The Universe Within (21 page)

Dirac continued throughout his life to initiate surprising and original lines of research. He discussed the existence of magnetic monopoles and initiated the first serious attempt to quantize gravity. Although he was one of quantum theory's founders, Dirac clearly loved the geometrical Einsteinian view of physics. In some ways, one can view Dirac as a brilliant technician, jumping off in directions that had been inspired by Einstein's more philosophical work.

In his
Scientific American
article in May 1963, titled “The Evolution of the Physicists' Picture of Nature,” he says, “Quantum theory has taught us that we have to take the process of observation into account, and observations usually require us to bring in the three-­dimensional sections of the four-dimensional picture of the universe.” What he meant by this was that in order to calculate and interpret the predictions of quantum
theory
, one often has to separate time from space. Dirac thought that Einstein's spacetime picture and the split into space and time created by an observer were fundamental and unlikely to change. But he suspected that quantum theory and Heisenberg's uncertainty relations would probably not survive in their current form. “Of course, there will not be a return to the determinism of classical physical theory. Evolution does not go backward,” he says. “There will have to be some new development that is quite unexpected, that we cannot make a guess about, which will take us still further from classical ideas.”

Many physicists regarded the unworldly Dirac with awe. Niels Bohr said, “Of all physicists, Dirac has the purest soul.” And “Dirac did not have a trivial bone in his body.”
78
The great U.S. physicist John Wheeler said, simply, “Dirac casts no penumbra.”
79

I met Dirac twice, both times at summer schools for graduate students. At the first, in Italy, he gave a one-hour lecture on why physics would never make any progress until we understood how to predict the exact value of the electric charge carried by an electron. During the school, there was an evening event called “The Glorious Days of Physics,” to which many of the great physicists from earlier days had been invited. They did their best to inspire and encourage us students with stories of staying up all night poring over difficult problems. But Dirac, the most distinguished of them all, just stood up and said, “The 1920s really were the glorious days of physics, and they will never come again.” That was all he said — not exactly what we wanted to hear!

At the second summer school where I met him, in Edinburgh, another lecturer was excitedly explaining supersymmetry — a proposed symmetry between the forces and matter particles. He looked to Dirac for support, repeating Dirac's well-known maxim that mathematical beauty was the single most important guiding principle in physics. But again Dirac rained on the parade, saying, “What people never quote is the second part of my statement, which is that if there is no experimental evidence for a beautiful idea after five years, you should abandon it.” I think he was, at least in part, just teasing us. In his
Scientific American
article
80
he gave no such caveat. Writing about Schrödinger's discovery of his wave equation, motivated far more by theoretical than experimental arguments, Dirac said, “I believe there is a moral to this story, namely that it is more important to have beauty in one's equations than to have them fit experiment.”

Dirac ended his article by advocating the exploration of interesting mathematics as one way for us to discover new physical principles: “It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.”

Dirac's God was, I believe, the same one that Einstein or the ancient Greeks would have recognized: the God that is nature and the universe, and whose works epitomize the very best in rationality, order, and beauty. There is no higher compliment that Dirac can pay than to call God “a mathematician of a very high order.” Note, even here, Dirac's understatement.

Perhaps because of his shy, taciturn nature and his technical focus, Dirac is far less famous than other twentieth-­century physics icons. But his uniquely logical, mathematical mind allowed him to articulate quantum theory's underlying principles more clearly than anyone else. After the 1930s, he initiated a number of research directions far ahead of his time. Above all, his uncompromising insistence on simplicity and absolute intellectual honesty continues to inspire attempts to improve on the formula he did so much to found.

· · ·

AS BEAUTIFUL AS IT
is, we know our magic formula isn't a final description of nature. It includes neither dark matter nor the tiny masses of neutrinos, both of which we know to exist. However, it is easy to conceive of amendments to the formula that would correct these omissions. More experimental evidence is needed to tell us exactly which one of them to include.

The second reason that the formula is unlikely to be the last word is an aesthetic one: as it stands it is only superficially “unified.” Buried in its compact notation are no less than nineteen adjustable parameters, fitted to experimental measurements.

The formula also suffers from a profound logical flaw. Starting in the 1950s, it was realized that in theories like quantum electrodynamics or electroweak theory, vacuum fluctuations can alter the effective charges on matter particles at very short distances, in such a way as to make theories inconsistent. Technically, the problem is known as the “Landau ghost,” after the Russian physicist Lev D. Landau.

The problem was circumvented by “grand unified” theories when they were introduced in the 1970s. The basic idea was to combine Glashow, Salam, and Weinberg's electroweak force and Gross, Politzer, and Wilczek's strong nuclear force into a single, grand unified force. At the same time, all the known matter particles would be combined into a single, grand unified particle. There would be new Higgs fields to separate out the strong and electroweak forces and distinguish the different matter particles from one another. These
theories
overcame Landau's problem, and for a while they seemed to be mathematically consistent descriptions of all the known forces except gravity.

Further encouragement came from calculations that extrapolated the strong force and the two electroweak forces to very short distances. All three seemed to unify nicely at a minuscule scale of around a ten-­thousand-trillionth the size of a proton, the atomic nucleus of hydrogen. For a while, from aesthetic and logical grounds as well as hints from the data, this idea of grand unification seemed very appealing. The devil is in the details, however. There turned out to be a great number of different possible grand unified theories, each involving different fields and symmetries. There are a large number of adjustable parameters that have to be fitted to the observed data. The early hints of unification at very tiny scales faded as measurements improved: unification could only be achieved by adding even more fields. Instead of making physics simpler and more beautiful, grand unified theories have, so far, turned out to make it more complex and arbitrary.

