Hyperspace (25 page)

Soon, three physicists (Daniel Freedman, Sergio Ferrara, and Peter van Nieuwenhuizen, at the State University of New York at Stony Brook) wrote down the theory of supergravity in 1976. Supergravity was the first realistic attempt to construct a world made entirely of marble. In a super-symmetric theory, all particles have super partners, called
sparticles
. The supergravity theory of the Stony Brook group contains just two fields: the spin-two graviton field (which is a boson) and its spin−3/2 partner, called the
gravitino
(which means “little gravity”). Since this is not enough particles to include the Standard Model, attempts were made to couple the theory to more complicated particles.

The simplest way to include matter is to write down the supergravity theory in 11-dimensional space. In order to write down the super Kaluza-Klein theory in 11 dimensions, one has to increase the components within the Riemann tensor vastly, which now becomes the super Riemann tensor. To visualize how supergravity converts wood into marble, let us write down the metric tensor and show how supergravity manages to fit the Einstein field, the Yang-Mills field, and the matter fields into one supergravity field (
Figure 6.3
). The essential feature of this diagram is that matter, along with the Yang-Mills and Einstein equations, is now included in the same 11-dimensional supergravity field. Supersymmetry is the symmetry that reshuffles the wood into marble and vice versa within the supergravity field. Thus they are all manifestations of the same force, the superforce. Wood no longer exists as a single, isolated entity. It is now merged with marble, to form supermarble (
Figure 6.4
)!

Figure 6.3. Supergravity almost fulfills Einstein’s dream of giving a purely geometric derivation of all the forces and particles in the universe. To see this, notice that if we add supersymmetry to the Riemann metric tensor, the metric doubles in size, giving us the super Riemann metric. The new components of the super Riemann tensor correspond to quarks and leptons. By slicing the super Riemann tensor into its components, we find that it includes almost all the fundamental particles and forces in nature: Einstein’s theory of gravity, the Yang-Mills and Maxwell fields, and the quarks and leptons. But the fact that certain particles are missing in this picture forces us to go a more powerful formalism: superstring theory
.

Physicist Peter van Nieuwenhuizen, one of supergravity’s creators, was deeply impressed by the implication of this superunification. He wrote that supergravity “may unify grand unified theories … with gravity, leading to a model with almost no free parameters. It is the unique theory with a local gauge symmetry between fermions and bosons. It is the most beautiful gauge theory known, so beautiful, in fact, that Nature should be aware of it!”
⁶

I fondly remember attending and giving lectures at many of these supergravity conferences. There was an intense, exhilarating feeling that we were on the verge of something important. At one meeting in Moscow, I remember well, a series of lively toasts were made to the continued success of the supergravity theory. It seemed that we were finally on the verge of carrying out Einstein’s dream of a universe of marble after 60 years of neglect. Some of us jokingly called it “Einstein’s revenge.”

On April 29, 1980, when cosmologist Stephen Hawking assumed the Lucasian Professorship (previously held by some of the immortals of physics, including Isaac Newton and P. A. M. Dirac), he gave a lecture with the auspicious title “Is the End in Sight for Theoretical Physics?” A student read for him: “[W]e have made a lot of progress in recent years and, as I shall describe, there are some grounds for cautious optimism that we may see a complete theory within the lifetime of some of those present here.”

Figure 6.4. In supergravity, we almost get a unification of all the known forces (marble) with matter (wood). Like a jigsaw puzzle, they fit inside Riemann
’s
metric tensor. This almost fulfills Einstein’s dream
.

Supergravity’s fame gradually spread into the general public and even began to have a following among religious groups. For example, the concept of “unification” is a central belief within the transcendental meditation movement. Its followers therefore published a large poster containing the complete equations describing 11-dimensional super-gravity. Each term in the equation, they claimed, represented something special, such as “harmony,” “love,” “brotherhood,” and so on. (This poster hangs on the wall of the theoretical institute at Stony Brook. This is the first time that I am aware of that an abstract equation from theoretical physics has inspired a following among a religious group!)

Peter van Nieuwenhuizen cuts a rather dashing figure in physics circles. Tall, tanned, athletic looking, and well dressed, he looks more like an actor promoting suntan lotion on television than one of the original creators of supergravity. He is a Dutch physicist who is now a professor at Stony Brook; he was a student of Veltman, as was’t Hooft, and was therefore long interested in the question of unification. He is one of the few physicists I have ever met with a truly inexhaustible capacity for mathematical punishment. Working with supergravity requires an extraordinary amount of patience. We recall that the simple metric tensor introduced by Riemann in the nineteenth century had only ten components. Riemann’s metric tensor has now been replaced by the super metric tensor of supergravity, which has literally hundreds of components. This is not surprising, since any theory that has higher dimensions and makes the claim of unifying all matter has to have enough components to describe it, but this vastly increases the mathematical complexity of the equations. (Sometimes I wonder what Riemann would think, knowing that after a century his metric tensor would blossom into a super metric many times larger than anything a nineteenth-century mathematician could conceive.)

