by Lee Smolin
As a consequence, we can keep the large ratios in the standard model, but to do so we have to pick the constants precisely. The larger the ratios we want the actual masses to have, the more finely we theorists have to tune the intrinsic masses (the masses absent quantum effects) to keep them apart. Just how finely depends on the kinds of particles involved.
The masses of the gauge bosons are not much of a problem; the symmetry basically prevents the rubber bands from pulling on their masses. And both before and after quantum effects are taken into account, a photon, which is the boson that carries the electromagnetic field, has no mass at all, so it is not a problem either. Nor are the constituents of matter, the quarks and the leptons; the parts of their masses that come from quantum effects are proportional to their intrinsic masses. If the intrinsic masses are small, so are the total masses. We say, therefore, that the masses of the gauge bosons and the fermions are protected.
The problem lies with the unprotected particles, which in the standard model of particle physics means the Higgs and the Higgs alone. It turns out that to protect the mass of the Higgs from being pulled up to the Planck mass, we have to tune the constants of the standard model to the amazing precision of thirty-two decimal places. Any inaccuracy in any one of those thirty-two decimal places and the Higgs boson ends up much heavier than it is predicted to be.
The challenge is then to tame the Higgs—to bring it down to size, so to speak. Many of the big ideas that particle physicists have explored since 1975 aim to do just that.
One way to tame the Higgs is to propose that it is not an elementary particle at all. If it were made of particles that behaved less wildly, the problem could be eliminated There are several proposals for what the Higgs boson might be made of. The most elegant and sparse theory hypothesizes that Higgs bosons are bound states of very heavy quarks or leptons. Nothing new is added at all—no new particles and no parameters to tune. The theory just posits that heavy particles stick together in new ways. The only problem with this kind of theory is that it is hard to do the calculations required to check it and work out the consequences. It was beyond our technology to do so when first proposed in the 1960s, and it still is.
The next-most-elegant hypothesis is that the Higgs boson is made up of a new kind of quark, different from those that make up protons and neutrons. Because this seemed at first a “technical” solution to the problem, these were called techniquarks. They are bound together by a new kind of force, similar to the strong nuclear force that binds quarks into protons and neutrons. Since the force in quantum chromodynamics is sometimes called “color,” the new force is called, of course, Technicolor.
This idea is more amenable to calculation. The problem is that it is hard to get this theory to agree with all aspects of the observations. But it’s not impossible, since there are many variants. Most have been ruled out; a few remain viable.
A third option is to make all the elementary particles into composite particles. This idea was pursued by a few people in the late 1970s. It was a natural thing to try: If protons and neutrons are made of quarks, why stop there? Perhaps there is a further level of structure, where quarks, electrons, neutrinos, and perhaps even the Higgs and the gauge bosons are seen to be made of particles that are even more fundamental and that we might call preons. Such theories worked very elegantly. Experiment had by then given us evidence for the forty-five fundamental fermions, and all could be put together from combinations of just two kinds of preons.
Moreover, these preon models explained some features observed in nature but unexplained in the standard model. For example, the quarks have two properties—color and charge—that seem unrelated. Each kind of quark comes in three versions called colors. This triplication provides the symmetry required for the gauge theory. But why three colors? Why not two, or four? Each quark also has an electric charge, and these come in units that are ⅓ and ⅔ of the electron’s charge. The number 3 occurs in each case, which suggests that these two properties, color and charge, could have a common origin. Neither the standard model nor, to my knowledge, string theory addresses this coincidence, but it is explained very simply by the preon model.
Unfortunately, there were major questions that the preon theories were not able to answer. These have to do with the unknown force that must bind the preons together into the particles we observe. The challenge was to keep the observed particles as small as they are while keeping them very light. Because preon theorists couldn’t solve this problem, preon models were dead by 1980. I’ve talked recently with well-known physicists who got their PhDs after this and have never even heard of them.
So, altogether, the attempts to make the Higgs boson a composite were not convincing. It seemed for a time that we theorists were running out of options. If the Higgs boson is elementary, then how can its properties be tamed?
One way to limit the freedom of a particle is to tie its behavior to another particle whose behavior is constrained. We know that the gauge bosons and the fermions are protected; their masses do not behave wildly. Could there be a symmetry that ties the Higgs to a particle whose mass is protected? If we could do that, perhaps the Higgs would be tamed at last. The only symmetry known to do this is supersymmetry, because supersymmetry relates fermions to bosons; hence, in a supersymmetric theory there will be a fermion that partners with the Higgs, called the Higgsino. (In supersymmetry-theory convention, the superpartners of fermions begin with an “s,” like the selectron, while the superpartners of bosons end in “ino.”) Because it is a fermion, the mass of the Higgsino will be protected from quantum weight gain. Well, supersymmetry tells us that two partners have the same mass. So the mass of the Higgs must be protected too.
This idea might well explain why the Higgs mass is low compared to the Planck mass. As stated, this idea is certainly elegant—but in practice it is complicated.
