Friday, January 14, 2005

Semiclassical vs. loop gravity

I simply can't resist the temptation to comment on the following paper that just appeared as the #1 on hep-th tonight:
The author claims that AUGER and GLAST will be testing "predictions of semiclassical gravity". If you look closely, you will see that these predictions have absolutely nothing to do with semiclassical gravity - they're rather predictions of a particular hypothetical understanding of loop gravity.

This reminds me of a layman who was writing about loop quantum gravity on a newsgroup and used the term "one-loop quantum gravity" instead of "loop quantum gravity" because the multiplicative factor "one" does not change anything. ;-) Is it the same way how the author of that paper determined that "loop gravity" may be renamed to "one-loop, i.e. semiclassical gravity"? :-)

There is a lot of difference between semiclassical gravity and loop gravity, for example these theories have a very different meanings:
• loop gravity is a combinatorial toy model that has nothing to do with gravity and probably nothing to do with any kind of physics in nearly smooth spacetimes; see the article about problems with loop quantum gravity
• on the other hand, semiclassical gravity is a perturbative treatment of quantized general relativity that takes classical physics and the first correction proportional to hbar - this first correction is called semiclassical physics - into account; semiclassical gravity is useful to explain the existence of gravitons, their leading scattering, and effects like black hole evaporation
Even if someone were confused and she thought that loop quantum gravity could be a theory of gravity, this formalism would be appropriate to describe a very different regime of quantum gravity:
• in the commercials, loop quantum gravity is described as a "non-perturbative" description of quantum gravity that has a simple form if one wants to describes the effects that take place on the Planck scale which is a very short distance - for example the geometry of Planckian surfaces
• on the other hand, semiclassical gravity is an expansion of gravity valid at very long distances at which all quantum corrections - non-perturbative as well as higher-order perturbative ones - can be neglected
It's not a good idea to confuse these two. OK, let's now pretend that we believe that loop quantum gravity can have something to do with gravity. What was the history of these AUGER/GLAST predictions?

First of all, it was realized by many people - including the proponents of loop quantum gravity - that this approach couldn't agree with the usual Lorentz invariance of local physics. It's very simple to see why - the spin networks are essentially a new kind of luminiferous aether that picks a priviliged reference frame, even in the hyper-optimistic case that they can conspire in such a way that smooth spacetime appears at long distances.

Note that General Relativity is based on a basic postulate - the principle of equivalence - that says , in one possible interpretation, that the freely falling observer sees local physics that is indistinguishable from physics without gravitational fields - which means physics of special relativity. It's the whole point of General Relativity that it is a theory of gravity that is compatible with special relativity and reduces to special relativity if the spacetime curvature can be neglected. This is why Einstein was looking for General Relativity in the first place.

A theory of gravity that does not respect special relativity in these limits is equally unacceptable for post-1905 physics as Newton's theory of gravity.

OK, let's forget about all these obvious facts. Loop quantum gravity offers us a "prediction" of the quantized areas. Is it really a prediction? No way. It's a basic assumption of loop quantum gravity - namely that the metric tensor can be expressed as a dual variable to a gauge field. Because the monodromies of the gauge field live in a compact space, the canonically dual variable to the gauge field is quantized (that's seen as the area quantization). Obviously, the area quantization does not follow from quantum gravity - and the metric tensor degrees of freedom themselves; it follows from the field redefinition that relates the metric tensor to the gauge field. This proves that this field redefinition, although it may be valid locally on the configuration space, is invalid globally.

Spin foam breaks Lorentz symmetry

This field redefinition - and the unphysical quantization of the areas - is also the primary source of the Lorentz violation in loop quantum gravity and the majority of other physical problems of loop quantum gravity. There cannot really be a sharp bound for a minimum positive area (or distance) in a Lorentz invariant theory because the Lorentz contraction can always lower this area (or distance), roughly speaking.

I used to think that this point had be completely obvious to anyone who has heard about the "luminiferous aether" and the story that Einstein had to abandon aether in order to preserve the principle of relativity: any discrete non-singular structure inserted to space picks a preferred frame which is not allowed by special relativity. But judging the number of questions I am getting all the time, this question is not so clear.

OK, let me formulate the proof in different words. Consider a spin foam - the time evolution of a spin network (a spin foam a structure made of 2-dimensional surfaces embedded in 3+1 dimensional space, and their junctions) - a spin foam that you believe to be typical configuration contributing to the path integral of what you want to call the "Minkowski vacuum". Assume that at long distances, the Lorentz symmetry is approximately preserved. Choose a large piece of a nearly null (but slightly space-like) 2-plane in the Minkowski space (a rectangle) and try to calculate its proper area. According to loop quantum gravity, the area is proportional to the number of intersections of this rectangle with your spin foam (weighted by coefficients of order one in Planck units, separated from zero by the assumption of area quantization). By Lorentz symmetry, the area must go to zero if the rectangle is becoming null because a boost can map it onto a very small, localized spacelike rectangle whose area should go to zero. This means that there can't really be any intersections of the spin foam with the null rectangle, and because it must be true for any null 2-plane, all faces of the spin foam must be parallel to all null 2-planes, which is easily seen to be impossible because different null 2-planes are not parallel to each other. In other words, every 2-plane in the Minkowski space intersects some null 2-planes, and therefore these null 2-planes will be assigned significant positive proper area by LQG, which is incorrect. If you have a spin foam, it either breaks Lorentz symmetry completely, or it will have to be infinitely dense. But you definitely can't get a non-singular Lorentz-invariant theory. Note that the violation of the Lorentz symmetry derived above is not "small" in any sense. The Lorentz contraction factor simply stays finite (of order one) if you approach the speed of light. There's nothing you can do about it: aether (or a spin foam) is a clearly wrong model of the Minkowski space.

