Lorentz violating severely restricted: Mqg/Mplank > 1200

[Ben Niehoff]

doesn't string theory compatification presented as a 6-dimensional yau-calibi manifold in every point in 4D spacetime imply discrete spacetime? If spacetime in string theory is infinitely smooth and continuous and infinitely divisible (even below the Planck length) how then can you speak of a 6-dimensional yau-calibi manifold in each point in spacetime:?

I think the pictures usually drawn are a bit deceiving, with little Calabi-Yaus attached at points along some grid...

A better way to think of it is this: A cylinder is really just a line, with circles attached to it at every point. These circles are linked together in a continuous fashion. If the cylinder is all wobbly instead of straight, we can regard this as having the circles changes shape and size (in a continuous way) as we move from point to point along a line. The curvature form of the resulting surface encodes the information as to exactly how these circles are connected together; hence all the talk of "connections".

In string theory, spacetime is similar, but replace our "line" with "4-D spacetime", and instead of attaching "circles", use "Calabi-Yau manifolds". The Calabi-Yaus are glued together, in a continuous fashion, at "right angles" to both themselves and to the 4-D spacetime. There is a 10-dimensional curvature form that encodes information as to how everything is connected together.

 

[atyy]

This paper has interesting comments on Lorentz invariance (or lack of) in spin foams and in the appendix, on condensed matter approaches to quantum gravity.

http://arxiv.org/abs/0901.4009
Quantum Histories and Quantum Gravity
Joe Henson

 

[ensabah6]

I think the pictures usually drawn are a bit deceiving, with little Calabi-Yaus attached at points along some grid...

A better way to think of it is this: A cylinder is really just a line, with circles attached to it at every point. These circles are linked together in a continuous fashion. If the cylinder is all wobbly instead of straight, we can regard this as having the circles changes shape and size (in a continuous way) as we move from point to point along a line. The curvature form of the resulting surface encodes the information as to exactly how these circles are connected together; hence all the talk of "connections".

In string theory, spacetime is similar, but replace our "line" with "4-D spacetime", and instead of attaching "circles", use "Calabi-Yau manifolds". The Calabi-Yaus are glued together, in a continuous fashion, at "right angles" to both themselves and to the 4-D spacetime. There is a 10-dimensional curvature form that encodes information as to how everything is connected together.

thanks,

so when mass-energy curves spacetime, does it curve 3+1 or does it curve all 11 dimensions in string theory?

so how is it these higher dimensions do not affect the propagation of a photon?

 

[lumidek]

I think that yes Distler has a point. But if you read the posts he does not give reasons why the fixed point doesn't exist. Instead he is concerned withe the reliability of the ERG. These concerns are valid but its the best tool we have to find evidence for a fixed point. Whats more if we were to find that by adding a term to the truncation destroyed the fixed point we would surely of found proof(?) that gravity is nonperturbativly nonrenormalizable which in turn would support string theory.

Actually I'm very interested in your comment about non-locality. Are you saying that string theory should allow information travel outside the light-cone? Or how do you see this non-locality? A "stretched horizon" of order the Planck length maybe?

Dear Finbar,

even when we decide that it is "uncertain" whether the fixed point exists, such a situation doesn't allow one to say that he has an alternative theory, does it? People can make bets according to their expectations. I would never bet on asymptotic safety, and frankly, i don't understand what valuable physics can possibly be obtained from a physical hypothesis "gravity is scale-invariant at short distances" before it is actually understood "why it should be scale-invariant there". I think that all other consequences of this hypothesis depend on the basic assumption whether it's possible, so before it's answered, the amount of interesting physics here is exactly zero and all these things are pure speculations.

Locality.

As the AdS/CFT correspondence, Matrix theory, and perhaps other pictures show, the black hole evolution is unitary, even when they evaporate. It means that the information must get out from the black hole after the matter has crossed the horizon. It means that it must tunnel out and violate the causal structure seen in the classical Penrose diagram i.e. travel along spacelike intervals in the vicinity of the black hole. Consequently, some nonlocality has to exist in quantum gravity as long it is consistent.

It is not enough for this violation to be of order 1 Planck length. The nonlocality must be able to go to arbitrary distances - the thermalization abruptly mixes the degrees of freedom around the whole horizon. The effect is "small" not because the range is short but because the amplitude is low. It is a kind of a quantum tunneling effect, suppressed exponentially, but it is enough to get the information out of the hole in time.

But I also meant the very entropy scaling for the entropy that contradicts field theory in the UV. In field theory, the entropy density really scales like Temperature^d where "d" is the number of spatial dimensions. For black holes, the entropy density is constant per unit area of the event horizon, which is a different power law. Because a consistent theory of quantum gravity must agree with the statement that black holes are the generic high-mass states, it can't be described by field theory in the limit of high masses (center of mass energies).

 

[lumidek]

The argument is on page 31 and subsequents, called "the problem with higher derivatives". Woodard says that higher derivatives make the theory very unstable.

heinz

Dear Heinz, the most obvious way to see that the statement is wrong is to simply calculate the effective action for gravity in *any* background in string theory - which is perfectly well-defined, stable, and in fact, supersymmetric (which implies stability). The higher-derivative terms with an arbitrary number of derivatives are always there. It's a basic rule of renormalization group that all these higher-derivative terms are always there unless their existence is banned by a conservation/symmetry law.

The argument on page 31 doesn't even use the right mathematical language. It is some game in classical mechanics. One surely can't answer such questions by comments about some calculations from the year 1850: it's downright silly.

There is no contradiction between higher derivatives and stability. If the scattering amplitude for four gravitons has an additional e.g. energy^400 piece in the scattering amplitude, there is inevitably a 400-derivative term (or so) in the effective action. Such a thing cannot possibly be proved incompatible with stability because there are many functions that contain energy^400 terms in their Taylor expansion, yet they satisfy any kind of inequality you want in order for the theory to be stable.

Actions with higher derivatives shouldn't be quantized along his procedure at all. In particular, having additional derivatives doesn't really add new degrees of freedom (as one would think if she imagined that they're additional initial conditions). The whole game on page 31 etc. simply has nothing to do with the proper calculations in effective field theories. By the way, he probably assumes that the exact action is polynomial, and such polynomials may have zeros or other important points. But the exact effective action is not polynomial: it contains corrections at arbitrary orders (plus nonperturbative ones), which is enough to see that his arguments would break down even if it were translated to the quantum field theory language in some way.

