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

by Lee Smolin

  Could any experiment see the effect of a breakdown in the structure of space and time at the Planck scale? Given modern electronics, very tiny differences in the arrival times of photons can be detected, but are modern electronics good enough to measure the even more minuscule effects of quantum gravity? For decades, we theorists have been teaching that the Planck scale is so small that no currently feasible experiment could detect it. Just as most physics professors a hundred years ago held that atoms were too small to see, we have told this lie in countless papers and lectures. And it is a lie.

  Remarkably, it took until the mid 1990s for us to realize that we could indeed probe the Planck scale. As sometimes happens, a few people recognized it but were in effect shouted down when they tried to publish their ideas. One was the Spanish physicist Luis Gonzalez-Mestres, of the Centre National de la Recherche Scientifique, in Paris. A discovery like this may be made several times independently until someone brings the point to the attention of the community of specialists in a way that sticks. In this case, it was Giovanni Amelino-Camelia, of the University of Rome. Now in his early forties, Amelino-Camelia is driven, focused, and passionate about physics, with all the charm and fire one associates with a southern Italian. The quantum-gravity community is lucky to count him as a member.

  When Amelino-Camelia was a postdoc at Oxford, he set himself the task of looking for a way to observe physics at the Planck scale. This seemed a completely crazy ambition at the time, but he challenged himself to prove common knowledge wrong and come up with some way to do it. He was inspired by the tests of proton decay. Proton decay (see chapter 4) was predicted to be an extremely rare event, but if you got enough protons together, you could expect to see it happen. The huge number of protons would function as an amplifier, making visible something extremely tiny and rare. The question Amelino-Camelia asked himself was whether any such amplifier could enable him to detect phenomena at the Planck scale.

  We have already noted two examples of useful amplification: cosmic rays and photons from gamma-ray bursts. In both cases, we use the universe itself as an amplifier. Its very size amplifies the probability of extremely rare events, and the enormous amount of time that light takes to travel across it can amplify tiny effects. That these kinds of experiments could theoretically signal a breakdown of special relativity had been pointed out before. What Amelino-Camelia discovered was that we could actually devise experiments to probe the Planck scale, and hence quantum gravity.

  A typical change in the speed of a photon due to quantum gravity would be incredibly tiny, but the effect is greatly amplified by the travel time from the gamma-ray burst, which can be billions of years. Physicists realized a few years ago, using rough estimates of the size of quantum gravity effects, that the time between the arrival of photons of different energy that had been traveling this long would be about 71,000 of a second. This is a tiny length of time, but it is well within the range that can be measured with modern electronics. Indeed, the newest gamma-ray detector, called GLAST (for Gamma Ray Large Area Space Telescope), has this kind of sensitivity. It is scheduled to launch in the summer of 2007 and its results are eagerly awaited.

  Since the barrier was first broken by Amelino-Camelia and his collaborators, we have discovered that there are many ways to probe the Planck scale with real experiments. Amelino-Camelia’s crazy question has become a respectable field of science.

  So suppose a new experimental result contradicts special relativity at the Planck scale. What would this tell us about the nature of space and time?

  I mentioned at the beginning of this chapter that there were two possibilities. We have already discussed one, which is that the principle of the relativity of motion is wrong—meaning that we could indeed distinguish absolute motion from absolute rest. This would reverse a principle that has been the linchpin of physics since Galileo. I personally find this possibility abhorrent, but as a scientist I must acknowledge that it is a real possibility. Indeed, if the results of AGASA, the Japanese cosmic-ray experiment, hold up, such a breakdown in special relativity may have already been seen.

  But is this the only possibility? Most physicists would probably say that if photons with different energies travel at different speeds, then special relativity is wrong. I would certainly have said this a decade ago. But I would have been mistaken.

  Einstein’s special theory of relativity is based on two postulates: One is the relativity of motion, and the second is the constancy and universality of the speed of light. Could the first postulate be true and the other false? If that was not possible, Einstein would not have had to make two postulates. But I don’t think many people realized until recently that you could have a consistent theory in which you changed only the second postulate. It turns out that you can, and working this out has been one of the most exciting things I’ve had the good fortune to participate in during my career.

  The new theory is called deformed or doubly special relativity—DSR for short. It came from asking a simple question, which seems to lead to a paradox.

  As noted, the Planck length is believed to be a kind of threshold below which is revealed a new kind of geometry, one that is intrinsically quantum mechanical. Different approaches to quantum gravity agree on one thing: The Planck length is in some sense the size of the smallest thing that can be observed. The question is, will all observers agree on what this shortest length is?

  According to Einstein’s special theory of relativity, different observers disagree on the lengths of moving objects. An observer riding on the meter stick will say it is a meter long. But any observer moving with respect to it will observe it to be shorter. Einstein called this the phenomenon of length contraction.

