I was asked to review Lee Smolin’s The Trouble With Physics by New Scientist. The review has now appeared, although with a couple of drawbacks. Most obviously, only subscribers can read it. But more importantly, they have some antiquated print-journal notion of a “word limit,” which in my case was about 1000 words. When I started writing the review, I kind of went over the limit. By a factor of about three. This is why the Intelligent Designer invented blogs; here’s the review I would have written, if the Man hadn’t tried to stifle my creativity. (Other reviews at Backreaction and Not Even Wrong; see also Bee’s interview with Lee, or his appearance with Brian Greene on Science Friday.)
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It was only after re-reading and considerable head-scratching that I figured out why Lee Smolin’s The Trouble With Physics is such a frustrating book: it’s really two books, with intertwined but ultimately independent arguments. One argument is big and abstract and likely to be ignored by most of the book’s audience; the other is narrow and specific and part of a wide-ranging and heated discussion carried out between scientists, in the popular press, and on the internet. The abstract argument — about academic culture and the need to nurture speculative ideas — is, in my opinion, important and largely correct, while the specific one — about the best way to set about quantizing gravity — is overstated and undersupported. It’s too bad that vociferous debate over the latter seems likely to suck all the oxygen away from the former.
Fundamental physics (for want of a better term) is concerned with the ultimate microscopic laws of nature. In our current understanding, these laws describe gravity according to Einstein’s general theory of relativity, and everything else according to the Standard Model of particle physics. The good news is that, with just a few exceptions (dark matter and dark energy, neutrino masses), these two theories are consistent with all the experimental data we have. The bad news is that they are mutually inconsistent. The Standard Model is a quantum field theory, a direct outgrowth of the quantum-mechanical revolution of the 1920’s. General relativity (GR), meanwhile, remains a classical theory, very much in the tradition of Newtonian mechanics. The program of “quantum gravity” is to invent a quantum-mechanical theory that reduces to GR in the classical limit.
This is obviously a crucially important problem, but one that has traditionally been a sidelight in the world of theoretical physics. For one thing, coming up with good models of quantum gravity has turned out to be extremely difficult; for another, the weakness of gravity implies that quantum effects don’t become important in any realistic experiment. There is a severe conceptual divide between GR and the Standard Model, but as a practical matter there is no pressing empirical question that one or the other of them cannot answer.
Quantum gravity moved to the forefront of research in the 1980’s, for two very different reasons. One was the success of the Standard Model itself; its triumph was so complete that there weren’t any nagging experimental puzzles left to resolve (a frustrating situation that persisted for twenty years). The other was the appearance of a promising new approach: string theory, the simple idea of replacing elementary point particles by one-dimensional loops and segments of “string.” (You’re not supposed to ask what the strings are made of; they’re made of string stuff, and there are no deeper layers.) In fact the theory had been around since the late 1960’s, originally investigated as an approach to the strong interactions. But problems arose, including the unavoidable appearance of string states that had all the characteristics one would expect of gravitons, particles of gravity. Whereas most attempts to quantize gravity ran quickly aground, here was a theory that insisted on the existence of gravity even when we didn’t ask for it! In 1984, Michael Green and John Schwarz demonstrated that certain potentially worrisome anomalies in the theory could be successfully canceled, and string mania swept the particle-theory community.
In the heady days of the “first superstring revolution,” triumphalism was everywhere. String theory wasn’t just a way to quantize gravity, it was a Theory of Everything, from which we could potentially derive all of particle physics. Sadly, that hasn’t worked out, or at least not yet. (String theorists remain quite confident that the theory is compatible with everything we know about particle physics, but optimism that it will uniquely predict the low-energy world is at a low ebb.) But on the theoretical front, there have been impressive advances, including a “second revolution” in the mid-nineties. Among the most astonishing results was the discovery by Juan Maldacena of gauge/gravity duality, according to which quantum gravity in a particular background is precisely equivalent to a completely distinct field theory, without gravity, in a different number of dimensions! String theory and quantum field theory, it turns out, aren’t really separate disciplines; there is a web of dualities that reveal various different-looking string theories as simply different manifestations of the same underlying theory, and some of those manifestations are ordinary field theories. Results such as this convince string theorists that they are on the right track, even in the absence of experimental tests. (Although all but the most fervent will readily agree that experimental tests are always the ultimate arbiter.)