Concerning the second question, No. The first subleading higher-derivative terms are of the same order as the would-be terms that cause the energy-dependence of the speed of light in Lorentz-violating theories: they're suppressed by powers of the Planck mass. However, the true higher-derivative terms are exactly Lorentz-invariant so they can't introduce any dependence of the speed of light on anything. Consequently, such terms can't be seen in any delays. One would have to make measurements that literally collide near-Planckian gravitons, or something like that. The relativistic higher-order terms are practically invisible at low energies - which is a part of their being consistent i.e. compatible with the low-energy principles. It also makes them hard to test, but it's apparently important for a theory of very high-energy phenomena to be hard to test, otherwise the separation of scales wouldn't work well.

Their Lorentz-violating counterparts would mess up the spacetime even at long distances - by adding delays etc. - which is a heuristic way to see that they're sick.

 

[lumidek]

what is the fundamental scale in string theory? What is the distance between one calabi-yau space and the adjacent one, in flat 3+1 space? Does curvature bring them closer or farther apart?

Haha, ensabah. I have already said this joke but I didn't expect that this was the real problem of yours.

The picture in the Elegant Universe where the Calabi-Yau is attached only to some points in a "grid" inside the 3+1-dimensional spacetime is just a caricature, and as far as I remember, Brian Greene even adds a footnote or sentence that explains the obvious point that the picture is misleading and that the Calabi-Yau space exists not only at points in the grid but at each point of space and time.

In other words, the distance between "adjacent" Calabi-Yau spaces is obviously zero, regardless of any curvature. The distance between "them" is infinitely small, there is no gap separating Calabi-Yau spaces at nearby points. The space is at least locally a Cartesian product of the large spacetime and the compact Calabi-Yau manifold. Everything is perfectly smooth about the background geometry, in all directions.

There are various fundamental scales in string theory - the Planck scale, the string scale, and others (they multiplicatively differ by powers of the coupling constant, which is a scalar field - different objects in different situations are governed by physics with different fundamental scales, physics is not that simple). But this fundamental scale doesn't imply that the Calabi-Yau spaces at nearby points are separated. It doesn't imply any discreteness of the naive, LQG type either. Any of these discrete features would be lethal for the theory.

 

[lumidek]

thanks,

so when mass-energy curves spacetime, does it curve 3+1 or does it curve all 11 dimensions in string theory?

so how is it these higher dimensions do not affect the propagation of a photon?

Dear ensabah,

in general, the stress-energy tensor curves the whole spacetime. So in a 11-dimensional field theory (that can be used to approximate string/M-theory, too), there is an 11-dimensional function "stress-energy tensor" with 11-dimensional indices, and the corresponding 11-dimensiona Ricci/Einstein tensor must be equal to the stress energy tensor at each point times the right constant.

But that doesn't mean that the four-dimensional Einstein's equations are unusable. If the matter distribution encoded in the stress-energy tensor is uniform as a function of the compact coordinates (or has a universal dependence on the compact dimensions), the corresponding Einstein tensor must also be uniform. That implies that the geometry of the compact manifold will be preserved at each point, and the effect of the mass on the geometry can be completely encoded in the 4-dimensional curved geometry. The geometry will still be a fibration of the same compact manifold over the 3+1 dimensions, and the parameters of the fibers at each field will be encoded as scalar fields in 3+1 dimensions. Those fields may be massive in which case the 3+1D geometry is the only light degree of freedom that is left.

Such curved geometry influences the propagation of a photon or anything else - and any other phenomenon - exactly in the same way as it does in 4-dimensional theories. This is the whole point of Kaluza-Klein theories that theories with compact dimensions can be rewritten as 4-dimensional theories with many (new) particle/field species, corresponding to "spherical harmonics" or "Fourier modes" propagating on the compact manifold (plus the components of the old fields with the new values of the indices, along the compact directions). Most of these fields are massive, and only influence the physics just like 4-dimensional massive fields (after they're integrating out).

Because all the interactions that govern physics in the 10/11-dimensional space are Lorentz-invariant i.e. under SO(3,1), all effective actions encoding how the subtle massive and wound objects will influence photons in 3+1D will be Lorentz-invariant, too. So there's never any predicted dispersion or anything like that. All the fundamental laws of string theory are exactly Lorentz-invariant, which means that all the effective laws obtained with them - and all predictions - will be Lorentz-invariant, too. Lorentz invariance implies that the speed of light is a universal constant.

 

[heinz]

...

The argument on page 31 doesn't even use the right mathematical language. It is some game in classical mechanics. One surely can't answer such questions by comments about some calculations from the year 1850: it's downright silly.

...

Concerning the second question, No. The first subleading higher-derivative terms are of the same order as the would-be terms that cause the energy-dependence of the speed of light in Lorentz-violating theories: they're suppressed by powers of the Planck mass. However, the true higher-derivative terms are exactly Lorentz-invariant so they can't introduce any dependence of the speed of light on anything. Consequently, such terms can't be seen in any delays.

...

Lubos, thank you again for your clear answer. Can I turn the argument around for a last question? String theory predicts deviations from general relativity at higher orders in R. Now, is there any way to detect such deviation in experiments? From what you say, it seems that the deviations are very small indeed, and need high energy probes to be detected. Does this mean that such deviations are only measurable near horizons and near the big bang - thus maybe never?

Not that I want to defend Woodard, but I want to mention another point he makes. He writes (p 43-45) that any theory of quantum gravity has very few domains where it differs from general relativity. He cites black hole evaporation, black hole collapse and inflation after the big bang. Is this truly pessimistic view correct? Also for string theory?

heinz

 

[lumidek]

Lubos, thank you again for your clear answer. Can I turn the argument around for a last question? String theory predicts deviations from general relativity at higher orders in R. Now, is there any way to detect such deviation in experiments? From what you say, it seems that the deviations are very small indeed, and need high energy probes to be detected. Does this mean that such deviations are only measurable near horizons and near the big bang - thus maybe never?

