Warped Passages (47 page)

Aftermath of the Revolution

In 1984, at the height of the “superstring revolution,” I was a graduate student at Harvard. It rapidly became apparent that in research, a beginning physicist had two choices. She could adopt string theory, following in the footsteps of Ed Witten and David Gross, who were then both at Princeton. Or she could remain a particle physicist with more immediate contact with experimental results, in the school of Howard Georgi and Sheldon Glashow, both then at Harvard. It might seem incredible that physicists interested in the same problems could have been so divided, but the notions of how to make progress were very different in the two camps.

The excitement at Harvard remained with particle physics, and many physicists there largely dismissed string theory. A number of problems in particle physics and cosmology remained unsolved—why not answer these questions before delving into the mathematical minefield that string theory was threatening to become? Was it acceptable for physics to extend into unmeasurable domains? With the many brilliant people and many exciting ideas about how to go beyond the Standard Model of particle physics using more traditional methods, there was not much motivation to jump ship.

Elsewhere, however, physicists were convinced that all of the questions about superstring theory would soon be solved, and that string theory was the physics of the future (and of the present). Superstring theory was in its early stages. Some believed that with enough man-hours devoted to it (and they were primarily man-hours), string theorists would ultimately derive known physics. In the 1985 paper about the heterotic string, Gross and his colleagues wrote, “Although much work remains to be done there seem to be no insuperable obstacles to
deriving all of known physics from the…heterotic string.”
^*
String theory promised to be the Theory of Everything. Princeton was in the vanguard of this effort. Physicists there were so certain that string theory was the road to the future that the department no longer contained any particle theorists who didn’t work on string theory—a mistake that Princeton has yet to correct.

Today, we can’t say whether or not the obstacles facing the theory are “insuperable,” but they are certainly challenging. Many major unanswered questions remain. Addressing the unresolved problems of string theory appears to require a mathematical apparatus or a fundamental new approach that goes well beyond the tools that physicists and mathematicians have so far developed.

Joe Polchinski, in his widely used string theory textbook, writes that “string theory may resemble the real world in its broad outline,”
^†
and so it does in some respects. String theory can include the particles and forces of the Standard Model, and can be reduced to four dimensions when other dimensions are curled up. However, although there is tantalizing evidence that string theory could incorporate the Standard Model, the program for finding the ideal Standard Model candidate is nowhere near completion after twenty years of searching.

Physicists initially hoped that string theory would make a unique prediction for what the world should be like, one that would be borne out by the world that we see. But there are now many possible models that can arise in string theory, each containing different forces, different dimensions, and different combinations of particles. We want to find the set that corresponds to the visible universe and the reason that this set is special. Right now, no one knows how to choose among the possibilities. And in any case, none of them look quite right.

For example, Calabi-Yau compactification can determine the number of generations of elementary particles. One possibility is indeed the three generations of the Standard Model. But there is not a unique Calabi-Yau candidate. Although string theorists originally
hoped that Calabi-Yau compactification would single out a preferred shape and unique physical laws, they were quickly disappointed. Andy Strominger described to me how within a week of discovering a Calabi-Yau compactification and thinking it was unique, his collaborator Gary Horowitz found several other candidates. Andy later learned from Yau that there were tens of thousands of Calabi-Yau candidates. We now know that string theories based on Calabi-Yau compactification can contain hundreds of generations. Which Calabi-Yau compactification, if any, is correct? And why? Even though we know that some of string theory’s dimensions must curl up or otherwise disappear, string theorists have yet to determine the principles that tell us the size and shape of the curled-up dimensions.

Moreover, in addition to the new heavy string particles arising from waves that oscillate many times along the string, string theory contains new low-mass particles. And we would expect that if they existed and were as light as string theory naively predicts, those particles would be visible to experiments in our world. Most models based on string theory contain many more light particles and forces than we observe at low energies, and it is not clear what singles out the right ones.

Getting string theory to match the real world is an enormously complicated problem. We have yet to learn why the gravity, particles, and forces derived from string theory should agree with what we already know to be true in our world. But these problems with particles, forces, and dimensions pale in comparison with the real elephant in the room—the gross overestimate for the energy density of the universe.

Even in the absence of particles, the universe can carry energy known as vacuum energy. According to general relativity, this energy has a physical consequence: it stretches or shrinks space. Positive vacuum energy accelerates the expansion of the universe, while negative energy makes it collapse. Einstein first proposed such an energy in 1917 in order to find a static solution to his equations of general relativity in which the gravitational effect of the vacuum energy would cancel that of matter. Although he had to abandon this idea for many reasons, including Edwin Hubble’s observed expansion of the universe in 1929, there is no theoretical reason that such vacuum energy should not exist in our universe.

Indeed, astronomers have recently measured the vacuum energy in our cosmos (it is also known as
dark energy
or the
cosmological constant
) and found a small positive value. They have observed that distant supernovas are dimmer than you’d expect unless they were accelerating away. The supernova measurements and the detailed observations of relic photons created during the Big Bang tell us that the expansion of the universe is accelerating, which is evidence that the vacuum energy has a small positive value.

This measurement is very exciting. But it also introduces a significant puzzle. The acceleration is very slow, which tells us that the value of the vacuum energy, though nonzero, is extremely tiny. The theoretical problem with the observed vacuum energy is that it is far smaller than anyone would estimate. According to string theory estimates, the energy should be much bigger. But if it were, this energy wouldn’t just lead to the hard-to-measure supernova acceleration. If the vacuum energy were big, the universe would long ago have collapsed (if negative) or quickly expanded away to nothing (if positive).