Once we know that the usual Lorentz invariance can't hold in a discrete model of gravity, one can try to propose weaker conjectures. For example, loop quantum gravity could agree with "doubly special relativity" (DSR), also known as "deformed special relativity". That's a nonlinear deformation of the Poincare algebra whose Lorentz subgroup is not modified at all, but the action on the momenta is altered. It has a parameter kappa that can be identified with the Planck scale. It's not such a big deal that such a deformation exists because we're really deforming the translational part of the Poincare symmetry only - and because the momenta commuted with each other anyway, it's not hard to preserve the Jacobi identity. Technically, we may also obtain this kappa-Poincare algebra as a limit of a q-deformed de Sitter algebra SO_q(d,1). The quantum deformation is claimed to be the reformulation of the cosmological constant term to the language of the LQG gauge fields - a potentially interesting relation that is, however, made irrelevant in LQG by the non-existence of any Lorentz or de Sitter symmetry in the first place. Nevertheless, even in string theory people (David Lowe etc.) have studied the possibility that the de Sitter space should carry a quantum deformation of the corresponding isometry group.

Doubly special relativity is a highly problematic picture as it stands - for example, the appearance of non-linear functions of momenta prove that the action of the Poincare transformations is non-local in spacetime and a Lorentz transformation can actually map a function (lion) in the interior of a region (cage) into a function (lion) outside the region, which is pretty dangerous. Moreover, the proposed modifications of the dispersion relations will give you different values of the speed of light for a composite particle than if you consider the particle to be elementary (imagine the proton as an example), which is pretty bad. Incidentally, on every normal Hilbert space - i.e. an infinite-dimensional separable Hilbert space - we can find a collection of 10 operators that form the four-dimensional Poincare algebra: even for an ordinary harmonic oscillator. It's simply because all Hilbert spaces are isomorphic to each other, and therefore the harmonic oscillator Hilbert space may be mapped to the Hilbert space of the Standard Model if we don't care that such a map is physically ludicrous. But that does not mean that all theories are Lorentz-invariant; we only accept the Poincare generators as "real symmetries" if they have simple commutators with the usual notions of time etc. (for example, we require that the rotation generators commute with the Hamiltonian).

But even if we forget about all these problems of doubly special relativity, I think that it is pretty clear that the conjectured relation of loop quantum gravity to doubly special relativity is just another speculation. Of course, the smooth space at long distance probably can't appear in LQG anyway (there is definitely no proof that it does appear, to say the least), and therefore LQG can't agree with DSR that does reduce to flat space at long distances.

If someone will tell you that semiclassical gravity predicts a violation of the relativistic dispersion relations for photons, for example, don't believe her. It's a conclusion based on shaky, speculative connections between various unrelated inconsistent ideas, each of which can easily be shown to disagree with reality.

1. So, Lubos, if AUGER or some other expt finds evidence for doubly special relativity or some other dispersive behavior, what does that mean for strings?

2. If doubly special relativity is demonstrated experimentally, then I am pretty confident that string theory will be falsified.

When I say this, I should also say that my estimated probability of this event is 10^{-15} or less.

3. Your argument against a minimal area using Lorentz boosts doesn't follow. By the same reasoning, spin can't possibly be quantized because we can always rotate J_z to any arbitrarily small value.

Don't you mean any two infinite dimensional separable Hilbert spaces are always isomorphic to each other? :)

4. Yes, by a Hilbert space, I meant a separable infinite-dimensional Hilbert space.

The difference between 4-vectors and the angular momentum is that the different components of the angular momentum don't commute with each other, while different components of 4-momenta - but analogously also the areas of different 2-surfaces (according to LQG) *do* commute with each other.

In the case of the angular momentum, you can't find a simultaneous eigenstate of all components with at least one nonzero eigenvalue. This prevents you from making my argument - obviously, the SU(2) algebra works and all of its generators have quantized eigenvalues.

However, in the case of the 4-momenta, it of course works. Lorentz symmetry guarantees that the energy can't be quantized, for example. You take an eigenstate of the 4-momentum and boost it, to prove that it is continuous. The same thing holds for distances and areas: take a common eigenstate of the area operators - which is called the spin network - and boost it by a Lorentz symmetry. The only way how can you obtain - even microscopically - similar state is if the spin network only contains the singular surfaces along the light cones. There is no regular solution: by averaging any spin network made out of regular areas over the noncompact Lorentz group, you will obtain an object totally overwhelmed by infinitely boosted areas, i.e. a singular one.

A discrete structure in spacetime is guaranteed to be incompatible with Lorentz symmetry as long as there are at least some local degrees of freedom.

5. As nasty as doubly special relativity is to start off with, is there any possible way string theory can accommodate it?

6. I liked your joke on one loop ..equal to loop since one is a multiplicative factor.

I completely agree with your comments. Also I didnt like the terms like "falsifiability" being used in the paper. I think some authors get too carried away with such notions. They are of course an important part of what science is but sometimes people abuse this.

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8. Dear Ramanan, right - falsifiability is important, but it's often used to politicize science. At any rate, I'll be happy if LQG is not only incorrect but also falsifiable, and I can't wait when this only claimed virtue of LQG is finally applied successfully. ;-)

For the previous colleague: it would be interesting if someone disagreed and gave some arguments, but I really think that there can't exist any "version" of string theory that accomodates doubly special relativity.

The purpose of string theory is not to accomodate any idea someone thinks of. String theory only accomodates some ideas - the ideas that it objectively does - and our experience suggests that it accomodates the good ideas that are useful to explain a world similar to ours.

