Lorentz violating severely restricted: Mqg/Mplank > 1200

[humanino]

Lubos,

is there of any non-string approach to quantum gravity you would consider worth if not pursuing at least being aware of ?

 

[skippy1729]

Very little of this thread has discussed the original cited paper. I have finally finished reading it and the supplementary information pages (I am an old, slow engineer, not a professional physicist). The one point that stands out for me is that the selection of the time of emission of the 31 GeV photon with respect to the rest of the gamma ray burst is most accurately described as speculation. Gamma ray bursts seem to come in some variety and have models that are, at best, qualitative.

I have no real horse in this race (Strings vs LQG) but to declare LQG dead as a result of this observation seems unfounded to me. The ultimate fate of discrete spacetime vs the continuum will ultimately be experimental but my hope for any ultimate continuum theory largely disappeared when I learned of the Banach-Tarski paradox.

Cheers, Skippy

 

[lumidek]

Lubos,

is there of any non-string approach to quantum gravity you would consider worth if not pursuing at least being aware of ?

Not as of August 2009. Science is not about trying to create or invent "diverse approaches"; it is about finding the right answers, and although there are many open detailed questions, string theory as a framework is pretty much a well-established unique framework to ask and answer questions about quantum gravity.

That doesn't mean that it's one method or one narrow-minded calculational procedure. There are dozens of approaches to questions about quantum gravity within string theory. Low-energy approximations, worldvolume theories, AdS/CFT, matrix theories, various perturbative expansions, general analyses of black hole thermodynamics and causal structures, calculations relying on supersymmetry, and many others.

 

[lumidek]

Very little of this thread has discussed the original cited paper. I have finally finished reading it and the supplementary information pages (I am an old, slow engineer, not a professional physicist). The one point that stands out for me is that the selection of the time of emission of the 31 GeV photon with respect to the rest of the gamma ray burst is most accurately described as speculation. Gamma ray bursts seem to come in some variety and have models that are, at best, qualitative.

I have no real horse in this race (Strings vs LQG) but to declare LQG dead as a result of this observation seems unfounded to me. The ultimate fate of discrete spacetime vs the continuum will ultimately be experimental but my hope for any ultimate continuum theory largely disappeared when I learned of the Banach-Tarski paradox.

Cheers, Skippy

Dear Skippy, given the known numbers, your statement about the speculations is just indefensible.

The burst occurred 10 billion light years away, i.e. roughly 3e17 seconds ago. The photons went up to 31 GeV which is over 1e-17 of the reduced Planck energy, and that's really the relevant typical scale.

An order-one energy-dependence should change the speed of light by at least 1e-17 of its value. If multiplied by 3e17 seconds, the lag should be at least 3 seconds. And I am being very generous here because the champions of the energy-dependence have claimed that the lag should even be several minutes or hours for such photons! That's what they boldly claimed after some MAGIC observations in 2007. But it's very clear from the newest, more accurate observation that the lag wasn't over 0.2 seconds, and it probably ("more likely than not") had to be smaller than 10 milliseconds. Just look at the colorful time series in the paper.

Assuming that all those 161 photons came within the short period by a combination of their being emitted at different moments - by those seconds - but delayed in such a way that they all arrive within the same second is extremely unlikely. It is really a conspiracy theory, not a sensible physical hypothesis.

At any rate, you will be proved wrong by further measurements. The more clear measurements of this kind one needs, the more appropriate it is to call him a denier of empirical evidence. Some of the future bursts will have a different duration and/or a different distance. That means that if the "conspiracy" worked for this particular burst, it couldn't work for other bursts to be seen in the future because the ratio "length of burst when it's created OVER the hypothetical delay" would be predicted to be different, and the synchronization should disappear. But it's clear that it will not. The probability of the conditions that need to be satisfied for the May 2009 to be a conspiracy that just masks an effect is negligible.

The opinion that the Banach-Tarski paradox has any consequences for physics or any natural science is downright ludicrous. It is pure maths, and very abstract and pathological maths. The most straightforward physical way to deal with the Banach-Tarski result is simply to deny the axiom of choice for infinite sets - one doesn't really need it in this form in any physically relevant maths. Without the axiom of choice, one cannot find non-measurable sets and the Banach-Tarski paradox can't be derived. Instead, one can consistently assume that all sets are measurable.

