Farewell to Reality (31 page)

Nobody was interested.

Enter Witten: the first superstring revolution

Schwarz continued his collaboration with both Neveu and Scherk. They worked on a variety of aspects of superstring theory and explored the possibility that the extra spatial dimensions demanded by the theory might somehow be responsible for spontaneous supersymmetry-breaking.

Supersymmetry was also becoming established as a four-dimensional extension of standard model quantum field theories. Supergravity was evolved, and Schwarz contributed to its development.

Whilst working for a few months at CERN in Geneva, Schwarz began collaborating with British physicist Michael Green, based at Queen Mary College in London. Together they explored aspects of three different kinds of superstring theory. These became known as Type I, Type IIA and Type IIB. All require ten spacetime dimensions but differ in the way that supersymmetries are applied. Like the MSSM, Type I superstring theory makes use of one supersymmetry. The Type II theories use two.

Although their work continued to be largely ignored, the theory was beginning to win a few advocates. Among them was Princeton mathematical physicist Edward Witten.

By the early 1980s, Witten was still relatively young but was already a force to be reckoned with. He had had a rather eclectic career. After studying history and linguistics at Brandeis University near Boston, he went on to read economics at the University of Wisconsin and embarked on a career in politics, working on George McGovern's 1972 presidential campaign.

After McGovern's overwhelming defeat by Richard Nixon, he abandoned politics and moved to Princeton to study mathematics. He migrated to physics shortly afterwards, following in the footsteps of his father, Louis, professor of physics at the University of Cincinnati. He studied for his doctorate under David Gross, securing his PhD in 1976. Just four years later he was a tenured professor at Princeton.

Witten was establishing a reputation as a bona fide genius, a modern-day Einstein. In 1982 he was awarded a MacArthur Foundation ‘genius' grant. Young Princeton graduate Peter Woit described the impression of being in contact with such a vastly superior intelligence. Following some paces behind Witten as he crossed the Princeton campus, Woit climbed the steps to the large plaza in front of the library:

When I reached the plaza [Witten] was nowhere to be seen, and it is quite a bit more than thirty feet to the nearest building entrance. While presumably he was just moving a lot faster than me, it crossed my mind at the time that a consistent explanation for everything was that Witten was an extra-terrestrial being from a superior race who, since he thought no one was watching, had teleported back to his office.
⁷

Witten's involvement in superstring theory was in itself sufficient to draw attention to the subject. He quickly persuaded Schwarz and Green that if superstring theory was to become a viable alternative to the standard model and a serious candidate as a theory of everything, then they needed to demonstrate that it was free of
anomalies
.

An anomaly occurs when the symmetry of the theory breaks down as a result of making so-called ‘one-loop' quantum corrections. If this happens, the mathematical consistency of the theory is lost and there's a chance that it might no longer make consistent predictions (for example, such an anomaly in QED might lead to the prediction of photons with three spin orientations or three polarization directions). Needless to say, in the quantum field theories of the standard model, all such anomalies cancel.

Different versions of superstring theory have different symmetry properties. Type IIA is mirror-symmetric, and the physicists could be confident that this theory would exhibit no residual anomalies. But look in a mirror. The world we inhabit is not mirror-symmetric.

In 1984, Witten and Spanish physicist Luis Alvarez-Gaumé pointed out that further anomalies would arise in superstring theory due to the gravitational field. But they went on to show that in a low-energy-approximation Type IIB theory, these anomalies did indeed cancel. This was encouraging, but still left a question mark over the Type I theory.

In the summer of 1984, Green and Schwarz discovered that in a low-energy-approximation Type I superstring theory based on the symmetry group SO (32), a group of rotations in 32 dimensions,
^*
the anomalies did indeed all cancel out. Witten picked up rumours of their
breakthrough, and called to find out more. They sent him a draft manuscript by Federal Express.

Things then happened very quickly.

Green and Schwarz published their paper in September 1984. Witten submitted his first paper on superstrings to the same journal later that same month.

At Princeton, David Gross, Jeffrey Harvey, Emil Martinec and Ryan Rohm (who would collectively come to be known as the Princeton String Quartet) found yet another version of the theory, called heterotic (or hybrid)
^*
superstring theory, in which the anomalies also cancelled. It turned out that there were two types of heterotic superstring theory, one based on the symmetry group formed from the product E
₈
× E
₈
, where E8 is an algebraic group with 248 dimensions, and the other based on the symmetry group SO(32). Both theories require ten spacetime dimensions. They submitted their paper for publication in November 1984.

The first superstring revolution had begun.

Hiding the extra dimensions: Calabi—Yau spaces

Kaluza discovered that by solving Einstein's field equations in a five-dimensional spacetime, Maxwell's equations would emerge naturally. Klein deduced that by rolling up — compactifying — the extra spatial dimension into a cylinder with a radius of sub-nuclear scale, its role in the theory could be preserved without the embarrassment of having to experience it directly.

Superstring theory couldn't settle for just one extra spatial dimension. It demanded an extra six. The reason is not so difficult to understand, once you have accepted the assumption that unification can be achieved by expanding the number of dimensions. Kaluza—Klein theory uses five dimensions to join gravity and electromagnetism, to which we must now add further dimensions to accommodate the weak and strong nuclear forces. Alternatively, if we make the string assumption, then we need enough ‘degrees of freedom' for the strings to vibrate
in if these vibrational patterns are to represent all the elementary particles and all the forces between them.

