The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next

by Lee Smolin

  “Doubly special relativity” is a stupid name, but it has stuck. The idea is an elegant one, by now much studied and discussed. We don’t know whether it describes nature, but we know enough about it to know that it could.

  The first responses to DSR were not encouraging. Some people said it was inconsistent; others said it was nothing more than a very complicated way of writing Einstein’s special relativity theory. A few people made both criticisms.

  We answered the second criticism by showing that the theory makes predictions different from those made by special relativity. A key role in these discussions was played by a highly cultured fan of heavy-metal music named Jerzy Kowalski-Glikman, from Warsaw. (Perhaps only a European could truly be both.) I believe he was the first person to really comprehend what Giovanni Amelino-Camelia was saying; I certainly understood his papers, which were short and crystal clear, before I understood Giovanni’s, which were long, printed in a small font, and full of asides and details. Jerzy found several of the important consequences of doubly special relativity, and it was he who straightened out the relationship between our efforts and the earlier mathematical work of his Polish colleagues.

  A watershed in my understanding of DSR and how the various approaches to it were connected was a discussion we had one afternoon at my girlfriend’s house in Toronto. Giovanni, Jerzy, João, and I had squeezed ourselves around a small table in her narrow dining room in an attempt to get to the bottom of our disagreements and misunderstandings. Jerzy insisted quietly that if anything was to make sense, it had to fit into a consistent mathematical structure, which for him meant the noncommutative geometries that he and his Polish colleagues had studied. João said that everything to do with physics could be understood without the fancy mathematics. Giovanni argued that it was easy to talk nonsense about these theories if you weren’t careful about which mathematical expressions corresponded to things that could be measured. At some point—I don’t recall the particular comment that set it off—Giovanni seized the formidable bread knife and howled, “If what you are saying is right, I slit my throat. Now!”

  We stared at him, and after a moment’s shocked silence, we collapsed laughing, and so did he. Only then were we each ready to start listening to what the others were saying.

  In fact, there are different versions of DSR, which give different predictions. In some, there is an energy that cannot be exceeded, analogous to the maximal speed of light. In others, there is no maximal energy but there is a maximal momentum. This is unfortunate, as it lessens the predictive power of the theory, but it doesn’t seem to take away from the theory’s consistency, so it’s something we have to live with.

  The consistency of DSR was shown by demonstrating that there is a possible universe in which it would be true. The possible universe is like our own, with one difference, which is that space has only two dimensions. It was discovered in the 1980s that quantum gravity can be precisely defined in a world with only two spatial dimensions. We call this 2 + 1 quantum gravity, for two dimensions of space and one of time. Moreover, if there is no matter, the theory can be exactly solved—that is, one can find exact mathematical expressions that answer any question that can be asked about the world the theory describes.

  It turns out that DSR is true in any world with two dimensions of space, quantum gravity, and matter. The particular form of DSR that is realized is the form originally discovered by Giovanni. When Jerzy and I looked back at the literature, we saw that several people had found features of this two-dimensional world that were aspects of DSR, but they had done so before the concept of DSR had been invented. Excited, we described this to Laurent Freidel, a colleague at Perimeter from France who works on quantum gravity. He told us that he not only already knew that but had tried to tell us about it earlier. I’m sure that’s true. In discussion, Friedel has more energy than I do, and I usually fail to understand what he is saying, to which he responds by talking faster and louder. In any case, we wrote a paper together that explained why DSR must be true of universes with two dimensions of space.4

  Sometime after that, Friedel, collaborating with Etera Livine, a French Tahitian postdoc at Perimeter, showed in detail how DSR works out in the theory of 2 + 1 dimensional gravity with matter.5 These are important results, because the fact that there is a model of a possible world where DSR is true guarantees the consistency of the theory.

  There was one more problem that had to be solved before DSR could be considered a viable theory. As noted, in many versions there is a maximal energy that a particle can have, which is usually taken to be the Planck energy. This is no problem experimentally, because the most energy that has been observed is that of the protons in the AGASA cosmic-ray detector, which is about a billionth of this maximum.

  But at first glance, it seems that the bound should apply to any sort of body: Not just electrons or protons, but dogs, stars, and soccer balls should all have an energy less than the maximum. This clearly contradicts nature, because any system with more than 1019 protons has more energy than the Planck mass. Dogs have about 1025 protons, stars even more. We call this the soccer-ball problem.

  The soccer-ball problem exists in a two-dimensional world, but there is no need to solve it there, since we don’t do experiments in that world. It is simply true, in that world, that any object has an energy of less than the Planck energy, no matter how many particles it’s composed of.

  There is a natural solution to the soccer-ball problem that might hold in our world of three spatial dimensions. João and I proposed this solution early on. The idea is that a body has a maximum energy that is one Planck energy for each proton it contains. Thus, a soccer ball, with about 1025 protons, cannot have an energy of more than 1025 Planck energies. There is, then, no problem with observation.