At any rate, these are purely aesthetic choices for a mathematician. The question whether all subsets of reals are measurable is clearly an unphysical question because it can't be associated with any operational test or measurement, not even in principle.

The fundamental laws of spacetime have to admit a description in terms of a priori continuous degrees of freedom. If they don't, they can't be fundamental.

Best wishes
Lubos

 

[Eelco]

The opinion that the Banach-Tarski paradox has any consequences for physics or any natural science is downright ludicrous. It is pure maths, and very abstract and pathological maths. The most straightforward physical way to deal with the Banach-Tarski result is simply to deny the axiom of choice for infinite sets - one doesn't really need it in this form in any physically relevant maths. Without the axiom of choice, one cannot find non-measurable sets and the Banach-Tarski paradox can't be derived. Instead, one can consistently assume that all sets are measurable.

I agree with you here: the axiom of choice is horsegarbage, and the tarski paradox a figment of the imagination of mathematicians.

As is the continuum, and completed infinity in general. It starts with Gallileo's paradox, and it goes downhill from there. Non-finitistic mathematics is not logically consistent, despite what mathematicians may tell you.

At any rate, these are purely aesthetic choices for a mathematician. The question whether all subsets of reals are measurable is clearly an unphysical question because it can't be associated with any operational test or measurement, not even in principle.

Fully agreed. More generally, there is in principle, never any need to allow for completed infinity in mathematical physics. That includes completed infinity with respect to division.

The fundamental laws of spacetime have to admit a description in terms of a priori continuous degrees of freedom. If they don't, they can't be fundamental.

You couldn't possibly sound more like Kant.

 

[Dmitry67]

I agree with you here: the axiom of choice is horsegarbage

The problem with the theory of set is much deeper the AC
Assuming 'not AC' or some weaker substitutions of AC does not really help,
because there are too many undecidable statements (even without AC)
which raises the questions what is a 'TRUTH' in the theory of set
and is it nothing more then just pure manupulation with character strings
containing symbols 'exists', 'all', 'belongs to' et cetera.

 

[Eelco]

The problem with the theory of set is much deeper the AC
Assuming 'not AC' or some weaker substitutions of AC does not really help,
because there are too many undecidable statements (even without AC)
which raises the questions what is a 'TRUTH' in the theory of set
and is it nothing more then just pure manupulation with character strings
containing symbols 'exists', 'all', 'belongs to' et cetera.

Yeah, I agree.

non-finitary mathemathics is horribly confused, AC or not.

 

[Dmitry67]

Dear Dmitry, there surely *is* a fundamental speed of light "c", and it represents the speed of light in the vacuum. It defines the null trajectories in spacetime and the light cones. A configuration with Casimir plates is not a vacuum.

Sorry, I don't understand.
I am just pure amater, so please tell me where I am wrong. Looks at the diagram.

"c" (null trajectory) is at 45 degrees. But photon has a chance to become a virtual pair traveling slower then c. So the speed of light in vacuum < "fundamental" c. In another words, the apparent speed of light is NOT on the null trajectory.

So, where I am wrong?

 

[marcus]

... champions of the energy-dependence have claimed that the lag should even be several minutes or hours for such photons! That's what they boldly claimed after some MAGIC observations in 2007...

Do you mean the MAGIC observations reported in 2007 here?
http://arxiv.org/abs/0708.2889
Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope
J. Albert et al. (for the MAGIC Collaboration), John Ellis, N.E. Mavromatos, D.V. Nanopoulos, A.S. Sakharov, E.K.G. Sarkisyan
(Submitted on 21 Aug 2007)
"We analyze the timing of photons observed by the MAGIC telescope during a flare of the active galactic nucleus Mkn 501 for a possible correlation with energy, as suggested by some models of quantum gravity (QG), which predict a vacuum refractive index..."

And are the "champions of the energy-dependence" in this case the string theorists Ellis, Mavromatos, Nanopoulos?

 

[Spinnor]

Sorry, I don't understand.
I am just pure amater, so please tell me where I am wrong. Looks at the diagram.

"c" (null trajectory) is at 45 degrees. But photon has a chance to become a virtual pair traveling slower then c. So the speed of light in vacuum < "fundamental" c. In another words, the apparent speed of light is NOT on the null trajectory.

So, where I am wrong?

