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?

 

[marcus]

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

wrong

(You don't make any sense, Micha. They worked hard to reproduce the 2+1 result and couldn't. So one expects no bending.)

==============

What one expects to be the case does not qualify as a miracle if it happens.
For any chance reader: what happens in different dimensions is often very different. What we are dealing with here is evidence about a first order coefficient. Even a theory that predicted some Lorentz bending could have zero first order and nonzero second orded. It's inefficient to have to go thru this kind of detail. People should really read Smolin's post at Bee's blog.

I will give the links again:
Bee Hossenfelder's blog
http://backreaction.blogspot.com/2009/08/that-photon-from-grb090510.html
where she is discussing the May 2009 Gammaray Burst.
Smolin's comment:
http://backreaction.blogspot.com/2009/08/that-photon-from-grb090510.html#c8923384582399562257

 

[skippy1729]

A "denier of empirical evidence"! I can't remember the last time anyone has thrown that at me. I really hope that there are more observations so a realistic limit can be placed on LIV and good models of GRB. It would be too bad if this turns out to be another Monopole balloon observation or SETI WOW signal.

I was not suggesting the Banach-Tarski paradox has any physical interpretation. What I was suggesting is that to take the concept of an infinitely divisible space SERIOUSLY for a physical model you must accept that your model has inherent flaws. Fortunately the hypothesis "spacetime is an infinitely divisible medium" is a falsifiable theory (just display a discrete model which correctly models all physical phenomenon!); while the hypothesis "spacetime is discrete at SOME energy level" is not falsifiable (there will always be higher energies and smaller distances, whether or not they will ever be accessible).

Rejecting the Axiom of Choice is fine but its use has become commonplace in topology and functional analysis texts (with and without specific mention). An example of its use in physics is the theorem of Geroch, Choqut–Bruhat that there exists a unique maximal Cauchy development from a given set of initial data: "Global aspects of the Cauchy problem in general relativity" http://www.springerlink.com/content/r137914u14277831/ (Zorn's lemma, which amounts to the same thing).

Skippy

 

[yossell]

Fortunately the hypothesis "spacetime is an infinitely divisible medium" is a falsifiable theory (just display a discrete model which correctly models all physical phenomenon!);

Not taking sides here, but finding a discrete model correctly modelling all physical phenomena would not *falsify* "spacetime is an infinitely divisible medium". Finding a ¬P model of a phenomenon is not falsifying P.

yossell

 

[Micha]

What one expects to be the case does not qualify as a miracle if it happens.
For any chance reader: what happens in different dimensions is often very different. What we are dealing with here is evidence about a first order coefficient. Even a theory that predicted some Lorentz bending could have zero first order and nonzero second orded. It's inefficient to have to go thru this kind of detail. People should really read Smolin's post at Bee's blog.

From Smolin's comment:

"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."

If Smolin expects things to be "very different" in 3+1 dimensions, he is hiding it quite well.

Arguing that first order terms could be zero without having a good argument for it (is there any?) to me sounds like quite a desperate move to save a theory.

 

[fleem]

Special relativity was derived solely from observations of the average, large-scale behavior of many objects. So are the concepts of continuums, manifolds, and even non-integral values. Yet the vast majority of scientists insist those 100% classical "fundamental" theories must unequivocally be the foundational theories for describing the behavior of a single one of those objects (a single particle-particle interaction). That's like insisting a theory that describes a swarm of bees be unequivocally used as the foundation of describing a single bee. In fact, I'll go so far as to say any theory describing single particle-particle interactions which uses those large-scale ideas, is suspect.

 

[atyy]

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.

http://relativity.livingreviews.org/Articles/lrr-2008-5/
"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."

Does this really unequivocally say that photon delay is not a prediction of LQG? The reference [67] is http://arxiv.org/abs/0804.0619 which seems to me to say that the delay is probably not due to violation of Lorentz invariance. This would suggest that Rovelli meant a violation of Lorentz invariance would indeed be a quantum gravity effect. But I do agree there is nothing definite to pin down by his specific choice of words - for example, he says "quantum gravity", rather than "loop quantum gravity" - in an article about "loop quantum gravity".

 

[marcus]

From Smolin's comment:

"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."

If Smolin expects things to be "very different" in 3+1 dimensions, he is hiding it quite well.

Arguing that first order terms could be zero without having a good argument for it (is there any?) to me sounds like quite a desperate move to save a theory.

I'm glad you read the comment at Bee's blog and it is fine with me whatever your attitude/interpretation. Mathematics is indeed sometimes very different in spaces of different dimensionality. It may be not crazy to guess at some analogy, but often the analogy doesn't turn out. In this case Freidel Livine proved something in 2005 for 3D and everybody was hoping they could do something analogous. What Smolin's sentence means is that it wasn't foolish to try, and they tried hard, but they could not get a proof in 4D.

