I have been deleting some comments, but am trying to err on the side of letting people say what the want to say.

Could you put the text of Lee Smolin’s reply letter in your next blog entry? It is buried
here among the postings of loonies and
it deserves to be more widely known (at
least parts of it) as it helps to understand
his position and motives better. If that is
impossible, can you at least remove the
two postings right after that letter that are
stupid, offensive and simply indecent.

Now it is a usual popular claim that Witten is the new Einstein or even the new Newton.

Sincerely, that is stupid. I’m sorry but Witten is not a 10% of a Feynman, regarding to physics.

Dan said

1- “there is no current experimental data that clearly goes beyond the SM and GR.” This is not true. There is experiments and data. SM was designed for typical accelerator physics experiments, if one continue to test it one probably fin nothing. Apply the SM to a molecule, for example, and after we will talk about that.

Has you computed the total orbit of Mercury using full GR (including non radial components)? Orbit programs use only some GR effects in perihelion and light deflection but ignore time delays in the computation of orbit. Why?

2- “theories that go beyond SM and GR such as ss/m-theory make predictions (10D-SUSY) that are not currently testable.” Incorrect again. Alternatives to GR are doing predictions about the future Gravity Prove B, alternatives to SM also can be verified in molecular experiments. There are proposals in literature for verifying the SM several orders of magnitude more exact that usual tests.

3- “there is no experimental evidence to guide theory.” False again, there are dozens and dozens of current anomalies in data that guide to us to new theoretical frameworks. For example, certain anomalies in tomahawk data arise from new forces do not predicted by QED.

In a recent Physical Review D:

“may reflect departures from both Newtonian gravity and GR on galactic and larger scales. Now alternatives to GR are traditionally required to possess an Newtonian limit for small velocities and potentials… also raises the possibility that the correct relativistic gravitational theory may be of a kind not considered hitherto.”

A “new” einstein will make predictions like the universe is not 10D and SUSY, I am practically sure.

“same can be said for other approaches, such as LQG-volume and area operators.” This is false; the existence of a quantum of volume and area can be proved. In fact, it has been theoretically proven that no existence of quantum invalidates some well-known experimental data. I mean an indirect verification of the quantum not one direct test (at least i don’t know any), somewhat like curved spacetimes in GR are not directly measured but compatible with many data.

1- there is no current experimental data that clearly goes beyond the SM and GR and

2- theories that go beyond SM and GR such as ss/m-theory make predictions (10D-SUSY) that are not currently testable.

3- there is no experimental evidence to guide theory.

if a “new” einstein makes predictions like the universe is 10D and SUSY — there would be no way to confirm it.

(same can be said for other approaches, such as LQG-volume and area operators).

so i don’t entirely understand smolin’s point. maybe the “new” einstein is alive and publishing and his name is witten, but we don’t have the technology to test witten’s theories.

Let me emphasize that I am not a string theorist – on the contrary, over the last years I have had strong disagreements with Lubos and others, especially over the role of diff anomalies. While initially a statistical physicist, the success of CFT made me interested in Lie algebras, where I discovered how to generalize the Virasoro algebra beyond 1D and developed its representation theory, together with mathematicians like Moody, Rao, Berman and Billig. In particular, the Virasoro algebra in 4D is the anomalous form of the algebra of 4-diffeomorphisms, which is the constraint algebra of GR in covariant formulations (in non-covariant canonical quantization the constraint algebra is modified).

So when I speak about diff anomalies, I do it as someone who has developed new mathematics which has not been absorbed by the physics community. You may wish to keep that in mind.

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.

Whereas I claim that this is true, it is not at all generally accepted. On the contrary, it is widely asserted that there are no pure gravitational anomalies in 4D, see e.g. Weinberg’s QT of F II, ch 22. Nevertheless, the constraint algebra of GR contains many subalgebras isomorphic to the infinite conformal symmetry in 2D, generated by vector fields of the form f(z) d/dz, where e.g. z = x^0 + ix^1 or z = x^2 + ix^3. Upon Fock quantization, these conformal subalgebras will in general acquire anomalies for the usual reason, making the whole shebang anomalous.

The reason why these anomalies cannot be seen in conventional field theory is that the relevant cocycles are functionals of the observer’s trajectory in spacetime. Unless this trajectory is introduced and quantized in conjunction with the fields, the relevant anomalies cannot be formulated. This is IMO the crucial obstruction to the quantization of gravity.

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.

Conventional quantization has turned out to describe nature in other contexts. I think this is a good reason to believe that it is the correct approach. In particular, CFT has been successfully applied to 2D condensed matter, where conformal anomalies have been measured experimentally. This is of course a different context and not directly relevant, but this fact has shaped my basic instinct that anomalies are very real things which cannot depend on the quantization method used.

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.

Yes, this is the crucial point. In any physical theory, there should be some positive operator which can be interpreted as a Hamiltonian; there is a physical requirement that energy be bounded from below. Of course, in GR there is a Hamiltonian constraint rather than a genuine Hamiltonian. This is another reason to introduce the observer’s trajectory; you can define a genuine Hamiltonian as the operator that translates the fields relative to the observer.

