The Universe_Leading Scientists Explore the Origin, Mysteries, and Future of the Cosmos

by John Brockman

  But in any case Maldacena’s conjecture has so far not been proven. There is quite a lot of evidence showing there is some relation between the two theories, but all of the results so far are consistent with a far weaker relationship holding between the two theories than the full equivalence Maldacena conjectured. This weaker relationship was originally formulated in a paper by Witten, shortly after the one of Maldacena. Except for a few special cases, which can be explained by special symmetry arguments, all the evidence is consistent with Witten’s weaker conjecture. We should here recall a basic principle of logic that when a collection of evidence is explained by two hypotheses, one stronger and one weaker, only the weaker one can be taken to be supported by the evidence.

  But Witten’s conjecture requires only that there be a partial and approximate correspondence between the two theories. It does not forbid either baby universes or the loss of information by black holes. For example, Witten shows how some black holes can be studied using results in the other theory, but again it turns out that these are atypical black holes, with positive specific heat.

  This discussion is related to a conjecture called the holographic principle (HP), an idea proposed by ’t Hooft (and a bit earlier Crane) that Susskind brought into string theory. Susskind proposes a strong form of the HP, which holds that a complete description of a system resides in the degrees of freedom on its boundary. He takes Maldacena’s conjecture as a demonstration of it. I believe here also the evidence better supports a weaker form (proposed with Markopoulou), according to which there is a relation between area and information but no necessity that the boundary has a complete description of its interior [i].

  I would urge a similar caution with respect to Susskind’s claim: “As repeatedly emphasized by ’t Hooft, black holes are the natural extension of the elementary particle spectrum. This is especially clear in string theory where black holes are simply highly excited string states. Does that mean that we should count every particle as a black hole?”

  As I mentioned, the only results in string theory that describe black holes in any detail describe only very atypical black holes. In those cases, they are related—at least by an indirect argument—to states described by string theory, but they are not in fact excitations of strings. They involve instead objects called D-branes. So Susskind must mean by “a highly excited string state” any state of string theory. But in this case the argument has no force, as stars, planets, and people must also be “highly excited string states.” In any case, until there are detailed descriptions of typical black holes in string theory, it is premature to judge whether Susskind and ’t Hooft have conjectured correctly.

  Susskind attempts to invoke Hawking’s authority here, and it is true that Hawking has announced that he has changed his view on this subject. But he has not yet put out a paper, and the transcript of the talk he gave recently doesn’t provide enough details to judge how seriously we should take his change of opinion.

  Next, Susskind refers to a paper by Horowitz and Maldacena, of which he says that “The implication is that if there is any kind of universe creation in the interior of the black hole, the quantum state of the offspring is completely unique and can have no memory of the initial state. That would preclude the kind of slow mutation rate envisioned by Smolin.”

  I read that paper and had some correspondence with its authors about it; unfortunately, Susskind misstates its implications. In fact that paper does not show that there is no loss of information, it merely assumes it and proposes a mechanism—which the authors acknowledge is speculative and not derived from theory—that might explain how it is that information is not lost. They do not show that information going into baby universes is precluded; in fact Maldacena wrote to me that “If black hole singularities really bounce into a second large region, I also think our proposal is false [j].”

  Finally, Susskind suggests that loop quantum gravity will be inconsistent unless it agrees with his conjectures about black holes. I should then mention that there are by now sufficient rigorous results (reviewed in [k]) to establish the consistency of the description of quantum geometry given by loop quantum gravity. Whether it applies to nature is an open question, as is what it has to say about black hole singularities, but progress in both directions is steady.

  Let me close with something Susskind and I agree about—which I learned from him back in graduate school: an idea called string/gauge duality according to which gauge fields, like those in electromagnetism and QCD have an equivalent description in terms of extended objects. For Susskind, those extended objects are strings. I believe that may be true at some level of approximation, but the problem is that we only know how to make sense of string theory in a context in which the geometry of spacetime is kept classical—giving a background in which the strings move.

  But general relativity teaches us that spacetime cannot be fixed; it is as dynamical as any other field. So a quantum theory of gravity must be background-independent. We should then ask if there is a version of this duality in which there is no fixed, classical background, so that the geometry of spacetime can be treated completely quantum mechanically. Indeed there is; it is loop quantum gravity. Moreover, a recent uniqueness theorem [l] shows essentially that any consistent background-independent version of this duality will be equivalent to loop quantum gravity. For this reason, I believe it is likely that if string theory is not altogether wrong, sooner or later it will find a more fundamental formulation in the language of loop quantum gravity.

  Indeed, what separates us on all these issues is the question of whether the quantum theory of gravity is to be background-independent or not. Most string theorists have yet to fully take on board the lesson from Einstein’s general theory of relativity; their intuitions about physics are still expressed in terms of things moving in fixed background spacetimes. For example, the view of time evolution that Susskind wants to preserve is tied to the existence of a fixed background. This leads him to propose a version of the holographic principle which can only be formulated in terms of a fixed background. The strong form of Maldacena’s conjecture posits that quantum gravity is equivalent to physics on a fixed background. The approaches string theory takes to black holes only succeed partially, because they describe black holes in terms of objects in a fixed background. Eternal inflation is also a background-dependent theory; indeed, some of its proponents have seen it as a return to an eternal, static universe.