First of all, a theory cannot be partly supersymmetric. If one particle has a superpartner, they all must. Thus, each quark comes with a bosonic partner, a squark. The photon is partnered with a new fermion, the photino. The interactions are then tuned so that if all quarks are replaced by squarks at the same time as we replace all photons by photinos, the probabilities of the various possible outcomes are unchanged.
Of course, there is a simpler possibility. Couldn’t two particles that we have already observed be partnered? Perhaps the photon and the neutrino go together? Or the Higgs and the electron? The discovery of a new relationship among known particles would certainly be elegant—and convincing.
Unfortunately, no one has ever successfully postulated a supersymmetry holding between two known particles. Instead, in all the supersymmetric theories the numbers of particles are at least doubled. A new superpartner is simply postulated to go along with each known particle. Not only are there squarks and sleptons and photinos, there are also sneutrinos to partner the neutrinos, Higgsinos with the Higgs, and gravitinos to go with the gravitons. Two by two, a regular Noah’s ark of particles. Sooner or later, tangled in the web of new snames and naminos, you begin to feel like Sbozo the clown. Or Bozo the clownino. Or swhatever.
For better or worse, nature is not like this. As noted, no experiment has ever produced evidence for a selectron. There appear to be, so far, no squarks, no sleptons, and no sneutrinos. The world contains huge numbers of photons (more than a billion for every proton), but no one has ever seen even a single photino.
The solution to this is to posit that supersymmetry is spontaneously broken. We discussed in chapter 4 how a symmetry is spontaneously broken. This spontaneous breaking can be extended to supersymmetry. Theories can be constructed that describe worlds in which the forces are supersymmetric but where those laws are cleverly adjusted so that the lowest energy state—that is, the state at which symmetry disappears—is not supersymmetric. As a result, the supersymmetric partner of a particle need not have the same mass that the particle has.
This makes for an ugly theory. To break the symmetry, we have to add still
more particles, analogous to the Higgs. They also need superpartners. There are still more free constants, which can be adjusted to describe their properties. All the constants of the theory then have to be adjusted so that all of these new particles are too heavy to be observed.
Doing this to the standard model of elementary-particle physics, with no additional assumptions, results in a contraption called the minimally supersymmetric standard model, or MSSM. As noted in chapter 1, the original standard model has about 20 free constants we have to adjust by hand to get predictions that agree with experiment. The MSSM adds 105 more free constants. The theorist is at liberty to adjust them all to ensure that the theory agrees with experiments. If this theory is right, then God is a techno-geek. He is the kind of guy or gal who likes a music system with as many dials as possible or a sailboat with 16 different lines to adjust the shape of each sail.
Of course, nature may be like this. The theory does have the potential to solve the fine-tuning problem. So what you get for increasing the number of dials from 20 to 125 is that none of the new dials have to be as finely tuned as the old dials. Still, with so many dials to adjust, the theory is difficult for experimentalists to prove or disprove.
There are many settings of the dials for which the supersymmetry is broken and each particle has a mass different from that of its superpartner. To hide all the missing better halves, we have to tune the dials in such a way that the missing particles all end up with a lot more mass than the ones we see. You have to get this right, for if the theory predicted that the squarks were lighter than the quarks, we would be in trouble. Not to worry. There turn out to be many different ways to tune the dials to ensure that all the particles we don’t see are so heavy that they’re as yet unseeable.
If the fine-tuning is to be explained, then the theory has to give an explanation for why the Higgs boson has the large mass we think it has. As noted, there is not an exact prediction for the Higgs mass even in the standard model, but it has to be more than about 120 times the mass of a proton. To predict this, a supersymmetric theory must be tuned so that at this scale the supersymmetry is restored. This means that the missing superpartners should have masses at about this scale, and if so, the LHC should see them.
Many theorists expect that this is what the LHC will see—lots of new particles that can be interpreted as missing superpartners. If the LHC does so, it certainly will be a triumph for the last thirty years of theoretical physics. However, I remind you that there are no clear predictions. Even if the MSSM is true, there are many different ways to tune its 125 parameters to agree with what is known at present. These lead to at least a dozen very distinct scenarios, which make quite different predictions about exactly what the LHC will see.
There are further worries. Suppose the LHC produces a new particle. Given that the supersymmetric theory comes in many different scenarios, it is possible that even if supersymmetry is wrong, it could still be adjusted to agree with the first observations from the LHC. To confirm supersymmetry, much more is needed. We’ll have to discover many new particles and explain them. And they may not all be superpartners of particles we know about. A new particle could be a superpartner of yet another new particle, still unseen.
The only unimpeachable way to prove supersymmetry true will be to show that there really is a symmetry—which is to say that the probabilities for the various possible outcomes of experiments don’t change (or change in certain very restricted ways) when we substitute one particle for its superpartner. But this is something that will not be easy for the LHC, at least initially. So even in the best of circumstances, it will be many more years before we know whether supersymmetry is the right explanation for the fine-tuning problem.
