized the points on which Greene and I disagree. There is no space here to enumerate the many points on which we agree. For both of us the most important and exciting fact is that during the last twenty years cosmology became an observational science. During the last five years, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite, an orbiting radio telescope designed by my friend David Wilkinson in Princeton, has given us more detailed and precise information about the history and structure of the cosmos than all earlier telescopes combined.

Observational cosmology has now entered its golden age, with the WMAP satellite continuing to scan the sky and with a variety of even more sensitive telescopes under construction. During the next decade we shall learn far more about the cosmos than we know today, and we shall probably find new mysteries to replace those that we shall solve. Greene and I agree that so long as observers continue to explore, cosmology will continue to deepen our understanding of where we stand and how we came to be.