The possibility that Lorentz might be bent, at very high energy, either first order or second order has been around for a long time. I think papers by non-Loop folks back in the 1990s may have pre-dated Smolin's involvement. I don't know the history. These quantities M_QG1 and M_QG2 have been around for many years, and has always been pointed out that first order deviation would be easier to detect or rule out.

If you look at a non-Loop paper like Ellis Mavromatos Nanopoulos they have this notation, and they consider both first and second order, try to control both, and they cite papers of theirs about this from way back in the 1990s.

There is no question of "desperate move to save a theory". Nobody's QG theory is being tested. The first/second order thing is just how Nature is, when you have a symmetry you need to be aware of the possibility that it might be bent. Don't assume you know everything up to infinitely high energy. It has always been acknowledged that if Lorentz is bent it might be first order or it might be second etc. ---and that the latter case would be much harder to detect.

So the first agendum is to rule out first order bending. If observations can rule it out, that's great. If observations can eventually rule second order deviation out, that will be great too.
I don't know of any theory that says there should be either kind of deviation, but it is only reasonable to be on the look-out, now that we have an instrument like Fermi-LAT with adequate sensitivity.

http://relativity.livingreviews.org/Articles/lrr-2008-5/
"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."

Does this really unequivocally say that photon delay is not a prediction of LQG? The reference [67] is http://arxiv.org/abs/0804.0619 which seems to me to say that the delay is probably not due to violation of Lorentz invariance. This would suggest that Rovelli meant a violation of Lorentz invariance would indeed be a quantum gravity effect. But I do agree there is nothing definite to pin down by his specific choice of words - for example, he says "quantum gravity", rather than "loop quantum gravity" - in an article about "loop quantum gravity".

That's right Thanks for reading carefully! Rovelli has never indicated that he thinks Lorentz bending is a LQG effect, derived from LQG. Indeed to the contrary, as in his 2002 paper where he takes the trouble to show LQG consistency with Lorentz.

What you quote means that QG-scale effects are now within reach of observational technology. This is good news for LQG research, as he is pointing out. It means the researchers will be getting guidance in the future from empirical data.

 

[atyy]

So the first agendum is to rule out first order bending. If observations can rule it out, that's great. If observations can eventually rule second order deviation out, that will be great too.
I don't know of any theory that says there should be either kind of deviation, but it is only reasonable to be on the look-out, now that we have an instrument like Fermi-LAT with adequate sensitivity.

I do - my favourite crackpot theories - Visser, Volovik, Wen - I still like them though

 

[marcus]

I do - my favourite crackpot theories - Visser, Volovik, Wen - I still like them though

QG with a condensed matter perspective! I should have thought of that! I don't know much about VV&W's work but I wouldn't cry crackpot just yet.
BTW the analog models people seem to have put up a strong showing at Vancouver.

 

[atyy]

QG with a condensed matter perspective! I should have thought of that! I don't know much about VV&W's work but I wouldn't cry crackpot just yet.
BTW the analog models people seem to have put up a strong showing at Vancouver.

I mean "crackpot" as a high compliment BTW, although AdS/CFT was derived from a different viewpoint, I would actually count it as instantiating the "emergent philosophy" of condensed matter - I think they've also got a session at Vancouver.

 

[Micha]

Sorry, Marcus.

there is no particular sentence in your reply which I can point to and say this is wrong. But all in all I have the impression I am arguing with a rubber band, always stretching so much, it is forced to in the light of new results.

The problem I have is I read Smolin's book (the one whose sales figures you analyzed here for months) and while I do not remember every single detail, I clearly remember the general line of thought. On the one hand there was string theory not being able to make any predictions and sticking exactly to Lorentz symmetry. On the other hand there were all these new approaches like DSR and LQG, where experimental results were around the corner, an energy dependent speed of light being the most important one.

Yes, I remember clearly, that Smolin also said in his book, that in 3+1 LQG there were so far no clear predictions about an energy dependent speed of light, but he would like to have them, before experimental results were coming in.

You can always put some ifs and whens, but according to you, the new experimental result makes not the slightest difference on how you view the different quantum gravity approaches. Not the slightest disappointment. No reference to Smolin's book. Nothing. Now Smolin suddenly is a figure on the sideline of LQG (which he might even be today). This makes me wonder what result ever would make an impression on you.

 

[marcus]

...Yes, I remember clearly, that Smolin also said in his book, that in 3+1 LQG there were so far no clear predictions about an energy dependent speed of light, but he would like to have them, before experimental results were coming in.

... according to you, the new experimental result makes not the slightest difference on how you view the different quantum gravity approaches...

