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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.

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