The coming of supergravity and super metric tensors has meant that the amount of mathematics a graduate student must master has exploded within the past decade. As Steven Weinberg observes, “Look what’s happened with supergravity. The people who’ve been working on
it for the past ten years are enormously bright. Some of them are brighter than anyone I knew in my early years.”
⁷

Peter is not only a superb calculator, but also a trendsetter. Because calculations for a single supergravity equation can easily exceed a sheet of paper, he eventually started using large, oversize artist’s sketch boards. I went to his house one day, and saw how he operated. He would start at the upper-left-hand corner of the pad, and start writing his equations in his microscopic handwriting. He would then proceed to work across and down the sketch pad until it was completely filled, and then turn the page and start again. This process would then go on for hours, until the calculation was completed. The only time he would ever be interrupted was when he inserted his pencil into a nearby electric pencil sharpener, and then within seconds he would resume his calculation without missing a symbol. Eventually, he would store these artist’s notepads on his shelf, as though they were volumes of some scientific journal. Peter’s sketch pads gradually became notorious around campus. Soon, a fad started; all the graduate students in physics began to buy these bulky artist’s sketch pads and could be seen on campus hauling them awkwardly but proudly under their arms.

One time, Peter, his friend Paul Townsend (now at Cambridge University), and I were collaborating on an exceptionally difficult super-gravity problem. The calculation was so difficult that it consumed several hundred pages. Since none of us totally trusted our calculations, we decided to meet in my dining room and collectively check our work. We faced a daunting challenge: Several thousand terms had to sum up to exactly zero. (Usually, we theoretical physicists can “visualize” blocks of equations in our heads and manipulate them without having to use paper. However, because of the sheer length and delicacy of this problem, we had to check every single minus sign in the calculation.)

We then divided the problem into several large chunks. Sitting around the dining-room table, each of us would busily calculate the same chunk. After an hour or so, we would then cross-check our results. Usually two out of three would get it right, and the third would be asked to find his mistake. Then we would go to the next chunk, and repeat the same process until all three of us agreed on the same answer. This repetitive cross-checking went on late into the night. We knew that even one mistake in several hundred pages would give us a totally worthless calculation. Finally, well past midnight we checked the last and final term. It was zero, as we had hoped. We then toasted our result. (The arduous calculation must have exhausted even an indefatigable workhorse like Peter. After leaving my apartment, he promptly forgot where his wife’s
new apartment was in Manhattan. He knocked on several doors of an apartment house, but got only angry responses; he had chosen the wrong building. After a futile search, Peter and Paul reluctantly headed back to Stony Brook. But because Peter had forgotten to replace a clutch cable, the cable snapped, and they had to push his car. They eventually straggled into Stony Brook in their broken car at 5:00 in the morning!)

The critics, however, gradually began to see problems with supergravity. After an intensive search, sparticles were not seen in any experiment. For example, the spin-1/2 electron does not have any spin-0 partner. In fact, there is, at the present, not one shred of experimental evidence for sparticles in our low-energy world. However, the firm belief of physicists working in this area is that, at the enormous energies found at the instant of Creation, all particles were accompanied by their super partners. Only at this incredible energy do we see a perfectly supersymmetric world.

But after a few years of fervent interest and scores of international conferences, it became clear that this theory could not be quantized correctly, thus temporarily derailing the dream of creating a theory purely out of marble. Like every other attempt to construct a theory of matter entirely from marble, supergravity failed for a very simple reason: Whenever we tried to calculate numbers from these theories, we would arrive at meaningless infinities. The theory, although it had fewer infinities than the original Kaluza-Klein theory, was still nonrenormalizable.

There were other problems. The highest symmetry that supergravity could include was called O(8), which was too small to accommodate the symmetry of the Standard Model. Supergravity, it appeared, was just another step in the long journey toward a unified theory of the universe. It cured one problem (turning wood into marble), only to fall victim to several other diseases. However, just as interest in supergravity began to wane, a new theory came along that was perhaps the strangest but most powerful physical theory ever proposed: the ten-dimensional superstring theory.

String theory is twenty-first century physics that fell accidentally into the twentieth century.

Edward Witten

E
DWARD
Witten, of the Institute for Advanced Study in Princeton, New Jersey, dominates the world of theoretical physics. Witten is currently the “leader of the pack,” the most brilliant high-energy physicist, who sets trends in the physics community the way Picasso would set trends in the art world. Hundreds of physicists follow his work religiously to get a glimmer of his path-breaking ideas. A colleague at Princeton, Samuel Treiman, says, “He’s head and shoulders above the rest. He’s started whole groups of people on new paths. He produces elegant, breathtaking proofs which people gasp at, which leave them in awe.” Treiman then concludes, “We shouldn’t toss comparisons with Einstein around too freely, but when it comes to Witten…”
¹

Witten comes from a family of physicists. His father is Leonard Witten, professor of physics at the University of Cincinnati and a leading authority on Einstein’s theory of general relativity. (His father, in fact, sometimes boasts that his greatest contribution to physics was producing his son.) His wife is Chiara Nappi, also a theoretical physicist at the institute.