The point about superstring theory is that it demands precisely nine spatial dimensions, no more and no fewer. But what must we now do with this embarrassment of riches? A lifetime of experience tells me that the world is stubbornly three-dimensional and I have little doubt that I will not find another six dimensions no matter how hard I look.

I feel another assumption coming on.

Klein had rolled up the extra dimension into a cylinder, but a further six dimensions demand a much more complex structure. In 1984, American theorist Andrew Strominger, then at the Institute for Advanced Study in Princeton, searched for an appropriate structure for this manifold in collaboration with British mathematical physicist Philip Candelas, then at the University of Texas. This was not a free choice. Supersymmetry places some fairly rigid constraints on precisely how these extra dimensions can be rolled up. Strominger's search led to the library, and a recent paper by Chinese-born American mathematician Shing-Tung Yau. The paper contained a proof of something called the Calabi conjecture, named for Italian-American mathematician Eugenio Calabi.

As Strominger explained: ‘I found Yau's paper in the library and couldn't make much sense of it, but from the little I did understand, I realized that these manifolds were just what the doctor ordered.'
⁸

Calabi's conjecture concerns the geometric structures that are allowed by different topologies, the various shapes that ‘mathematical' spaces can possess. Although this was a problem in abstract geometry, solutions to such problems have been of interest to physicists ever since Einstein established the connection between geometry and gravity in the general theory of relativity. One interpretation of the Calabi
conjecture is that it suggests that in certain spaces, gravity is possible even in the absence of matter.

Yau developed a proof of the conjecture, which he discussed with Calabi and Canadian-born American mathematician Louis Nirenberg on Christmas Day 1976.
^*
The proof confirmed the existence of a series of shapes — now called Calabi—Yau spaces — that satisfy Einstein's field equations in the absence of matter. It was indeed just what the doctor ordered.

Strominger and Candelas got in touch with Gary Horowitz, at the University of California in Santa Barbara, a physicist who had worked with Yau as a postdoctoral associate. Strominger also visited Witten, to discover that the latter had independently arrived at the same conclusion. At Strominger and Witten's request, on a flight from San Diego to Chicago Yau worked out the structure of a Calabi—Yau space that would generate three families or generations of matter particles.

The four theorists collaborated on a paper which was published in 1985. Thus was born the idea of ‘hidden dimensions'. If I mark an infinitesimally small point on the desk in front of my keyboard, and could somehow zoom in on this point and magnify it so that a distance of a billionth of a trillionth of a trillionth of a centimetre becomes visible, then superstring theory says that I should perceive six further spatial dimensions, curled up into a Calabi—Yau shape (see Figure 8).

On the one hand, this is a perfect example of how we make progress in science. We know that abstract point particles lead to problems. Abstract one-dimensional strings appear to offer better prospects. We reach for supersymmetry because we want a theory that describes fermions as well as bosons, and this eliminates some of the problems of the original string theory (such as tachyons) and yields theories free of anomalies. Superstrings demand a ten-dimensional spacetime, so we borrow concepts from mathematics and tuck the six extra spatial dimensions out of sight in a Calabi—Yau space. We can find a Calabi—Yau space that is consistent with three generations of elementary matter particles. This all seems perfectly logical and reasonable.

Figure 8
The Calabi—Yau manifolds or Calabi—Yau shapes are complex, high-dimensional algebraic surfaces. They appear in superstring theory as manifolds containing the six additional spatial dimensions required for the strings to vibrate in. Because they have dimensions of the Planck length, these manifolds are far too small to be visible. Source: Wikimedia Commons.

But then there is the other hand. On what basis do we choose strings, as opposed to any other kind of abstract construction? Because of a (possibly rather tenuous) relationship between the behaviour of strings and the beta function identified in the scattering of mesons by Veneziano. On what basis do we assume supersymmetry between fermions and bosons? Because this is the only way to get both kinds of particles into the same picture. What is the basis for assuming that six dimensions must be hidden in a Calabi—Yau space? Because it is our experience that the universe is four-dimensional.

I think you get the point. Although this is all perfectly logical and reasonable, what we are actually doing is piling one grand assumption
on top of another. I want to emphasize that there is no experimental or observational basis for these assumptions. This is a theory with little or no foundation in empirical reality. It is rather a loose assemblage of assumptions, ideas or hypotheses that say rather more about how we would like the universe to be than how it really is.
^*

I don't think it's uncharitable to suggest that this is looking increasingly like a house of cards.

Of course, the Theory Principle tells us that this is still okay. Science is a very forgiving discipline in that it never really matters overmuch
how
you arrive at a theory. If it can be shown to work better than existing alternatives, then no matter how much speculation or luck was involved, you can sit back and wait patiently for the Nobel Prize committee to reach the right decision.

Before we take a look at superstring theory's predictions, we have to deal with the fact that there appear to be at least five different versions of the theory — Type I, Type IIA, Type IIB and two versions of heterotic superstring theory. This is a little embarrassing for a theory that has pretensions to be
the
theory of everything.

Resolving this issue would require the biggest assumption of all, one that sparked the second superstring revolution.