Isn't your picture one of many possible endpoints for the electron-positron pair. Don't you have to do some averaging process? Would that averaging lead to a speed of c?

 

[humanino]

So, where I am wrong?

This is just a drawing. It does not correspond to a physical process. Are you suggesting that QED alone allows light not to propagate at c ?

There are many issues with your drawing, assuming I correctly interpret it as external photon legs on-shell (real photons). First of all, you are assuming a single Feynman diagram to give you the amplitude for a physical process. Related to this issue, what would prevent light from traveling faster than c, provided your electron-positron fluctuation decides to go on the other side of the light-cone ? Another problem is that I can cut your diagram and end up with a different total energy-momentum, so I would naively suspect that you do not have the proper conservation at each vertex. However, it's hard to tell because you seem to mix up position and momentum representations.

 

[lumidek]

The problem with the theory of set is much deeper the AC
Assuming 'not AC' or some weaker substitutions of AC does not really help,
because there are too many undecidable statements (even without AC)
which raises the questions what is a 'TRUTH' in the theory of set
and is it nothing more then just pure manupulation with character strings
containing symbols 'exists', 'all', 'belongs to' et cetera.

There is no problem with incomplete sets of axioms and there is no unique "true" answer to these unphysical questions. Get used to it.

In fact, as you should know, even in pure mathematics, a theorem by Gödel says that every sufficiently strong system of axioms (and all systems that naturally incorporate "all functions", as needed in physics, are sufficiently strong!) *has* to admit undecidable statements. That's the incompleteness theorem.

So if you're complaining against this fact, i.e. against the very existence of undecidable statements, then you're complaining against a mathematical inevitability. It is therefore on par with complaining that 2+2=4. You don't like it? Too bad.

This is no "paradox" in mathematics. One can carefully design constructively, in the Zermelo-Frenkel template, an infinite and physically sufficient class of questions that are decidable. And the undecidable ones are, in a very meaningful sense, physically uninteresting, quasi-recursive and self-referring logical games.

I wasn't trying to reject Gödel's incompleteness theorem, as you did. I was just explaining that these games in set theory don't have any negative implications for the consistency of continuous objects - numbers, functions, and functional spaces, among others.

 

[lumidek]

Do you mean the MAGIC observations reported in 2007 here?
http://arxiv.org/abs/0708.2889
Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope
J. Albert et al. (for the MAGIC Collaboration), John Ellis, N.E. Mavromatos, D.V. Nanopoulos, A.S. Sakharov, E.K.G. Sarkisyan
(Submitted on 21 Aug 2007)
"We analyze the timing of photons observed by the MAGIC telescope during a flare of the active galactic nucleus Mkn 501 for a possible correlation with energy, as suggested by some models of quantum gravity (QG), which predict a vacuum refractive index..."

And are the "champions of the energy-dependence" in this case the string theorists Ellis, Mavromatos, Nanopoulos?

Yes, I do. That's the papers. The statement that the multi-minute delay seen by MAGIC was due to the journey through the Cosmos is now known to be ludicrous because the delay can't exceed a second, and probably not even 10 millisecond (and by theoretical reasons, it's almost certainly zero).

The delay seen by MAGIC was therefore created during the burst itself, not during the journey through the Universe, and Ellis et al. were spectacularly wrong about this point.

John Ellis is a top physicist but he is *not* a string theorist. What they wrote about Lorentz violation was clearly not string theory, in the sense taught by textbooks on "String theory" or "Superstring theory".

 

[lumidek]

Sorry, I don't understand.
I am just pure amater, so please tell me where I am wrong. Looks at the diagram.

"c" (null trajectory) is at 45 degrees. But photon has a chance to become a virtual pair traveling slower then c. So the speed of light in vacuum < "fundamental" c. In another words, the apparent speed of light is NOT on the null trajectory.

So, where I am wrong?

Dear Dmitry,

you're just taking these spacetime diagrams too seriously - and you seem to think that the complicated answers such as the "speed of something" can be "directly" read out of these naive pictures. Well, that's not the case. When done properly, they should be Feynman diagrams. Such diagrams must be integrated over the momenta - or, if you wish, over the positions of the vertices in spacetime. But there are many more steps you have to do before you can evaluate amplitudes - and the speed of photons. Let's look.

The results of the integral - in this case, a one-loop integral - will be divergent and one must regulate it. This procedure involves various complicated subtractions. If you use a brute cutoff, one may indeed "slow down the light", more precisely generate a mass term for the photon.