But it’s been a long time since the last revolution, and contact with data seems no closer. Indeed, the hope that string theory would uniquely predict a model of particle physics appears increasingly utopian; these days, it seems more likely that there is a huge number (10500 or more) phases in which string theory can find itself, each featuring different particles and forces. This embarrassment of riches has opened a possible explanation for apparent fine-tunings in nature — perhaps every phase of string theory exists somewhere, and we only find ourselves in those that are hospitable to life. But this particular prediction is not experimentally testable; if there is to be contact with data, it seems that it won’t be through predicting the details of particle physics.
It is perhaps not surprising that there has been a backlash against string theory. Lee Smolin’s The Trouble With Physics is a paradigmatic example, along with Peter Woit’s new book Not Even Wrong. Both books were foreshadowed by Roger Penrose’s massive work, The Road to Reality. But string theorists have not been silent; several years ago, Brian Greene’s The Elegant Universe was a surprise bestseller, and more recently Leonard Susskind’s The Cosmic Landscape has focused on the opportunities presented by a theory with 10500 different phases. Alex Vilenkin’s Many Worlds in One also discusses the multiverse, and Lisa Randall’s Warped Passages enthuses over the possibility of extra dimensions of spacetime — while Lawrence Krauss’s Hiding in the Mirror strikes a skeptical note. Perhaps surprisingly, these books have not been published by vanity presses — there is apparently a huge market for popular discussions of the problems and prospects of string theory and related subjects.
Smolin is an excellent writer and a wide-ranging thinker, and his book is extremely readable. He adopts a more-in-sorrow-than-in-anger attitude toward string theory, claiming to appreciate its virtues while being very aware of its shortcomings. The Trouble with Physics offers a lucid introduction to general relativity, quantum mechanics, and string theory itself, before becoming more judgmental about the current state of the theory and its future prospects.
There is plenty to worry or complain about when it comes to string theory, but Smolin’s concerns are not always particularly compelling. For example, there are crucially important results in string theory (such as the fundamental fact that quantum-gravitational scattering is finite, or the gauge/gravity duality mentioned above) for which rigorous proofs have not been found. But there are proofs, and there are proofs. In fact, there are almost no results in realistic quantum field theories that have been rigorously proven; physicists often take the attitude that reasonably strong arguments are enough to allow us to accept a claim, even in the absence of the kind of proof that would make a mathematician happy. Both the finiteness of stringy scattering and the equivalence of gauge theory and gravity under Maldacena’s duality are supported by extremely compelling evidence, to the point where it has become extremely hard to see how they could fail to be true.
Smolin’s favorite alternative to string theory is Loop Quantum Gravity (LQG), which has grown out of attempts to quantize general relativity directly (without exotica such as supersymmetry or extra dimensions). To most field theorists, this seems like a quixotic quest; general relativity is not well-behaved at short distances and high energies, where such new degrees of freedom are likely to play a crucial role. But Smolin makes much of one purported advantage of LQG, that the theory is background-independent. In other words, rather than picking some background spacetime and studying the propagation of strings (or whatever), LQG is formulated without reference to any specific background.
It’s unclear whether this is really such a big deal. Most approaches to string theory are indeed background-dependent (although in some cases one can quibble about definitions), but that’s presumably because we don’t understand the theory very well. This is an argument about style; in particular, how we should set about inventing new theories. Smolin wants to think big, and start with a background-independent formulation from the start. String theorists would argue that it’s okay to start with a background, since we are led to exciting new results like finite scattering and gauge/gravity duality, and a background-independent formulation will perhaps be invented some day. It’s not an argument that anyone can hope to definitively win, until the right theory is settled and we can look back on how it was invented.
