### Lee Smolin disproves his critics politely

Loop Quantum Gravity researcher Lee Smolin has answered 'critics' (mainly string 'theorists' who believe in unobservables) on Peter Woit's blog, LQG for Skeptics, http://www.math.columbia.edu/~woit/wordpress/?p=330. Lubos (Lumos) Motl of Harvard and some others rushed in with all sorts of 'arguments' trying to simply ridicule the spin foam vacuum approach to understanding quantum gravity (unifying general relativity and Feynman path integrals), when in fact they were just plain ignorant. Smolin then had to politely correct all their miscomprehensions:

Lee Smolin Says: January 20th, 2006 at 6:13 pm

Hi Peter, Thanks for mentioning this. After a quick look I can say that there are some statements they make that I agree with (such as about the difficiulties of relating the spin foam to the Hamiltonian constraint theory) and others with which I disagree, such as their statements about uv finiteness.

In particular, the point you quote, “the need to fix infinitely many couplings in the perturbative approach….” seems to disagree with old, well understood results. (Not to mention they don’t seem to make a detailed argument for their claim.) In fact, there is a well understood and detailed explanation for how the theory is cutoff. I won’t repeat the argument here (see hep-th/0408048) but the key points are that, as a result of the finitess of area and volume, one can show that the Planck length cannot suffer an infinite normalization if the theory is to reproduce the finiteness of black hole entropy,and the appearence of gravitons in perturbations around weave states. Thus, the theory is uv cutoff and the divergences do not have to cancel as they were never there in the first place. The key issue is then how is this finite cutoff length compatible with the symmetry of the ground state, which leads to the expectation that the symmetry is DSR.

But honest criticism based on detailed study is always welcome and I will read the paper carefully before seeing if I have any more substantial reponse to make.

In case anyone is interested, I am teaching a course on LQG, and video’s of lectures will be available as they are given at http://streamer.perimeterinstitute.ca:81/mediasite/viewer/FrontEnd/Front.aspx?&shouldResize=False

Thanks,

Lee

Lee Smolin Says: January 21st, 2006 at 9:51 am

On reading NP I am grateful for the hard work that they put in, but I end up feeling that they still miss the point, because they have prejudices about what a quantum theory of gravity should do coming from old expectations. They appear to evaluate LQG and spin foam models as if they were proposed as a unique theory which was a proposals for a final theory of everything. This is in my view a misunderstanding. One should understand these as a large set of models for studying background and diffeo invariant QFT’s. These are based on quantization of a set of classical field theories which are constrained topological field theories. There are three key claims: 1) these theories exist, rigorously. i.e. there are uv finite diffeo invariant QFT’s based on quantization of constrained TQFT’s. 2) there is a common mathematical and conceptual language and some calculational tools which are useful to study such models and 3) there are some common generic consequences of these models, which are relevant for physics.

Nothing NP say questions these key claims. Unfortunately, they do not mention key papers which support these key claims, such as the uniqueness theorems (gr-qc/0504147, math-ph/0407006) which show the necessity of the quantization LQG uses. And while they mention the non-seperability of the kinematical Hilbert space they fail to mention the seperability of the diffeomorphism invariant Hilbert space, (grqc/ 0403047). It is unfortunate that they omit reference to such key results which resolve issues they mention.

A second misunderstanding concerns uv divergences. NP do not discuss the results on black hole entropy, so they miss the point that the finiteness of the black hole entropy fixes the ratio of the bare and low energy planck length to be a finite number of order one. Calculations on a class of semiclassical states they do not discuss-the weave states-lead to the same conclusion (A. Ashtekar, C. Rovelli, L. Smolin, Weaving a classical metric with quantum threads,” Phys. Rev. Lett. 69 (1992) 237.). So there can be no infinite refinement of spin foams and no infinite renormalization. These theories are uv finite, period. This is one of the generic features I mentioned. Thus, their main claim, that the fact that there are many LQG or spin foam models is the same as the problem of uv divergent is just manifestly untrue. The freedom to specify spin foam amplitudes does not map onto the freedom to specify parameters of a perturbatively non-renormalizable theory. For one thing, few if any spin foam models are likely to have a low energy limit which is Poincare invariant, a property shared by all perturbative QFT’s, renormalizable or not, defined in Minkowski spacetime. In fact, we know from recent results that in 2+1 none do-the low energy limit of 2+1 gravity coupled to arbitrary matter is DSR. So their argument is false. They do get a number of things right. The following are open issues, much discussed in the literature: 1) whether there is any regularization of the Hamiltonian constraint that leads to exchange moves, 2) whether thus there are any links between the spin foam amplitudes and Hamiltonian evolution, 3) whether the sum over spin foam diagrams is convergent or, more likely, Borel resummmable (although they miss that this has been proven for 2+1 models, hep-th/0211026). I don’t agree with all the details of their discussion of these issues, but these certainly are open issues.