On the other hand, we know that string theory covers many concepts that were not thought to be directly related to it - e.g. non-commutative geometry. But in the case of noncommutative geometry, we know a field - the B-field - whose condensate gives the noncommutativity. I think it's obvious that no field or degree of freedom we can think of would lead to deformed special relativity.

In perturbative string theory, the spacetime coordinates are fields on the worldsheet, and they're bound to preserve the Lorentz invariance at short spacetime distances.

I've erased a comment by Quantoken - one that repeated several times that I am doing some "mistake", but it seems that the "mistake" I was doing was the simple statement that GR and SR were related and GR extended SR. Of course that GR extends SR and must reduce to SR at short distances, in the inertial frames, and it seems inappropriate for a participant who did not bother to learn absolute basics of physics to contaminate the comment section.

9. Maybe we can do spin networks and M-theory only in light-cone gauge.

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12. Smolin is the master of coctail-party physics.

The more you debunk him the stronger he will become.

13. "It's the whole point of General Relativity that it is a theory of gravity that is compatible with special relativity and reduces to special relativity if the spacetime curvature can be neglected. This is why Einstein was looking for General Relativity in the first place.
"

This is not correct. Sean Carroll and others have proposed gravitational lagrangians containing terms proportional to the *reciprocal* of the scalar curvature. Obviously these theories do not admit flat spacetime as solutions, and do not reduce to special relativity in the limit of vanishing curvature. Indeed, this is the point: these authors want to develop a theory which *deviates* from ordinary GR in the limit of *small* curvature, because [in their view] the current acceleration of the universe is evidence that GR breaks down precisely when the curvature is *small*. After all, nobody believes that special relativity is exactly true --- spacetime curvature is never exactly zero. So being able to reduce to special relativity in the limit of exact flatness is not a physical requirement. If you don't believe me, take a look at http://arxiv.org/abs/astro-ph/0306438 which has been cited over 100 times. There are objections to these theories but not on the basis that they are inconsistent with some basic principle of GR.

14. Lubos,

I read your cited critique of LQG, and while I don't claim to understand all of it, it seems to me that your criticisms fall into three categories:

a) LQG doesn't predict a bunch of things like extra-dimensions, supersymmetry, and particles which, however, have not (yet) been observed.

b) Matters of taste, like treating GR as an exact theory to be quantized instead of an effective field theory, or considering it more important to preserve some features of relativity than others.

c) Accusations of mathematical, physical, and logical inconsistency that should be publishable if provable. Why haven't you published them if you can prove them?

If you guys are right, and Rovelli owes his fame more to his rhetorical skills than to his work, why not publish your refutations? On the other hand, if these really are matters of different approach to an unsolved problem (as Rovelli argues), why are you so strident? Anger and sarcasm are inimical to dispassionate inquiry, so what's the point?

15. Lubos, you said: ...Of course that GR extends SR and must reduce to SR at short distances, in the inertial frames...

It's not so clear to me what you mean by this. If you mean that local inertial frames exist in GR, I suppose that's true (except for singularities), but isn't it also true that empty spacetime GR admits non Lorentzian solutions?

It's not clear to me that your statement means anything except that the GR solutions form a manifold with Lorentzian signature. GR extends SR in much the same sense as Maxwell's equations extend Coulomb's Law - it reduces in some special and especially uninteresting cases.

Also, it is not clear to me why you say quantization of area necessarilly implies loss of Lorentz invariance. Can you explain that?

16. For the anonymous poster before CIP:

First point. Sean Carroll was not the only person who played with these models. I've played with them, too, and Nima has posted papers on them.

Second. These models are not GR. They don't satisfy the equivalence principle because a gravitational field can't be replaced by a zero gravitational field with an accelerating observer - simply because the zero gravitational field does not solve the equations of motion.

This implies the third point. These theories are not GR itself; they're small deformations of GR, and you can get rid of the deformations by sending some parameters to zero or infinity.

Fourth point, if you already talk about "no one believes": Virtually every particle physicist believes that no local violation of the Lorentz symmetry of the physical laws will ever be observed. Certainly, none has been observed so far. The CMB does not violate the Lorentz symmetry of the physical laws: it's just a specific state with "stuff" in it, and such states of course break typically all symmetries. CMB also breaks the rotational symmetry because the temperature depends on the direction.

Summary: you're just confusing yourself by confusing examples and confusing terminology, but you can't eliminate the fact that the Lorentz invariance is an important symmetry of Nature that every meaningful candidate fundamental theory must reproduce, at least in some zeroth approximation. LQG can't do it because it breaks the Lorentz symmetry completely.

17. Dear CIP,

concerning your first posting. You're just a bit too sloppy in interpreting the points. Your interpretations have something to do with physics and you use the right words, but the details how you combine them into sentences show that you're not getting the point.

a) the problem is not just whether LQG "predicts" this particle or another particle. (Of course that it does not predict any particle, and it will never be able to say anything about any particle we know or we will know - not even the graviton whose very existence is an undecided question in LQG.) The really major problem of this kind is that LQG assumes that you can forget about all physics except for the metric tensor. That's not right. First of all, in the actual particle physics, we know that other forces don't go to zero near the Planck scale and you can't turn them off (the electroweak and strong forces). Second of all, we know pretty well that there must be other new physics that regularizes the problems of GR.

b) Whether or not GR is an exact theory that can be directly quantized to get the right quantum theory is definitely not a "matter of taste". Physics is not about "tastes", CIP, even though you apparently think the other way around. It is an essential question concerning quantum gravity that one must answer before she tries to say anything about quantum gravity beyond the classical (and perhaps semiclassical) approximation. It is not a "religious" question as you try to suggest. It is a completely scientific question, and one of the possible answers is incorrect. Even before string theory, we've known many other examples that show that UV nonrenormalizable divergences signal new physics that was neglected in the low-energy effective theory, and GR is another example.

c) the theory of LQG is easily shown to be inconsistent with the desired long-distance physics as well as internally, but I definitely don't think that LQG and/or its inconsistency is an interesting and serious enough topic that it should appear in the journals. If we were writing papers about every incorrect other paper on the web, or about every proposal of every crank, there would be exist almost no papers except those about wrong papers. ;-) If you're living in the propaganda that LQG is a competition to string theory, be aware that I won't join you.