There are other aspects of Smolin’s book that, as a working physicist, rub me the wrong way. He puts a great deal of emphasis on connection to experimental results, which is entirely appropriate. However, he tends to give the impression that LQG and other non-stringy approaches are in close contact with experiment in a way that string theory is not, and I don’t think there’s any reasonable reading on which that is true. There may very well be certain experimental findings — which haven’t yet happened — that would be easier to explain in LQG than in string theory. But the converse is certainly equally true; the discovery of extra dimensions is the most obvious example. As far as I can tell, both string theory and LQG (and every other approach to quantizing gravity) are in the position of not making a single verifiable prediction that, if contradicted by experiment, would falsify the theory. (I’d be happy to hear otherwise.)
Smolin does mention a number of experimental results that have already been obtained, but none of them is naturally explained by LQG any more than by string theory, and most of them are, to be blunt, likely to go away. He mentions the claimed observation that the fine-structure constant is varying with time (against which more precise data has already been obtained), certain large-angle anomalies in the cosmic microwave background anisotropy, and the possibility of large-scale modifications of general relativity replacing dark matter. (Bad timing on that one.) I don’t know of any approach to quantum gravity that firmly predicts (or even better, predicted ahead of time) that any of these should be true. That’s the least surprising thing in the world; gravity is a weak force, and most of the universe is in the regime where it is completely classical.
Smolin also complains about the tendency of string theorists to hype their field. It is hard to argue with that; as a cosmologist, of course, it is hard to feel morally superior, either. But Smolin does tend to project such a feeling of superiority, often contrasting the careful and nuanced claims of LQG to the bombast of string theory. Yet he feels comfortable making statements such as (p. 232)
Loop quantum gravity already has elementary particles in it, and recent results suggest that this is exactly the right particle physics: the standard model.
There are only two ways to interpret this kind of statement: either (1) we have good evidence that quantum spacetime alone, without additional fields, supports excitations that have the right kinds of interactions and quantum numbers to be the particles of the Standard Model, which would be the most important discovery in physics since the invention of quantum mechanics, or (2) it’s hype. Time will tell, I suppose. The point being, it’s perfectly natural to get excited or even overenthusiastic when one is working on ideas of fantastic scope and ambition; at the end of the day, those ideas should be judged on whether they are right or wrong, not whether their proponents were insufficiently cautious and humble.
To date, the string theorists are unambiguously winning the battle for support within the physics community. Success is measured primarily by faculty positions and grant money, and these flow to string theorists much more than to anyone pursuing other approaches to quantum gravity. From an historical perspective, the unusual feature of this situation is that there are any resources being spent on research in quantum gravity; if string theory were suddenly to fall out of favor, it seems much more likely that jobs and money would flow to particle phenomenology, astrophysics, or other areas of theory than to alternative approaches to quantum gravity.
It seems worth emphasizing that the dominance of string theory is absolutely not self-perpetuating. When string theorists apply for grants, they are ultimately judged by program officers at the National Science Foundation or the Department of Energy, the large majority of whom are not string theorists. (I don’t know of any who are, off the top of my head.) And when string theorists apply for faculty jobs, it might very well be other string theorists who decide which are the best candidates, but the job itself must be approved by the rest of the department and by the university administration. String theorists have somehow managed to convince all of these people that their field is worthy of support; I personally take the uncynical view that they have done so through obtaining interesting results.
Smolin talks a great deal about the need for physics, and academia more generally, to support plucky upstart ideas and scholars with the courage and vision to think big and go against the grain. This is a larger point than the specific argument about how to best quantize gravity, and ultimately far more persuasive; it is likely, unfortunately, to be lost amidst the conflict between string theory and its discontents. Faculty positions and grant money are scarce commodities, and universities and funding agencies are naturally risk-averse. Under the current system, a typical researcher might spend five years in graduate school, three to six as a postdoc, and another six or seven as an assistant professor before getting tenure — with an expectation that they will write several competent papers in every one of those years. Nobody should be surprised that, apart from a few singular geniuses, the people who survive this gauntlet are more likely to be those who show technical competence within a dominant paradigm, rather than those who will take risks and pursue their idiosyncratic visions. The dogged pursuit of string theory through the 1970’s by Green and Schwarz is a perfect example of the ultimate triumph of the latter approach, and Smolin is quite correct to lament the lack of support for this kind of research today.
