by Lee Smolin
Theorists are also busy trying to predict what we might see in the Auger and GLAST experiments, both of which will indicate whether special relativity breaks down at Planck energies. One great advantage of background-independent approaches is their ability to make predictions for such experiments. Is the principle of the relativity of inertial frames preserved or broken? Is it modified, as in DSR theories? As I have emphasized, no background-dependent theory can make a real prediction for these experiments, because the question is already answered by the choice of background. String theory, in particular, assumes that the relativity of inertial frames remains true in the form originally given by Einstein in his special theory of relativity. Only a background-independent approach can make a prediction for the fate of the principles of special relativity, because the properties of classical spacetime emerge as the solution to a dynamical problem.
Loop quantum gravity promises to be able to make a sure prediction. In the models in which space has only two dimensions, it has already done so: It predicts that DSR is right. There are indications that the same prediction holds for our three-dimensional world, but so far there is no convincing proof of this.
What about the other big problems, such as unification of the particles and forces? Until recently, we thought that loop quantum gravity had little to say about problems other than quantum gravity. We could put matter in the theory and the good results would not be changed. If we wanted, we could put in the entire standard model of particle physics—or any other model of particle physics we wanted to study—but we didn’t think loop quantum gravity had anything specific to contribute to the problem of unification. Lately we have realized that we were wrong about this. Loop quantum gravity already has elementary particles in it, and recent results suggest that this is exactly the right particle physics: the standard model.
Last year, Fotini Markopoulou proposed a new way to approach the problem of how the geometry of space could emerge from a more fundamental theory. Markopoulou is the young physicist working on quantum gravity who most often surprises me with unlikely ideas that turn out to be right, and this was one of her best. Rather than asking directly whether or not the geometry of quantum spacetime can emerge as a classical spacetime, she proposed a different approach, based on identifying and studying the motion of particles in quantum geometry. Her idea was that a particle must be some kind of emergent excitation of quantum geometry, traveling through that geometry much as a wave travels through a solid or a liquid. However, in order for the physics we know to be reproduced, these emergent particles have to be describable as pure quantum particles, ignoring the quantum geometry through which they travel.9
Normally when a particle is in interaction with an environment, information about its state dissipates into the environment—we say that it decoheres. It’s difficult to prevent this decoherence from happening; this, by the way, is why it’s hard to make a quantum computer, which depends for its efficacy on a particle’s being in a pure quantum state. The people who make quantum computers have ideas about when a quantum system will stay pure even in contact with an environment. While working with experts in this area, Markopoulou realized that their insights applied to the problem of how a quantum particle could emerge from a quantum spacetime. She pointed out that to draw predictions from theories of quantum gravity, you can identify such a quantum particle and show it moving as if it were in ordinary space. In her analogy, the environment is the quantum spacetime, which, being dynamical, is constantly changing. The quantum particle must move through it as though it were a fixed, nondynamical background.
Using these ideas, Markopoulou and her collaborators could show that some background-independent theories of quantum gravity have emergent particles. But what are these particles? Do they correspond to anything that has been observed?
At first the problem seemed difficult, because the quantum geometries predicted by loop quantum gravity are very complicated. The particle states are associated with graphs drawn in three-dimensional space. The space is a background, but it has no properties except for its topology; all the information about measures of geometry—like lengths, areas, and volumes—come from the graphs. But because the graphs have to be drawn in space, the theory has a lot of extra information in it that seems to have nothing to do with geometry. This is because of the infinite number of ways the edges of a graph can knot, link, and braid in three-dimensional space.
What is the significance of the knotting, linking, and braiding of the graphs? This question has been with us since around 1988. All this time, we had no idea what the knotting, linking, and braiding meant. Markopoulou saw that emergent particles are coded in these topological structures.
