Lee Smolin wrote an interesting responses to comments in the comment section of my posting about his Physics Today piece entitled “Why No New Einstein?”. I’m reposting it here.
“Dear Peter and colleagues,
I am grateful for the attention given to my essay. I only want to emphasize a few points here. The main thing is that the essay is carefully written. It does not advocate more funds to LQG or any other program. It explicitly advocates more support and positions for young, ambitious theorists pursuing their own research programs who are unaffiliated with any larger program. Several proposals are made for how to accomplish this. I would hope that the focus of the discussion could be on these proposals.
-String theory is criticized in the essay mainly because it is currently sociologically dominant, and so subject to the problems mentioned. It was necessary to do so as many readers of physics today will be unfortunately unaware that there are any problems with string theory, or any viable alternatives. Anyone with a long enough memory will know that the sociological issues in high energy theory predate string theory, and have hurt physics in the past, i.e. in the case of S-Matrix theory.
-I hope I don’t have to say that I am not anti-string theory. My current last paper on the ArXiv is a technical paper in string theory, and I have 14 more in past years, plus 8 papers on related topics such as the landscape. I wouldn’t have written these papers if I didn’t think there was a good chance string theory is relevant to nature. The fact that someone like me who contributes sometimes, but not exclusively, to string theory, is not considered “a string theorist” is part of the sociological problems my essay criticizes. Similarly, the fact that one can elicit angry responses, and be called “anti-string” for carefully and correctly recounting the actual status of various conjectures is a sign of an unhealthy sociology. No one calls someone anti-LQG or anti-QCD when they do a similarly honest summary of what is known and not known in those fields.
-I would claim that the sociological issues mentioned in the essay have hurt string theory even more than they have hurt the alternative programs, because they greatly limit the range of ideas worked on, and because people with a lot of imagination and intellectual independence are either selected out or choose themselves to work within communities which are more friendly to diversity and imagination. As a result, key issues such as the question of a background dependent formulation, or perturbative finiteness, don’t get a lot of attention, in spite of their centrality for the whole program.
-I was grateful that someone noted the range of subjects at the LQG meetings. This was not planned, it is a natural outcome of the more open and curious atmosphere among people who work on the subject. We don’t believe we should have a meeting without inviting people from alternative and rival programs to report to us what they are doing, as well as to serve as critics. At the meeting in Marseille last May we even invited a persistent critic of LQG-Ted Jacobson-an early contributor who is now very critical of the subject-to give a talk to lay out his criticisms. I think it would be very good for string theory if the organizers of their meetings took a similar attitude.
-Someone asked for a blanket term for LQG, CDT, causal sets etc. We use background independent approaches to quantum gravity. There is a lot of interchange of ideas, techniques and people among these programs, and many of us have contributed to more than one. There is a very different intellectual climate, in which diversity, creativity and independence are strongly encouraged.
-Someone is asking for what is “LQG proper?” But the fact is that a lot of different things are now going on roughly under the name of or related to LQG. After all, this is now a community of > 100 people and there is no orthodoxy and no one trying to control what people work on. We agree generally on what has been achieved and what problems remain open, but not much beyond that. There is a healthy variety of approaches and attitudes towards the open problems. If there is one thing we all agree on it is that no approach is likely to achieve the right theory that is not background independent at its foundations. Come to the meeting and see what is happening.
-While the point of my essay was not to advocate more funding to any particular direction, if you ask me I will of course say that I think that people working on background independent approaches to quantum gravity deserve much more support. Among them are Loll and Freidel, that I am glad someone mentioned, but there are many others.
-I did not, as Lubos implies, advocate funding a large number of people who do nothing but think about the foundations of quantum theory. What I do advocate is much more support for the kind of person who might be inclined to work on foundational issues. These are deep and independent thinkers who believe that the road to progress in physics is confronting the hard problems directly. But there is no need to argue about whether more funding for foundations of quantum mechanics would be fruitful. The experiment has been done. For decades there was no support at all, and slow progress. Then, because of the possibility that quantum computers could break codes, there has been a lot of support for the last few years. And a lot of progress has been made, both experimentally and theoretically on aspects of foundations of QM.
-Although this essay was not written to advocate LQG, since it is attacked in response I should try to clear some things up. Someone asks for an accounting of the present status of the field. I among others, have given one in hep-th/0408048, shortly to be updated.
As to the issue of anomalies, i.e. the claim that we ignore the established knowledge that “INFINITE-DIMENSIONAL CONSTRAINT ALGEBRAS generically acquire anomalies on the quantum level…” is simply false. It is contradicted by rigorous existence and uniqueness theorems in LQG. As a few people do nevertheless take this seriously let me start from a point we can agree about and see if we can clear this up for good. I would hope we can all agree that:
1) The approach to quantization of constrained systems is different in string theory and LQG. The former approach depends on a gauge fixing that refers to a fixed background metric. It results in the construction of a Fock space. The latter is background independent and involves no background metric, no gauge fixing and results in a state space unitarily inequivalent to a Fock space.