NP seem to argue as if one has to prove a QFT rigorously exists in order to do physics with it, by which standard we would believe no prediction from the standard model. They mention that there are no rigorous constructed, semiclassical states, which are exact solutions to the dynamics, but this is the case in most QFT’s. This does not prevent us from writing down and deriving predictions from heuristic semiclassical states (hep-th/ 0501091), or from constructing reduced models to describe black holes or cosmologies and likewise deriving predictions (astro-ph/0411124), Nor does it prevent Rovelli et al from computing the graviton propagator and getting the right answer, showing there are gravitons and Newtonian gravity in the theory (gr-qc/0502036).

But, someone may ask, if LQG is the right general direction, shouldn’t there be a unique theory that is claimed to be the theory of nature? Certainly, but should the program be dismissed because no claim has yet been made that this theory has been found? To narrow in on the right theory there are further considerations, all under study:

-Not every spin foam model is ir finite.-Not every spin foam model is likely to have a good low energy limit.-The right theory should have the standard model of particle physics in it.

In addition it must be stressed that there can in physics be generic consequences of classes of theories, leading to experimental predictions. Here are some historical examples: light bending, weak vector bosons, confinement, principle of inertia, existence of black holes. All of these observable features of nature are predicted by large classes of theories, which can be as a whole confirmed or falsified, even in the absence of knowing which precise theory describes nature, and prior to proving the mathematical consistency of the theory. LQG predicts a number of such generic features: discreteness of quantum geometry, horizon entropy, removal of all spacelike singularities, and I believe will soon predict more including DSR, emergence of matter degrees of freedom.

One reason for this is of course that most of the parameters in such classes of such theories are irrelevant in the RG sense, and do not influence large scale predictions. Since we know the theory is uv finite this does not affect existence. The lack of a uv unique theory does not prevent us from testing predictions of QFT in detail, and it is likely to be the same for quantum gravity. The old idea that consistency would lead to a unique uv theory that would give unique low energy predictions was seductive, but given the landscape, it is an idea that is unsupported by the actual results. Having said all this, I hope that NP will put their hard won expertise to work, and perhaps get their hands dirty and do some research in the area.

Sorry to go on so long,

Thanks, Lee

Lee Smolin Says: January 21st, 2006 at 1:09 pm

To Zorq, I apologise that the one argument I gave is far from the whole story. I agree that to define a theory you have first to define a regulated theory and then study the limit as the regulator is removed and show that the expressions for observables that result have the symmetries and gauge invariances of the classical theory. The physical parameters are parameters of the resulting theory. But this was exactly what was done in the hamiltonian construction of LQG, the observables such as area and volume are constructed through a limit of regulated operators and then the limit is taken. The result is finite, diffeomorphism invariant observables. The parameters of the finite, diffeo inv. theory include the bare Newton’s and cosmological constant-not as coefficients in the dynamics but as coefficients in the algebra of observables. The diffeo invariance is proved restored in the limit. And don’t be confused, the bare planck scale was not the regulator, there was another regulator, that has already been taken to zero. Please study the details of the construction.

So what you ask for has been done-the logic is not circular and the theory is finite. I was addressing the proposal to still take a limit of the parameters vanishing, even after the limit of the regulator to zero is taken. This would be non-standard, and it leads to results in disagreement with the semiclassical theory.

To quantoken: obviously it would be better to have precise predictions than generic ones. But generic ones can still distinguish between classes of theories. If GLAST sees an energy dependent, polarization independent speed of light, thus confirming that the symmetry of the vacuum is DSR, this obviouosly kills theories that predicted either broken or naive Poincare invariance and supports the plausibility of theories that predict-even generically DSR.

