Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone)
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In a similar vein, if supersymmetry were somehow a “broken” symmetry, then perhaps the superpartners of ordinary particles could behave differently than the particles we know. If, for example, they were much more massive—too massive, say, to have been created in current particle accelerators—then that might explain why none of them has yet been discovered. Here one might wonder what the point is of inventing a new symmetry in nature and then coming up with a reason why it doesn’t seem to apply to what we see. If this were all that were involved, the whole process would resemble intellectual masturbation. (I am motivated here perhaps by an infamous quip by Richard Feynman that physics is to mathematics as sex is to masturbation.) It is more than this, however—at least probably more than this—in part because the existence of broken supersymmetry might resolve the hierarchy problem.
One of the many interesting aspects of virtual particles is that their indirect effects on physically measurable quantities depend upon the spins of the virtual particles—that is, whether they are bosons (integral spin) or fermions (half-integral spin). Given otherwise identical fermions and bosons (i.e., masses, charges, etc.), the fermions will produce contributions identical in magnitude to the bosons, but opposite in sign. This means that in a fully supersymmetric world, virtual particles can yield zero quantum mechanical corrections to physical quantities because for every boson there is a fermion of identical mass and charge, and the two sets of particles can produce equal and opposite contributions to all the processes. Thus, the effects of virtual particles at GUT scales, or at Planck scales, can disappear, so the low-energy mass scale of the particles we observe will be protected.
Of course, we do not live in a fully supersymmetric world. If supersymmetry exists, it is broken, and we would expect the fermionic partners of bosons, and vice versa, to have large masses. However, if the masses of the superpartners of ordinary matter are not too much larger than the masses of the heaviest particles we have now measured, then it is still possible for naturalness to be maintained even with a large hierarchy between the GUT scale and the scale of ordinary particles.
This is because the same virtual particle cancellation that in the fully supersymmetric world yields zero now yields an inexact cancellation. The magnitude of its inexactness will be precisely of the order of the mass difference between particles and their superpartners. If this mass difference is much smaller than the GUT scale, and is on the order of the weak scale masses, say, then virtual particle corrections will not induce masses for ordinary particles that are much larger than the weak scale. The hierarchy between the GUT scale and the weak scale then, while still uncomfortable, would at least be technically natural.
In the same year that Witten presented his argument regarding supersymmetry and the hierarchy problem, another calculation was performed that further bolstered the argument for both broken supersymmetry and grand unification. Recall that when one calculated the strengths of the three nongravitational forces as a function of scale assuming a desert between presently observed scales and the GUT scale, the strengths of the three forces would not converge together precisely at a single scale. However, if instead one assumes that a whole new set of superpartners of ordinary particles might appear with masses close to the weak scale, this would change the calculation. One then finds, given the current best-measured strengths of the three forces, a beautiful convergence together at a single GUT scale. There are other indirect arguments that suggest that broken supersymmetry may actually be a property of nature. For example, it turns out that, in supersymmetric models, various otherwise apparently puzzling features of measured elementary particle properties can be explained. These include most importantly the strange fact that the so-called top quark (the heaviest known quark) is 175 times heavier than the proton, and almost 40 times heavier than the next heaviest quark, the bottom quark, and the fact that a predicted particle called the Higgs particle, associated with the breaking of the symmetry between the weak and electromagnetic interactions, has both thus far escaped detection but yet still could yield the quantum mechanical corrections necessary in the weak interaction to preserve agreement between theoretical predictions and observation. Finally, broken supersymmetry rather naturally predicts the existence of heavy, stable, weakly interacting particles that might make up the dark matter inferred to dominate the mass of our galaxy and all other galaxies.
But even before all of this—indeed, within a few years of the first GUT proposal and of Wess and Zumino’s elucidation of the possibility of supersymmetry in our four-dimensional universe—there was another reason proposed for considering a supersymmetric universe, but this time not in four dimensions, but rather in eleven dimensions.
As I keep stressing, the development of GUTs set the stage for far more ambitious theoretical speculations about nature. Once scientists were seriously willing to consider scales a million billion times smaller than current experiments could directly measure, why not consider scales a billion billion times smaller? This scale is the Planck scale, where as I have mentioned one must come face to face with the problems of trying to unite gravity and quantum mechanics. Thus it was that from 1974 onward, a growing legion of physicists began to turn their attentions to this otherwise esoteric legacy of Einstein.