Not that I want to defend Woodard, but I want to mention another point he makes. He writes (p 43-45) that any theory of quantum gravity has very few domains where it differs from general relativity. He cites black hole evaporation, black hole collapse and inflation after the big bang. Is this truly pessimistic view correct? Also for string theory?

heinz

Dear heinz,

the questions are good but may already hide some confusion. A lot of it. As we said, it is a disputable terminological issue whether the higher-derivative diff-invariant terms, like R^n, deviate from "general relativity". What do you mean by general relativity? They deviate from the Einstein-Hilbert (exact) action. But in the modern sense, general relativity is allowed to have all these terms as long as they are diff-invariant. They only influence very high-energy physics.

But these terms are not really a specific prediction of string theory. Any quantum theory of the UV will generate all these terms at low energies - this is a trivial qualitative conclusion of the renormalization group. Any theory that violates these basic rules about the "production" of such terms fails to be a consistent quantum field-like theory, even at the very qualitative level.

Are these terms measurable? Well, near the Big Bang, you could do it, if you could also repeat the Big Bang many times to train. ;-)

I don't think that you can realistically measure any of these terms near the event horizons of large black holes. All the macroscopically detectable physics near the event horizon is, once again, low-energy effective physics - e.g. Hawking radiation - and it is almost unaffected by these high-derivative terms, too. It's a great ability of quantum gravity that all limits are described by low-energy physics, including the very high center-of-mass energy (which is dominated by black holes which have again low curvatures etc.).

In practice, I would bet 999:1 that these Planck-suppressed terms will never be measured. The only way how they could be measured would be to isolate an effect that doesn't exist without these terms at all, but appears as their consequence. I don't think that any such a phenomenon may exist, even in principle, because the higher-derivative terms mix with the lower-derivative terms if one changes the RG scale, so one can't even objectively say what the coefficients of these terms are - they depend on the RG scale. The only exceptions could be higher-derivative terms that violate a conservation law that is "accidentally" satisfied by the leading terms.

I agree with Woodard that quantum gravity has to agree with GR in most limits - in fact, I independently wrote it above. But I completely disagree that it is disappointing in any way.

Why it's disappointing? What were you/they "hoping" for and why? Science's goal is not to confirm someone's predetermined "hopes" but to search for the correct answers regardless of all the preconceptions. I think it's a beautiful feature of quantum gravity that it is constraining and "learnable". The known low-energy physics governs both limits - very low energies and very high trans-Planckian energies (it's the most universal type of a UV/IR connection, linking low-energy physics and high-energy physics) - and the nontrivial ability of the full quantum theory of gravity is to interpolate between the two regions where the "classical" laws should approximately apply. That's why the "special" physics of quantum gravity is only relevant for the "intermediate" i.e. nearly Planckian scales.

Once again, you're not the only one who assigns strange, ad hoc emotional labels with insights - even important insights - but I just don't get it. It seems like an irrational, unscientific attitude to me. Whenever we learn something correct about the Universe, it's a good news. Well, there may be cases in which we learn that something will remain (or probably remain) forever unknown, like in the anthropic principle, and this can possibly be disappointing. But what we see here is not a similar situation. Here we're learning that we can predict what happens in all limiting situations. What's so bad about the ability to predict? It's not disappointing by any stretch of imagination.

In my favorite analogy, the other "limit" of the Atlantic Ocean was found by Columbus to be qualitatively similar to Europe. Some people may have hoped to see infinite waterfalls, dragons, or giant turtles underlying the Earth in its Western corners. Well, their hopes could have been disappointed. But their hopes had nothing to do with science. Science cares about what there actually is, and having continents on both sides of the ocean makes a lot of sense - and is deeply satisfying from a scientific viewpoint.

At the same moment, the full quantum gravity in the "inaccessible region" of the energy scales (near the Planck scale) is not less constrained but more constrained by the requirement that it interpolates between the two "low-energy limits", much like the laws of the ocean must obey the fact that it can be surrounded by continents on both sides (so for example, one can't indefinitely produce tons of water there, like in the infinite waterfalls). It's great news, too. Moreover, it seems obvious that there's only one framework that solves the interpolation homework: string/M-theory. I am just not getting the sorrow - probably because I have found it obvious, from my childhood, that quantum gravity effects couldn't be measured by cheap gadgets in the labs designed for low-energy physics: they belong to a completely different world that can be accessed only with a lot of mathematics and ability to derive complicated conclusions indirectly; this is why I have loved theoretical high-energy physics and whoever doesn't share this attitude of mine shouldn't have studied high-energy physics.

This must have something to do with the fact that so many laymen so enthusiastically adopt the attitude of the vitriolic physics haters such as Smolin and Woit suggesting that correct theories should be generating "easy to see" or "bizarre" effects. It must have something to do with the general laymen's hatred against mathematics - the language in which God wrote the world, using Galileo's words. Galileo was the first one to realize that mathematics will govern all the cutting-edge laws of physical sciences, and since Isaac Newton, this expectation was actually seen in practice: cutting-edge physics has always been linked to the state-of-the-art mathematical structures.

On the other hand, their desire to see "inconsistent effects" all the time is a completely wrong opinion. Valuable theories should not predict effects that would be "easy to see" if they existed. Valuable theories should predict exactly the effects that can be seen, and not predict effects that can't be seen: valuable theories should be correct rather than hyped or pornographic. This is a huge difference in our understanding of the basic values in science, and maybe not only science. In science, one should be searching for the truth which can often be very subtle and demand a lot of sensitivity and accuracy on our side. People like Smolin are searching for pornographic hype, sensationalism, conclusions that don't require any thinking, and profit from books sold to uneducated people (who usually hate maths) which is something completely different than the search for the truth, which is why I consider Smolin et al. to be very low-quality people from the moral perspective.

Best wishes
Lubos

 

[Fra]

...which is why I consider Smolin et al. to be very low-quality people from the moral perspective.

Surely everyone has the right to their own considered opinon - I do, and so do you - and it's interesting to share our reasoning here regardless of anything else.

But it's exactly your reasoning, your view on science and the scientific process that I really disagree strongly with. In your desire to clear the fog, by means of informing us which are low quality people, and which have inferior intelligence, I encourage everyone reading this to make their own evaluation of his, and the reasoning embracing it.

If I didn't read on the internet that Lubos was a professional physicists I wouldn't have guessed. Surely your well educated but your way of reasoning and your superior attitude is one of the hallmarks of crackpots to me.