  But this implies that there cannot be such a thing as a “shortest length.” No matter how short something is, you can make it still shorter by moving relative to it very close to the speed of light. Thus there appears to be a contradiction between the idea of the Planck length and special relativity.

  Now, you might think that anyone professionally involved in the problem of quantum gravity would have stumbled on this contradiction. You might even think that some bright undergraduate in a first-year physics course would have raised the question. After all, each of the brilliant physicists responsible for the most difficult work in string theory and quantum gravity was once a naïve student. Wouldn’t at least a few have seen the problem? But to my knowledge very few did, until recently.

  One who did was Giovanni Amelino-Camelia. At some point in 1999, he came upon the paradox just described, and he solved it. His idea was to extend the reasoning that had led Einstein to special relativity.

  The second postulate of special relativity, which says that the speed of light is universal, appears to be almost contradictory in itself. Why? Consider a single photon, tracked by two observers. Assume that the two observers move with respect to each other. If they measure the speed of that single photon, we would normally expect them to get different answers, because this is the way normal objects behave. If I see a bus pull ahead of me at what looks to me like a speed of 10 kilometers an hour because I am in a car screaming down the highway at 140 kilometers per hour, an observer standing on the side of the road will see the bus moving at 150 km/hour. But if I observe a photon under the same circumstances, special relativity says that the roadside observer will measure the photon to have the same speed that I think it has.

  So why is this not a contradiction? The key is that we do not measure speed directly. Speed is a ratio: It is a certain distance per a certain time. The central realization of Einstein is that different observers measure a photon to have the same speed, even if they are moving with respect to each other, because they measure space and time differently. Their measurements of time and distance vary from each other in such a way that one speed, that of light, is universal.

  But if we can do this for one constant, why not for another? Could we play the trick for distance as well? That is, we understand that, generally, observ
ers measure a moving meter stick to be less than a meter long. This will be true for most lengths, but can we arrange things so that when we finally get all the way down to the Planck length, the effect goes away? This means that if a stick is exactly a Planck-length long, all observers will agree on its length, even if it is moving. Could we then have two universal quantities, a speed and a length?

  Einstein got away with the first trick because nothing can go faster than light. There are two kinds of things in the world—things that go the speed of light and things that go less than the speed of light. If one observer sees something go less than the speed of light, all observers will. And if one observer sees something go exactly the speed of light, all observers will agree about that, too.

  Amelino-Camelia’s idea was to play the same game with length. He proposed modifying the rules by which space and time measurements differ from one observer to another, so that if something is the Planck length, then all observers will agree it is a Planck-length long, and if it is longer than that, all observers will agree about that, too. This scheme can be consistent, because nothing can be smaller than the Planck length, for any observer.

  Amelino-Camelia quickly found that there is a modification of Einstein’s special-relativity equations that realizes this idea. He called it doubly special relativity, because the trick that made relativity special had now been played twice. I had been following his efforts to invent ways to probe the Planck scale, but in 2000, when he circulated a preprint on the idea of doubly special relativity, I didn’t at first understand it.1

  That’s embarrassing enough, but here’s something even more embarrassing. About ten years earlier, I had run into the very same paradox. It arose in work I was doing on a theory of quantum gravity called loop quantum gravity. The details aren’t important—the point is that our calculations in loop quantum gravity appeared to contradict Einstein’s special theory of relativity. Now I understand that those particular calculations actually did contradict Einstein’s special theory. But at the time, that possibility was too scary to contemplate, and after struggling with this, I dropped the whole line of research. Indeed, this was the first in a series of steps that eventually led me to forsake loop quantum gravity and work for a time on string theory.

  But just before I dropped it, I had a thought: Perhaps special relativity could be modified so that all observers, moving or not, agree about what the Planck length is. This was the key idea of doubly special relativity, although I wasn’t imaginative enough to do anything about it. I thought about it for a bit, couldn’t make any sense of it, and then went on to something else. Even seeing Amelino-Camelia’s paper ten years later did not bring it back to me. I had to come to the idea from another direction. At this time, I was a visiting professor at Imperial College in London, and I was getting to know a remarkable scientist there named João Magueijo, a bright young cosmologist from Portugal, about the same age as Giovanni Amelino-Camelia and with an equally intense Latin temperament.

  João Magueijo was known for having a really crazy idea, which was that light traveled faster in the very early universe. This idea makes inflation unnecessary, because it explains how every region of the early universe could have been in causal contact and thus at the same temperature. There would have been no need for an exponential expansion in the earliest moments in order to bring this about.

  That’s nice, but the idea is nuts—really nuts. It disagrees with both special and general relativity. There is no other word for it but “heretical.” However, the British academic world has a soft spot for heretics, and Magueijo was thriving at Imperial College. Had he been in the United States, I doubt he would even have been hired as a postdoc with an idea like that.