Anyway, in all applications of Lie algebras to physics so far, the reps have been of lowest-weight type. At least for finite-dimensional Lie algebras, all unitary irreps are of this type.

There are other reps of Diff(S^1 ) that are non-anomalous but in which L_0 is not positive.

If you consider the restriction to the algebra of polynomial vector fields, generated by L_m with m >= -1, then all irreps have a vacuum vector (or are dual to such a rep).

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.

OK. I disagree.

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.

Contrary to string theorists, I claim that anomaly freedom is not a necessary requirement. To illustrate this point, let me again use the bosonic string as an example and quote from GSW, subsection 2.4: ‘Classical free string theory can be consistently formulated for any spacetime dimension, but quantization with a ghost-free spectrum requires D less than or equal to 26. [...] In the special case of D=26 and a=1 the spectrum is entirely tranverse, with many decoupled zero-norm states.’

Thus, D=26 is special, but D less than 26 is not ruled out by consistency requirements. It is only in 26D that it is possible to pass to the reduced Hilbert space by imposing the physical state condition L_m|phys)=0, but when D less than 26 this is not necessary, because the full, unreduced Hilbert space is already positive-definite.

Thus, my position is that some diff and gauge anomalies are good, making it possible to break diff and gauge symmetry on the quantum level, such as the string in D less than 26 illustrates. This does not mean that all gauge anomalies are good, of course. On the contrary, I recently gave a simple algebraic argument why conventional gauge anomalies, due to chiral fermions and proportional to the third Casimir, indeed are inconsistent. This argument does not apply to observer-dependent anomalies, which are proportional to the second Casimir.

The idea that diff and gauge anomalies may be consistent is of course very controversial.

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.

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.

I agree that a diff invariant quantization of gravity cannot use Fock space, and I am convinced that such a quantization does not exist. However, a diff covariant Fock space quantization of gravity may very well exist. By this I mean a quantization in analogy with the string for D less than 26: the unreduced Hilbert space is consistent in itself, and diffeomorphisms are promoted to a genuine but anomalous symmetry acting on the full Hilbert space.

A step in this direction was taken in hep-th/0504020. Sure, there are problems: the (manifestly covariant) regularization has not quite been removed, no invariant inner product has been found, and no hard predictions have been extracted. But there is a Hamiltonian which is bounded from below in the regularized theories, the analogous construction for the harmonic oscillator has a spectrum bounded from below (it is not quite right, and I discuss why), and infinities cancel best (though not quite, so I am doing something wrong) in 4D. Most importantly, since phase space variables are promoted to operators in the usual way, this is genuine quantization, which is witnessed by the presence of anomalies.

Finally, I didn’t express myself very well on the sociological issues. I agree with you about the problems with string theory, and I did not mean that funding to LQG should be stopped. However, given what I feel is a major problem (the harmonic oscillator spectrum), and that LQG already is the second biggest player in QG, I cannot really think that it is badly underfunded at present levels.

I smell moral pressure from string theorists on this issue. It is considered immoral to say that string theorists aren’t superhuman geniuses. Let me say this: I have met and talked to many of them, and they seem to me to be no more intelligent on average than a typical mathematician or theoretical physicist. Just as it is OK to exaggerate how bad Hitler or Saddam Hussein were, for example by saying that they ate babies, it is OK to exaggerate how clever string theorists are. A person who says that Saddam didn’t eat babies can be attacked for being a Saddam-sympathizer, and a person who dares to say that all of this “string theorists are all geniuses” talk is mere propaganda can be attacked for claiming to be more intelligent than string theorists, which nobody is entitled to do unless they know more than all the string theorists about heteroskedastic fibrations over David-Letterman manifolds.

String theorists aren’t the smartest guys on the planet. They’re just enmeshed in a macho culture where they have to claim to be super-geniuses, and they can conceal their mediocrity behind a cloak of gibberish which one must become a string theorist to see through.

It seems to me that any progress that has been made has been in the realm of taking the previously existing understanding of QM and applying it to new systems. People have talked about qubits and Shor’s algorithm and quantum registers and have demonstrated quantum teleportation, but these are all straightforward applications of the previously known and well-understood formalism of quantum mechanics.
I think that this is no more indicative of progress being made on the foundations of quantum mechanics than the successful factorization of a large number constitutes progress on the foundations of arithmetic.

An example of a genuine non-trivial thing that
quantum mechanics says is the following:
Suppose there are N experiments with the
following properties:
1. Each experiment has only two possible results.
2. If we perform the same experiment twice, then
we get the same result.
3. If we know in advance with certainty that a
particular experiment will give a particular
result, then the probabilities of the possible
results for all other experiments are 50%.

Then N is less than or equal to three.

Nobody has ever attempted to address questions like why this should be true. Instead, it seems that the quantum computation people have agreed amongst themselves that they like the many-worlds interpretation and have left the foundations there.