Recall that one of the issues that led to the development of supersymmetry, in the context of dual strings, was the realization that there appeared to be an unfortunate asymmetry in nature, wherein forces seem to be transmitted by bosons, while matter is made up of both bosons and fermions. In the context of general relativity this asymmetry is exacerbated. Namely, general relativity relates force (i.e., gravity) as a geometric quantity on the one hand, to the energy of matter on the other. Thus, force and matter are integrally related, and one might wonder if apparent distinctions between them are actually artificial. One step in this direction was taken in 1978 by Eugene Cremmer, Bernard Julia, and Joel Scherk, who were following up on work a few years earlier exploring the possibility of “local supersymmetry,” or, as it has become known, “supergravity,” as a symmetry of nature. In the case of supergravity, the duality between bosons and fermions is extended to the case of the gravitational force. If one tries to model gravity as a quantum theory like electromagnetism, then the carrier of the gravitational force should be a massless particle called the graviton. It is a boson, like the photon, but instead of having spin one, it has spin two. Indeed, it would be the only known fundamental particle of spin two in nature, which is why gravity behaves so differently than the other forces. Now, if supersymmetry is also a symmetry appropriate to gravity, then there would be a fermionic partner of the graviton, which is conventionally called the gravitino. This particle would couple to all other matter just as the graviton does, except that, being a fermion, it would be more comparable to the particles that make up ordinary matter, such as electrons and quarks, rather than the particles that carry forces, such as photons and gravitons.
Thus, in supergravity, the moment one introduces a graviton to carry the gravitational force, one also automatically must include a matter particle whose interactions are also determined purely by the gravitational force. Cremmer, Julia, and Scherk realized that this relation between matter particles and the gravitational force in supergravity is in fact dimension dependent. In some sense one can think of this as being due to the fact that in many more dimensions, there are many more axes that a spinning particle can spin about, so that there are many more independent states in which a particle with fixed spin can be. In four dimensions, a particle of spin zero can only be in one state, a particle of spin one-half can exist in two spin states (which we often label up and down), and so on. It turns out that in precisely eleven dimensions only a single type of supergravity theory is allowed. The mathematical relationships between particles of different spins that are determined by supersymmetry in this case is so restrictive that only one combination of particles that can include the graviton is possible if one is to achieve mathematical consistency. In eleven dimensio
ns the graviton (which I remind you is a boson with quantum mechanical spin value equal to 2) has 44 independent states, and the gravitino (a fermion with quantum mechanical spin value of 3/2) has 128 independent states. Since supersymmetry implies that if a graviton exists, so must its fermionic partner. This presents a problem, because the total number of fermionic states and bosonic states are not the same, as is also required by supersymmetry. Therefore, there must be eighty-four other bosonic states that can partner with the fermions, which one can think of as making up all the allowed particles of matter in this theory.
Eleven-dimensional supergravity can be thought of, therefore, as an ultimate theory, in which gravity and supersymmetry together determine all the allowed particles. Force and matter are uniquely determined. Of course, once again the astute reader will note that in our fourdimensional universe there are many particles which have nongravitational interactions. Well, it turns out that in ten dimensions—which, as you may recall, happens to be the critical allowed number for dual strings with fermions included—gravity and supersymmetry almost completely constrain everything, but there turns out to be just enough wiggle room to have additional particles and their superpartners, which in fact can have Yang–Mills interactions.
By the early 1980s, therefore, there were numerous independent reasons for serious physicists to actually consider ten or maybe eleven dimensions as real possibilities in theories that might unify gravity and the other interactions in nature. (The independent argument I mentioned earlier—that eleven dimensions might be necessary for a Kaluza-Klein theory incorporating all known forces—was actually derived much later.) The circle was at that point almost complete; just one more ingredient was needed to close it.
Once again, we return to 1974. In that fateful year, two pioneers of dual string models, Joel Scherk and John Schwarz, realized that while these models proved a failure for describing the strong interaction, they had even greater potential. Recall that what dual string models did so well was get rid of pesky apparent infinities in the calculation of processes where particles of higher and higher spin were involved. Remember also that one of the negative features of the dual string models, besides producing incorrect predictions for scattering rates, was that they predicted a number of massless particles that had not yet been seen—in particular, a massless spin two particle.
Scherk and Schwarz argued that dual strings still might be the correct solution, but that perhaps they had been looking at the wrong problem: Maybe the apparently beautiful feature of dual strings could be combined with one of their negative features, not to describe a theory of the strong interaction, but instead to unify gravity and quantum mechanics!
After all, one of the reasons that gravity confounded all attempts to quantize it was that it involved a series of infinities in calculations because of the exchange of a massless spin two particle, the graviton. Here, string theory not only provided a possible way to remove such infinities, but also automatically predicted the existence of a particle with precisely the properties of a graviton. Indeed, as Richard Feynman had first demonstrated, any relativistic theory involving the exchange of a massless spin two particle could be shown to reproduce precisely Einstein’s equations of general relativity.