2) There is a body of rigorous results that support each kinds of quantization. Hence it cannot be a question of which is correct mathematically. Both are correct, within their contexts. It is a question only of which construction is appropriate for which theories and which describes nature.
3) The treatment of constraints in string theory depends on certain technical features of 1+1 dimensional theories, particularly the fact that there is a gauge in which L_0 plays the role of a Hamiltonian and therefore should, in that gauge, be quantized so as to have a positive spectrum. The anomalies are not generic, as asserted above, rather they depend on the additional condition that L_0 should be a positive operator. There are other reps of Diff(S^1 ) that are non-anomalous but in which L_0 is not positive. So a choice is made in the standard quantization of string theory, which his motivated by the physics. This does not mean it is the right choice for all physical theories.
4) Conversely the existence and uniqueness theorems which support the LQG quantization work only in 2+1 dimensions and above for the reason that gauge fields don’t have local degrees of freedom in 1+1 dimensions. The existence theorems tell us that there are quantizations in 2+1 and higher of diffeo invariant gauge theories that have unitary, anomaly free realizations of diffeo invariance. The uniqueness theorem tells us that the resulting state space we use in LQG is unique.
5) Now it is true that Starodubstev and Thiemann have found it an interesting exercise to apply the LQG techniques to free string theory. Not surprisingly they get a theory that is unitarily inequivalent to the usual one. This does not mean that the usual quantization of string theory is wrong, nor does it mean that the LQG techniques are wrong when applied to other problems, where the existence and uniqueness theorems together with a large number of results prove their worth. All we learn is that the two quantizations are inequivalent, which was to have been expected.
6) With regard to the non-standard quantization, in which holonomies, but not local field operators are well defined, it is of course true that when applied to standard systems this leads to inequivalent results. “This apparently leads to unphysical consequences, such as an unbounded spectrum for the harmonic oscillator.” But, give me a break, do you really think someone is proposing to replace the standard quantization of the harmonic oscillator with the alternative one? What is being proposed is that the quantization used in LQG is well suited to the quantization of diffeo invariant gauge theories.
In case it is not obvious, let me emphasize that harmonic oscillators are not relevent here, and can play no role in a background independent quantum theory, precisely because the division of a field into harmonic modes requires a fixed background metric. Thus, the physics of the problem REQUIRES an alternative quantization.
The detailed motivation is, I think, well argued in the papers, and are supported by the results as well as the existence and uniqueness theorems. First, is well known that a complete coordinatization of the gauge invariant configuration space for a non-Abelian gauge theory requires the holonomies. Second, using them gives rise to the unitary non-anomolous reps of the spatial diffeomorphisms.
Nor is anyone proposing using non-seperable Hilbert spaces for the full theory, the point is that when one mods out by the piecewise smooth spatial diffeos one is left with a seperable Hilbert space.
I am frankly puzzled why someone who claims to know the literature well would throw up examples like the harmonic oscillator up in this context. I can try to understand their point of view, but it certainly reads as if they either are choosing to ignore the basic point, which is that background independent quantizations cannot use fock space, or they are looking to make debating points to impress ignorant outsiders. They must know comments like this are not going to influence experts, because they are, after all, taken from our own papers, written precisely because we wanted to clarify the difference between the new and standard quantizations and the limits of the applicability of each.
With regard to the sociology of the string-loop division, “Roughly speaking, string theorists are fundamentally particle theorists with a strong understanding of quantum theory, whereas loop people are gravitists with a background in GR”, this is a myth. Rovelli, myself and many other people in LQG were trained as particle physicists, myself at Harvard in the late 70’s. Most of the physical motivation for LQG comes directly from ideas about formulating gauge theories in terms of loops that were studied by Polyakov, Wilson, Migdal, Mandelstam, Neilsen and others. LQG is squarely an outgrowth of their intellectual tradition. The only thing we added was to correctly treat the diffeomorphism invariance exactly in the quantum theory. This led to new results just as the exact treatment of gauge invariance in lattice gauge theory led to new results. I would claim that we made progress in LQG precisely because we had a very good grounding in QFT.
String theory, as it is practiced, makes much more contact with the general relativity tradition, especially the once discredited tradition of extending general relativity to add dimensions and degrees of freedom in the search for a unified field theory. You are much more likely to read a paper which studies solutions to a generalizationsof the Einstein equations, with hbar=0, by a string theorist than by someone working on a background independent approach to quantum gravity.
This of course does not mean that string theory is wrong. But I believe it does mean that by enforcing a narrowly restrictive notion of what constitutes good work, the community of string theorists has hampered progress in string theory by excluding from consideration the lessons learned by attempts to do what string theory must do eventually if it is to be a real theory: which is to find a background independent formulation of a quantum theory of spacetime.”
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