But a mass term for the photon would prevent us from decoupling the unphysical, time-like and longitudinal modes of the electromagnetic field, which would make some probabilities negative. That's inconsistent, so the gauge invariance has to be preserved, and the photon has to stay massless.

So the right "counterterms" have to be added to the Feynman diagram (the same diagram, with the electron loop replaced by a new two-legged small "cross vertex" inserted to the middle of the photon propagator) so that the photon mass remains zero (this is automatic if you evaluate the divergent integrals e.g. in dimensional regularization or any other regularization that respects the gauge invariance: no counterterms subtracting the photon mass are needed in that case).

At any rate, when you do the right integrals and subtract the things you need to subtract to preserve gauge invariance (for positivity of probabilities), you will obviously return to a theory where the mass of the photons is zero, so the speed must be the speed of light.

I also wanted to say (previously) that it's easy to see that in the right variables, the true information can never propagate faster than the speed of light. How? E.g. in the Heisenberg picture.

The operators satisfy the same equations as the classical fields. The classical field equations are known to affect the future light cone and its interior only, so it must be true in quantum field theory, too. This statement is easily seen in infinitesimal pieces of spacetime because in such small regions, one can neglect (by dimensional analysis) all the terms except for the kinetic ones, and one is back to wave equations for individual particles and/or particle "splitting/mergers". This has to be true in the presence of matter, Casimir plates, or anything else. Of course, a nonlocal field redefinition may obscure the causality and it may produce a picture where it "looks like" the information propagates superluminally, but there always exist variables in which it does not.

 

[metron]

What they wrote about Lorentz violation was clearly not string theory, in the sense taught by textbooks on "String theory" or "Superstring theory".

Hi Lubos,

Yes, and it seems they knew it.

http://arxiv.org/abs/gr-qc/0005100

They used a world-sheet Liouville approach to non-critical string theory.

 

[marcus]

What they [e.g. Nick Mavromatos...?] wrote about Lorentz violation was clearly not string theory, in the sense taught by textbooks on "String theory" or "Superstring theory".

And likewise claims of Lorentz violation are not derived from the regular LQG, in the sense taught by Rovelli's textbook or Ashtekar's standard review of the subject.

 

[marcus]

On the other hand, if one's idea of what is string theory is not narrowly restricted then one could mistake Dimitri Nanopoulos for a highly cited string phenomenologist/theorist based on publications such as these

The Flipped SU(5) x U(1) String Model Revamped.
Ignatios Antoniadis, John R. Ellis, J.S. Hagelin, Dimitri V. Nanopoulos, (CERN) . CERN-TH-5442-89, CTP-TAMU-37-89, MIU-THP-89-42, Jul 1989. 18pp.
Published in Phys.Lett.B231:65,1989.
TOPCITE = 250+
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 413 times

Precision LEP data, supersymmetric GUTs and string unification.
John R. Ellis, (CERN) , S. Kelley, (Maharishi U. of Management) , Dimitri V. Nanopoulos, (Texas A-M & HARC, Woodlands) . CERN-TH-5773-90, CTP-TAMU-60-90, ACT-11, Jun 1990. 16pp.
Published in Phys.Lett.B249:441-448,1990.
TOPCITE = 250+
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 407 times

Supersymmetric Flipped SU(5) Revitalized.
Ignatios Antoniadis, John R. Ellis, (CERN) , J.S. Hagelin, (Maharishi U. of Management) , Dimitri V. Nanopoulos, (Wisconsin U., Madison) . CERN-TH-4710-87, MAD-TH-87-10, MIU-THP-87-012, May 1987. 9pp.
Published in Phys.Lett.B194:231,1987.
TOPCITE = 250+
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 388 times

Cosmological String Theories and Discrete Inflation.
Ignatios Antoniadis, C. Bachas, John R. Ellis, (CERN) , Dimitri V. Nanopoulos, (Wisconsin U., Madison) . CERN-TH-5054/88, MAD/TH/88-14, May 1988. 12pp.
Published in Phys.Lett.B211:393,1988.
TOPCITE = 100+
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 247 times