I am writing about it on my blog for the people who are interested in physics but don't work on it - because LQG is a rather good example of many typical errors that these interested laymen also tend to make. The research of the LQG people is very similar to the research of the "interested laymen". I certainly don't think that the real physicists need to be explained why LQG is nonsense. Everyone either ignores LQG because this is just one particular weird paradigm that has not affected the physicist, or - if the physicist is familiar with LQG - he knows very well why LQG is misguided because it contradicts virtually everything that physics works with and needs. There is no reason to write papers about it. But of course that I could.

I assure you that I am equally strident about every other proposal in physics that is based on misunderstanding of some basic points.

18. Dear CIP, concerning your second posting:

You don't appreciate how non-trivial the Lorentz symmetry is. Most solutions in GR don't look globally like the Minkowski space, of course, but ALL solutions in GR are manifolds of Lorentzian signature. The small regions on this manifold are open sets from the Minkowski space and they preserve the same symmetries.

The very definition of a Riemannian manifold is that it is locally a Minkowski space, and therefore the Lorentz symmetry at short distances is recovered with any precision you want.

This respect for the Lorentz symmetry is a very nontrivial requirement - LQG violates it, for example - and it is only with this requirement that General Relativity is special.

Best
Lubos

19. Dear CIP,

I've updated the discussion in the article why the area quantization breaks Lorentz invariance, inside the article. I hope it will be completely clear what I mean and why it's true.

Cheers,
Lubos

20. Lubos:

Putting the tease aside. I do see your points in your description how a quantum of area in LQG violates the Lorentz invariance.

I definitely agree with you that Lorentz invariance is important and anything that violates it can not be right. But I personally know Lee Smolin and his intelligence and his understand of physics deserves so respect. He certainly knows the importance of Lorentz symmetry. There must be a reason that trivial discussions of Lorentz invariance like yours do not convince the LQG camp people. No, the reason can not be because those LQG people are stupid. You have to look at some where else for the reason why they disagree with you.

You are still missing the point I pointed out. You need to pay attention to the fact that at microscopic scale, things are discrete, not continuous. If you still hold the philosophy belief that the nature is inheritantly continuous, even if we observe discreteness, then I have nothing further to say.

But most people do accept discreteness at microscopic scales as a fact. You have to be very carefully applying the physics laws we obtained in the macroscopic world, into what happens in the microscopic scale. Because these laws all based on differential equations that rely on the continuity of spacetime coordinates.

For example, the speed. To discuss Lorentz invariance, discussing of speed and inertial frame transformation is necessary. But how do you define what SPEED is in Planck Scale?

If you look at it at Planck Scale, in one quanta of time, the thing does not move a bit and the speed is zero, in another quanta of time, it moves just one quanta of posotion so the speed equals to C. So you lack of an exact definition of what speed is, and it keep jumping randomly to be either C or zero. And it is hard to apply the continuous form of Lorentz transformation if you don't have a precise definition of speed!!!

My whole point is discussing a CLASSICAL theory, SR, in the microscopic scale where spacetime is quantized, is invalid. As long as the theory can return to the case of Lorentz invariance in the macroscopic world, then it is OK and has not violated Lorentz invariance.

Quantoken

21. Lubos,

I appreciate your clarification of your point about area, but there is one point that still bothers me. You say that a different Lorentz observer will see a different area because of the contraction. That seems to me like saying a different Lorentz observer will observe a different energy state because of the time dilation. What the different Lorentz observers observe in both cases are different probabilities of energy (or area) states.

22. CIP, you're just deliberately confusing yourself. You must be very careful to distinguish the proper area and the coordinate areas and so forth, and I was very careful about it.

You just seem to suggest "I, CIP, am confused about the difference between the proper area and the coordinate area, and therefore you are definitely confused, too".

No, I am not confused. I used the rules of LQG to calculate the *proper* physical area of a given surface - I am absolutely sure that I did not forget to emphasize that it was the proper area - and this observable is independent of the reference frame. In your analogy, it is analogous to the rest mass of a particle.

23. Lubos, you said: Assume that at long distances, the Lorentz symmetry is approximately preserved. Choose a large piece of a nearly null (but slightly space-like) 2-plane in the Minkowski space (a rectangle) and try to calculate its proper area. According to loop quantum gravity, the area is proportional to the number of intersections of this rectangle with your spin foam (weighted by coefficients of order one in Planck units, separated from zero by the assumption of area quantization). By Lorentz symmetry, the area must go to zero if the rectangle is becoming null because a boost can map it onto a very small, localized spacelike rectangle whose area should go to zero. This means that there can't really be any intersections of the spin foam with the null rectangle, and because it must be true for any null 2-plane, all faces of the spin foam must be parallel to all null 2-planes, which is easily seen to be impossible because different null 2-planes are not parallel to each other....

I previously plead guilty to being confused, but didn't accuse you of being confused. Your point about proper area is a good one, but it seems to me that you are thinking of the spin foam as something that lives in the spacetime, instead of something that "is" the space time. The areas you talk about going to zero can hardly be proper areas if they are observer dependent.