I can’t agree with your equivalanece of LQG and string theory just because of the vast imbalence in how much work has been put into each. For each point about string theory there are dozens of papers, so the ins and outs of each issue have been often thoroughly explored. Key facts about LQG still rest, in many cases on one or a few papers. There are many obvious things to do that have not been tried for lack of people. So there is a lot still do to, for example to turn generic predictions into precise predictions.

And I don’t “believe” nature is discrete, we showed this is a generic property of a large class of diffeo invariant QFT’s.

I’ll reply to the rest later,

Lee

Lee Smolin Says: January 22nd, 2006 at 8:58 am

Zorq, the distinction between a finite theory and a uv fixed point is the following: a lattice QFT or condensed matter physics model with a fixed lattice spacing is a finite theory. You can still apply the RG to study the infrared behavior. The point in LQG is that AFTER carrying out the regularization procedure and defining the diffeo invariant states and operators from the limit of the regulator removed, there remains a theory with a fixed, but spatially diffeo invariant cutoff. So it is like a lattice theory in being intrinsically finite, except that all the states are spatially diffeo invariant. So the physical theory has a fixed cutoff. One place this is explained in detail is Rovelli’s book, pages 280-282, another is my review hep-th/0408048. To see how this is done rigorously see Thiemann’s gr-qc/0110034 or Ashtekar-Lewandowski GR-QC 0404018.

Lubos, the finiteness is achieved kinematically, once the procedure just described is done the theory is uv finite WHATEVER the dynanmics, again just as in a lattice QFT with fixed lattice spaceing. But, to continue with my example of 2+1, which you misunderstood, is that the symmetry of the groundstate is not put in, it is determined dynamically. In 2+1 it turns out to be kappa-Poincare. This cannot agree with perturbation theory carried out as an expansion around Minkowski spacetime, which order by order assumes ordinary Poincare invariance.

I agree there is an issue in the Hamiltonian theory with full spacetime diffeo invariance, which is one of several reasons I always discuss dynamics in the spin foam picture.

Thomas and Aaron, this has been discussed before. For QFT the harmonic oscillator kind of quantization leads to Fock space. The inner product of Fock space depends on the background metric, hence this quantization will never arise in a background independent formalism. So we do not avoid it because we are stupid, it is simply not an option. The question is then to find an inner product for states which are functionals of a connection mod spatial diffeos. The only known way to do this is to first construct a kinematical Hilbert spaced that carries an exact non-anomalous rep of the spatial diffeos and then use that unitary rep to mod out by the diffeos .

The uniqueness theorems tell us the result is unique. If you don’t like this please at least acknowledge the argument just described and either accept it or propose an alternative background independent quantization and do the work to show it is consistent.

Anonomous: See my talk at the loops 05 conference, details are in a paper under preparation.

## 2 Comments:

copy of a comment to Christine Dantas' blog:

http://christinedantas.blogspot.com/2006/01/smolins-online-course-on-qg-available.html

Sunday, January 22, 2006

Smolin´s online course on QG available in video

Lee Smolin´s Introduction to Quantum Gravity is now available in video! [ http://streamer.perimeterinstitute.ca:81/mediasite/viewer/FrontEnd/Front.aspx?&shouldResize=False ] Just scroll down the left side menu and you´ll find two presentations already there. I am watching the first part right now (and it´s 2 am! You see, sometimes it´s the only way to find time, just substract your precious sleeping hours and you get it...).

posted by Christine at 2:10 AM

Christine,

The background independence as Smolin presents it is very mathematically sophisticated. Part 1 of Smolin, going through spatial topology and Hilbert graphs, valent modes, Penrose's spin networks and arriving at the way to use these to deal with gravity by Feynman's sum over histories, is very good.

Part 2, showing with background independent (no metric)electromagnetism as field theories in Einstein's GR notation, is again interesting.

Special relativity (SR) is incompatible with spin foam vacuum because SR denies the spacetime fabric (i.e. accelerations resulting from curvature / spacetime fabric).

If you put any forces (accelerations of matter) into SR, you get paradoxes like the twins paradox.

This was one reason Einstein build general relativity (GR) which is not SR + gravity, contrary to Lubos Motl's ignorance.