I think with a little bit of humbleness and respect for those with differing opinion your words would have much more weight.

I see someone who is well educated, but with a very special suspect way of reasoning, this alone makes me question your conclusions. Your entire reasoning comes out as very risky, since you clearly do not acknowledge your own lack of perfection. This latter is what I thought most educated people learn to do, because the more you learn the more you understand how little you know. You reason as is your inferences were deductions, this alon signals a totally twisted (IMHO) view of the learning process, implicit science.

/fredrik

 

[lumidek]

Surely everyone has the right to their own considered opinon - I do, and so do you - and it's interesting to share our reasoning here regardless of anything else.

But it's exactly your reasoning, your view on science and the scientific process that I really disagree strongly with. In your desire to clear the fog, by means of informing us which are low quality people, and which have inferior intelligence, I encourage everyone reading this to make their own evaluation of his, and the reasoning embracing it.

If I didn't read on the internet that Lubos was a professional physicists I wouldn't have guessed. Surely your well educated but your way of reasoning and your superior attitude is one of the hallmarks of crackpots to me.

I think with a little bit of humbleness and respect for those with differing opinion your words would have much more weight.

I see someone who is well educated, but with a very special suspect way of reasoning, this alone makes me question your conclusions. Your entire reasoning comes out as very risky, since you clearly do not acknowledge your own lack of perfection. This latter is what I thought most educated people learn to do, because the more you learn the more you understand how little you know. You reason as is your inferences were deductions, this alon signals a totally twisted (IMHO) view of the learning process, implicit science.

/fredrik

Dear Fredrik, your comment has clearly nothing whatsoever to do with science. It's just a personal attack. You should shut up in a discussion about physics if you know nothing about physics because it's just painful.

The fact that you wouldn't have guessed the right answers to simple questions related to science - as you admitted yourself - should be just another reason for you to realize that you are not qualified to participate in this discussion and you should avoid proclamations about this topic, especially far-reaching ones.

Concerning Lee Smolin and being a crackpot, indeed, there is a lot of difference between the opinions of uneducated, brainwashed laymen on one side, and professional physicists on the other side. It is easy to check that the first category, represented by a journalist, thinks that Lee Smolin is not a crackpot, while the second category, represented e.g. by the bulk of the Santa Barbara physics department (plus KITP), starting with its chair and including a Nobel prize winner, thinks that Lee Smolin is a crackpot. See

http://online.kitp.ucsb.edu/online/resident/johnson2/rm/qt.html

And sure enough, I agree with the second group. I know Smolin and his thinking quite a lot. Be sure that one doesn't have to be "perfect" to get to this elementary conclusion. Quite generally, science only makes sense because it allows imperfect mortal human beings to determine certain things. If it were only making the results accessible to perfect creatures (God?), it wouldn't be science.

 

[humanino]

Dear Fredrik, your comment has clearly nothing whatsoever to do with science. It's just a personal attack. You should shut up in a discussion about physics if you know nothing about physics because it's just painful.

But do you realize that you are one of the most prominent figures in personal attacks ? We on PF do not know your personal reasons to display such hatred towards non-string approaches. It cannot be that you just disagree with their scientific approach. It is very painful for us too, even if we favor string theory on a personal level, to have high level physics discussion mixed together with personal attacks. So why are you allowed to personal attacks towards people not even present to defend themselves ? This is very cruel.

 

[ccdantas]

Lubos,

In my previous post, I have mentioned the "response-paper" by Thiemann,

http://arxiv.org/abs/hep-th/0608210

but have not asked you explicitly to comment about your impressions on it. I would like to ask you now.

I suppose that your position is that Thiemann have not answered/clarified certain objections from Nicolai et al.'s paper. It would be extremely interesting and pedagogical if you care to list the main points/criticisms raised by Nicolai et al. (and possibly by the paper by Helling et al., also mentioned by Thiemann), and relate why you think the response by Thiemann was not satisfactory.

This is an exercise that I am doing myself and encourage and serious student on quantum gravity to do the same. However, given your strong objection to LQG, it would be extremely clarifying to learn about your conclusions about those papers.

Concerning Fermi's recent data, and data in general, it is true that a single experiment may challenge a theory to a point of falsifying it, however, it is important to note that the scientific method relies on the capability of repeatibility, and cosmological observations differ from laboratory experiments in that regard. Lab experiments can (and should) be repeated as many times as one desires (under the limit of financial contraints, etc), but cosmological *observations* are not that kind of experiments, they are observations, as the name implies, and independent statistical assembly of data is fundamental. There are other issues as well, but it doesn't matter. One should be careful about reaching strong conclusions at this point.

Finally, Fermi's data do challenge a certain class of Lorentz violation quantum gravity models, but I would not agree at this point that the entire LQG programme is challenged from that single observation. Does LQG necessarily relies (or predicts) Lorentz violation, whatever its form? I think that a rational answer at this point of the programme is: it is not clear.

There are technical subtleties that flash large red allerts in front of me and I am certain that not everyone is ready to take strong conclusions at this point. But we all know that you have already taken your (strong) conclusions, and I have always found this a very curious attitude. I think it is not logical to assume that others should be as convinced as you are. I am very skeptical about any theory under development. This is why I am curious on your understanding of the above mentioned exchange Nicolai et al.-Thiemann.

If you find the space in PF inappropriate for that elucidation, may I suggest you to write a technical paper and submit it to the arxiv, with the following title:

Loop Quantum Gravity: a 100% Certain View

I am not joking.

Thanks,
Christine

 

[Fra]

Lubos, I'm not attacking you as a person - since I don't know you, but I do attack the intolerance you display so very clearly, and that you proclaim as if you were preaching the truth which is not the case. Every response you make just confirms my point.

Why not just add your opinon like everyone else, without beeing so downputting towards others. Note that I am not trying to be downputting towards You, I am only attacking your downputting and attitude.

If you think this is irrelevant to science, and the selfcritisim is irrelevant to learning and the scientific method then from my point of view you are the one living an illusion.

Science needs both selection and diversity, but from your reasoning I doubt you see why.