  On the other hand, those who have concentrated on quantum gravity have learned, from loop quantum gravity and other approaches, how to do quantum spacetime physics in a background-independent way. After the many successful calculations which have been done, we have gained a new and different intuition about physics, and it leads to different expectations for each of the issues we have been discussing. There is still more to do, but it is clear there need be—and can be—no going back to a pre–Einsteinian view of space and time. Anyone who still wants to approach the problems of physics by discussing how things move in classical background spacetimes—whether those things are strings, branes or whatever—are addressing the past rather than the future of our science.

  References:

  [a] Lee Smolin, Scientific alternatives to the anthropic principle, hep-th/0407213.

  [b] Leonard Susskind, Cosmic natural selection, hep-th/0407266.

  [c] E. Hawkins, F. Markopoulou, H. Sahlmann, Evolution in quantum causal histories, hep-th/0302111.

  [d] In particular, global unitarity is automatically present whenever there is a global time coordinate, but need not be if that condition is not met. Quantum information accessible to local observables is propagated in terms of density matrices following rules that conserve energy and probability, because a weaker property, described in terms of completely positive maps, is maintained.

  [e] G. J. Milburn, Phys. Rev A44, 5401 (1991).

  [f] Rodolfo Gambini, Rafael Porto, Jorge Pullin, Realistic clocks, universal decoherence and the black hole information paradox hep-
th/0406260, gr-qc/0402118 and references cited there.

  [g] L. Smolin, How far are we from the quantum theory of gravity? hep-th/0303185; M. Arnsdorf and L. Smolin, The Maldacena conjecture and Rehren duality, hep-th/0106073.

  [h] This is one of several key cases in which conjectures, widely believed by string theorists have not so far been proven by the actual results on the table. Another key unproven conjecture concerns the finiteness of the theory.

  [i] F. Markopoulou and L. Smolin, Holography in a quantum spacetime, hep-th/9910146; L. Smolin, The strong and the weak holographic principles, hep-th/0003056.

  [j] Juan Maldacena, email to me, 1 November 2003, used with permission.

  [k] L. Smolin, An invitation to loop quantum gravity, hep-th/0408048.

  [l] By Lewandowski, Okolow, Sahlmann and Thiemann, see p. 20 of the previous endnote.

  12

  Science Is Not About Certainty

  Carlo Rovelli

  Theoretical physicist, Professeur de classe exceptionelle, Université de la Méditerranée, Marseille; author, The First Scientist: Anaximander and His Legacy

  INTRODUCTION by Lee Smolin

  Carlo Rovelli is a leading contributor to quantum gravity who has also made influential proposals regarding the foundation of quantum mechanics and the nature of time. Shortly after receiving his PhD, he did work that made him regarded as one of the three founders of the approach to quantum gravity called loop quantum gravity—the other two being Abhay Ashtekar and me. Over the last twenty-five years, he has made numerous contributions to the field, the most important of which developed the spacetime approach to quantum gravity called spin-foam models. These have culminated over the last five years in a series of discoveries that give strong evidence that loop quantum gravity provides a consistent and plausible quantum theory of gravity.

  Rovelli’s textbook, Quantum Gravity, has been the main introduction to the field since its publication in 2004, and his research group in Marseille has been a major center for incubating and developing new talent in the field in Europe. Carlo Rovelli’s approach to the foundations of quantum mechanics is called relational quantum theory. He also, with the mathematician Alain Connes, has proposed a mechanism by which time could emerge from a timeless world—a mechanism called the thermal time hypothesis.

  Science Is Not About Certainty

  We teach our students: We say that we have some theories about science. Science is about hypothetico-deductive methods; we have observations, we have data, data require organizing into theories. So then we have theories. These theories are suggested or produced from the data somehow, then checked in terms of the data. Then time passes, we have more data, theories evolve, we throw away a theory, and we find another theory that’s better, a better understanding of the data, and so on and so forth.

  This is the standard idea of how science works, which implies that science is about empirical content; the true, interesting, relevant content of science is its empirical content. Since theories change, the empirical content is the solid part of what science is.

  Now, there’s something disturbing, for me, as a theoretical scientist, in all this. I feel that something is missing. Something of the story is missing. I’ve been asking myself, “What is this thing missing?” I’m not sure I have the answer, but I want to present some ideas on something else that science is.

  This is particularly relevant today in science, and particularly in physics, because—if I’m allowed to be polemical—in my field, fundamental theoretical physics, for thirty years we have failed. There hasn’t been a major success in theoretical physics in the last few decades after the standard model, somehow. Of course there are ideas. These ideas might turn out to be right. Loop quantum gravity might turn out to be right, or not. String theory might turn out to be right, or not. But we don’t know, and for the moment Nature has not said yes, in any sense.