In the real world, it’s difficult to see what to do about the problem. I would be happy to see longer-term postdocs, or simply fewer postdocs before people move on to assistant professorships. But faculty positions are extremely rare — within fundamental theory, a good-sized department might have two per decade, and it would be hard to convince a university to take a long-shot gamble on someone outside the mainstream just for the greater good of the field as a whole. And a gamble it would certainly be. Smolin stacks the deck by contrasting the “craftsmen” who toil within string theory to the “seers” who pursue alternatives, and it’s pretty obvious which is the more romantic role. Many physicists are more likely to see the distinction as one between “doers” and “dreamers,” or even (among our less politic colleagues) between “scientists” and “crackpots.”
To be clear, the scientists working on LQG and other non-stringy approaches to quantum gravity are not crackpots, but honest researchers tackling a very difficult problem. Nevertheless, for the most part they have not managed to convince the rest of the community that their research programs are worthy of substantial support. String theorists are made, not born; they are simply physicists who have decided that this is the best thing to work on right now, and if something better comes along they would likely switch to that. The current situation could easily change. Many string theorists have done interesting work in phenomenology, cosmology, mathematical physics, condensed matter, and even loop quantum gravity. If a latter-day Green and Schwarz were to produce a surprising result that convinced people that some alternative to string theory were more promising, it wouldn’t take long for the newcomer to become dominant. Alternatively, if another decade passes without substantial new progress within string theory, it’s not hard to imagine that people will lose interest and switch to other problems. I would personally bet against this possibility; string theory has proved to be a remarkably fruitful source of surprising new ideas, and there’s no reason to expect that track record to come to a halt.
Smolin is right in the abstract, that we should try to nurture a diversity of approaches to difficult questions in physics, even if his arguments on the specific example of string theory and its competitors are less compelling. But he is also right that string theorists are not always as self-critical as they could be, and can even occasionally be a mite arrogant (although I haven’t found this quality to be rare within academia). The best possible consequence of the appearance of The Trouble with Physics and similar books would be that physicists of all stripes are moved to take an honest look at the strengths and weaknesses of their own research programs, and to maintain an open mind about alternatives. (The worst possible consequence would be for large segments of the public, or the student population, or even physicists in other specialties, to misunderstand why string theorists find their field so compelling.) Sometimes a little criticism can be a healthy thing.
Lee–
Thanks for the response. Briefly:
1) You misunderstood what I was saying about background independence; perhaps I was not clear. Parenthetically, it is certainly not the case that quantum gravity must necessarily be background-independent; I could easily imagine, for example, a set of overlapping descriptions in different regimes, each of which referred to some background, but when taken as a whole described the entire theory. (Tom Banks has discussed ideas along these lines.)
But that’s not what I was talking about. The “style” I referred to was the style of developing new theories, not what the theories looked like. Whether or not we someday find a background-independent formulation of quantum gravity, that has nothing to do with some imaginary requirement that we will only make progress toward that goal by insisting on background-independence from the start. Perhaps we will get there eventually, as we eventually got to quantum mechanics through Bohr’s quantization rules and so on. I just don’t know; but since nobody else does either, at the moment it’s simply a guess, which different people are welcome to have.
2) We’ll just have to disagree about the rigorous-results issue. Of course I never claimed that it is or would be impossible to prove things rigorously, only that we can make substantial progress without doing so (for example, in every realistic quantum field theory).
3) My claim was not that quantum GR is non-unique or ill-defined, it was that it is ill-behaved. These are not the same thing; I know plenty of people, for example, who exist and are unique and well-defined yet very ill-behaved. There is no reason to think that gravity has an ultraviolet fixed point or some other nice behavior, and there is every reason to believe that non-gravitational degrees of freedom will play a crucial role in understanding the behavior of gravity at short distances. Jacques spelled all of this out very clearly in his posts:
http://golem.ph.utexas.edu/~distler/blog/archives/000612.html
http://golem.ph.utexas.edu/~distler/blog/archives/000639.html
and I haven’t seen anyone even attempt to answer his questions.
The swipe at my understanding of the subject was gratuitous; let’s stick to substantive arguments, shall we? It’s true that I haven’t gone through the details of the proof of the LOST theorem, so I can’t judge how general its hypotheses really are, or what the implications of the result might be in detail. But the claim is that there is a unique representation of the “kinematical algebra.” I don’t see how this has much bearing on the issue at hand, which is about dynamics, not kinematics. How does having a unique representation help you derive the low-energy effective theory, for example?