/Fredrik

 

[Finbar]

Dear Finbar,

even when we decide that it is "uncertain" whether the fixed point exists, such a situation doesn't allow one to say that he has an alternative theory, does it? People can make bets according to their expectations. I would never bet on asymptotic safety, and frankly, i don't understand what valuable physics can possibly be obtained from a physical hypothesis "gravity is scale-invariant at short distances" before it is actually understood "why it should be scale-invariant there". I think that all other consequences of this hypothesis depend on the basic assumption whether it's possible, so before it's answered, the amount of interesting physics here is exactly zero and all these things are pure speculations.

No one doesn't have a alternative theory one has a quantum theory of Einstein's gravity defined by the metric tensor. QCD is also an asymptotically safe theory (with a Gaussian fixed point so we say free) but nobody expects this theory to be final we expect unification. There is a large amount of physical information contained in the RG flow of a theory so learning something about this flow can tell us a lot.

Locality.

As the AdS/CFT correspondence, Matrix theory, and perhaps other pictures show, the black hole evolution is unitary, even when they evaporate. It means that the information must get out from the black hole after the matter has crossed the horizon. It means that it must tunnel out and violate the causal structure seen in the classical Penrose diagram i.e. travel along spacelike intervals in the vicinity of the black hole. Consequently, some nonlocality has to exist in quantum gravity as long it is consistent.

It is not enough for this violation to be of order 1 Planck length. The nonlocality must be able to go to arbitrary distances - the thermalization abruptly mixes the degrees of freedom around the whole horizon. The effect is "small" not because the range is short but because the amplitude is low. It is a kind of a quantum tunneling effect, suppressed exponentially, but it is enough to get the information out of the hole in time.

So information can travel arbitrary distances non-locally? Is this not a violation of the principles of relativity? Let me get this straight it is points on the horizon that information can move between non-locally?

But I also meant the very entropy scaling for the entropy that contradicts field theory in the UV. In field theory, the entropy density really scales like Temperature^d where "d" is the number of spatial dimensions. For black holes, the entropy density is constant per unit area of the event horizon, which is a different power law. Because a consistent theory of quantum gravity must agree with the statement that black holes are the generic high-mass states, it can't be described by field theory in the limit of high masses (center of mass energies).

In classical field theory yes the entropy density diverges. But when quantum effects are taken into account there is no certainty that this picture persists.

 

[lumidek]

Lubos,

In my previous post, I have mentioned the "response-paper" by Thiemann,

http://arxiv.org/abs/hep-th/0608210

but have not asked you explicitly to comment about your impressions on it. I would like to ask you now.

I suppose that your position is that Thiemann have not answered/clarified certain objections from Nicolai et al.'s paper. It would be extremely interesting and pedagogical if you care to list the main points/criticisms raised by Nicolai et al. (and possibly by the paper by Helling et al., also mentioned by Thiemann), and relate why you think the response by Thiemann was not satisfactory.

This is an exercise that I am doing myself and encourage and serious student on quantum gravity to do the same. However, given your strong objection to LQG, it would be extremely clarifying to learn about your conclusions about those papers.

Concerning Fermi's recent data, and data in general, it is true that a single experiment may challenge a theory to a point of falsifying it, however, it is important to note that the scientific method relies on the capability of repeatibility, and cosmological observations differ from laboratory experiments in that regard. Lab experiments can (and should) be repeated as many times as one desires (under the limit of financial contraints, etc), but cosmological *observations* are not that kind of experiments, they are observations, as the name implies, and independent statistical assembly of data is fundamental. There are other issues as well, but it doesn't matter. One should be careful about reaching strong conclusions at this point.

Finally, Fermi's data do challenge a certain class of Lorentz violation quantum gravity models, but I would not agree at this point that the entire LQG programme is challenged from that single observation. Does LQG necessarily relies (or predicts) Lorentz violation, whatever its form? I think that a rational answer at this point of the programme is: it is not clear.

There are technical subtleties that flash large red allerts in front of me and I am certain that not everyone is ready to take strong conclusions at this point. But we all know that you have already taken your (strong) conclusions, and I have always found this a very curious attitude. I think it is not logical to assume that others should be as convinced as you are. I am very skeptical about any theory under development. This is why I am curious on your understanding of the above mentioned exchange Nicolai et al.-Thiemann.

If you find the space in PF inappropriate for that elucidation, may I suggest you to write a technical paper and submit it to the arxiv, with the following title:

Loop Quantum Gravity: a 100% Certain View

I am not joking.

Thanks,
Christine

Dear Christine,

a discussion of this paper by Thiemann involves some technicalities which are not terribly interesting. Thiemann is a champion of the spin foam models (unlike Ashtekar and others), and he criticizes Nicolai et al. for not giving much attention to spin foams.

Indeed, they don't give enough time to spin foams. But any consistent theory can be, at least in principle, formulated via the spacetime perspective, like in spin foams, or in the time-sliced perspective, like in the canonical quantization. The results must be automatically equivalent when done correctly.

So Thiemann doesn't address any of the main points by Nicolai et al. He's just redirecting the discussion elsewhere. For example, Nicolai show, in the operator approach, that the algebra doesn't close. Thiemann doesn't find any mistake in Nicolai et al. Instead, he presents a calculation in his formalism, leading him to the conclusion that the algebra closes - but he can only say up to zeroth order in hbar. That's really entertaining because it's like saying that the classical diffeomorphism groups etc. exist.

Similarly, Nicolai et al. explain that many constructions are ambiguous and must be allowed to lead to objects with many possible values. Thiemann doesn't show anything wrong about the multiparameter classes of solutions: he just presents a random one among them and declares it to be the right answer, without showing that his answer is any better than any other answer in any way.

I think it's obvious that Thiemann doesn't disprove any basic propositions by Nicolai et al. That's not because Thiemann is not bright enough in this case: it's because the Nicolai et al. arguments are correct so they cannot really be disproved in any way.

Note that despite the self-promoting character of the LQG community - that makes sure that all published papers about LQG are "positive" and hide all the inconsistencies under the rug - the Nicolai et al. paper still beats Thiemann by citations. It probably makes no sense to write new papers of the Nicolai et al. type (or to rewrite the arguments into the spin foam language) because the people who have already gotten the message would learn nothing new, and the people who haven't gotten it will probably never get it, either because they're blinded by preconceptions, or because they're just intellectually limited.