Last spring, I happened to see a preprint by a young Australian particle physicist called Sundance O. Bilson-Thompson. In it he presented a simple braiding of ribbons that quite remarkably captured precisely the structure of the preon models of particle physics I discussed in chapter 5. (Recall that these are models positing the hypothetical particles called preons as the fundamental constituents of protons, neutrons, and other particles the standard model deems elementary.) In his model, a preon is a ribbon, and the various kinds of preons correspond to the ribbon being twisted to the left, right, or not at all. Three ribbons can be braided together, and the various ways to do this correspond precisely to the various particles of the standard model.10
As soon as I read the paper, I knew this was the missing idea, because the braids Bilson-Thompson studied could all occur in loop quantum gravity. This meant that the different ways to braid and knot the edges of the graphs in a quantum spacetime must be different kinds of elementary particles. So loop quantum gravity is not just about quantum spacetime—it already has elementary-particle physics in it. And if we could discover Bilson-Thompson’s game working precisely in the theory, it would have the right elementary-particle physics. I asked Markopoulou if his braids could be her coherent excitations. We invited Bilson-Thompson to collaborate with us, and after several false starts we saw that the argument indeed worked all the way through. Making some mild assumptions, we found a preon model describing the simplest of these particle-like states in a class of quantum-gravity theories.11
This result raises many questions, and answering them is now my primary goal. It is too early to tell if it works well enough to give unambiguous predictions for the upcoming experiments at the Large Hadron Collider at CERN. But one thing is clear. String theory is no longer the only approach to quantum gravity that also unifies the elementary particles. Markopoulou’s results suggest that many of the background-independent quantum theories of gravity have elementary particles in them as emergent states. And a given theory does not lead to a vast landscape of possible theories. Rather, it shows promise of leading to unique predictions, which will either be in agreement with experiment or not. Most important, this obviates the need to revise the scientific method by invoking the anthropic principle, as Leonard Susskind and others have advocated (see chapter 11). Science done the old-fashioned way is moving ahead.
Plainly, there are different approaches to the five fundamental problems in physics. The field of fundamental physics beyond string theory is progressing rapidly, and in several directions, including but not limited to causal dynamical triangulations and loop quantum gravity. As in any healthy field of science, there is a lively interaction with both experiment and mathematics. While there aren’t as many people (perhaps two hundred, all told) in these research programs as there are in string theory, it’s still quite a lot of people to be tackling foundational problems on the frontiers of science. The big leaps of the twentieth century were made by far fewer. When it comes to revolutionizing science, what matters is quality of thought, not quantity of true believers.
I want to be clear, though, that there is nothing in this new, post-string atmosphere that excludes the study of string theory per se. The idea it is based on—the duality of fields and strings—is, as I have pointed out, one shared with loop quantum
gravity. What has led to the present crisis in physics is not this core idea but a particular kind of realization of it, worked out in a background-dependent context—a context that ties it to risky proposals such as supersymmetry and higher dimensions. There is no reason why a different approach to string theory—one more in tune with foundational issues like background independence and the problems in quantum theory—might not be part of the final story. But to find this out, string theory needs to be developed in an open atmosphere, in which it is considered as one idea among several, without any presuppositions as to its ultimate success or failure. What the new spirit of physics cannot tolerate is a presumption that one idea has to succeed, whatever the evidence.
While there is today an exciting sense of progress among quantum-gravity theorists, there is also a strong expectation that the road ahead will bring at least a few surprises. Unlike string theorists in the exhilarating days of the two superstring revolutions, few of the people working on quantum gravity believe they have their hands on a final theory. We recognize that the accomplishments of background-independent approaches to quantum gravity are a necessary step in finishing Einstein’s revolution. They show that there can be a consistent mathematical and conceptual language that unifies quantum theory and general relativity. This gives us something string theory does not, which is a possible framework in which to formulate the theory that solves all five of the problems I listed in chapter 1. But we are also fairly sure that we do not yet have all the pieces. Even with the recent successes, no idea yet has that absolute ring of truth.
When you look back at the history of physics, one thing sticks out: When the right theory is finally proposed, it triumphs quickly. The few really good ideas about unification appear in a form that is compelling, simple, and unique; they do not come with a list of options or adjustable features. Newtonian mechanics is defined by three simple laws, Newtonian gravity by a simple formula with one constant. Special relativity was complete on arrival. It may have taken twenty-five years to fully formulate quantum mechanics, but from the beginning it was developed in concert with experiment. Many of the key papers in the subject from 1900 on either explained a recent experimental result or made a definite prediction for an experiment that was shortly done. The same was true of general relativity.
Thus, all the theories that triumphed had consequences for experiment that were simple to work out and could be tested within a few years. This does not mean that the theories could be solved exactly—most theories never are. But it does mean that physical insight led immediately to a prediction of a new physical effect.
Whatever else one says about string theory, loop quantum gravity, and other approaches, they have not delivered on that front. The standard excuse has been that experiments on this scale are impossible to perform—but, as we’ve seen, such is not the case. So there must be another reason. I believe there is something basic we are all missing, some wrong assumption we are all making. If this is so, then we need to isolate the wrong assumption and replace it with a new idea.
What could that wrong assumption be? My guess is that it involves two things: the foundations of quantum mechanics and the nature of time. We have already discussed the first; I find it hopeful that new ideas about quantum mechanics have been proposed recently, motivated by studies of quantum gravity. But I strongly suspect that the key is time. More and more, I have the feeling that quantum theory and general relativity are both deeply wrong about the nature of time. It is not enough to combine them. There is a deeper problem, perhaps going back to the origin of physics.