A second reason to question grand unification is that its most striking predictions have not been confirmed. If at the most fundamental level there is only one type of particle, and if all of the differences between the particles we see are due to Higgs fields in the vacuum, then there should be physical processes allowing any one kind of particle to turn into any other kind of particle by burrowing quantum-mechanically through the grand unified Higgs field. One of the most dramatic such processes is proton decay, which would cause the proton, one of the basic constituents of atomic nuclei, to decay into lighter particles. If the prediction is correct, then all atoms will disappear, albeit at an extremely slow rate. For many years, researchers have searched for signals of this process in very large tanks of very clean water, observed with highly sensitive light detectors capable of detecting the process of nuclear decay, but so far without success.

But the strongest reason to doubt grand unification is that it ignores the force of gravity. At a scale not too far below the grand unified scale — about a thousand times smaller — we reach the Planck scale, a ten-million-­trillionth the size of a proton, where the vacuum fluctuations start to wreak havoc with Einstein's theory of gravity. As we go to shorter wavelengths, the quantum fluctuations become increasingly wild, causing space­time to become so curved and distorted that we cannot calculate anything. As beautiful as it is, we believe Einstein's theory, as included in the formula, to be only a stand-in. We need new mathematical principles to understand how spacetime works at very short distances.

At the far right of the formula, the Higgs potential energy,
V
, also poses a conundrum. Somehow, there is an extremely fine balance in the universe between the contribution from
V
and the contributions from vacuum fluctuations, a fine balance that results in a minuscule positive vacuum energy. We do not understand how this balance occurs. We can get the formula to agree with observations by adjusting
V
to 120 decimal places. It works, but it gives us no sense that we know what we are doing.

To summarize: all the physics we know can be combined into a formula that, at a certain level, demonstrates how powerful and connected the basic principles are. The formula explains many things with exquisite precision. But in addition to its rather arbitrary-looking pattern of particles and forces, and its breakdown at extremely short distances due to quantum fluctuations, it has two glaring, overwhelming failures. So far, it fails to make sense of the universe's singular beginning and its strange, vacuous future.

In practice, physicists seldom use the complete formula. Most of physics is based on approximations, on knowing which parts of the formula to ignore and how to simplify the parts you keep. Nevertheless, many predictions based on the formula have been worked out and verified, sometimes with extreme precision. For example, an electron has spin, and this causes it to behave in some respects like a tiny bar magnet. The relevant parts of the formula allow you to calculate the strength of this little bar magnet to a precision of about one part in a trillion. And the calculations agree with experiment.

For anything even slightly more complicated — like the structure of complex molecules, or the properties of glass or aluminum, or the flow of water — we are unable to work out all of the predictions because we are not good enough at doing the math, even though we believe the formula contains within it all the right answers. In the future, as I will describe in the next chapter, the development of quantum computers may completely transform our ability to calculate and to translate the magic formula directly into predictions for many processes far beyond the reach of computation today.

HOW SHALL THE BASIC
problems of the indescribable beginning and the puzzling future of the universe be resolved? The most popular candidate for replacing our formula for all known physics is a radically different framework known as string theory, as mentioned in the previous chapter. String theory was discovered more or less by accident in 1968, by a young Italian post-doctoral researcher named Gabriele Veneziano, working at the European Organization for Nuclear Research (
CERN
) in Geneva. Veneziano wasn't looking for a unified theory; he was trying to fit experimental data on nuclear collisions. By chance, he came across a very interesting mathematical formula invented by the eighteenth-­century Swiss mathematician Leonhard Euler — the very same Euler whose mathematical discoveries are central to the formula for all known physics.

Veneziano found he could use another formula of Euler's, called “Euler's beta function,” to describe the collisions of nuclear particles in an entirely new way. Veneziano's calculations caused great excitement at the time, and even more so when it was realized that they were describing the particles as if they were little quantum pieces of string, an entirely different picture from that of quantum fields. Ultimately, the idea failed as a description of nuclear physics. It was superseded by the field theories of the strong and weak nuclear forces, and by the understanding that nuclear particles are complicated agglomerations of fields held together by vacuum fluctuations. But the mathematics of string theory turned out to be very rich and interesting, and during the early 1970s, it was developed rapidly.

String is envisaged as a form of perfect elastic. It can exist as pieces with two ends or in the form of closed loops. Waves travel along it at the speed of light. And pieces of string can vibrate and spin in a myriad ways. One of string theory's most attractive features is that just one entity — string — describes an infinite variety of objects. So string theory is a highly unified theory.

In 1974, French physicist Joël Scherk and U.S. physicist John Schwarz realized that a closed loop of string, also spinning end over end, behaved like a graviton, the basic quantum of Einstein's theory of gravity. And so it turned out that string theory automatically provided a theory of quantum gravity, a totally unexpected discovery. Even more surprising, string theory seems to be free of the infinities that plague more conventional approaches to quantum gravity. In the mid-1980s, just as hopes for a grand unified theory were fading, string
theory
came along as the next candidate for a theory of everything.