I don't plan to read Thiemann's paper or any other paper on LQG because this story is over and no sensible person should continue to waste her time with this stuff. And I surely don't plan to become Thiemann's personal historian because I don"t think that he deserves one. Do you understand the concept that in science, one eliminates theories that have been falsified and focus on the viable ones? Do you really think that people like me should be wasting time with obscure LQG papers a week after the event that has falsified LQG and all similar research programs?

Best wishes
Lubos

 

[lumidek]

But do you realize that you are one of the most prominent figures in personal attacks ? We on PF do not know your personal reasons to display such hatred towards non-string approaches. It cannot be that you just disagree with their scientific approach. It is very painful for us too, even if we favor string theory on a personal level, to have high level physics discussion mixed together with personal attacks. So why are you allowed to personal attacks towards people not even present to defend themselves ? This is very cruel.

No, I don't realize that I am the most prominent figure in the discipline you wrote.

Indeed, it is not true that I disagree just with scientific propositions. I disagree with their moral values (or, more precisely, the absence of values). I disagree with their nasty plans to politicize science, their focus on populism and brainwashing of ordinary people, and their desire to transform science into another left-wing mouthpiece. I protest against their double-faced approaches and hypocrisy, and about their readiness to deny evidence or facts whenever they find it convenient. Indeed, this is about much more than a disagreement about a technicality in science.

I think that these people are not good ones. Still, the amount of my attacks against them is negligible relatively to their attacks on good science and its fundamental principles.

For example, I didn't put "Rise of Smolins, fall of science" into the subtitle of my books I wrote so far, even though such a subtitle would be very accurate because the rise of this crap and loud sub-par would-be scientists is really threatening to cause a fall of science. I want to do everything I can to stop the influence of these people on this world which has been devastating for science and all other values I find important.

 

[humanino]

Dear Lubos

...

I sincerely appreciate that you clarified your position. Thank you very much.

I also apologize to those who think I polluted this thread, but I do believe that strong opinions expressed earlier in this thread must be read in the light of this political position.

 

[lumidek]

1. No one doesn't have a alternative theory one has a quantum theory of Einstein's gravity defined by the metric tensor. QCD is also an asymptotically safe theory (with a Gaussian fixed point so we say free) but nobody expects this theory to be final we expect unification. There is a large amount of physical information contained in the RG flow of a theory so learning something about this flow can tell us a lot.

2. So information can travel arbitrary distances non-locally? Is this not a violation of the principles of relativity? Let me get this straight it is points on the horizon that information can move between non-locally?

3. In classical field theory yes the entropy density diverges. But when quantum effects are taken into account there is no certainty that this picture persists.

1. QCD is not only asymptotically "safe": it is asymptotically free (which means that the coupling goes to zero in the UV, instead of a finite constant, as in asymptotically safe theories). And it is a great example of yours showing what I meant.

QCD only became a sensible theory worth studying when the people understood why it was asymptotically free - the negative beta-function. That's what the QCD fathers finally got their Nobel prize for. Before that point, one couldn't say anything sensible, deep, or useful about QCD, which is why no one should have studied it. The situation with asymptotic safety is analogous except that there's no understanding why gravity should be asymptotically safe. So no one should really study it because all insights depend on it, and predictions of any other questions are probably at least as difficult as the "proofs" of asymptotic safety. So the output from asymptotic safety is at most as large as the input. One wants to believe it's there, and given this assumption, it's there, but one can't learn anything else because any other question is as difficult as the proof that it's asymptotically safe, and this proof doesn't exist.

2. Yes, once again, the information getting out of the black hole violates the causal rules as classically determined from the black hole causal diagram. It is a violation of relativity in the same sense as quantum tunneling may violate the energy conservation law for a while, by allowing the particle to be in classically inaccessible regions.

Let me just say that this is what pretty much all experts think that actually happens in string theory = quantum gravity (regardless of the approach). There's nothing paradoxical about it. The metric tensor is a fluctuating quantum degree of freedom and the causality defined by it simply cannot be quite exact for objects whose lifetime is finite.

3. I didn't talk about any classical field theories. I talked about the full quantum field theories, the entropy density was not divergent, but finite, and it was determined fully by the conformal invariance i.e. dimensional analysis. In field theory (and this term always means "quantum field theory" in these HEP discussions!), it is C times Temperature^d where d is a spatial dimension. You seem to respond to something that has nothing to do with my argument, and is clearly irrelevant for this discussion because it's just some artifact of classical field theories. Again, we are talking about (asymptotically safe) quantum field theories, right?

 

[atyy]

The situation with asymptotic safety is analogous except that there's no understanding why gravity should be asymptotically safe. So no one should really study it because all insights depend on it, and predictions of any other questions are probably at least as difficult as the "proofs" of asymptotic safety. So the output from asymptotic safety is at most as large as the input. One wants to believe it's there, and given this assumption, it's there, but one can't learn anything else because any other question is as difficult as the proof that it's asymptotically safe, and this proof doesn't exist.

I agree that the major question about asymptotic safety is its existence. But suppose the UV fixed point for gravity exists, and the critical surface is finite dimensional - will that be enough to make predictions, or will there still be a problem coming in from electroweak theory not having a continuum limit (ie. can asymptotically safe gravity and electroweak theory be combined at Planck scale energies)?

 

[MTd2]

That's what the QCD fathers finally got their Nobel prize for. Before that point, one couldn't say anything sensible, deep, or useful about QCD, which is why no one should have studied it.

There would be no QCD fathers if they thought like that before studying it.

 

[heinz]

In practice, I would bet 999:1 that these Planck-suppressed terms will never be measured. The only way how they could be measured would be to isolate an effect that doesn't exist without these terms at all, but appears as their consequence. I don't think that any such a phenomenon may exist, even in principle, because the higher-derivative terms mix with the lower-derivative terms if one changes the RG scale, so one can't even objectively say what the coefficients of these terms are - they depend on the RG scale. The only exceptions could be higher-derivative terms that violate a conservation law that is "accidentally" satisfied by the leading terms.

I agree with Woodard that quantum gravity has to agree with GR in most limits - in fact, I independently wrote it above. But I completely disagree that it is disappointing in any way.

Lubos,

thank you again for the clear answer. The reason I added "disappointing" is that the situation you describe is now the following: general relativity (with Einstein-Hilbert action) and string theory differ only by terms which cannot be measured in experiments (your 999:1 bet).