24. CIP: "You are thinking of the spin foam as something that lives in
the spacetime, instead of something that "is" the space time."

CIP, these may be good words in philosophy, but if the spin foam is something that exists in reality, it must exist "somewhere" in the spacetime. Moreover, people in LQG assume that the topology of the spin foam must be trivial, and therefore it's directly embedded into the space as we know it.

Alternatively, of course, you can say that the spin foam *is* some other type of spacetime. Then my proof shows that this can't be our spacetime.

CIP: "The areas you talk about going to zero can hardly be proper areas if they are observer dependent."

This sentence makes no sense. I am talking about the proper areas, and the proper areas are always observer independent. It's just you who is repeatingly claiming that I am talking about some observer dependent quantities. No. I am talking about physical quantities.

I take very particular surfaces - along the null planes - whose proper area must be equal to zero by Lorentz symmetry. And then I easily show that the proper area is not zero according to loop quantum gravity, and I have really no idea what can you find so difficult about this simple argument.

25. Or are you questioning that the proper area of null surfaces must be zero, by Lorentz symmetry? Do you at least agree that it is zero if you calculate it using the standard Lorentzian metric? Please if you continue to write something, think twice and try to write something that makes more sense.

26. The Hamiltonian constraint does not commute with the area operator. The area operator is only defined with respect to the timeless reformulation of general relativity. This means the area of a null surface isn't the number of intersections it makes with the spin foam.

27. Anon: "The area operator is only defined with respect to the timeless reformulation of general relativity. This means the area of a null surface isn't the number of intersections it makes with the spin foam."

Dear Anon,

what you're saying is more or less the same thing that I am saying. One cannot define a meaningful area operator in LQG in such a way that the definition is shared by different observers. You need a different definition for a different observer - which is equivalent to the statement that the theory breaks Lorentz symmetry.

If one wants to obtain the area of a different surface in spacetime than a surface within the t=0 hypersurface, then the correct prescription can't be given by the loop quantum gravity expression - which is the sum over the intersections.

Once again, the rules to calculate geometrical properties are only valid in one reference frame, which means that the framework does not preserve Lorentz invariance, not even approximately, and therefore it is not an acceptable physical theory.

Best
Lubos

28. You have been more then kind in explaining to the laymen

Lubos:But even if we forget about all these problems of doubly special relativity, I think that it is pretty clear that the conjectured relation of loop quantum gravity to doubly special relativity is just another speculation.For me it was trying to decipher Smolin's position exactly. In terms of his statue in the science I have been most appreicative, but my realization if most appropriate would say, that he has stopped with the Srian approach and does not care to venture in GRian idealizations?

Would this be a correct summation?

29. Hi, Lubos. You mentioned string theory preserves Lorentz invariance. Perhaps it is useful to keep in mind string theory also have other flux backgrounds that manifestly break Lorentz invariance, such AdS_5*S^5, pp-waves, et al.

30. Lubos said:
"CIP, these may be good words in philosophy, but if the spin foam is something that exists in reality, it must exist "somewhere" in the spacetime."

You seem to suggest that ANY thing that exists in reality at all has to exist some where within the spacetime. That's reasonable because it is indeed mind buggling to imagine something that does not exist in spacetime.

But still there are plenty of things that definitely exist in reality, but obviously do not live in spacetime. Spacetime itself is one of them. String theory is another. Regardless whether string theory is right or wrong, it does exist in reality, because there does exist a group of people researching it. String theory is something that exists in reality but do not live in spacetime, it lives in the minds of some of the people. You don't want to say that string theory does not exist, do you?

Actually, since according to Einstein, absolute reference frame of spacetime does not exist, the only spacetime that exists is the spacetime in the reference frame of an observer. Therefore, spacetime itself is none-real since it is totally observer dependent, and nothing actually lives in spacetime.

Quantoken

31. Dear Quantoken,

various things - like the ideas - can exist "outside" spacetime. But I thought that loop quantum gravity was meant to describe the spacetime, not the space of ideas.

String theory certainly does, and its spacetime may be identified with the spacetime around us. I don't know what's the answer to the question whether "spacetime is inside spacetime". In my opinion, the answer is "yes", but I'm not interested in the answer anyway.

All the best
Lubos

32. Lubos said:
"various things - like the ideas - can exist "outside" spacetime. But I thought that loop quantum gravity was meant to describe the spacetime, not the space of ideas."

No no no. All theories exist not to describe the nature, but to describe the ideas we have about the nature! For example the Newton Gravity Theory does not describe the nature but Newton's ideas, since the nature behaves in slightly different ways as we know today thanks to Einstein.

Since there does not seem to be an ultimate physics theory that could never be replaced in the future, all theories we humen developed would just be theories describing our ideas, and exist in the space of ideas, as they would look terribly primitive and shallow by an alien civilization which is much more advanced and has a much better understanding of the nature than us.

You also said:
"String theory certainly does, and its spacetime may be identified with the spacetime around us. I don't know what's the answer to the question whether "spacetime is inside spacetime". In my opinion, the answer is "yes", but I'm not interested in the answer anyway."

Einstein taught us that there is no unique and absolute spacetime. There's a different set of spacetime for each different reference frame. Is it not what the LQG camp people criticize your String camp for, that string theory provides one unique and absolute spacetime, and so is background dependent, which is not allowed by Relativity? Is it not what the LQG people claim a victory over yours, in that theirs is background independent and yours is background dependent?