Meanwhile, a great many theorists appear to believe in supersymmetry. And there are a few good reasons for thinking it is an improvement on older ideas of unification. First, the Higgs boson, if not pointlike, does not appear to be very large. This favors supersymmetry while ruling out some (though not all) Technicolor theories. There is also an argument that comes from the idea of grand unification. As we discussed earlier, experiments done at the unification scale should not be able to distinguish between electromagnetism and the nuclear forces. The standard model predicts this kind of unified scale but requires slight adjustments. The supersymmetric version gives unification more directly.
Supersymmetry is certainly a very compelling theoretical idea. The idea of a unification of forces and matter offers a resolution of the deepest duality in fundamental physics. No wonder so many theorists cannot imagine that the world is not supersymmetric.
At the same time, some physicists do worry that supersymmetry, if real, should have already been seen in experiment. Here is a fairly typical quote, from an introduction to a recent paper: “Another problem comes from the fact that LEP II [the Large Electron-Positron accelerator, also at CERN] did not discover any superparticles or the Higgs boson.”1 Paul Frampton, a distinguished theorist at the University of North Carolina, recently wrote me that,
One general observation I have made over the last decade or more is that the majority of researchers (there are a few exceptions) working on the phenomenology of TeV scale supersymmetry breaking think that the probability that TeV scale supersymmetry will show up in experiment is much less than 50 percent, an estimate of 5 percent being quite typical.2
My own guess, for what it’s worth, is that (at least in the form so far studied) supersymmetry will not explain the observations at the LHC. In any case, supersymmetry is decidable by experiment, and whatever our aesthetic preferences, we will all be thrilled to have an answer to the question of whether or not it is a true picture of nature.
But even if supersymmetry were detected, it would not in itself be a solution to any of the five big problems I listed in chapter 1. The constants of the standard model would not be explained, because the MSSM has many more free constants. The possible choices for a quantum theory of gravity would not be narrowed, because the leading theories are all consistent with the world’s being supersymmetric. It may be that the dark matter is made up of superpartners, but we would need this to be confirmed directly.
The reason for this larger inadequacy is that while supersymmetric theories have much more symmetry, they are not simpler. They are in fact much more complicated than theories with less symmetry. They do not decrease the number of free constants—they increase them, drastically. And they fail to unify any two things we already know about. Supersymmetry would be absolutely compelling—as compelling as Maxwell’s unification of electricity and magnetism—if it uncovered a deep commonality between two known things. If the photon and electron turned out to be superpartners, say, or even the neutrino and the Higgs, it would be fantastic.
But this is not what any of the supersymmetry theories have done. Instead, they posit a whole new set of particles and make each particle symmetric with either a known particle or another unknown particle. This kind of theoretical success is far too easy. To invent a whole new world of the unknown and then make a theory with many parameters—parameters that can be tuned to hide all the new stuff—is not very impressive, even if it’s technically challenging to pull off. It is the kind of theorizing that can’t fail, because any disagreement with present data can be eliminated by tweaking some constants. It can fail only when confronted with experiment.
Of course, none of this means that supersymmetry is not real. It may be, and if it is, there is a chance it will be discovered in the next few years, at the LHC. But the fact that supersymmetry does not do all that we hoped suggests that its proponents are sitting way out on a limb, far from the sturdy trunk of empirical science. Perhaps that is the cost of looking to drill, as Einstein said, where the wood is thin.
6
Quantum Gravity: The Fork in the Road
WHILE MOST physicists were ignoring gravity, a few brave souls in the 1930s began to think about reconciling it with the rapidly developing quantum theory. For more than half a century, no mo
re than a handful of pioneers would work on quantum gravity, and few would pay them any attention. But the problem of quantum gravity could not be ignored forever. Of the five questions I described in the first chapter, it is the one that cannot go unsolved. Unlike the others, it seeks nothing less than the language in which the laws of nature are written. To try to solve any of the other problems without solving this one would be like trying to negotiate a contract in a country without law.
The search for quantum gravity is a true quest. The pioneers were explorers in a new landscape of ideas and possible worlds. Now there are more of us, and some of the landscape has been well mapped. Some trails were explored only to lead to dead ends. And while some are still being blazed and a few are even becoming crowded, we cannot yet say that the problem is solved.
Much of this book was written in 2005, the centenary of Einstein’s first great achievements. The year was full of conferences and events to mark the anniversary. It was as good an excuse as any to draw attention to physics, but it was not without irony. Some of Einstein’s discoveries were so radical that even now they are insufficiently appreciated by many theoretical physicists; chief among these is the understanding he achieved of space and time in general relativity.
The main lesson of general relativity is that the geometry of space is not fixed. It evolves dynamically, changing in time as matter moves about. There are even waves—gravitational waves—that travel through the geometry of space. Until Einstein, the laws of Euclidean geometry we learned in school were seen as eternal laws: It always was and always would be true that the angles of a triangle add up to 180 degrees. But in general relativity the angles of a triangle can add up to anything, because the geometry of space can curve.