It is fun to see, when you google for "string theory" and "deviations from general relativity", that many pages come up. So thank you for stating so clearly that in fact, these deviations are probably not of any "measurable" importance.

Obviously, this distinguishes string theory from all other theories that predict deviations from general relativity, but it does not distinguish string theory from general relativity itself. We thus can confirm string theory only in the particle physics domain, not in the gravitation domain. I think that is a powerful conclusion. Thanks for saying this so clearly!

heinz

 

[Finbar]

1. QCD is not only asymptotically "safe": it is asymptotically free (which means that the coupling goes to zero in the UV, instead of a finite constant, as in asymptotically safe theories). And it is a great example of yours showing what I meant.

Yes QCD is asymptotically safe, asymptotic freedom is a special case of asymptotic safety where the fixed point is Gaussian, as I said. But note that Newtons constant would be asymptotically free in asymptotically safe gravity as it has a negative mass dimension.

QCD only became a sensible theory worth studying when the people understood why it was asymptotically free - the negative beta-function. That's what the QCD fathers finally got their Nobel prize for. Before that point, one couldn't say anything sensible, deep, or useful about QCD, which is why no one should have studied it.

But by that logic the people who found the negative beta-function shouldn't of been studying it. People study the RG flow of gravity to see whether the beta-function's of gravitational constants have fixed points. Evidence has been found for the fixed so also it makes sense to look at the physical implications.



I was thinking of fields on black hole spacetimes in the entropy discussion. Sorry. Can you give me a reference with the calculation that entropy goes as T^d in a full QFT? I was looking at Susskind's book (BH, information and the ST revolution) where he notes this relationship S~V T^3 for a free scalar field. He then goes on to show that this implies the entropy diverges near the horizon. This though is at least a semi-classical calculation. Obviously a full theory of quantum gravity should solve this problem. It also doesn't seem unreasonable that within asymptotic safety this problem could be solved; the coupling of gravity to matter fields is asymptotically free so effects near the horizon should be reduced.

 

[ccdantas]

a discussion of this paper by Thiemann involves some technicalities which are not terribly interesting. (...)

Thanks for your clarifications (although I was expecting a more detailed elaboration; but never mind). This is certainly something I should work myself.

Do you really think that people like me should be wasting time with obscure LQG papers a week after the event that has falsified LQG and all similar research programs?

Evidently, every one is free to do whatever one desires, I'm not here to try to convince anyone otherwise.

Also, there is nothing particularly wrong in establishing one's own standard against which a given theory is found not to deserve further investiment of one's energy and time, so I have nothing to criticize you on thinking that LQG is a waste of your time. However, I do not agree to conclude that it has been "falsified and period". I think there is still a long way to ascertain the situation. This is quite normal in science. I am generally as skeptical as science requires, and I think it is healthy to keep that way. Evidently there is a limit to that and the limit is not often as clear as desirable. The situation in quantum gravity is exactly like that.

You should realize that your standard is not necessarily in agreement with other people's, not because other people are stupid and you are a genius, but just because in the present case, it is clear that there are still subtleties in the LQG formalism (I believe you would agree with this?). These are open for debate, and people are interested in investigating them further. This is not a big issue (although you do often make a big issue on this). You are free to put an end to your own curiosity about LQG, by your own standards. But this does not mean that you are 100% correct. What is needed is clean cut predictions and clean cut observations/experiments. LQG is not at that point yet; Fermi data lead to some interesting (possible) constraints, that need to be established with more data. More understanding of the source, a clear bound on the emission time of the highest energy photon.

A similar situation concerns your preferred approach, string theory, which is often claimed to be under construction. One needs clean cut predicitons of the theory in order to falsify it.

Thanks.
Christine

 

[Micha]

Hi Lubos,
as Christine and others pointed out, we are talking about one photon. I don't think that it is appropriate to say, that some theory has been falsified by measuring one photon. Never. Of course this does not change anything in all the arguments exchanged in this very interesting thread. You can always add the small if clause "if the result is confirmed then..." and then we can put a probability to that. But by completely dropping it, I think you make your position attackable at a point, where it is not necessary. Because whether this is confirmed or not we can just wait and see. No point to put energy into this if you are a theorist.

 

[Eelco]

Lubos:

While I am myself unsure of the merits of LQG, you make some fundemantally flawed claims concerning discrete spacetime. Small scale physics that breaks some laws deduced from macroscopic observations are perfectly capable of reproducing these macroscopic properties in the large scale limit. As an elementary example, just think of wave propagation over a mass-spring chain, which is dispersive but has the continuum wave propagation for wavelengths much larger than the grid spacing.

My impression of you and your likes, is that you are terrified of the possibility that all these fancy theories you have invested your life in, will be falsified by some future experiment. To claim victory over one photon merely shows desperation. But even if these dipersion predictions are falsified, at least that's more than string theory can lay claim to.

Since you seem to know so well, do you dare make any predictions that might be tested with the LHC? What if supersymmetric particles are not found, will that mean anything for your position on string theory?

 

[MTd2]

will be falsified by some future experiment.

Not really. Just string theory models he likes best. The one by Mavromatos shows an average distribution for light speed, not of fundamental nature, and could fit possibly delayed fotons.

 

[humanino]

You know MTd2, Lubos admitted that he is on a political fight against LQG. I am not sure what is the point to continue any scientific argumentation for or against here, we merely have lobbying activity and it is against PF rules. So I am not sure how much will be necessary and whether it is worth pushing in this direction, for instance Lubos made several references to "God" which should be enough for moderation of a "regular" member.

 

[Micha]

for instance Lubos made several references to "God" which should be enough for moderation of a "regular" member.

That statement is completely ridiculous and you know it. The reference to God was clearly not made in a scientific sense.

 

[Sauron]

I would like to present the relevance from an slighly different viewpoint.

There are two asic options:
a) LQG predicts dispersion of speed of light. Them it has benn falsified.

b) It doesn't predict that dispersion. Them it doesn't predict anything measurable AFAIK. That's contrary to one of it's declared main purposes, to sacrify "ambition" of beeing an unified theory for the predictivity power.

Anyway this result is very bad for LQG.