4) Again, I think we’ll just have to disagree. In my personal experience, the reason why more jobs have not been allocated to people working in non-stringy approaches to quantum gravity is not because those people are too modest and careful about stating their results.
5) Of course it would be interesting and exciting to get experimental data relevant to the Planck scale, and of course things like extra dimensions are not a unique signature of string theory. As I said in the review, in both string theory and other approaches, we have ideas for experimental results that would be compatible with the theory, but no firm predictions that would falsify it if they were not found. Does LQG make a prediction about ultra-high-energy cosmic rays that, if data from Auger were inconsistent with the prediction, would rule out the theory once and for all?
Hi Lee —
Can you list some people who believe that string theory will not eventually be background independent (modulo boundary issues)? You go on radio programs talking about these deep philosophical differences going back hundreds of years, and as best I can tell, they don’t exist. We’ve all read MTW, and some of us have even read Hawking and Ellis. Why do you continually place yourself in the role of the defender of Einstein when none of us are attacking him?
What there is, as Sean states, is a difference of approaches, but that hardly is indicative of this grand historical context that you seem so fond of.
This is true of GR with compact boundary conditions, and certainly not true of AdS/CFT which has a large group of global symmetries, What AdS/CFT doers show us is that a global internal symmetry can be dual to a global spacetime symmetry, but this is not background independence.
It’s good to know that background independence is still a moving target, though.
The central result in the whole subject of LQG is a rigorous theorem, the LOST theorem (math-ph/0407006, gr-qc/0504147). It asserts that there is a unique quantization of a diffeo invariant gauge theory with 2 or more spatial dimensions, subject to some technical, but physically reasonable conditions.
As far as I can tell, it does not do any such thing. The LOST theorem discusses a particular representation of a particular algebra before the imposition of all the constraints. The physical aspect of the theory is the Hilbert space with all the constraints imposed and, as best I’ve been able to discern, the LOST theorem has little to say about that.
Don’t you think we should be careful about `hyping’ our results?
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I’m afraid I don’t understand this statement.
In a noncompact space one only mods out by diffeomorphisms that go to the identity at infinity. In asymptotically flat spacetimes, this means that Poincaré acts a global symmetry of the gravitational theory.
And bona fide observables (e.g., the ADM energy) transform as nontrivial representations of Poincaré.
Similarly, in asymptotically AdS space, there is a group of global symmetries, and bona fide observables transform in nontrivial representations of that symmetry group.
And, therefore, it is true in any theory containing quantum field theory as a systematic approximation. Which is to say, it is true of any theory of “fundamental physics” that we might possibly be interested in.
There seems to be a tremendous amount of confusion (if not outright misinformation) about the status of that subject. See here for a discussion of what is (and is not) known.
Berenstein, Maldacena and Nastase (and their successors) showed that the duality holds well beyond the supergravity approximation. That, and the myriad of other checks, makes it hard to see how any weaker form of the conjecture could hold, but not the strong form.
Do you have a proposal for some weaker form of the conjecture that is actually consistent with all the currently-known evidence?
There is no example of a sensible nontrivial quantum field theory, defined by its perturbation theory. So there is no reason to expect that string theory will either. If it were, then string theory would be dead in the water. So it’s rather a good thin that its perturbation series is not convergent.
We’ve spent the past decade learning tantalizing things about aspects of nonperturbative string theory. It’s rather like the blind men and the elephant., but what we do know about string theory is far more interesting that what one learns from string perturbation theory alone..
Hi Lee,
We’re all waiting to read your response to
Jacques’Jeff’s question over on Asymptotia. You asked for members of the community to respond directly to your book’s contents, and he’s done so – asking again the question about why you seem to have downplayed the role of research which tries to apply string theory to the strong interactions in a book that criticises the program of research in string theory for not being relevant to experiment.We’re all very curious to read your answer.
Best,
-cvj
I believe you mean Jeff’s question. While I might appreciate being mistaken for Jeff Harvey, I’m not sure he would be so thrilled.