  Magueijo had developed his idea with a young professor at Imperial named Andreas Albrecht, who as a graduate student at the University of Pennsylvania had been one of the inventors of inflation. Albrecht had recently left England to move back to America. After I had been at Imperial for a few months, I found Magueijo at my door. He wanted to see whether there was a way to make his idea of a variable-speed-of-light (VSL) cosmology consistent with special and general relativity. Somehow he felt that talking with me could help.

  I didn’t know at the time that this had already been done. Indeed, the whole VSL cosmology had been developed earlier, by that imaginative Toronto physics professor John Moffat. A heretic many times over, Moffat had invented the idea and worked it out in a way that was consistent with both special and general relativity, but his attempts to publish his theory in a scientific journal had met with rejection.

  As João tells the story in his 2003 book, Faster Than the Speed of Light, he learned of Moffat’s work when he and Albrecht tried to publish their own paper.2 It is characteristic of João that his response was to embrace Moffat as a friend—and, indeed, they remain close. He knew of Moffat’s work by the time he started to talk with me, but I don’t think he understood that it had solved the problem he was trying to solve. Or if he did, he didn’t like the way this had been done.

  John Moffat is now a friend and colleague of mine at the Perimeter Institute for Theoretical Physics. There is no one I respect more for his boldness and originality. I’ve also said how much I admire Giovanni Amelino-Camelia for his revelations about probing the Planck scale. So it pains me to admit that João and I ignored the work of both of them. In a sense, it’s good we did, for we found a different solution to the problem of how to make a variable speed of light consistent with the principles of relativity. I certainly would not have tried if I had known that the problem had already been solved—and not once, but twice.

  João came to me often with this problem. I always made time to talk with him, because I was attracted by his energy and his fresh way of seeing physics. But for many months, I didn’t think very hard about what he was saying. The turning point came when he showed me an old book in which the problem was discussed. It was a textbook on general relativity by a famous Russian mathematical physicist named Vladimir Fock.3 I knew some of Fock’s work in quantum field theory (all physicists do), but I had never seen his book on relativity. The problem João was trying to get me to think about was a homework problem in Fock’s book. Once I saw it, I recalled my idea from ten years earlier, and the whole thing came together. The key was indeed to keep the principles of Einstein’s special theory but to change the rules so that all observers agree that both the speed of light and the Planck scale are universal. Actually, the speed that is constant is no longer the speed of all photons, only very low-energy ones.

  At first we didn’t see what to do with this idea. We had a story, with some pieces of the math, but not yet a full theory. At about this time, I went on a trip that included a stop in Rome, where I spent many hours talking with Giovanni Amelino-Camelia. All of a sudden I understood what he was saying. He had come to the same idea we were developing, and he had come to it earlier and worked it out first. Nevertheless, there was a lot about the way he had worked out the idea that I didn’t understand. The math seemed complicated, and it appeared to be tied to a formalism invented some ten years earlier by a group of Polish mathematical physicists—a formalism that I certainly couldn’t penetrate.

  It would take me many years to appreciate the mathematical subtleties of the subject. I found it impenetrable until I started reading early papers by an English mathematician named Shahn Majid, who was one of the inventors of quantum groups. His work was closely related to the mathematics the Polish group was using. Majid had begun with some visionary ideas about how to express the essential insights of relativity and quantum theory in a single mathematical structure. This had led him to quantum groups (which are a revolutionary extension of the idea of a symmetry) and then to modifications of relativity theory based on a subject we call noncommutative geometry. His insights are at the core of the mathematics required to express DSR clearly, but they were lost—at least, to me—in the complicated papers where I had first seen them expressed.

  In any case, Jo
ão and I ignored mathematics and kept talking about physics. Our progress was interrupted by my move to Canada, to the newly founded Perimeter Institute, in September of 2001. A month later, João came to Perimeter as its second visitor. The theory finally fell into place the afternoon after he arrived. We were working in a café in uptown Waterloo called the Symposium, with comfortable couches. He was jetlagged. I was traumatized and exhausted, having just returned from a weekend in New York following the events of September 11. I fell asleep as João was talking, then woke up to find him dozing. I remembered something he had said as I was losing consciousness, and I played with it on a pad, then fell asleep again. I woke up when he started talking, and we had a few mutually lucid minutes before he fell asleep again. And so the afternoon went, as we talked, calculated, and dozed in turn. I can only imagine what the café staff thought. But at some point during that afternoon, we hit on a key factor that had evaded us for months, having to do with trading momenta for positions. When we were done, we had invented a second version of DSR, much simpler than the one developed by Giovanni Amelino-Camelia. Now it is known to experts as DSR II.

  This was roughly what João had wanted. In our version, photons that have more energy travel faster. Thus, in the very early universe, when the temperature was very high, the speed of light was, on average, faster than it is now. As you go farther back in time and the temperature approaches the Planck energy, the speed of light becomes infinite. It took somewhat longer to show that this led to a version of a variable-speed-of-light theory that was also consistent with the principles of general relativity, but we eventually got there, too. We call this theory Gravity’s Rainbow, after Thomas Pynchon’s novel.