## Saturday, September 03, 2005 ... //

### John Baez and quantum gravity

In his Week in mathematical physics, John Baez argues that the research of quantum gravity has been stagnant recently which was his reason to focus on pure math - and the so-called operads (which I probably don't want to learn about - evidence that this is unreasonable is welcome) dominate his "Week". Well, most of the things he says are based on true facts but some of them may require some comments.

String theory

Concerning the landscape, it should be known that the anthropic reasoning is a rather active and slightly fashionable direction that a relatively small subset of typically very smart string theorists considers promising as the likely ultimate explanation; this subset co-operates with a larger group that likes to study various technical questions about the stabilized vacua. The majority of roughly 80%, as shown in the poll in Toronto, opposes the anthropic reasoning.

This is probably a fair ratio reflecting our ignorance about the right answer. While the majority seems to share my opinion that much stronger evidence would be needed for us to accept that the predictibality of particle physics should be crippled in this radical, anthropic fashion, no one can yet use string theory to prove that the anthropic scenario is impossible as a rule for this world.

If we really live in a random background of string theory which only differs from most others in a huge ensemble called the landscape by its ability to create somewhat intelligent beings like us, and if we ever find quantitative evidence that this is the case, it would be a true revolution (or at least a counter-revolution) in physics. This is why it's an interesting game that many incredibly smart and patient colleagues continue to investigate so seriously. Unfortunately, I think that it is virtually impossible to find such evidence - unless we directly observe the other Universes in one form or another.

Otherwise, only non-trivial quantitative predictions of something would convince others that the anthropic principle constrains the predictability as advertised and the much larger multiverse is relevant for physics. But they're unlikely to appear exactly because the anthropic principle itself says that many important things can't be predicted which probably implies, because all parts of the world are coupled to each other, that nothing can really be predicted if this scenario is true.

Nevertheless, because of the importance of the other answer that would surprise us, a group of researchers is looking at some very serious math and is investigating the possibility that the masses of elementary particles and various couplings are as much historical coincidences as the radii of planetary orbits. This scenario is usually embedded in eternal inflation and involves something like the flux vacua - the most popular vacua that often allow complete moduli stabilization.

But it is not fair to say that string theory has become anthropic. We simply do not know yet what are the correct rules for vacuum selection - no one has convinced others about some amazing progress in the search for a "unique" realistic vacuum - and an anthropic, random selection remains a logical possibility.

Once again, it is important to stress that even though this basic unsolved question about the vacuum selection - that may perhaps be answered only after we understand string theory in some background independent way that allows one to answer questions about cosmology and the primordial quantum evolution of the moduli and other things - is reducing the number of the people who would otherwise believe that string theory describes the real world, we have not found any demonstrable internal inconsistencies in string theory or inconsistencies between string theory and the real world, or at least its qualitative features.

And there are some relatively interesting directions "inside" string theory - those that don't immediately try to connect the theory with the real world but that show us some new mechanisms inside the theory; some of them may turn out to be helpful in the search for the more universal definition of string theory. This issue is not the focus of this text.

Loop quantum gravity

The progress in loop quantum gravity has been more straightforward and most of the conjectures that loop quantum gravity could be another consistent quantum theory that includes gravity at long distances have been more or less safely falsified. There is growing evidence that