Whoops! Will correct…. Short term memory shot to pieces so that I forget thing while moving between two browser windows. Thanks.
-cvj
Hi, Lee.
If you are interested in background independence in 4D, why not start by looking at background independence on the circle, where diffeomorphisms are well understood? There the situation is like this:
1. There is a unique theory with c = 0, namely the trivial one.
2. There are many unitary theories with c > 0.
As I pointed out above, the notion of an anomalous dimension is background independent, since the dilaton operator does not involve the metric. Therefore, you should find the same anomalous dimensions with and without a background metric.
Dear Lee,
I’d be interested in your answer to my question on Clifford’s
blog as well. Since you want feedback and I don’t have the time to collect all my questions and responses in one place, I’ll ask another question here.
One of your main criticisms of string theory involves the possible landscape
of solutions to string theory. For example, in the introduction, on page xiv,
you have a paragraph that starts with “Part of the reason string theory
makes no new predictions is that it appears to come in an infinite number
of versions.” and ends with “No experiment will ever be able to prove it true.”
There are many other places in the text where you focus on this point as
one of the central flaws of string theory.
I have two responses. The first, which I mentioned on the radio show, is
that the existence of an infinite number of solutions does not at all
imply a lack of predictions or falsifiability. QFTs are infinite in number, but
once you make a choice of QFT (gauge group, representation of matter
fields, values of masses and couplings) you can make definite dynamical
predictions which of course in the Standard Model have been tested rather
precisely. There is no reason that string theory could not have similar
features. In fact, there seem to be certain fairly universal results in string
theory. These include the computability of black hole entropy in a wide
variety of backgrounds and the universality of the viscosity to entropy
ration in the QGP. I agree with you that the landscape (if it exists) is
problematic for the initially hoped for prediction of parameters of the Standard
Model, but this is not the only conceivable way of testing string theory.
My second response is really a question to you. You end your discussion
of the Landscape in Chapter 10 with a statement of your own point of view
on the problem. You say “If you insist on those standards, then you will not
believe in the vast number of new theories, because the evidence for any theory in the current landscape is pretty minimal according to the old standards. This is the point of view I find myself leaning toward, most of
the time. It just seems to me the most rational reading of the evidence.”
My question: Why do you criticize string theory for having a property that you don’t believe it has, at least most of the time?
If I may, let me amend Jeff’s question with my own – how large is the space of all background-independent quantum field theories, do we have a reason to believe it is not infinite?
While the issue with Lee Smolin is being cleared up, I thought it important that people read KC’s article for themself and think about what has manifested in the comment section supplied in regards to “The Tea CUP,” as well as Peter Woit’s Corrections post.
As a lay person as I watched the debate. I learned of what is important to science people. This was a lesson for me, and I hope one the public will appreciate.
Hi,
Thanks for the different questions and responses. If I may, I’ll quickly answer a few now and come back to others that require more thought later.
To Jeff, First, thanks for taking the time to do the radio show.
“Why do you criticize string theory for having a property that you don’t believe it has, at least most of the time?”
This is a fair point. If we don’t accept the KKLT and related flux vacua, there are then two possibilities: 1) There are no non-supersymmetric consistent string perturbation theories, and 2) There are consistent non-supersymmetric string perturbation theories yet to be found.
If 1) is true then there may be a problem incorporating the observed dark energy in string theory altogether. This would be one way to disconfirm string theory. Alternatively, to show that 2) is true we should find a new way to construct non-supersymmetric string theories.
I certainly don’t know which of the three possibilities is right, I hope people are working on both alternatives to the KKLT etc landscape.
To Moshe:, “how large is the space of all background-independent quantum field theories, do we have a reason to believe it is not infinite?” I don’t think we know. At the Hamiltonian level it is pretty hard to get the gravity parts of the quantum constraints to close, but once they do it seems possible to add different forms of matter and maintain that property. At the spin foam level we don’t have good control on the space of possible amplitudes or of RG flow through them, I have been urging people to work more on this for a long time; perhaps due to the few number of people involved, most have been concentrating on first understanding the properties of Barrett-Crane and related models.