Whether "spacetime" is inside "spacetime" is not a trivial and silly philosophical question. Everything that does exist exists in "reality", since "spacetime" do seem to exist it also exist in reality, and is part of reality. In that sense, spacetime(s) have to exist in reality and is only part of reality. So surely reality does not live exclusively in spacetime, because how could something living on just part of its existence?

It is important for us to understand that spacetime is only part of the physics reality, and not every existence exist in spacetime. This notion became important every since we found that the Newtonian absolute spacetime do not exist. You can not move the physics of spacetime further without a deep understanding that spacetime is not the whole, but just a small portion, of the reality!!!

If it is mind buggling, you may try to imagine that your soul (not your material body, but just your soul) went to a different universe, in which exists just one single electron, and nothing else. That's a physically real universe because there is some substance: that one electron. Does spacetime exist there? Not really, you do not have any ruler to measure space, nor do you have anything to use to measure time. It could be one Planck Time or it could be billions of years, but you don't know. Without any way to measure spacetime, it might as well does not exist. But still that one electron exists.

The point I want to make is the existence of spacetime is a secondary derivation from the existence of the material world. Matters do not exist in spacetime. Instead, spacetime exists in matters. We first have matters exist in existence, and then the material world enables us to make rulers to do spacetime measurements, and then spacetime came into existence.

It is not the other way around, in which we first construct a Newtonian absolute space time, then hang out atoms and elementary particles into that spacetime background one by one to construct the universe. The God does not construct the universe in that way since we know absolute spacetime never existed.

Quantoken

33. Quantoken, science is something very different than you imagine. Science is a human enterprise to study Nature itself, not just "ideas that people have about Nature". The research of "ideas that people have about Nature" is not science; it is perhaps social science (philosophy of science). The rest of your text is also misled, but I am sure that most readers know why anyway, and we don't have to waste more time with your text.

34. Lubos said: "Science is a human enterprise to study Nature itself, not just "ideas that people have about Nature". "

Yes, definitely. Science is a HUMAN enterprise, not a monkey enterprise or an alien enterprise. So certainly science are HUMAN ideas. But science is certainly more than just ideas, it is ideas that subject itself to rigorous scientific ways of testing by evidences in the nature that is independent of our ideas.

You seem to never had any training in philosophy. Not surprising form some one came from the former communist bloc where Marxism was the only allowed philosophy ever taught. You have learned all the mathematical formalisms of physics, but have not grasbed the soul of physics, the philosophy that had guided the discovery of physics laws.

How could you research a fundamental physics theory, without some deep thinking of what spacetime actually means?

Quantoken

35. No, Quantoken, really not. Science is only science if its conclusions are independent of the race, gender, political orientation, religion, or the species into which the scientist belongs. Science is about objective features of Nature. Things that are related to humans are called "humanities", not sciences. If monkeys or dolphins could do science properly, it would be the same science - they would be certainly closer to the "ordinary" science than you.

36. In Smolin's general summary of theories of quantum gravity here, he says (p. 23):

Spin foam models appropriate for Lorentzian quantum gravity, called causal spin foams, have quantum analogues of all the basic features of general relativistic spacetimes14. These include dynamically generated causal structure, light cones and a discrete analogue of multifingered time, which is the freedom to slice the spacetime many different ways into sequences of spatial slices[90]. The spatial slices are spin networks, which are quantum analogues of spatial geometries.When he says "Lorentzian quantum gravity", does this mean a theory that preserves Lorentz-invariance? Or would your criticism that LQG introduces a preferred reference frame apply to the models he describes above as well?

37. Hi Anon,

normally, the word "Lorentzian" should always mean that the local Lorentz symmetry is preserved, but it's not the case here.

The word "Lorentzian" as opposed to "Euclidean" means that what you're trying to describe are the phenomena that one sees in the usual spacetime; the usual spacetime has the Lorentzian signature -+++ and usually it preserves the Lorentz symmetry. However, if you define a theory meant for the Lorentzian spacetime, it does not guarantee that it will preserve the Lorentz symmetry.

It only means that you're not working with the Euclidean path integral - whose spacetime has signature ++++, and it is only good as Feynman's definition of quantum field theory that must be analytically continued to imaginary time before it is interpreted physically.

Best
Lubos

38. Is there any sort of preferred reference frame in the models he describes? He says that these models contain a discrete analogue of multifingered time, which is the freedom to slice the spacetime many different ways into sequences of spatial slices[90]. The spatial slices are spin networks, which are quantum analogues of spatial geometries. Would the different spin networks generated by different "slices" obey identical laws, or would the laws governing spin networks work differently depending on how you slice the spin foam?

39. Dear Lubos,

Just as you have given us a bunch of reasons as to why you think LQG is to quote you "nonsense", could you take time off to explain to a researcher starting off his career, and looking for good problems, what problems in "gravity" string theory has so far "solved"?

Also, I think it is very unprofessional of you to bicker about LQG on a daily basis and to resort to slander on quantum gravity people.

So, please give me an objective list of points as to why I should trash all my LQG preprints and start believing that strings is the end of the story. Should I also pack my bags, since you have solved everything anyway?

40. Dear Anonymous,

the collection of problems from quantum gravity that string theory has already solved is impressive, and equally impressive is the list of the questions that have not been solved yet.

Among the solved big problems, one of the biggest ones is the understanding of the microscopic origin of the black hole entropy that has been worked out quantitatively in many contexts and for black holes of many types that can have as many as 7 parameters, including the leading corrections away from extremality. In all cases, the Bekenstein-Hawking formula is recovered.

Also, another large category of essentially solved problems includes the understanding of timelike (static) singularities. String theory has allowed us to study physics near these singularities and physics is completely non-singular, due to the existence of new light states and new phenomena that are under control. This category includes the understanding of topology changing transitions.

