The Elegant Universe (32 page)

You should bear in mind two things, though. Even if superpartner particles are found, this fact alone will not establish that string theory is correct. As we have seen, although supersymmetry was discovered by studying string theory, it has also been successfully incorporated into point-particle theories and is therefore not unique to its stringy origins. Conversely, even if superpartner particles are not found by the Large Hadron Collider, this fact alone will not rule out string theory, since it might be that the superpartners are so heavy that they are beyond the reach of this machine as well.

Having said this, if in fact the superpartner particles are found, it will most definitely be strong and exciting circumstantial evidence for string theory.

Fractionally Charged Particles

Another experimental signature of string theory, having to do with electric charge, is somewhat less generic than superpartner particles but equally dramatic. The elementary particles of the standard model have a very limited assortment of electric charges: The quarks and antiquarks have electric charges of one-third or two-thirds, and their negatives, while the other particles have electric charges of zero, one, or negative one. Combinations of these particles account for all known matter in the universe. In string theory, however, it is possible for there to be resonant vibrational patterns corresponding to particles of significantly different electric charges. For instance, the electric charge of a particle can take on exotic fractional values such as 1/5, 1/11, 1/13, or 1/53, among a variety of other possibilities. These unusual charges can arise if the curled-up dimensions have a certain geometrical property: Holes with the peculiar property that strings encircling them can disentangle themselves only by wrapping around a specified number of times.18 The details are not particularly important, but it turns out that the number of windings required to get disentangled manifests itself in the allowed patterns of vibration by determining the denominator of the fractional charges.

Some Calabi-Yau shapes have this geometrical property while others do not, and for this reason the possibility of unusual electric-charge fractions is not as generic as the existence of superpartner particles. On the other hand, whereas the prediction of superpartners is not a unique property of string theory, decades of experience have shown that there is no compelling reason for such exotic electric-charge fractions to exist in any point-particle theory. They can be forced into a point-particle theory, but doing so would be as natural as the proverbial bull in a china shop. Their possible emergence from simple geometrical properties that the extra dimensions can have makes these unusual electric charges a natural experimental signature for string theory.

As with the situation with superpartners, no such exotically charged particles have ever been observed, and our understanding of string theory does not allow for a definitive prediction of their masses should the extra dimensions have the correct properties to generate them. One explanation for not seeing them, again, is that if they do exist, their masses must be beyond our present technological means—in fact, it is likely that their masses would be on the order of the Planck mass. But should a future experiment come across such exotic electric charges, it would constitute very strong evidence for string theory.

Some Longer Shots

There are yet other ways in which evidence for string theory might be found. For example, Witten has pointed out the long-shot possibility that astronomers might one day see a direct signature of string theory in the data they collect from observing the heavens. As encountered in Chapter 6, the size of a string is typically the Planck length, but strings that are more energetic can grow substantially larger. The energy of the big bang, in fact, would have been high enough to produce a few macroscopically large strings that, through cosmic expansion, might have grown to astronomical scales. We can imagine that now or sometime in the future, a string of this sort might sweep across the night sky, leaving an unmistakable and measurable imprint on data collected by astronomers (such as a small shift in the cosmic microwave background temperature; see Chapter 14). As Witten says, “Although somewhat fanciful, this is my favorite scenario for confirming string theory as nothing would settle the issue quite as dramatically as seeing a string in a telescope.”19

Closer to earth, there are other possible experimental signatures of string theory that have been put forward. Here are five examples. First, in Table 1.1 we noted that we do not know if neutrinos are just very light, or if in fact they are exactly massless. According to the standard model, they are massless, but not for any particularly deep reason. A challenge to string theory is to provide a compelling explanation of present and future neutrino data, especially if experiments ultimately show that neutrinos do have a tiny but nonzero mass. Second, there are certain hypothetical processes that are forbidden by the standard model, but that may be allowed by string theory. Among these are the possible disintegration of the proton (don’t worry, such disintegration, if true, would happen very slowly) and the possible transmutations and decays of various combinations of quarks, in violation of certain long-established properties of point-particle quantum field theory.20 These kinds of processes are especially interesting because their absence from conventional theory makes them sensitive signals of physics that cannot be accounted for without invoking new theoretical principles. If observed, any one of these processes would provide fertile ground for string theory to offer an explanation. Third, for certain choices of the Calabi-Yau shape there are particular patterns of string vibration that can effectively contribute new, tiny, long-range force fields. Should the effects of any such new forces be discovered, they might well reflect some of the new physics of string theory. Fourth, as we note in the next chapter, astronomers have collected evidence that our galaxy and possibly the whole of the universe is immersed in a bath of dark matter, the identity of which has yet to be determined. Through its many possible patterns of resonant vibration, string theory suggests a number of candidates for the dark matter; the verdict on these candidates must await future experimental results establishing the detailed properties of the dark matter.

And finally, a fifth possible means of connecting string theory to observations involves the cosmological constant—remember, as discussed in Chapter 3, this is the modification Einstein temporarily imposed on his original equations of general relativity to ensure a static universe. Although the subsequent discovery that the universe is expanding led Einstein to retract the modification, physicists have since realized that there is no explanation for why the cosmological constant should be zero. In fact, the cosmological constant can be interpreted as a kind of overall energy stored in the vacuum of space, and hence its value should be theoretically calculable and experimentally measurable. But, to date, such calculations and measurements lead to a colossal mismatch: Observations show that the cosmological constant is either zero (as Einstein ultimately suggested) or quite small; calculations indicate that quantum-mechanical fluctuations in the vacuum of empty space tend to generate a nonzero cosmological constant whose value is some 120 orders of magnitude (a 1 followed by 120 zeros) larger than experiment allows! This presents a wonderful challenge and opportunity for string theorists: Can calculations in string theory improve on this mismatch and explain why the cosmological constant is zero, or if experiments do ultimately establish that its value is small but nonzero, can string theory provide an explanation? Should string theorists be able to rise to this challenge—as yet they have not—it would provide a compelling piece of evidence in support of the theory.