Around the beginning of the seventeenth century, Descartes and Galileo both made a most wonderful discovery: You could draw a graph, with one axis being space and the other being time. A motion through space then becomes a curve on the graph (see Fig. 17). In this way, time is represented as if it were another dimension of space. Motion is frozen, and a whole history of constant motion and change is presented to us as something static and unchanging. If I had to guess (and guessing is what I do for a living), this is the scene of the crime.
Fig. 17. Since Descartes and Galileo, a process unfolding in time has been represented as a curve on a graph, with an additional dimension representing time. This “spatialization” of time is useful but may be challenged as representing a static and unchanging world—a frozen, eternal set of mathematical relations.
We have to find a way to unfreeze time—to represent time without turning it into space. I have no idea how to do this. I can’t conceive of a mathematics that doesn’t represent a world as if it were frozen in eternity. It’s terribly hard to represent time, and that’s why there’s a good chance that this representation is the missing piece.
One thing is clear: I can’t get anywhere thinking about this kind of problem within the confines of string theory. Since string theory is limited to the description of strings and branes moving in fixed-background spacetime geometries, it offers nothing for someone who wants to break new ground thinking about the nature of time or of quantum theory. Background-independent approaches offer a better starting point, because they have already transcended the classical picture of space and time. And they are simple to define and easy to play with. There’s an added bonus, which is that the mathematics involved is close to the one a few mathematicians have used to explore radical ideas about the nature of time—an area of logic called topos theory.
One thing I do know about the question of how to represent time without its turning into a dimension of space is that it comes up in other fields, from theoretical biology to computer science to law. In an effort to shake free some new ideas, the philosopher Roberto Mangabeira Unger and I recently organized a small workshop at Perimeter bringing together visionaries in each of these fields to talk about time. Those two days were the most exciting I’ve spent in years.12
I won’t say more about this, because I want to move on to a different question. Suppose an intellectually ambitious young person with an original and impatient mind wants to think deeply about the five great questions. Given our failure to definitively solve any of them, I can’t imagine why such a person would want to be limited to working in any of the current research programs. Clearly, if string theory or loop quantum gravity by themselves were the answer, we would know it by now. They may be starting points, they may be parts of the answer, they may contain necessary lessons. But the right theory must contain new elements, which our ambitious young person is perhaps uniquely qualified to search for.
What has my generation bequeathed to these young scientists? Ideas and techniques they may or may not want to use, together with a cautionary tale of partial success in several directions, resulting in a general failure to finish the job that Einstein started a hundred years ago. The worst thing we could do would be to hold them back by insisting that they work on our ideas. So the question for the last part of the book is a question I ask myself every morning: Are we doing all we can to support and encourage young scientists—and, by virtue of this, ourselves—to transcend what we have done these last thirty years and find the true theory that solves the five great problems of physics?
IV
LEARNING FROM EXPERIENCE
16
How Do You Fight Sociology?
IN THIS LAST PART of the book, I want to return to the questions I raised in the Introduction. Why, despite so much effort by thousands of the most talented and well-trained scientists, has fundamental physics made so little definitive progress in the last twenty-five years? And given that there are promising new directions, what can we do to ensure that the rate of progress is restored to what it was for two centuries before 1980?
One way to describe the trouble with physics is to say that there is no work in theoretical elementary-particle physics over the last three decades that is a sure bet for a Nobel Prize. The reason is that a condition of the prize is that the advance has been checked by experiment. Of course, ideas such as supersymmetry or inflation may be shown by experiment to be true, a
nd if they are, their inventors will deserve Nobel Prizes. But we cannot now say that a discovery of any hypothesis about physics beyond the standard model of particle physics is assured.
The situation was very different when I entered graduate school in 1976. It was abundantly clear that the standard model, which had been put in final form only three years earlier, was a definitive advance. There had already been substantial experimental confirmation of it and more was on the way. There was no serious doubt that its inventors would sooner or later be awarded Nobel Prizes for their work. And, in time, they were.
Nothing like that is true now. There have been many prizes awarded for work in theoretical particle physics in the last twenty-five years, but not the Nobel. The Nobel is not given for being smart or successful; it is given for being right.
This is not to deny that there have been great technical advances in each of the research programs. It is said that there are more scientists working now than in the whole history of science. This is certainly true of physics; there may be more professors of physics in a large university department today than there were a hundred years ago in the whole of Europe, where almost all the advances were being made. All these people are working, and much of the work is technically very sophisticated. Moreover, the technical level of young theoretical physicists is much higher today than it was a generation or two ago. There is more for young people to master, and they somehow manage to do it.
Still, if we judge by the standards of the two hundred years before 1980, it does appear that the pace of irreversible progress in elementary-particle theory has slowed.