  I suspect that this might be in part because of the wrong ideas we have about science, and because methodologically we’re doing something wrong—at least in theoretical physics, and perhaps also in other sciences. Let me tell you a story to explain what I mean. The story is an old story about my latest, greatest passion outside theoretical physics—an ancient scientist, or so I say even if often he’s called a philosopher: Anaximander. I’m fascinated by this character, Anaximander. I went into understanding what he did, and to me he’s a scientist. He did something that’s very typical of science and shows some aspect of what science is. What is the story with Anaximander? It’s the following, in brief:

  Until Anaximander, all the civilizations of the planet—everybody around the world—thought the structure of the world was the sky over our heads and the earth under our feet. There’s an up and a down, heavy things fall from the up to the down, and that’s reality. Reality is oriented up and down; Heaven’s up and Earth is down. Then comes Anaximander and says, “No, it’s something else. The Earth is a finite body that floats in space, without falling, and the sky is not just over our head, it’s all around.”

  How did he get this? Well, obviously, he looked at the sky. You see things going around—the stars, the heavens, the moon, the planets, everything moves around and keeps turning around us. It’s sort of reasonable to think that below us is nothing, so it seems simple to come to this conclusion. Except that nobody else came to this conclusion. In centuries and centuries of ancient civilizations, nobody got there. The Chinese didn’t get there until the 17th century, when Matteo Ricci and the Jesuits went to China and told them. In spite of centuries of the Imperial Astronomical Institute, which was studying the sky. The Indians learned this only when the Greeks arrived to tell them. In Africa, in America, in Australia—nobody else arrived at this simple realization that the sky is not just over our head, it’s also under our feet. Why?

  Because obviously it’s easy to suggest that the Earth floats in nothing, but then you have to answer the question, Why doesn’t it fall? The genius of Anaximander was to answer this question. We know his answer—from Aristotle, from other people. He doesn’t answer this question, in fact: He questions this question. He asks, “Why should it fall?” Things fall toward the Earth. Why should the Earth itself fall? In other words, he realizes that the obvious generalization—from every heavy object falling to the Earth itself falling—might be wrong. He proposes an alternative, which is that objects fall toward the Earth, which means that the direction of falling changes around the Earth.

  This means that up and down become notions relative to the Earth. Which is rather simple to figure out for us now: We’ve learned this idea. But if you think of the difficulty when we were children of understanding how people in Sydney could live upside-down, clearly this required changing something structural in our basic language in terms of which we understand the world. In other words, “up” and “down” meant something different before and after Anaximander’s revolution.

  He understands something about reality essentially by changing something in the conceptual structure we use to grasp reality. In doing so, he isn’t making a theory; he understands something that, in some precise sense, is forever. It’s an uncovered truth, which to a large extent is a negative truth. He frees us from prejudice, a prejudice that was ingrained in our conceptual structure for thinking about space.

  Why do I think this is interesting? Because I think this is what happens at every major step, at least in physics; in fact, I think this is what happened at every step in physics, not necessarily major. When I give a thesis to students, most of the time the problem I give for a thesis is not solved. It’s not solved because the solution of the question, most of the time, is not in solving the question, it’s in questioning the question itself. It’s realizing that in the way the problem was formulated there was some implicit prejudice or assumption that should be dropped.

  If this is so, then the idea that we have data and theories and then we have a rational agent who constructs theories from the data using his rationality, his mind, his intelligence, his
conceptual structure doesn’t make any sense, because what’s being challenged at every step is not the theory, it’s the conceptual structure used in constructing the theory and interpreting the data. In other words, it’s not by changing theories that we go ahead but by changing the way we think about the world.

  The prototype of this way of thinking—the example that makes it clearer—is Einstein’s discovery of special relativity. On the one hand, there was Newtonian mechanics, which was extremely successful with its empirical content. On the other hand, there was Maxwell’s theory, with its empirical content, which was extremely successful, too. But there was a contradiction between the two.

  If Einstein had gone to school to learn what science is, if he had read Kuhn, and the philosophers explaining what science is, if he was any one of my colleagues today who are looking for a solution of the big problem of physics today, what would he do? He would say, “OK, the empirical content is the strong part of the theory. The idea in classical mechanics that velocity is relative: forget about it. The Maxwell equations: forget about them. Because this is a volatile part of our knowledge. The theories themselves have to be changed, OK? What we keep solid is the data, and we modify the theory so that it makes sense coherently, and coherently with the data.”

  That’s not at all what Einstein does. Einstein does the contrary. He takes the theories very seriously. He believes the theories. He says, “Look, classical mechanics is so successful that when it says that velocity is relative, we should take it seriously, and we should believe it. And the Maxwell equations are so successful that we should believe the Maxwell equations.” He has so much trust in the theory itself, in the qualitative content of the theory—that qualitative content that Kuhn says changes all the time, that we learned not to take too seriously—and he has so much in that that he’s ready to do what? To force coherence between the two theories by challenging something completely different, which is something that’s in our head, which is how we think about time.