SR is false because the principle of constancy of light speed duplicates the contraction. Remember, physically FitzGerald in 1889 and Lorentz in 1893 used the contraction (of distance in direction of motion) to save the spacetime fabric + variance of light speed.

The Michelson-Morley experiment of 1887 showed that you can't measure the speed of light difference due to the direction and speed of the Earth's motion.

FitzGerald said it was because the distance the light beam had to travel was physically shortened, due to the spacetime fabric pressure inducing physical compression of everything electrically held together (atoms) in the direction of motion in the ratio [1 - (v^2)/(c^)]^1/2

SR contains both the postulate of that light speed appears the same to all observers, plus the contraction and no spacetime, which is too much.

My feeling is that SR is completely bogus.

Einstein did not do SR + gravity = GR. He wrote in 1916 that SR is the restricted approximation which doesn't deal with accelerations, so SR doesn't apply to any spacetime fabric (curvature and acceleration).

Motl's claim that SR should result from a physical gravity model (spin foam vacuum) is a fraud.

GR is really Newtonian gravity + equivalence principle + consistent tensor analysis of Ricci and Levi-Civita.

Ignoring the indices, Newton's law in tensors is R = 4 Pi GT. To get to the field equation of GR you introduce the contraction which arises several ways for mathematica consistency or conservation of gravitational potential energy which Newton's equation doesn't deal with when expressed in tensor calculus:

GR: R– ½gr = 8 Pi GT

The contraction term, -½gr, is the special thing which introduces all the special things about GR that Newton does not.

‘The Michelson-Morley experiment has thus failed to detect our motion through the aether, because the effect looked for – the delay of one of the light waves – is exactly compensated by an automatic contraction of the matter forming the apparatus…. The great stumbing-block for a philosophy which denies absolute space is the experimental detection of absolute rotation.’ – Professor A.S. Eddington (who confirmed Einstein’s general theory of relativity in 1919), Space Time and Gravitation: An Outline of the General Relativity Theory, Cambridge University Press, Cambridge, 1921, pp. 20, 152.

‘Recapitulating, we may say that according to the general theory of relativity, space is endowed with physical qualities... According to the general theory of relativity space without ether is unthinkable.’ – Albert Einstein, Leyden University lecture on ‘Ether and Relativity’, 1920. (Einstein, A., Sidelights on Relativity, Dover, New York, 1952, pp. 15-23.)

Of course, Motl argues on his blog that SR is entirely right because Dirac's equation is supposedly SR + QM. But Dirac was just using the mathematical results of SR, which by the equivalence principle, are the same in GR. I've demonstrated how the contraction of FitzGerald-Lorentz gives the gravitational contraction (of radius, time, etc) on my site (although my presentation is not very neat as I don't have much time).

Therefore Dirac's equation doesn't prove SR is the right formulation. Dirac himself didn't pay attention to SR's denial of acceleration/fabric:

‘… with the new theory of electrodynamics [vacuum filled with virtual particles] we are rather forced to have an aether.’ – Paul A. M. Dirac, ‘Is There an Aether?,’ Nature, v168, 1951, p906. (If you have a kid playing with magnets, how do you explain the pull and push forces felt through space? As ‘magic’?) See also Dirac’s paper in Proc. Roy. Soc. v.A209, 1951, p.291.

Contrary to Motl, EM does imply a spacetime fabric with physical properties:

‘It has been supposed that empty space has no physical properties but only geometrical properties. No such empty space without physical properties has ever been observed, and the assumption that it can exist is without justification. It is convenient to ignore the physical properties of space when discussing its geometrical properties, but this ought not to have resulted in the belief in the possibility of the existence of empty space having only geometrical properties... It has specific inductive capacity and magnetic permeability.’ - Professor H.A. Wilson, Modern Physics, Blackie & Son Ltd, London, 4th ed., 1959, p. 361.

QFT also implies a spacetime fabric:

‘All charges are surrounded by clouds of virtual photons, which spend part of their existence dissociated into fermion-antifermion pairs. The virtual fermions with charges opposite to the bare charge will be, on average, closer to the bare charge than those virtual particles of like sign. Thus, at large distances, we observe a reduced bare charge due to this screening effect.’ – I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424.