Micha, I'm glad you remember so clearly from that popular 2006 book! I read some of it when it came out. It had an important function, but it was not something to learn all about LQG from! In this case what you remember is right. As we know, a number of people tried hard including top people like Freidel and Kowalski-Glikman. The result just doesn't seem to extend to 4D! Maybe sometime we will understand the underlying reason. Or even it could happen that some new approach to QG will actually imply some kind of Lorentz bending, and it will check out observationally! We are at the beginning stages of observational QG. Theories don't stand still either.

I have an idea to propose to you. Since you show signs of being a thoughtful reader, how about you try Rovelli's 2008 review of LQG?
This is a scholarly review article, not a popular-written book. The popular-written books can not and do not properly characterize an intellectual discussion, obviously.

BTW my introduction to QG was basically the online 2003 draft of Rovelli's book. That book is still worth looking at, for its depth. But I mention the review article because shorter and more up-to-date. It is true that I tend to see LQG "thru Rovelli glasses" so to speak. I also follow AsymSafe QG of Reuter/Percacci/Weinberg and the Triangulations QG of Loll's group. These are all exciting QG approaches in a phase of rapid growth and change.

It is useless to harp on the past. Like what looked hopeful in 2003 to someone writing an informal memoir for a poplar online magazine
LQG has gone thru enormous change even since 2006. A new spinfoam model is now the basis of a new dynamics. (Before there was no satisfactory dynamics, and no good grasp of the semiclassical limit.) The cosmo subfield LQC has also been completely revolutionized since 2006. Basic equations of LQC changed, and fresh results. It is really time now for a new Smolin-type book that will bring the general audience readership up to date.

I guess I should point out that my personality or your personality or what we think of each others thought process is not the issue. We are talking about the real research world out there.

 

[Micha]

I guess I should point out that my personality or your personality or what we think of each others thought process is not the issue. We are talking about the real research world out there.

I agree with that.

But it is also true that real research is paid by the general society. So the public deserves to get an accurate picture about the status of various research approaches. It is a moral requirement and public perception surely also has an effect on funding agencies and hiring at universities and so on, although you will never be able to exactly quantify that. And the physics forum is a small piece of this public perception. So therefore it is not unimportant, what is written here. And as you are a key contributor to this forum, I think, that you have a responsibility as well.

Best regards Michael.

PS: I haven't anything against you personally. To the contrary. I am just curious about scientific truth.

 

[MTd2]

Unfortunantely, this forum is not supported by any public agency.

 

[Micha]

Unfortunantely, this forum is not supported by any public agency.

I don't think, this invalidates any of my points.

 

[MTd2]

I don't think, this invalidates any of my points.

Of course it does not invalidate your points. But many of us do not have much time left because of our jobs, family, etc. And many of the recent developments in most of new areas did have a proper conference on the subject, so there is not much consolidation even among experts.

 

[MTd2]

What if lorentz violating effects were supressed like 1-sech(Mpl/Mqg^2)? I guess that wouldn't rule out DSR, right?

Edit: perhaps, a 1-erf^2

http://en.wikipedia.org/wiki/Error_function

 

[Micha]

Hi MTd2,
as any smooth function, the Lorentz violating effects, in this case the deviation of the speed of high energy photons from the known speed of light as a function of energy, can be developed into a Taylor expansion. So whatever the exact form of the function is, it is zero in the low energy limit (the speed of light of low energy photons is what it is) and then what you first would notice are linear effects. These have been excluded by the measured result now (if confirmed). Quadratic or higher order terms can't be excluded so far. Maybe quadratic terms can be measured or excluded by the experiment in the future, but not yet. So you can save a Lorentz violating theory by having it only predict quadratic effects at maximum. This however smells like a trick, if you don't have a good reason, why the linear term should be zero.

 

[MTd2]

Hi Micha, look at this:

http://backreaction.blogspot.com/2009/08/that-photon-from-grb090510.html

At 12:06 PM, August 25, 2009, Daniel de França MTd2 said...
You mean, the linear dispertion was not ruled out?

At 12:25 PM, August 25, 2009, Lee Smolin said...
Dear Daniel de França MTd2,

This is a key question which was covered in many places, for example my paper with Amelino-Camelia or my post above. See those for details.

The linear correction is parity odd in the case of Lorentz symmetry breaking and parity even in the case of DSR. The former is ruled out by several orders of magnitude because it leads to rotations of planes of polarization, see the reference by Gleiser and Kozemeh I mentioned above. The latter, DSR, parity even case is not ruled out, although further observations by Fermi may be able to do that.

The distinction between broken and deformed lorentz invariance is a key point in this whole discussion.

Thanks,

Lee

Thanks,

Lee

 

[Micha]

Yes I read it.

When I read your discussion of the error function, I just thought, that I remind people of the Taylor expansion. It is a trivial point of course.