An Expanding Universe in String Theory.
Ignatios Antoniadis, C. Bachas, (Ecole Polytechnique) , John R. Ellis, (CERN) , Dimitri V. Nanopoulos, (Texas A-M) . CERN-TH-5231-89, CPTH-A890-0389, MAD-TH-88-23, CTP-TAMU-83-89, Nov 1988. 35pp.
Published in Nucl.Phys.B328:117-139,1989.
TOPCITE = 100+
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 242 times

Observables in Low-Energy Superstring Models.
John R. Ellis, K. Enqvist, Dimitri V. Nanopoulos, F. Zwirner, (CERN) . CERN-TH-4350-86, Jan 1986. 19pp.
Published in Mod.Phys.Lett.A1:57,1986.
TOPCITE = 100+
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 222 times

Experimental Predictions from the Superstring.
E. Cohen, John R. Ellis, K. Enqvist, Dimitri V. Nanopoulos, (CERN) . CERN-TH-4222/85, Jul 1985. 16pp.
Published in Phys.Lett.B165:76,1985.
TOPCITE = 100+
References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Cited 217 times

http://slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+EA+NANOPOULOS%2C+DIMITRI+V&FORMAT=www&SEQUENCE=citecount%28d%29

 

[Micha]

And likewise claims of Lorentz violation are not derived from the regular LQG, in the sense taught by Rovelli's textbook or Ashtekar's standard review of the subject.

Do you have a reference for Rovelli's take on this?

 

[atyy]

And likewise claims of Lorentz violation are not derived from the regular LQG, in the sense taught by Rovelli's textbook or Ashtekar's standard review of the subject.

Technically, this text is ambiguous, although perhaps suggestive that Lorentz invariance is violated by LQG.

http://relativity.livingreviews.org/Articles/lrr-2008-5/
"The best possibility for testing the theory seems to be via cosmology. However, the investigation of the possibility that quantum gravity effects are observable is constantly under investigation. Various possibilities have been considered, including quantum gravitational effects on light and particle propagation at very long distances [130, 8], which could perhaps be relevant for observations in progress such as AUGER and GLAST, and others. For an overview, see for instance [277, 199]. ... The MAGIC telescope collaboration has recently reported the measurement of an energy-dependent time delay in the arrival of signals from the active galaxy Markarian 501. The measured phenomenological parameter governing this dependence is on the Planck scale [1]. Energy-dependent time delays in the arrival of signals from far away sources have long been suggested as possible quantum gravity effects [14, 15]. A quantum-gravity interpretation of the MAGIC observation does not appear to be likely at present (see for instance [67]), but the measurement shows that quantum-gravity effects are within the reach of current technology. "

The above-mentioned reference [277] is Smolin's http://arxiv.org/abs/hep-th/0408048 , which is quite unequivocal:
"The assumptions, made by other approaches, that spacetime is smooth and lorentz invariant at arbitrarily short scales, are not used in the quantization procedure, and in fact turns out to be contradicted by the results."

But Smolin tempered his statements later http://arxiv.org/abs/hep-th/0605052 :
"Gambini and Pullin ... They showed that for correction terms that are only linearly suppressed by the Planck scale ( = 1) one would inevitably end up predicting birefringence for light waves. ... Note that while Gambini and Pullin worked within the framework of loop quantum gravity [18, 19, 20, 21], their scenario depends on the assumption of a particular and nonphysical ground state for that theory. Thus, their scenario should not be viewed as a definite prediction of loop quantum gravity or more generally of other quantum theories of gravity. ... Unfortunately, this is typical of the current state of the art, in which theories of quantum gravity suggest possible new phenomena that can be searched for experimentally, without so far making precise predictions for them [22]."

 

[marcus]

Do you have a reference for Rovelli's take on this?

Take on what? I've read or looked at a large portion of his work. There is one tentative note that went unpublished for some time describing a physical mechanism by which a DSR like dispersion could arise. It is not based on LQG formalism and does not predict that dispersion will be found. It speculates along the lines: "if some dispersion were found, here is a way to picture the physical mechanism by which it might have arisen."

http://arxiv.org/abs/0808.3505
A note on DSR
Carlo Rovelli
6 pages, 2 figures
(Submitted on 26 Aug 2008 (v1), last revised 29 Aug 2008 (this version, v2))
"I study the physical meaning of Deformed, or Doubly, Special Relativity (DSR). I argue that DSR could be physically relevant in a certain large-distance limit. I consider a concrete physical effect: the gravitational slowing down of time due to the gravitational potential well of a massive-particle, and its effect on the dynamics of the particle itself. I argue that this physical effect can survive in a limit in which gravitation and quantum mechanics can be disregarded, and that taking it into account leads directy to the Girelli-Livine DSR formalism. This provides a physical interpretation to the corresponding 5d spacetime, and a concrete physical derivation of DSR."