This picture of QFT, which is experimentally justified by the reduction in the EM coupling constant from 137 to 128 or less when electrons and positrons were collided at very high energy (they penetrate the polarised vacuum particle "shield" and expose more of the core charge), is actually INCOMPATIBLE with SR:

Quantum field theory is moving towards an ether picture of the Feynman path integral, due to problems with renormalisation in the purely abstract mathematical model.

See arXiv: hep-th/0510040, page 85, the virtual particles in the vacuum contradict special relativity and imply a Dirac sea because:

'...it is not possible anymore to define a state which would be recognised as the vacuum by all observers'.

So SR is incompatible with QFT.

So the 'spin foam vacuum' of loop quantum gravity is a Dirac sea or spacetime fabric, which does not obey SR philosophy, but GR + Lorentz-FitzGerald spacetime fabric dynamics!

Sorry for the length and style of this post, I just feel Smolin is being too mathematical and nice about it, so Motl et al. can abuse his kindness.

Best wishes

nigel

From:Nigel Cook

To:callegari05@aol.com

Sent:Monday, January 23, 2006 12:04 PM

Subject:Re: 1.87Hz

Hi Ciao, Tony and Jaga,

Yes I saw your letter in Jan 06 EW, very interesting. I do not subscribe to NS at present, but I'll have a look when I next visit the library. I'm interested in the 1.87 Hz signals because it seems to me that "radio" is a distortion in the background field of electromagnetism. The model I go along with is Feynman's exchange process, where all charges are continuously exchanging energy ("gauge bosons"), which causes force. Radio seems to me to be a oscillating form of this energy.

An analogy is thermodynamics, with real photon (infrared, etc) exchange. At constant temperature, you can imagine that no photons are being exchanged. But when temperature is varying in time, you notice the change.

A radio won't detect the gauge bosons being exchanged normally, because their rate of arrival doen't vary in space or time, so they don't induce any current. The laws that tell you when you do get currents are time dependent (Faraday's law and Maxwell's "displacement current" equation, which is in some ways misleading).

So my picture is that every charge is exchanging energy with every other charge, normally at a steady enough rate that we can't detect it, apart from as a steady electric, magnetic or gravity force field. But where there are periodic variations, they are detectable by radio or other means.

According to the orthodox picture of plasma attenuation, the Earth's ionosphere should absorb all radio below about 80-100 MHz.

However, the maths behind that omits the Feynman exchange approach. If all charges are exchanging energy and this exchange is interrupted partially in some directions by planetary or moon motions, this could vary slightly the background field in a periodic way at any frequency, such as a few Hertz or less. This would not be attenuated by the ionosphere because the force causing gauge bosons of electromagnetism don't seem to have a frequency as such, they don't cause radio noise!

Therefore the gauge boson radiation, varying in time with a frequency of say 1.87 Hz, would not behave like radiowaves of 1.87 Hz in being attenuated.

I think what happens is that the frequency of the force field created by gauge boson exchange is simply the variation in the number of gauge bosons arriving per second, and has nothing to do with a frequency of an individual gauge boson. Therefore, at such extremely low frequencies, you could measure effects due to processes in outer space and deep inside the earth without the shielding that would occur if the frequency of the radiation were associated with individual photons.

My effort to get the gravity model into a form that will convince people is very difficult. I see a lot of independent evidence from different places, but it is difficult to select and assemble the evidence in a convincing way. One interesting thing is that Lee Smolin's Loop Quantum Gravity suggests that gravity is mediated by a spin foam vacuum, and this is the main rival to string theory.

As I see it, string theory is an empty frame work to describe an unobserved graviton theory using unobserved 10/11 dimensional spacetime and predicting unobserved SUSY (super symmetry) partners. There is no effort in string theory to describe or model anything observable, and the claim that it predicts gravity is empty, as it just predicts and unobserved gravity mediation scheme, without any dynamics.

Smolin's Loop Quantum Gravity is completely different. His recent two lectures at the Perimeter Institute on 18 Jan, "Introduction to Quantum Gravity", are available on line if you have a fast internet connection. His pesentation is very mathematical, following the style of some of the material in Penrose's book The Road to Reality.