There is of course the new possibility found in recent work of Markopoulou and Krebs that shows that a large set of pure quantum gravity models have additional conserved quantities and local excitations that carry them. These are naturally interpreted as particles, and their properties should be computable with no additional parameters. But we have a long way to go to understand if the dynamics comes out right, even if there are preliminary indications that something like a preon model comes out.
Dear Sean, with regard to LOST: “I don’t see how this has much bearing on the issue at hand, which is about dynamics, not kinematics.” The point is that the theory is then unique (for a fixed value of the cosmological constant) also at the spatially diffeomorphism invariant level, because the unique kinematical representation carries a rep of the spatial diffeo group and this lets one construct rigorously and explicitly the Hilbert space of spatially diffeo invariant states. One can then argue that any operator product in the kinematical Hilbert space that is defined re the limit of a regularization procedure, such that it gives rise to a well defined operator on the Hilbert space of diffeomorphism invariant states, has no uv divergences. This is confirmed in many calculations and results.
So the existence of the Ashtekar-Lewandowski representation (of the kinematical algebra) allows us to construct a Hilbert space of spatially diffeo invariant states on which the hamiltonian constraint and other operators are represented by uv finite operators. This is pretty important, it is how uv finiteness is shown. Then the LOST theorem tells us that this construction is unique.
Now this may or may not prevent there from being some space of parameters that govern possible consistent Hamiltonian constraint operators. But it does appears that matter content is not tightly restricted by uv finiteness, because of Thiemann et al’s results that the consistency of the quantum constraints on this Hilbert space is not altered by adding different matter fields and couplings.
This is, so far as I can tell, a proof that quantum general relativity a) exists and is uv finite and b) does so with a variety of fundamental matter couplings or with no matter at all. These results then, directly contradict your assertion: “There is no reason to think that gravity has an ultraviolet fixed point or some other nice behavior, and there is every reason to believe that non-gravitational degrees of freedom will play a crucial role in understanding the behavior of gravity at short distances.”
So we have a genuine disagreement. It seems to me that either you have to concede you are wrong or find an error in the LOST theorem or related results.
To be completely clear, one possibility is still that the Hamiltonian formulation these results refer to do not have a low energy limit that reproduces classical GR. We have several indications that this is so, but so far no proof, so on present results it is still possible that while quantum GR exists as these results show it does not have GR as a low energy limit (i.e just as quantum YM theory does not have classical YM’s theory as a low energy limit.) Indeed, it may be that only the path integral form of the theory captured in spin foam models has GR as a low energy limit. So there is not yet a claim that LQG passes all the tests for a good quantum theory of gravity. But there is the claim that at both the Hamiltonian and path integral levels there is a well defined theory which corresponds to the quantization of GR that is well defined and uv finite, which contradicts your assertions.
Thanks,
Lee
Thanks Lee, my point is of course that is that if and when LQG will make contact with low energy effective field theory, all indications are that it will have its own landscape to deal with.
I have to say the discussion regarding tachyons in non-SUSY vacua (in Clifford’s space) sounds awfully familiar, maybe someone else will have something more convincing to say.
Finally, congratulations! hope you are getting a bit of sleep already.
So we have a genuine disagreement. It seems to me that either you have to concede you are wrong or find an error in the LOST theorem or related results
It is also possible that the LOST theorem is correct but that some assumption (e.g. no diff anomalies) is not realized in nature.
Dear Plato,
The neutrino wasn’t a non-testable prediction but a FACT from experimental data on beta decay spectra.
Experiments show that beta particles, which are the most common decay mechanism in the chart of nuclides, have a continuous spectrum of energies (unlike gamma rays, which are line spectra, indicating that they occur from quantum-type energy state transitions in the nucleus).
The beta spectrum curve does have an upper limit however, and the mean energy of the beta particles is around 30% of the upper limit.
The data indicated that the mean energy emitted by the beta particles was far less than the total energy lost per beta decay. There are only two ways of accounting for this: (1) abandon law of conservation of energy (which Niels Bohr wanted to do, or at least make that law subject to statistical indeterminancy and wishy-washyness) or (2) postulate a new particle.