Let's go with some of the subleties. Some people claim that LQG in fact doesn't predict that dispersions. Lubos, on the contrary, gives a general argument about the lack of imaginary values for areas in LQG (something shared by all the approach to LQG,canonical, spin foams, CDT's if I am not wrong) impliying, whatever LQG people agrees or not that dispersions. Well, I would like to see if Lubos has some reference for an actual paper where that argument is elaborated in detaill.

The other subletie I see is that some people claim that as an experimental result the conclusions are not absolutly settled because it is argued that it is necessary to obtain result for ensemmbles of photons because the dispersion is an average result. Aout this particlar point Lubbos says that the natural thing would be to do an satatistic about the number of collisions of the photon with the "atoms of space time" (inthe markopolulos justification of the phenomena). Form this viewpoint a single photon will have by far enought numer of collisions to do a good statistichal average as far as I see (I think that is the essence of Lubos argument).

About the question of predictions of string theory surelly Lubos can give more detaills (and correct me if I make some mistake in what I say about F-theory). I can point to the F-theory GUT scenaries. In the strings 2009 Vafa gave a brief account of results stating two clear predictions. One was the there were not WIMP's candidates foro dark matter. That implied that the apparent excess of positrons observed by ARTIC and PAMELA were false. Curiously FERMI/GLAST could also prove this.

For the LHC it is predicted some particular particle (I don't remembberthe name just now), with a very clear trace when leaving the detectors.

If that results are found that particular approach, the F-theory GUTS will be clearly favoured. If not that particular approach of string theory (a very good one which reproduces all the characteristics of the standard model) will have been falsified. Still it is possible that other phenomenological models based on string theory could be shown valids.

 

[Finbar]

Let's go with some of the subleties. Some people claim that LQG in fact doesn't predict that dispersions. Lubos, on the contrary, gives a general argument about the lack of imaginary values for areas in LQG (something shared by all the approach to LQG,canonical, spin foams, CDT's if I am not wrong) impliying, whatever LQG people agrees or not that dispersions. Well, I would like to see if Lubos has some reference for an actual paper where that argument is elaborated in detaill.

Nice post. I just want to know more about this lack of imaginary area. Does this stem from the Hamilton approach of LQG where by they split space time d=3+1 such that areas can only be real i.e spatial? I see then that this could crop up in CDT as there they seem to give time a direction. As I see it the singling out time could well be the downfall of these theories if this makes them break Lorentz invariance physically. On the other hand it could be that this singling out of time is no more than a gauge fixing procedure for example if one gauge fixes a Lagrangian in the path integral approach this breaks Lorentz invariance in the Lagrangian but the theory still gives the correct gauge independent results.

Clearly a lack of imaginary areas seems like we area seriously restricting the number of metrics that we include in a path integral approach like CDT. Perhaps this restriction is to server on the other hand restriction is needed such that double counting doesn't occur.

In my opinion if your starting principles are general relativity and quantum mechanics and you end up with a theory that breaks local Lorentz invariance you haven't applied those principles. If this is so then you should really restate your guiding principles, change your approach, so you retain Lorentz invariance, or give up on the theory altogether. I must say that the first one seems least appealing therapeutically but experimentally it obviously leads to predictions.

 

[marcus]

...
Anyway this result is very bad for LQG.
...

I don't understand your reasoning, Sauron. LQG researchers tried for some years to derive a prediction of dispersion, but could not make the 4D theory yield such a prediction.
This observation makes dispersion less likely. If it is born out by other similar observations then this will help guide their development of LQG and save them trouble.

It certainly does not falsify the approach since there was no prediction that actually derived from the theory. I see this kind of Fermi-LAT observation as stimulating for LQG and the other QG approaches.

The task of deriving predictions still remains, and various avenues are being explored. But that is a separate topic. All this observational result does is give more direction and focus to the effort. Or? Please explain if you see it differently.

 

[atyy]

I don't understand your reasoning, Sauron. LQG researchers tried for some years to derive a prediction of dispersion, but could not make the 4D theory yield such a prediction.
This observation makes dispersion less likely. If it is born out by other similar observations then this will help guide their development of LQG and save them trouble.

It certainly does not falsify the approach since there was no prediction that actually derived from the theory. I see this kind of Fermi-LAT observation as stimulating for LQG and the other QG approaches.

The task of deriving predictions still remains, and various avenues are being explored. But that is a separate topic. All this observational result does is give more direction and focus to the effort. Or? Please explain if you see it differently.

What's your take on Henson's http://arxiv.org/abs/0901.4009 ? He claims spin foams violate Lorentz invariance, specifically photon dispersion tests.

 

[Micha]

I don't understand your reasoning, Sauron. LQG researchers tried for some years to derive a prediction of dispersion, but could not make the 4D theory yield such a prediction.
This observation makes dispersion less likely. If it is born out by other similar observations then this will help guide their development of LQG and save them trouble.

It certainly does not falsify the approach since there was no prediction that actually derived from the theory. I see this kind of Fermi-LAT observation as stimulating for LQG and the other QG approaches.

The task of deriving predictions still remains, and various avenues are being explored. But that is a separate topic. All this observational result does is give more direction and focus to the effort. Or? Please explain if you see it differently.

I must have dreamt when I read Smolin's book. Lubos Motl concludes, that LQG is dead. Where is your voice, Marcus?

 

[marcus]

What's your take on Henson's http://arxiv.org/abs/0901.4009 ? He claims spin foams violate Lorentz invariance, specifically photon dispersion tests.

I guess you know Joe Henson is not a Lqg researcher. He is a postdoc currently at Perimeter who has done almost all his work in Causal Sets. He indicates that Carlo Rovelli and Daniele Oriti (more experienced representatives of mainstream Lqg) had serious objections to the paper. The paper is iffy and handwaving. It says if such and such then maybe so and so. Ultimately doesn't derive hard prediction.

You asked my take. Well, in essence that paper seems to have been Joe's contribution to one of the parallel sessions at the Potsdam Loops 2005 conference,
http://loops05.aei.mpg.de/index_files/abstract_henson.html
I am not sure why it didn't get published earlier. The preprint is January 2009. Before spending a lot of time on it, I would wait to see how it fares in peer review and the normal publication channels. If he thinks the idea is good maybe he will follow it up with something less tentative.