Otherwise there is nothing by Rovelli arguing for dispersion (energy dependent speed) that I know, indeed there is a negative paper that is often cited.
It proves that strict Lorentz is compatible with LQG.

This is a 2003 paper (posted arxiv 2002) with Speziale. I will get the link
http://arxiv.org/abs/gr-qc/0205108
Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
Carlo Rovelli, Simone Speziale
12 pages, 3 figures
(Submitted on 25 May 2002)
"A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted observer could see the minimal length further Lorentz contracted. We show that this is not the case within loop quantum gravity. In loop quantum gravity the minimal length (more precisely, minimal area) does not appear as a fixed property of geometry, but rather as the minimal (nonzero) eigenvalue of a quantum observable. The boosted observer can see the same observable spectrum, with the same minimal area. What changes continuously in the boost transformation is not the value of the minimal length: it is the probability distribution of seeing one or the other of the discrete eigenvalues of the area. We discuss several difficulties associated with boosts and area measurement in quantum gravity. We compute the transformation of the area operator under a local boost, propose an explicit expression for the generator of local boosts and give the conditions under which its action is unitary."
=============

Technically, this text is ambiguous, although perhaps suggestive that Lorentz invariance is violated by LQG.

Perhaps suggestive. Perhaps not suggestive. No clear prediction.

http://relativity.livingreviews.org/Articles/lrr-2008-5/
"The best possibility for testing the theory seems to be via cosmology.

That's right! And that has nothing to do with DSR or energy-dependent dispersion. Gravitational wave imprints on the CMB. Ways people are working on to distinguish LQC bounce models from other big bang models.

The rest of your quote is the inclusiveness that a review article author must show. Everybody's work must be mentioned whether the review author subscribes to it or not.

However, ... Various possibilities have been considered, including quantum gravitational effects on light and particle propagation at very long distances [130, 8], which could perhaps be relevant ... The MAGIC telescope collaboration has recently reported ...A quantum-gravity interpretation of the MAGIC observation does not appear to be likely at present (see for instance [67]), but the measurement shows that quantum-gravity effects are within the reach of current technology. "

What he explicitly says here is that there is NOT a prediction of photon delay derived from Loop at present. And you have referenced an authoritative recent Loop review article, so that basically should settle the issue.

 

[Haelfix]

I would say this result more or less rules out doubly special relativity and other 'time varying speed of light' theories! Not exactly a big surprise frankly.

I doubt it effects CDT, or any other lattice gravity program (eg Regge calculus) so long as you insist that the continuum limit is taken. In which case the lorentz group is restored as a residual symmetry. You could and should worry about Planckian entropy density and violation of unitarity (b/c of the topological restrictions from the choice of foliation) but that's something else.

We already knew that you couldn't have strict spacetime discreteness anyway (b/c inflation would generically blow it up to observable levels after 60 efolds).

LQG, I couldn't say what they predict. The whole semiclassical limit has always been a sort of fuzzy and confused issue with no consensus. -Shrug-

 

[metron]

I have just read http://backreaction.blogspot.com/2009/08/that-photon-from-grb090510.html#c8923384582399562257".

At 9:13 AM, August 22, 2009, Lee Smolin said...

Hi,
I wonder if I could clarify some issues raised here. More details and references are in a recent paper by Amelino-Camelia and myself in arXiv:0906.3731.

First, LQG in 3+1 dimensions has not been shown to break or deform Lorentz invariance. There were some papers, starting in the 90s, studying excitations of non-physical ansatz’s for vacuum states (ie that didn’t satisfy the quantum constraints) that showed evidence for Lorentz symmetry breaking. These were not prediction of LQG, they were consequence of an ansatz for the ground state that broke both Lorentz invariance and diffeomorphism invariance. They could be characterized as exploratory, but very far from definitive. There is no definitive result concerning the symmetry of the ground state in LQG in 3+1 dimensions.