• the "spin foam" (path integral) approach to these ideas does not lead to unitary S-matrices, not even approximately - the LQG proponents say themselves that global unitarity is violated and they even elevate this to a virtue (this is the real reason why they promote the obscure "relational interpretation of quantum mechanics" in which information is only conserved "locally", see page 64 here, which also requires one to believe that Maldacena's correspondence is wrong - wow)
• assuming a realistic smooth space limit, the spin foam heavily violates Lorentz invariance because any spin foam intersects null two-planes roughly as many times as it intersects all other planes, and their area therefore cannot be (close to) zero as required by the Lorentz symmetry
• this could possibly be resolved if you imagine that most of the spin foam is degenerate; in fact, the generic simplices in the spin foam are indeed degenerate as shown by Baez et al. (the degenerate 4-simplices dominate the ensemble) which completely ruins the idea of the spin foam as a "regulator" giving nice results but does not still guarantee that at least a smooth space made out of degenerate simplices exists
• independently of that, all attempts to derive the flat space limit at long distances seem to fail unless one makes an ad hoc assumption that the configurations that don't look as flat space must be eliminated by hand
• the spin foam is not quite equivalent to the "canonical" (and currently unpopular among the "mainstream" LQGers) approach based on spin networks and the Hamiltonian favored by T. Thiemann, among others
• that the Hamiltonian in the canonical approach cannot be defined as a finite object unless infinitely many parameters are undetermined or unless all points in space remain isolated forever; this has been the focus of Nicolai et al.
• that the original calculation of the black hole entropy in loop quantum gravity was mathematically flawed; in August, the 17th proposal what the "right" numerical pre-factor (the Immirzi parameter) should be appeared
• this means that the number involving log(3) is not the desired number to match LQG with the Bekenstein-Hawking formula; but independently of that, it is absolutely certain that the quasinormal modes of non-Schwarzschild black holes don't lead to the right constant log(3) either
• in other words, the previous arguments about the ability of LQG to explain the value of the black hole entropy were based on an equality between the results of two calculations; both calculations are known to be seriously wrong, in different ways (in fact, one wrong side would be enough to kill this argument)
• more generally, there still exists no consistency check in LQG - a thing that can be calculated or derived in two inequivalent ways
• one could continue with comments like those summarized here

But there are still new and new attempts. On Tuesday, Carlo Rovelli claimed to have derived the graviton propagator from the Euclidean spinfoam version of LQG. In his framework, the regular tetrahedral simplices dominate the spin network state. This not only violates the calculation of Baez et al. mentioned above that implied that singular simplices dominate, but also the condition for Lorentz invariance in the Minkowski version of LQG. Moreover, it is not derived in the new paper; instead, it is (correctly or incorrectly) assumed that smooth-space-like behavior is impossible if the degenerate spin networks dominate. Also, this seems to acknowledge that one effectively needs a background after all - something that tries to keep the space nearly flat or, equivalently, keep the tetrahedra nearly regular.

I wonder how a worse collection of discouraging insights about a candidate theory could look like for someone to admit that LQG cannot be a consistent theory of quantum gravity. It's not a tragedy if someone's favorite theory or formula has been proved wrong and everyone should be assured that the other physicists won't kill anyone for this insight. It's much more worrisome if someone feels pressure - for example, existential pressure - to defend a theory that is known to be inconsistent.

The previous comments about loop quantum gravity (LQG) may sound incoherent because they reflect the actual topics studied in LQG rather than a rational approach to quantum gravity.

Jacques Distler gives a rather nice description why the alternatives to string theory are unlikely to solve the real combined problems of quantum gravity. I completely agree with his description of some of the major difficult problems and their resolution in string theory:

• gravity can't ever be quite decoupled from other forces; in fact, it is probably bound to be the weakest one and therefore it is not physically realistic to study "pure quantum gravity"; we will mention some additional consequences below
• there's no problem in using gravity as a low-energy effective quantum field theory, but the number of parameters (the coefficients of the higher-derivative terms) grows indefinitely if one wants to predict physics in the Planckian regime (and a cutoff can't really be defined in a diffeomorphism-invariant way which always means a slight non-decoupling of the unphysical modes of the graviton)
• one can't imagine that gravity is classical; my simpler argument for the same statement is that the fate of the Schrodinger cat is decided probabilistically (via the radioactive atom), and because a dead cat creates a different gravitational field than an alive cat (imagine a planetary-size cat if you have problems to imagine a cat's gravitational field), the gravitational field can't evolve "classically" either: everything must be probabilistic if something is probabilistic
• in other words, it is impossible to combine classical and quantum physics in one consistent theory, and it is apparently also impossible to deform the Schrodinger equation in a non-linear way while preserving the conservation of probabilities (recall how linearity is crucial for your proof of the conservation of probabilities in the Schrodinger equation) as well as some kind of locality (one may want to "normalize" the probabilities so that they sum up to one, but this would introduce testably non-local and superluminal interactions)
• the discretization of quantum gravity - much like loop quantum gravity - is morally equivalent to defining a theory near the Planckian cutoff; infinitely many parameters - the coefficients of the terms that are equivalent to the higher-derivative terms - remain undetermined (in the case of LQG, this is discussed by Nicolai et al., but the LQG proponents don't seem to care about this "detail" of having infinitely many undetermined and important parameters)
• the predictable theories of this type for the Planckian physics could only exist if there exists a non-trivial UV fixed point of gravity (a scale-invariant effective description of general relativity that would be valid at extremely short distances) - a hypothetical possibility that we discussed recently - such that its conformal symmetry is broken near the Planck scale and flows to general relativity at low energies; it seems that such a UV fixed point does not exist
• even if this UV fixed point existed, it would probably prevent you from adding non-gravitational physics because other forces completely change the UV behavior
Jacques continues by explaining how string theory solves these problems. There are other arguments that eliminate the very same "alternative" theories and lead you to string theory as the unique solution - for example those based on Lorentz invariance:
• The Minkowski vacuum cannot have any "discrete structure" that could a priori be in many different microstates that are more or less equally good approximations of an empty space because this would lead to a Planckian entropy density and the same huge Lorentz violation as in the theories of aether. This eliminates the attempts to discretize gravity.
• In this sense, the full theory must look like a generalized quantum field theory.
• Only infinitely many new fields have the capacity to soften the UV problems of gravity.
• Only if these fields arise from the same fundamental object(s), the number of undetermined parameters may stay finite.
• Strings are the only objects whose quantization leads to a realistic QFT-like theory perturbatively - one that automatically involves both gravity as well as fermions and gauge theories; in fact, the number of non-dynamical parameters is exactly zero in string theory.
• Other (higher-dimensional) objects also occur in consistent theories of quantum gravity and in all the known cases, they are part of string theory. There should be a description of string theory that does not have to start with strings at all and defines what kind of theories with infinitely many new objects (and correlated couplings) are plausible, and we should try to find it.
String theory solves both related sets of the problems because the extra massive fields arising from excited strings (and the non-perturbative objects that morally lead to the same story) provide you with the counterparts of the W,Z bosons that soften the Fermi four-fermion theory; in the stringy case they soften gravity. There is an infinite tower of these states but all of their masses and couplings are determined by their stringy origin. One can prove that the resulting amplitudes are Lorentz-invariant, finite, unitary, and every conceivable deformation of this theory destroys at least one of these roughly three symptoms of consistency. Strings are the only objects that can lead to such a result constructively and perturbatively.

Also, string theory always leads you to calculate the right observables, for example the S-matrix or its slightly different anti-de-Sitter counterpart (and we don't know what are the right observables to study in completely generic cosmological backgrounds), and various potential paradoxes arising from other observables and their subtle tension with the diffeomorphism invariance are therefore avoided in string theory. Jacques also argues that a generic discrete theory of gravity would also naturally lead to a Planckian cosmological constant. While this comment is true, it may be painful for a string theorist (or any other theoretical physicist, for that matter) to use this as an argument to kill a different theory. ;-)

Whether or not we count LQG as a discretization of gravity is an irrelevant verbal game. At any rate, one can derive that the spin networks form a basis of its Hilbert space, and infinitely many terms in the Hamiltonian must be considered, as argued by Nicolai et al., much like in other attempts to discretize gravity.

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SPAM ENDED....

Sorry guys, these three very fast examples have led me to introduce the word verification.

Dear Lumo,

Please take a look at t'Hooft's suggestion at *http://eskesthai.blogspot.com/2005/08/fifth-dimension-is-spacetime-fabric.html*

I've been interested in this for a decade, and have a pressure calculation for gravity strength which is correct. I've had the preliminary calculation go on Cern document server (preprint EXT-2004-007, http://cdsweb.cern.ch/search.py?recid=706468&ln=en) and published in 12 pages of the magazine Electronics World (4 pages in the August 2002 issue, 6 in the April 2003 issued, and 2 other pages of letters; http://www.softcopy.co.uk/electronicsworld/ ).

However, with t'Hooft's recent ideas it now looks a part of 5-D spacetime. It would be nice to have someone put a paper about it on arxiv, which I did using my university email address for verification in 2002, but they removed my paper about 2 minutes later. The prejudices in science are inexcusible. What makes it so bad is the propaganda supporting 10-D spacetime speculation for ST.

Why not 5-D string theory?

Best wishes,
Nigel