A similar class of problems - namely the spacelike singularities, such as the big bang and the black hole singularity, are largerly unsolved.

Another class of problems in quantum gravity is graviton scattering; black hole evaporation. The microscopic description of these things in a subset of backgrounds is under control, too, the understanding in completely universal backgrounds is not available yet.

Another huge subindustry in physics that works very well is the holographic duality - usually studied as AdS/CFT - that allows one to identify the origin of the holographic principle, at least in some backgrounds connected with the anti de Sitter space. In quantum gravity, the information can be encoded to areas whose dimension is smaller by one than the dimension of the full space, and AdS/CFT allows one to study a huge number of phenomena - black holes, strings, branes, their interactions etc. - using the language of local quantum field theory (usually conformal field theory or its deformations).

Your sentence about "quantum gravity people" shows that you may be confused about the meaning of the words "quantum gravity". "Quantum gravity" certainly does not mean "loop quantum gravity". "Loop quantum gravity" is just one of a plenty of naive and problematic approaches to quantum gravity - one that has not led to convincing results so far and most likely has nothing to do with gravity.

I am not criticizing "quantum gravity people"; I am criticizing "loop quantum gravity people" which is something very different.

It's your free decision whether you think that loop quantum gravity is a serious enterprise. I think that today there is enough material available freely on the internet to help anyone understand that it's not quite a serious enterprise. If you need a text by others that looks at LQG without irrational hype, look e.g. at the new paper that appeared 30 minutes ago,

http://www.arxiv.org/abs/hep-th/0501114

that discusses a main problem of LQG, namely defining the Hamiltonian constraint.

All the best
Lubos

41. Thanks Lubos for the reference, I see that it is from people at the Albert Eisneien Institut and I will definitely read it.

Thanks also for the list of achievments from the string side.

I might ask a question at this point: what is your opinion of
Renata Loll's work on dynamical triangulation ( essentially a non-perturbative path integral approach), which from an outsider's point of view seems to be more "result" oriented than
loop approaches, and has recently produced a few interesting ones.

42. Renata Loll is a smart woman.

What nice can I say more... Well, I think that all discretized approaches to quantum gravity share most of the flaws - like the Lorentz violation; the inability to cure the real divergences of the theory.

Triangulations may be a good calculational tool in numerical GR, but the assumption that they define a meaningful quantum theory essentially includes the assumption that there is no new physics beyond GR necessary to make sense of short UV physics in quantum gravity. And I think that there is just enough evidence that new physics is needed and none of the discrete approaches really has the right physics.

In the path-integral discrete formulations, the divergences are exhibited by "crumpled" spacetime - the typical configurations to the path integral don't even have the right Hausdorff dimension. People may try to fix it by hand and remove the unwanted configurations, but that's a kind of cheating that breaks unitarity anyway.

And once again, quite generally, any discrete structure inserted to the Minkowski spacetime will break the Lorentz symmetry. All of these things are aether - for special relativity it is just totally necessary that the vacuum is unique and Lorentz transformations don't alter it.

All the best
Lubos

43. Lubos daid:
"No, Quantoken, really not. Science is only science if its CONCLUSIONS are independent of the race, gender, political orientation, religion, or the species into which the scientist belongs. Science is about objective features of Nature. Things that are related to humans are called "humanities", not sciences. If monkeys or dolphins could do science properly, it would be the same science - they would be certainly closer to the "ordinary" science than you."

Sigh, you really do not have proper training in thinking philosophically. Unfortunately that make you merely a technician in your camp and never a master.
As you said, conclusions of science are objective and should match the nature regardless the background in which the theory was first raise. BUT, science is more than calculation results. A science theory contains at least three parts:
A.Some basic principles or postulations.
B.Mathematical formulations and logical reasonings.
C.Results and predictions.
Only C is purely objective and needs to be matched against nature. B is totally within the realm of human invention, imagination and other creative activities. A came from observation of the nature but is interpreted by human mind.
Science is a form of art. There can be multiple ways of describing the same thing and all of them leads to the same conclusion. Certainly we tend to accept the easier or more simpler explanation. But isn't easiness or simplicity an opinion dependent thing and therefore none-objective? Take QM, we have Heisenberg Picture and Schrodinger Picture. They leads to the same results. The specific form Heisenberg Picture and Schrodinger Picture took are totally none-objective, and were purely due to the happentness of that two guy's education background and their preference. We could have some other different pictures of QM.

Another example is the specific form GR took. It's purely by chance that Einstein knew some mathematician, who taught him something about Lieman geometry. And so it seem fit and it because the math tool he used. In a different occasion he could have used some different approaches, although the end result will probably be the same.

Science is art and it involves more than just the objective things in the nature, but also subjective imagination and creativity of human kind.

Quantoken

44. Lubos said:
"In quantum gravity, the information can be encoded to areas whose dimension is smaller by one than the dimension of the full space"

You are wrong, Lubos, but wrong only by 4 missing letters at the end of your sentence. All the establish camp people, including Hawking, are wrong the same way. You need to add 4 more letters: "time". The last word in your sentence should be amended to "spacetime".

The entropy is porportional to the 3-D surface area of the 4-D spacetime, not the 2-D surface area of a a 3-D space. That one-dimention discrepancy is the whole reason that cuased that 120 orders of magnitude discrepancy in the so called "cosmological constant problem".

It's rather strange, Einstein taught us that space and time are really none-separable. But still people keep dealing with space only and forget the time, or time only and forget space. Why cut the 3-D space off from the 4-D spacetime, when time and space can be transformed in Lorentz transformation.