  We could see that this solution would work, but we did not know why it had to be true. An explanation was recently given by Etera Livine and Florian Girelli, another Perimeter postdoc from France. They found a marvelous way to reformulate the theory so that this solution pops out.6 Now that the soccer-ball problem has been solved, there is no obstacle I know of to DSR being true of our world. It may well be confirmed by Auger and GLAST observations made over the next few years; if not, it will at least be shown to be false, which means that DSR is a real scientific theory.

  We can now return to the question of what the implications would be for different theories of quantum gravity if special relativity broke down. We have seen that such a breakdown can mean two different things, depending on what the experiments tell us. Special relativity could break down completely at this scale, which would mean there really is an absolute distinction between motion and rest. Or special relativity could be preserved but deepened, as in DSR.

  Would string theory survive either change? Certainly all known string theories would be proved false, since they depend so heavily on special relativity holding. But might there still be a version of string theory that could be consistent with either type of breakdown? Several string theorists have insisted to me that even if special relativity were seen to break down or be modified, there might someday be invented a form of string theory that could accommodate whatever the experiments see. They’re possibly right. String theory has, as noted, many fields that are not observed. There are a lot of ways to change the background of string theory so that there is a preferred state of rest, so that the relativity of motion is wrong. Perhaps in this way a version of string theory could be engineered that agreed with experiment.

  What about DSR? Could there be a version of string theory consistent with it? As of this writing, João Magueijo and I are the only people who have investigated this question, and the evidence we found was mixed. We were able to construct a string theory that satisfied some tests for consistency, but we didn’t succeed in finding a clear answer with respect to other tests.

  So, while all the known versions of string theory are consistent with special relativity, it is also the case that if special relativity proves f
lawed, string theorists might be able to accommodate such a discovery. What puzzles me is why string theorists think this helps their cause. To me, it’s more an indication that string theory is unable to make any predictions because it is no more than a collection of theories, one for each of a vast number of possible backgrounds. The question at issue in the GLAST and Auger observations is the symmetry of space and time. In a background-dependent theory, this is decided by the choice of background. As long as a theory allows it, you can get any answer you need to get by choosing an appropriate background. This is very different from making a prediction.

  What about other approaches to quantum gravity? Have any predicted a breakdown of special relativity? In a background-independent theory, the situation is very different, because the geometry of spacetime is not specified by choosing the background. That geometry must emerge as a consequence of solving the theory. A background-independent approach to quantum gravity must make a genuine prediction about the symmetry of space and time.

  As I discussed earlier, if the world had two dimensions of space, we know the answer. There is no freedom; the calculations show that particles behave according to DSR. Might the same be true in the real world, with three dimensions of space? My intuition is that it would, and we have results in loop quantum gravity that provide evidence, but not yet proof, for this idea. My fondest hope is that this question can be settled quickly, before the observations tell us what is true. It would be wonderful to get a real prediction out of a quantum theory of gravity and then have it shown to be false by an unambiguous observation. The only thing better would be if experiment confirmed the prediction. Either way, we would be doing real science.

  15

  Physics After String Theory

  IN THE LAST two chapters, we saw that there is reason to expect dramatic progress in the search for the laws of nature. There are hints that surprising experimental discoveries may be around the corner. And a far-reaching extension of relativity theory offers predictions for experiments in progress. Whether doubly special relativity is right or not, it is real science, because experiments now under way will either confirm or refute its main predictions.

  The theorists and experimentalists whose work I described in the last two chapters have already inaugurated the post-string era in fundamental physics. In this chapter, I will take you on a tour of this new world, highlighting the most promising ideas and developments. Looking beyond string theory, we find a healthy resurgence of fundamental theory done the old-fashioned way—through hard, concentrated thought about basic questions, mindful of developments in both mathematics and experimental physics. In all the frontier fields—quantum gravity, foundations of quantum physics, elementary-particle physics, and cosmology—bold new ideas are evolving in tandem with fascinating new experiments. These initiatives have to be nourished or they’ll die on the vine, but they show great promise.

  Let us start with a field in which we are seeing rapid progress: approaches to quantum gravity that embrace rather than evade Einstein’s great discovery that the geometry of spacetime is dynamical and contingent.

  As I have emphasized several times, it is not enough to have a theory with gravitons made from strings wiggling in space. We need a theory about what makes up space, a background-independent theory. As described earlier, the success of general relativity demonstrates that the geometry of space is not fixed. It is dynamical and it evolves in time. This is a basic discovery that cannot be reversed, so any further theory must incorporate it. String theory does not, so if string theory is valid, there must lie behind it a more fundamental theory—one that is background-independent. In other words, whether string theory is valid or not, we still have to discover a background-independent theory of quantum gravity.