He starts off with spatial topology, sets of all graphs possible with or without edges, embeddings in all possible graphs, valent nodes on graphs (by analogy to chemistry, I presume). He defines Hilbert spaces on an orthagonal basis, then Penrose's "spin networks". Finally he shows how Feynman's "sum over histories" approach to quantum mechanics arises in the vacuum: each interaction is a graph and you sum over all the graphs describing interactions in spacetime to arrive at the "sum over histories".

Smolin's second lecture dealt with "background independence" which is the problem with special relativity and the spin foam vacuum (an aether physically). He starts out by showing which of Maxwell's equations are background independent and finds that divergence equations, like Gauss's law, are background independent. I do not like his approach to Maxwell's equations. It demonstrates he is a mathematician, who prefers to prove results rigorously with sophisticated maths, instead of using simple, lucid intuitive or experimental facts to obtain the same results. My feeling is that SR must be dumped as a postulate-driven endeavour and replaced by a causal mechanism for the contraction, mass increase, time dilation and energy-mass equivalence using the physical effects of the spin foam vacuum.

Peter Woit has allowed my anonymous comments on this (below).

Best wishes,

Nigel

http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7837

anonymous Says:

January 21st, 2006 at 1:19 pm

Lumos has a long list of publications about speculation on unobservables. So I guess he’s well qualified to make vacuous assertions. What I’d like to see debated is the fact that the spin foam vacuum is modelling physical processes KNOWN to exist, as even the string theorists authors of http://arxiv.org/abs/hep-th/0601129 admit, p14:

‘… it is thus perhaps best to view spin foam models … as a novel way of defining a (regularised) path integral in quantum gravity. Even without a clear-cut link to the canonical spin network quantisation programme, it is conceivable that spin foam models can be constructed which possess a proper semi-classical limit in which the relation to classical gravitational physics becomes clear. For this reason, it has even been suggested that spin foam models may provide a possible ‘way out’ if the difficulties with the conventional Hamiltonian approach should really prove insurmountable.’

Strangely, the ‘critics’ are ignoring the consensus on where LQG is a useful approach, and just trying to ridicule it. In a recent post on his blog, for example, Motl states that special relativity should come from LQG. Surely Motl knows that GR deals better with the situation than SR, which is a restricted theory that is not even able to deal with the spacetime fabric (SR implicitly assumes NO spacetime fabric curvature, to avoid acceleration!).

When asked, Motl responds by saying Dirac’s equation in QFT is a unification of SR and QM. What Motl doesn’t grasp is that the ‘SR’ EQUATIONS are the same in GR as in SR, but the background is totally different:

‘The special theory of relativity … does not extend to non-uniform motion … The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion. Along this road we arrive at an extension of the postulate of relativity… The general laws of nature are to be expressed by equations which hold good for all systems of co-ordinates, that is, are co-variant with respect to any substitutions whatever (generally co-variant). …’ – Albert Einstein, ‘The Foundation of the General Theory of Relativity’, Annalen der Physik, v49, 1916.

anonymous Says:

January 23rd, 2006 at 6:10 am

QFT has a spacetime fabric, the Dirac sea, the foam of virtual particles in the vacuum. So does GR! This doesn’t contradict Dirac’s unification of the equations of ‘SR’ with QM, because the equations of SR are background independent: long before Einstein they were obtained by FitzGerald (1889) and Lorentz (1893) from some of Maxwell’s physical theory of electromagnetism.

General relativity is not the invention of a metric, but the effect of applying the tensor calculus of Ricci and Levi-Civita to Newtonian gravity (which must be put into GR by hand), correcting the resulting field equation for consistency, and applying the equivalence principle.

String theorists falsely and conveniently “believe” GR = SR + Newton. Thus, they claim that SR is a vital component of GR, instead of being a replacement of SR which implies a spacetime fabric (if there is no fabric for curvature, there is no GR). So they use the no-accelerations permitted, no gravity permitted, no-spacetime fabric, naked SR (better called “restricted relativity”) to try to discredit the spin foam vacuum which is a fabric approach.

----- Original Message -----

From:callegari05@aol.com

To:nigelbryancook@hotmail.com

Sent:Sunday, January 22, 2006 2:31 PM

Subject:1.87Hz

Hi Nigel,

Just a short note.How is the research going?Did you see my letter in EW Jan.06?,and outsiders NS 21Jan.page 44?

Ciao,Tony and Jaga

Post a Comment

<< Home