Quantoken

45. All of these things are aether - for special relativity it is just totally necessary that the vacuum is unique and Lorentz transformations don't alter it.Hi Lubos, can you address my earlier question about Smolin's comment about slicing spacetime foams into different possible sequences of spin networks? Would the laws of physics governing the spin networks work differently depending on what set of slices you use? If not, then this wouldn't really be much like "aether", since there would be no preferred reference frame.

46. I think that it has been showed above that the laws affecting matter in spacetime *do* depend on the direction of the slicing of the spin foam. Does not it answer your question?

47. I couldn't follow all the details of the argument--I have only an undergraduate degree in physics, so obviously loop quantum gravity is a bit over my head. But I was wondering if you have any direct familiarity with the models Smolin is talking about there--if not, is it possible that these models define a "slicing" of the spin foam differently than you're imagining it? Given your discussion with Capitalist Imperialist Pig earlier, you seem to think that the space the foam is embedded in has a real physical significance, so perhaps you're thinking of a "slice" as a flat 3D hyperplane cross-section of this space, but I was under the impression that the embedding space had only topological importance (like the embedding space for knots in knot theory), in which case a "slice" might be something different, like a subset of vertices that, depending on your choice of embedding, might not lie on a single hyperplane at all.

48. The spin foams summed over in LQG have the same topology as the spacetime on which you define them - which means that there exists a continuous map to the spacetime which embeds the spin foam, and because it's continuous, it also transforms the slices of spacetime into slices of spin foam and vice versa.

49. I emailed Lee Smolin about this, he said that loop quantum gravity does not imply a preferred reference frame, or a violation of Lorentz-invariance:
The rules that attribute to each spin foam history an amplitude are
independent of how they are sliced.  They are of the form of a product
of amplitudes, one for each elementary event or unit of four volume.
Thus, the product is independent of, and in fact does not refer to, a
slicing of the quantum spacetime history into space and time.
Furthermore, detailed rules have been found, I'd be curious where that
piece of disnformation comes from.
[This was in reference to a comment I made that I was under the impression no detailed rules for the dynamics of spin networks were known] There are several explicit propoosals
which have been studied in a lot of detail. The best studied is called the
Barrett-Crane model. Its rules are explicitly lorentz invariant.  It has
also benn proved analytically and checked numerically that the resulting
amplitudes are ultraviolet finite.

50. Dear Lubos,

Personally, I did not like Smolin's article mainly because it does actually predict anything!! and hence does not live upto the promise of the title of the paper.

However, the ensuing discussion focuses on the pros and cons of Loop quantum gravity.

However lets for a moment talk just about DSR. DSR does not require LQG as a precursor, hence the DSR idea might still have some merit (it does have a long distance limit) independent of LQG and irrespective of whether LQG is tenable or not.

in your opinion is that assessment correct?

I want to mention one more thing. It seems that the LQG community (the young researchers) ARE beginning to take the criticisms seriously. I see Laurent Freidel and a few others exploring alternatives, and I think it should be acknowledged that some people are interested in making progress, even if they have loopy connections. Anyway, It would be nice to hear about DSR from you.

51. Yes, I completely agree that LQG is independent of DSR - that was one of my points. My estimate for the probability that DSR will be proved correct is clearly smaller than yours, but it's fine. ;-) Yes, it could be true, in principle, but I don't see any natural dispersion relation of the DSR type that could apply to the individual particles (the coefficients have to depend on the particle species because the dispersion relations don't have a uniform degree, and therefore depend on the particle being treated as elementary vs. composite). Yes, there are potential other indications - from AdS/CFT and dS/CFT - that the cosmological constant could imply a quantum deformation of the rotational group that could be displayed as DSR. I just find it unlikely because it is not useful to explain anything we know, and it disagrees with our natural theories as we know them - QFT and string theory. Therefore I would guess that DSR works with probability 10^{-10} or less. But of course, I can be wrong.

52. Thanks Lubos on your comments about DSR. Well, I don't have a personal stake in either LQG or DSR, at least not for now---so I really don't have an estimate on the probability of DSR being correct or not.
I do work on quantum gravity---but not LQG. but that is about all I can reveal. But I am a curious grad student, and I kinda like the DSR idea.

I think it is too soon to say that DSR disagrees with QFT. At this point, I do not want to delve in philosophy, but if DSR is a potentially new symmetry near the planck regime, then quite possibly it shold be investigated what "new" things it can predict for QFT. Off and on, some people (who do not want to publish these statements, because you know they want to be careful) hae expressed the opinion that QFT as we undretand it today might have to undergo some revisions at high energies.

I am interested in DSR for its potential connections with ADS/CFT and noncommutative geometry ---- and it still might be an interesting idea on "its own". I lend support to the opinion that we should'nt adhere to LQG as a "father" of DSR. That simply is not a progressive attitude. So what if it is? will it shed light on the problems of LQG? the closure of the constraints? NO!!! so why is this connection useful?

53. dear lubos,

i have not studied lqg or strings deeply enough to understand all that you have said, but it seems that you are making statements about the loop approach (such as lqg not being lorentz invariant)that smolin says are false or at least not a deathblow to the loop approach.

perhaps it is possible that smolin and his collaborators understand something about loop quantum gravity, having studied it in depth for such a long time, that you are overlooking or that fixes the problem.

it seems that it would be more productive, and beneficial to new students of quantum gravity, if there was a more cooperative atmosphere between people working in strings and people working in loop quantum gravity.

I would like to see a review of LQG (and of strings) that both sides could agree on, at least as far as what the theory predicts and assumes. If there is a differing opinion about the aesthetics of the theory, so be it. I think it is good to have people working on aesthetically different theories, so long as what they are doing is not plain wrong.

regards, martin