String theory has yet to explain why the universe’s vacuum energy is as small as we know it must be. Particle physics has no answer to this problem either. However, unlike string theory, particle physics does not purport to be a theory of quantum gravity—it’s less ambitious. A particle physics model that cannot explain the energy is unsatisfying, but a string theory that gets the energy wrong is ruled out.

The question of why the energy density is so extraordinarily tiny is an entirely unsolved problem. Some physicists believe that there is no true explanation. Although string theory is a single theory with a single parameter—the tension of the plucked string—string theorists cannot use it to predict most features of the universe. Most physical theories cannot yet use it to predict most features of the universe. Most physical theories contain physical principles which allow you to decide which of the many possible physical configurations a theory would actually predict. For example, most systems will settle down into the configuration that has the lowest energy. But that criterion doesn’t seem to work for string theory, which looks as if it might give rise to an infinite number of different configurations that don’t have the same vacuum energy—and we don’t know which of them, if any, is preferred.

Some string theorists no longer try to find a unique theory. They look at the possible sizes and shapes of rolled-up dimensions and the different options for the energy a universe could contain, and conclude that string theory can only delineate a landscape that describes the huge number of possible universes in which we might live. These string theorists don’t think that string uniquely predicts the vacuum energy. They believe that the cosmos houses many different disconnected regions with different values of the vacuum energy, and we live in the portion of the cosmos that contains the right one. Of the many possible universes, only the one that can give rise to structure could (and does) contain us. Those physicists think that we live in a universe with such an incredibly unlikely value for the vacuum energy because any larger value would have prevented the formation of galaxies and structure in the universe—and hence prevented us.

This reasoning has a name: the anthropic principle. The anthropic principle diverges substantially from the original string theory goal of predicting all the features of the universe. It says that we don’t have to explain the small energy. Disconnected universes with many possible values of the vacuum energy exist, but we live in one of the few where structure can form. The value of the energy in this universe is ridiculously small, and only exceptional versions of string theory would predict this minuscule value, but we could exist only in a universe with minuscule energy. This principle might be discredited by future advances, or it could be vindicated by more thorough investigations. Unfortunately, however, it will be difficult (if not impossible) to test. A world in which the anthropic principle is the answer would certainly be a disappointing and not very satisfying scenario.

In any case, string theory in its current state of development certainly does not predict the features of the world, even though it is a single theory in its underlying formulation. Once again, we are faced with the question of how to connect a beautiful symmetric theory to the physical realities of our universe. The simplest formulation of the theory is too symmetric: many dimensions and many particles and forces that we know must be different appear to be on the same footing. And to make the connection to the Standard Model, and the world we see, this huge order must be disturbed. After symmetry
breaking, the single string theory can manifest itself in many different guises, according to which of the symmetries get broken, which particles become heavy, and which dimensions distinguish themselves.

It is as if string theory is a beautifully designed suit that doesn’t quite fit. In its current state, you can hang it on a rack and admire its fine stitching and intricately woven pattern—it really is beautiful—but you can’t wear it until you make the necessary adjustments. We’d like string theory to accommodate everything we know about the world. But “one size fits all” rarely looks good on anybody. Right now, we don’t even know whether we have the right tools to tailor string theory correctly.

Since we don’t really know all of the theory’s implications, and it is not clear that we ever will, some physicists simply define string theory as whatever resolves the paradox of quantum mechanics and general relativity at small distances. Certainly most string theorists believe that string theory and the correct theory are the same, or at least very closely connected.

There’s clearly a lot left to learn. It is still too early to decide the ultimate merits of a string theory description of the world. Perhaps more elaborate mathematical machinery will permit physicists to truly understand string theory, or perhaps physical insights garnered from applying string theory’s implications to the surrounding universe will provide the critical clues. Addressing the unresolved problems of string theory appears to require a fundamentally new approach that goes well beyond the tools that mathematicians and physicists have so far developed.

Nonetheless, string theory is a remarkable theory. It has already led to important insights into gravity, dimensions, and quantum field theory and it’s the best candidate we know of for a consistent theory of quantum gravity. Furthermore, string theory has led to incredibly beautiful mathematical advances. But string theorists have yet to make good on the promises they made in the 1980s to connect string theory to the world. We still don’t know most of string theory’s implications.

In fairness, questions in particle physics were not immediately answered either. Many of the particle physics problems that were known in the 1980s have still not been solved. These questions include
an explanation of the origin of the disparate masses for the elementary particles and determining the correct solution to the hierarchy problem. Moreover, model builders are still waiting for the experimental clues that tell us which of the myriad possibilities correctly describe physics beyond the Standard Model. Until we explore energies higher than a TeV, we are unlikely to know with certainty the answers to the questions we care most about.

Today, both the string theory and the particle physics communities have a more sober view of their level of understanding than they did in the 1980s. We are trying to address difficult questions, and they will take time to answer. But this is an exciting time, and despite (or perhaps because of) the many unsolved problems, there is good reason to be optimistic. Physicists now have a better grasp of many consequences of both particle physics and string theory, and open-minded physicists today stand to profit from the achievements of both schools. That is the middle ground that some physics colleagues and I prefer—and it has led to many of the exciting results that we will shortly encounter.