So, unfortunately, it is not correct to claim that this or any such result rules out LQG. I say unfortunately because it would be nice if we knew what the prediction was of LQG for deformed dispersion relations, but despite some effort we don’t.


I have published two papers arguing that a form of DSR is a consequence of generic quantum theories of gravity in the semiclassical approximation, plus certain scaling assumptions: hep-th/0501091v2, arXiv:0808.3765v1. These derivations make several assumptions, particularly as to the scaling dimensions of certain operators, which have not been confirmed in LQG or any theory. If there is no linear dispersion (order l_Planck) then we learn that one of the assumptions of these arguments are wrong, and my guess is it would be these scaling assumptions.


One can also deduce the significance of these scaling relations from some general considerations that derive kappa Poincare symmetry from quantum deformed (A)dS symmetry, this was shown in hep-th/0306134 and hep-th/0307085.


In fact, in 2+1 dimensions the argument from quantum group theory is correct and the low energy symmetry is kappa-Poincare (hep-th/0512113, hep-th/0502106). This suggests its not crazy that to hypothesize that the same is true in 3+1 but this is not a proof, it is a suggestion of a line of argument.


Whether string theory allows deformed Poincare symmetry is unknown, in hep-th/0401087, Magueijo and I showed that there are consistent free bosonic string theories with deformed energy-momentum relations, to my knowledge no one has followed up to investigate what happens to this when interactions are included. Otherwise string theory assumes perfect Lorentz invariance.


Further, Lorentz symmetry breaking at order l_Pl is already ruled out by several orders of magnitude by observations of polarized radio galaxies which constrain the bi-frengence from the parity odd term in the effective action for Maxwell fields that appears at dimension five. What might be the case, but is now somewhat constrained, is parity even deformation of Poincare invariance. It also should be emphasized that order l_Pl^2 effects are not strongly constrained by any observation so that there could still be Planck scale Lorentz symmetry breaking at that order.


Coming to the recent observations, that Fermi was capable of putting order L_Pl limits on dispersion has been clear for a while and was discussed in detail by Amelino-Camelia and myself in arXiv:0906.3731. My reading of the recent Fermi collaboration paper on GRB090520 is that the conservative bound of about 1.2 M_Pl is reliable, while the stricter limits are based on assumptions about the sources which are at this time speculative. I might make a couple of other comments on the results in this important paper.

- -Even the most conservative bound > 1.2 M_{Pl} conflicts with the claims of Ellis et al in the Magic and subsequent papers to make a measurement of an effect of around .1 M_{Pl}.

-They also give a very interesting bound on the advanced case, s=-1 which is also around 1.2M_{Pl}. This is much better than the best bound so far which so far as I know is the one in Giovanni and my paper: 3.2 X 10^17 GeV .

Thanks,

Lee

 

[MTd2]

Well, it seems there is a really small correcton to the speed of light in QED:

Formula 42 of this article:

http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+EPRINT+HEP-PH/9803216

Quantum Corrections to the QED Vacuum Energy

Xinwei Kong, Finn Ravndal (University of Oslo)
(Submitted on 2 Mar 1998 (v1), last revised 11 Mar 1998 (this version, v2))
At energies much less than the electron mass $m$ the effects of quantum fluctuations in the vacuum due to virtual electron loops can be included by extending the Maxwell Lagrangian by additional non-renormalizable terms corresponding to the Uehling and Euler-Heisenberg interactions. This effective field theory is used to calculate the properties of the QED vacuum at temperatures $T << m$. By a redefinition of the electromagnetic field, the Uehling term is shown not to contribute. The Stefan-Boltzmann energy density is thus found to be modified by a term proportional with $T^8/m^4$ in agreement with the semi-classical result of Barton. The speed of light in blackbody radiation is smaller than one. Similarly, the correction to the energy density of the vacuum between two metallic parallel plates diverges like $1/m^4z^8$ at a distance from one of the plates $z \to 0$. While the integral of the regularized energy density is thus divergent, the regularized integral is finite and corresponds to a correction to the Casimir force which varies with the separation $L$ between the plates as $1/m^4L^8$. This result is in seemingly disagreement with a previous result for the radiative correction to the Casimir force which gives a correction varying like $1/mL^5$ in a calculation using full QED.