Pauli decided to write down all the charcateristics he could about the postulated new particle. Using conservation of angular momentum and other laws, Pauli was able to predict the spin and other characteristics of neutrinos. He wanted to call it the neutron, but Chadwick stole that name for another particle, so Pauli settled on the neutrino name.
FINALLY, Pauli DID say it was possible to TEST the neutrino theory:
http://www.math.columbia.edu/~woit/wordpress/?p=389#comment-10746
Wolfgang Pauli’s letter of Dec 4, 1930 to a meeting of beta radiation specialists in Tubingen:
‘Dear Radioactive Ladies and Gentlemen, I have hit upon a desperate remedy regarding … the continous beta-spectrum … I admit that my way out may seem rather improbable a priori … Nevertheless, if you don’t play you can’t win … Therefore, Dear Radioactives, test and judge.’
(Quoted in footnote of page 12, http://arxiv.org/abs/hep-ph/0204104 )
All it took to test was a strong source of neutrinos. It is telling that Enrico Fermi, who worked out the original theory of beta decay, also invented the nuclear reactor, which was used to discover the neutrino 😉
Best,
nc
LQG, if successful, would have the relationship to General Relativity that QED has to classical electromagnetism. How would a landscape arise?
Arun, loop “quantization” is an attempt to generalize QFT in a way that preserves backround-independence explicitely. The attempts so far are to reproduce pure gravity (and if I may add, quantum mechanics), but as Lee emphasizes one can do the same thing to gravity coupled to any form of matter, with any dynamics and any couplings, and so far there seems to be no difference. So the number of low energy universes coming from the theory is apriori infinite, unless one finds some “selection principle”, or more pessimistically the number ends up being zero.
Moshe, LQG is a modelling process, not a speculation. Smolin et al. show that a path integral is a summing over the full set of interaction graphs in a Penrose spin network. The result gives general relativity without a metric (ie, background independent). Next, you simply have to make gravity consistent completely with standard model-type Yang-Mills QFT dynamics to get predictions (cf comment#29).
Lee– I don’t have time right now for anything but a quick response, but to my mind the fact that you have a Hilbert space and some Hamiltonian, but don’t know whether the theory recovers GR (or some close relative thereof) in the classical limit, is not a minor technicality. It’s basically the whole point. To me, “quantum GR” does not mean “a diffeomorphism-invariant representation on Hilbert space”, it means “a quantum-mechanical theory that reduces to GR in the classical limit.”
In particular, again, I don’t see how the model answers “Georgi’s objection” discussed in Jacques’s posts linked to above. String theory has an answer, and I think that any competitor should as well.
They don’t have a definite Hamiltonian last I checked. I could be wrong on this point, though.
Moshe:
Does classical general relativity have a landscape problem? After all, one can put any kind of matter with any dynamics and coupling into it. I do not expect LQG to any more constrain matter than GR does. The fact that LQG or GR does not constrain matter is not the landscape problem that string theory has. The string theory landscape problem as I understand it is that the degrees of freedom are supposedly exactly known (at least at high energy) but can manifest themselves in the low energy limit in myriads of inequivalent ways.
If LQG works, then the theory of (not everything, but everything we know about) will be LQG + the Standard Model. If we discover something know at LHC, the theory will be LQG + the Standard Model + LHC extensions. And so on. No landscape problem here.
Of course, “Georgi’s objections” make it unlikely that LQG will work. Perhaps even more than finding a classical limit, this objection needs to be addressed (in my highly inexpert opinion).
-Arun
Question to Sean: does the gravitation theory that emerges in the “classical limit” of string theory have the principle of equivalence, or is there plenty of low energy matter that doesn’t?
Arun, all of ordinary physics — e.g., classical or quantum field theory — has a “landscape problem,” in that there are a gajillion (really, an infinite number of) possible models. It used to be thought that we would distinguish between them by doing experiments, which makes sense to me. Of course it would be great if there were some profound principle that picked one out as unique, but the absence of such a principle doesn’t seem like such a disaster to me.
In modern parlance, “violating the principle of equivalence” just means “having some new long-range forces of approximately gravitational strength.” String theory could have such forces (the dilaton is an obvious candidate), but it’s not necessary, as the forces would be undetectable if their associated fields were given a relatively large mass.
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