An Appraisal

The history of physics is filled with ideas that when first presented seemed completely untestable but, through various unforeseen developments, were ultimately brought within the realm of experimental verifiability. The notion that matter is made of atoms, Pauli’s hypothesis that there are ghostly neutrino particles, and the possibility that the heavens are dotted with neutron stars and black holes are three prominent ideas of precisely this sort—ideas that we now embrace fully but that, at their inception, seemed more like musings of science fiction than aspects of science fact.

The motivation for introducing string theory is at least as compelling as any of these three ideas—in fact, string theory has been hailed as the most important and exciting development in theoretical physics since the discovery of quantum mechanics. This comparison is particularly apt because the history of quantum mechanics teaches us that revolutions in physics can easily take many decades to reach maturity. And compared to today’s string theorists, the physicists working out quantum mechanics had a great advantage: Quantum mechanics, even when only partially formulated, could make direct contact with experimental results. Even so, it took close to 30 years for the logical structure of quantum mechanics to be worked out, and about another 20 years to incorporate special relativity fully into the theory. We are now incorporating general relativity, a far more challenging task, and, moreover, one that makes contact with experiment much more difficult. Unlike those who worked out quantum theory, today’s string theorists do not have the shining light of nature—through detailed experimental results—to guide them from one step to the next.

This means that it’s conceivable that one or more generations of physicists will devote their lives to the investigation and development of string theory without getting a shred of experimental feedback. The substantial number of physicists the world over who are vigorously pursuing string theory know that they are taking a risk: that a lifetime of effort might result in an inconclusive outcome. Undoubtedly, significant theoretical progress will continue, but will it be sufficient to overcome present hurdles and yield definitive, experimentally testable predictions? Will the indirect tests we have discussed above result in a true smoking gun for string theory? These questions are of central concern to all string theorists, but they are also questions about which nothing can really be said. Only the passage of time will reveal the answers. The beautiful simplicity of string theory, the way in which it tames the conflict between gravity and quantum mechanics, its ability to unify all of nature’s ingredients, and its potential of limitless predictive power all serve to provide rich inspiration that makes the risk worth taking.

These lofty considerations have been continually reinforced by the ability of string theory to uncover remarkably new physical characteristics of a string-based universe—characteristics that reveal a subtle and deep coherence in the workings of nature. In the language introduced above, many of these are generic features that, regardless of currently unknown details, will be basic properties of a universe built of strings. Of these, the most astonishing have had a profound effect on our ever evolving understanding of space and time.

Part IV. String Theory and the Fabric of Spacetime

Quantum Geometry

I

n the course of about a decade, Einstein singlehandedly overthrew the centuries-old Newtonian framework and gave the world a radically new and demonstrably deeper understanding of gravity. It does not take much to get experts and nonexperts alike to gush over the sheer brilliance and monumental originality of Einstein’s accomplishment in fashioning general relativity. Nevertheless, we should not lose sight of the favorable historical circumstances that strongly contributed to Einstein’s success. Foremost among these are the nineteenth-century mathematical insights of Georg Bernhard Riemann that firmly established the geometrical apparatus for describing curved spaces of arbitrary dimension. In his famous 1854 inaugural lecture at the University of Göttingen, Riemann broke the chains of flat-space Euclidean thought and paved the way for a democratic mathematical treatment of geometry on all varieties of curved surfaces. It is Riemann’s insights that provide the mathematics for quantitatively analyzing warped spaces such as those illustrated in Figures 3.4 and 3.6. Einstein’s genius lay in recognizing that this body of mathematics was tailor-made for implementing his new view of the gravitational force. He boldly declared that the mathematics of Riemann’s geometry aligns perfectly with the physics of gravity.

But now, almost a century after Einstein’s tour-de-force, string theory gives us a quantum-mechanical description of gravity that, by necessity, modifies general relativity when the distances involved become as short as the Planck length. Since Riemannian geometry is the mathematical core of general relativity, this means that it too must be modified in order to reflect faithfully the new short-distance physics of string theory. Whereas general relativity asserts that the curved properties of the universe are described by Riemannian geometry, string theory asserts that this is true only if we examine the fabric of the universe on large enough scales. On scales as small as the Planck length a new kind of geometry must emerge, one that aligns with the new physics of string theory. This new geometrical framework is called quantum geometry.

Unlike the case of Riemannian geometry, there is no ready-made geometrical opus sitting on some mathematician’s shelf that string theorists can adopt and put in the service of quantum geometry. Instead, physicists and mathematicians are now vigorously studying string theory and, little by little, piecing together a new branch of physics and mathematics. Although the full story has yet to be written, these investigations have already uncovered many new geometrical properties of spacetime entailed by string theory—properties that would almost certainly have thrilled even Einstein.

The Heart of Riemannian Geometry

If you jump on a trampoline, the weight of your body causes it to warp by stretching its elastic fibers. This stretching is most severe right under your body and becomes less noticeable toward the trampoline’s edge. You can see this clearly if a familiar image such as the Mona Lisa is painted on the trampoline. When the trampoline is not supporting any weight, the Mona Lisa looks normal. But when you stand on the trampoline, the image of the Mona Lisa becomes distorted, especially the part directly under your body, as illustrated in Figure 10.1.