This one is simple in termos of math, but the resul is the same:

http://arxiv.org/abs/hep-ph/9709220v1

Radiative Corrections to the Stefan-Boltzmann Law

Finn Ravndal
(Submitted on 2 Sep 1997)
Photons in blackbody radiation have non-zero interactions due to their couplings to virtual electron-positron pairs in the vacuum. For temperatures much less than the electron mass $m$ these effects can be described by an effective theory incorporating the Uehling and Euler-Heisenberg interactions as dominant terms. By a redefinition of the electromagnetic field, the Uehling term is shown not to contribute. The Stefan-Boltzmann energy is then modified by a term proportional with $T^8/m^4$ in agreement with the semi-classical result of Barton. The same effects give a speed of light smaller than one at non-zero temperatures as has also recently been derived using full QED.

***********

And the black body contribution was pretty higher in the early universe?

 

[marcus]

I have just read http://backreaction.blogspot.com/2009/08/that-photon-from-grb090510.html#c8923384582399562257".

At 9:13 AM, August 22, 2009, Lee Smolin said...
...

Metron, I liked your Smolin quote very much.
Lee Smolin is a great guy, creative, explores widely, develops new ideas, though he does not at all represent mainstream LQG

His interests have taken him far afield since the time when he was primarily focused on Loop.
Last year the main Loop conference was at Nottingham UK and Smolin was invited to give a plenary talk but he did not even attend.
This year the Loop conference was in Beijing, I'm sure they would have loved if he'd come.

The core people in LQG are folks like Ashtekar, Rovelli, Freidel, Barrett, their co-authors and grad students. Smolin does other valuable things, like explore entirely new approaches and stimulate people to do research along entirely different lines.

That said, I thought your quote from Smolin was absolutely correct. Thanks!
====================

[EDIT: Metron knows this already, but some other readers of this thread might not. So I will leave the following in as context.]
Whether energy-dependent dispersion is POSSIBLE is a totally other question! Sure it's possible. No need for anyone to deny the possibility of some DSR thing happening at very high energy and small scale. Admit our ignorance But prediction is something else. It is where you bet the life of your theory on some future observation or experiment and if it comes out different then you chuck the theory. The prediction has to be an inescapable logical consequence of the core precepts of the theory so that if the prediction proves wrong it logically falsifies the theory.

 

[marcus]

Atyy just cited section 7 (Physical Effects) of Rovelli's 2008 Review of LQG:
http://relativity.livingreviews.org/Articles/lrr-2008-5/

It says that there is no prediction of dispersion derived so far from LQG.

The idea has been talked about, and Rovelli gives references to other people's papers, but not actually derived.

That was as of May 2008. That should settle the issue as far as LQG goes.
Rovelli's review is the current authoritative survey of the field.

===================
Metron just noticed a comment by Lee Smolin on Bee Hossenfelder's blog
http://backreaction.blogspot.com/2009/08/that-photon-from-grb090510.html
where she is discussing the May 2009 Gammaray Burst.

It's really clear, says exactly what should be said about various predictions & non-predictions. Apparently he just posted it today:
http://backreaction.blogspot.com/2009/08/that-photon-from-grb090510.html#c8923384582399562257

 

[metron]

Marcus,

Whether energy-dependent dispersion is POSSIBLE is a totally other question! Sure it's possible. No need for anyone to deny the possibility of some DSR thing happening at very high energy and small scale. Admit our ignorance But prediction is something different. It is where you bet the life of your theory on some future observation or experiment and if it comes out different then you chuck the theory. The prediction is an inescapable logical consequence of the core precepts of the theory.

This is obvious.

I didn't try to argue in favor of anything. My post was just about what Smolin thinks concerning Fermi's observations.

 

[marcus]

Marcus,
This is obvious.

I didn't try to argue in favor of anything. My post was just about what Smolin thinks concerning Fermi's observations.

You are absolutely right. It is obvious. Maybe it's OK to include to provide context for any other readers who are just learning about the issues. Maybe I'll edit it to bring that out.

I'm appreciate very much your relaying to us that comment from Bee's blog.

 

[metron]

Maybe I'll edit it to bring that out.

feel free

 

[marcus]

feel free

done

 

[Micha]

So if I understand correctly, 2+1 dimensional LQG has strictly shown to break Lorentz invariance, but 3+1 dimensional LQG so far hasn't. I seem to remember this now as the state of affairs.

In other words if no miracle happens at 3+1 dimensions, LQG is dead, right?