Moreover, if dual strings were instead to be viewed as models of quantum gravity, then one more of those notorious warts in the theory could be turned into a beauty mark. Remember that dual strings require higher dimensions to make sense—either twenty-six or ten, depending upon the type of model. As applied to a theory of the strong interaction, this strained the bounds of credibility. However, as we have seen, ever since the time of Kaluza and Klein, efforts to unify gravity and other forces had focused on the possible existence of extra dimensions. In this sense, Scherk and Schwarz could claim they were following a noble tradition, rather than heading down a blind alley.
So it was that by 1981 all the independent ingredients were now in the air: GUTs, strings, supersymmetry, and a newfound desire to unify all the forces in nature. It would take some years, and a few more miracles, before many people other than Scherk (who sadly died in 1980), Schwarz, and a few other diehards would join in the harvest, but the seeds had been planted. A growing group of physicists began to seriously believe that our four-dimensional universe really might be just the tip of a cosmic iceberg, with six or seven hidden dimensions lying, literally, just beneath the surface. The new love affair with extra dimensions had begun.
C H A P T E R 1 4
SUPER TIMES FOR THE SUPERWORLD
If it is possible that there could be regions with other dimensions, it is very likely that God has somewhere brought them into being.
—Immanuel Kant
The year in which many in the particle physics community first experienced a “conversion” was a full decade after the apparent 1974 demise of dual strings—and, perhaps appropriately, a century after the publication of Edwin Abbott’s Flatland. The twentieth century had brought more change in our technology and our fundamental understanding of the universe than anyone could have imagined in 1884. Yet at the beginning of the twenty-first century our fascination with hidden extra dimensions has, if anything, become even stronger, in large part because of the remarkable resurrection of an idea left for dead.
The road from Yang-Mills theories in 1954 to the proposal that strings might be a theory of gravity in the 1970s to the rise of supersymmetry in the early 1980s was, as I have described, a long and winding one. Most of all, it was not a road from which the destination was clearly visible on the horizon. Many different aspects of the problem were being explored independently by separate individuals and groups, and it was certainly not at all obvious in advance, in spite of the natural way in which gravity appeared to be embeddable in string theory, that much would amount from this effort.
First, as the saying goes, “Once bitten, twice shy.” Many physicists had already seen how dual strings, the dominant fad of the late 1960s because of their great potential to resolve apparent mathematical inconsistencies of the strong interaction, had in fact been almost completely off the mark. Given this, it was understandable that they would be hesitant to embrace the theory again, even when applied in a different context. In the second place, dual strings still suffered from embarrassing problems in 1974. While the theory might predict a graviton, it still also appeared to predict a tachyon, for example. And finally, no one had yet shown that it would produce fully consistent quantum mechanical predictions for either gravity or other forces in nature. And of course, there was still the question of those pesky extra dimensions.
What is remarkable is that, as we have seen, piece by piece, different components seemed to fall into place to make the theory less unattractive and, at the same time, less removed from the rest of particle physics. Supersymmetry seemed to be needed once one put fermions on strings. GUTs suggested that the goal of unification itself was worth exploring, and then supersymmetry again seemed to offer the most attractive, and viable, scenarios for GUTs. Finally, applying supersymmetry to gravity seemed to once again suggest that extra dimensions might be called for. Still, even with this growing level of attraction, string theories needed serious work to resolve their outstanding issues, which required the dedicated efforts of a small cadre of individuals, two of whom we have already encountered: Joel Scherk and John Schwarz.
John Schwarz appeared twice in the previous chapter: once associated with the effort to put fermion modes on strings, and once with the initial proposal (along with Scherk), suggesting that strings might yield a quantum theory of gravity. But his role will be even more significant in what follows. For a full decade during which much of the rest of the community was focused elsewhere, Schwarz and various collaborators—notably Joel Scherk, who tragically died before string theories truly achieved wide recognition—continued to do work on the theory, convinced that it must have something to do with nature. I have known John Schwarz for over twenty years, and I am hard pressed to think of a time when he wasn’t smili
ng, even when I was disagreeing with him. An indefatigably cheerful individual, John always seems to be optimistic. I believe, in fact, that his temperament has been an essential part of his ultimate success. Were this not the case, it is hard to imagine that he would have kept plugging away on what was apparently such a long shot. From 1974 until 1984 he and other string devotees labored in almost complete isolation on a model in which, frankly, almost no one other than they was interested. Without unflagging optimism they might have given up.