  Luckily, thanks to work over the last twenty years, we know a lot about how to make such a theory. The field of background-independent approaches to quantum gravity took off in 1986, just two years after the first string theory revolution. The catalyst was the publication by the theoretical physicist Abhay Ashtekar, then at Syracuse University, of a reformulation of general relativity that made the equations much simpler.1 Interestingly enough, it did so by expressing Einstein’s theory in a form very close to that of the gauge theories—the theories that underlie the standard model of particle physics.

  Unfortunately, most string theorists have paid no attention to the remarkable progress made in the field of quantum gravity these last twenty years, so the two fields have developed separately. This lack of communication may seem strange to an outsider. It certainly seems strange to me, which is why I have done my best to reverse it by arguing to each community the merits of the other. But I can’t say I’ve had much success. The failure to get people who work on the same problem from different perspectives to communicate with each other is part of what led me to believe that physics was in crisis—and to think hard about how to rescue it.

  The whole atmosphere of the field of quantum gravity is different from that of string theory. There are no grand theories, no fads or fashions. There are just a few very good people working hard on several closely related ideas. There are several directions being explored, but there are also some unifying ideas that give the field an overall coherence.

  The main unifying idea is simple to state: Don’t start with space, or anything moving in space. Start with something that is purely quantum-mechanical and has, instead of space, some kind of purely quantum structure. If the theory is right, then space must emerge, representing some average properties of the structure—in the same sense that temperature emerges as a representation of the average motion of atoms.

  Thus many quantum-gravity theorists believe there is a deeper level of reality, where space does not exist (this is taking background independence to its logical extreme). Since string theory requires the existence of a background-independent theory to make sense, many string theorists have indicated that they agree. In a certain limited sense, if the strong form of the Maldacena conjecture (see chapter 9) turns out to be true, a nine-dimensional geometry will emerge out of a fixed three-dimensional geometry. It is thus not surprising to hear Edward Witten say, as he did in a recent talk at the Kavli Institute for Theoretical Physics at UC Santa Barbara, that “most string theorists suspect that spacetime is an ‘emergent phenomenon,’ in the language of condensed matter physics.”2

  Some string theorists have finally begun to appreciate this point, and one can only hope they will follow up by studying the concrete results that have already been obtained. But in fact, most people in quantum gravity have in mind something more radical than the Maldacena conjecture.

  The starting point is nothing like geometry. What many of us in quantum gravity mean when we say that space is emergent is that the continuum of space is an illusion. Just as the apparent smoothness of water or silk hides the fact that matter is made of discrete atoms, we suspect that the smoothness of space is not real and that space emerges as an approximation of something consisting of building blocks that we can count. In some approaches, it is just assumed that space is made of discrete “atoms”; in others, this assumption is rigorously derived by combining the principles of general relativity and quantum theory.

  Another unifying idea is the importance of causality. In classical general relativity, the spacetime geometry tells light rays how to propagate. Since nothing can travel faster than light, once you know how light propagates, you can determine which events a particular event might have caused. Given two things that happen, the first can be the cause of the second only if a particle has propagated from the first to the second going at or less than the speed of light. Thus, the spacetime geometry contains information about which events cause which other events. This is referred to as the causal structure of a spacetime.

  It is not only the case that the spacetime geometry determines what the causal relations are. This can be turned around: Causal relations can determine the spacetime geometry, because most of the information you need to define th
e geometry of spacetime is fixed, if you know how light travels.

  It’s easy to talk about space or spacetime emerging from something more fundamental, but those who have tried to develop the idea have found it difficult to realize in practice. Indeed, several early approaches failed. We now believe they failed because they ignored the role that causality plays in spacetime. These days, many of us working on quantum gravity believe that causality itself is fundamental—and is thus meaningful even at a level where the notion of space has disappeared.3

  The most successful approaches to quantum gravity to date combine these three basic ideas: that space is emergent, that the more fundamental description is discrete, and that this description involves causality in a fundamental way.

  The current study of quantum gravity is in some respects analogous to physics one hundred years ago, when people believed in atoms but didn’t know the details of atomic structure. But despite this ignorance, Ludwig Boltzmann, Einstein, and others could understand quite a lot about matter using only the fact that it was made of atoms. Knowing nothing more than the approximate size of an atom, they were even able to make predictions of observable effects. Similarly, we have been able to derive important results from simple models based only on the three principles of emergence, discreteness, and causality. Given our ignorance about the details, these models make the simplest possible assumptions about the discrete units of spacetime and then see what can come of them. The most successful of these models was invented by Renate Loll and Jan Ambjørn and is called causal dynamical triangulations.4 This is perhaps too technical a name for an approach with a very simple strategy, which is to represent the basic causal processes by simple building blocks, which indeed look like the blocks that children play with (see Fig. 14). It might be called the Buckminster Fuller approach. The basic idea is that a spacetime geometry is made by piling up a large number of blocks, each of which represents a simple causal process. There are a few simple rules that govern how the blocks can be piled up and a simple formula that gives the quantum-mechanical probability for each such model of a quantum space-time.