# Fermi (GLAST) almost kills all Lorentz violating theories.

marcus
Gold Member
Dearly Missed
There is no need to "critique" your understanding, Jon. You are just mistaken.

LQG researchers tried unsuccessfully around 2005-2006 to derive a prediction of energy-dependent speed of light, from the theory in 4D.

The authoritative review paper on LQG, as of May 2008, is Rovelli's article in Living Reviews of Relativity. As I recall, it examines the issue and points out that LQG does not predict energy-dependence of the speed that photons travel.
http://relativity.livingreviews.org/Articles/lrr-2008-5/ [Broken]

The impression that it does has been given in one or more hostile blogs, but that is misinformation. BTW be careful about relying on Wikipedia.

We've discussed this in several other threads.
Thanks for your interest, Jon, and the best of luck with your quantum gravity self-education!

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tom.stoer
The old LQG calculations from which violation of Lorentz invariance (or better: deformation in the sense of DSR) seemed to follow were mostly based on crude approximations like weave states which are not solutions to the full LQG theory. So the Lorentz violation was an artefact of "wrong" or unphysical spin network states.

I am not absolutely sure about that; Marcus, do you remember?

marcus
Gold Member
Dearly Missed
Off the top of my head, as I recall it, before 2006 there was a lot of wishful thinking, mainly on the part of Smolin. Smolin and a few others WANTED to have a prediction which could be tested.

In 2005 and 2006, GLAST was getting near time to launch and Smolin felt it was urgent to derive some kind of testable prediction, so he wrote some inconclusive papers involving guesswork. I think he motivated some younger people, like Freidel and Kowalski-Glikman, to work on the general problem. Freidel got a result for 3d gravity, but it could not be extended to the interesting case of 4d. Kowalski-Glikman studied DSR and found that (contrary to most people's expectation) it did NOT imply a variation in photon speed. I'm not clear on how that conclusion was drawn--there seem to be several versions of DSR. It wasn't clear which version, if any, was related to 4d LQG.

Essentially a Perimeter group tried to prove that LQG predicted variation in the speed of light, back then, because they wanted to be able to TEST LQG when GLAST was launched. In science your theory has to make a prediction BEFORE the experiment. So there was a time-pressure which Smolin and a few others felt. But despite their good efforts, they were unable to derive such a prediction. So in 2008 GLAST was launched without their going on record with something definite.

This was not representative of the broader LQG community. The main community did not think LQG had any prediction like that and they didn't bother with it. As far as I can tell, at this time it is only outsiders who imagine that LQG should imply variation in speed of photons.

About the earlier wishful thinking, and the handwaving arguments, I regret to say I don't remember what the technical grounds were.

It's worth pointing out that Jon is talking about the issue of energy-dependent photon speed: a separate issue from DSR (deformed special rel), which you asked about.
I'm sorry to say I don't know what the deal is currently with DSR. I'll try to find out.

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atyy
In science your theory has to make a prediction BEFORE the experiment.

But we'll make an exception for mercury's perihelion precession, right?

I'm sorry to say I don't know what the deal is currently with DSR. I'll try to find out.

marcus
Gold Member
Dearly Missed

Spot on! It does not seem to make a rigorous connection with LQG, and I don't see an energy-dependent speed of light, but it is probably the best indication of the current status of this question. We can learn by studying this paper!
http://arxiv.org/pdf/0903.3475
Page 2:
==quote==
Very interesting results have been obtained in the 3d context [16, 17, 18] where it has been shown that eﬀective models with quantum group symmetries and a non-commutative spacetime structure (although diﬀerent from the DSR one) arise very naturally when considering the coupling of point particles to a spin foam model for 3d quantum gravity, in the Riemannian setting, with the physics of these particles being that of non-commutative ﬁeld theories on Lie algebra spaces. While no similarly solid links between spin foam models and non-commutative ﬁeld theories have been discovered in the 4d context, several arguments have been put forward suggesting that these links should exist and that the relevant eﬀective models in 4d should indeed be of the DSR type [19, 20].

For reasons that should become apparent in the following, group ﬁeld theories are a natural framework for establishing such links,...
...
...What we do in this paper is to apply the same procedure to the more technically challenging case of four spacetime dimensions, and Lorentzian signature, and derive from a group ﬁeld theory model related to 4-dimensional quantum gravity an eﬀective non-commutative ﬁeld theory of the DSR type and living on κ-Minkowski spacetime.

As said, not only this is the ﬁrst example of a derivation of a DSR model for matter from a more fundamental quantum gravity model, and one further example of the link between non-commutative geometry and quantum gravity formulated in terms of spin foam/loop quantum gravity ideas, but it is of great interest from the point of view of quantum gravity phenomenology. It is also interesting, more generally, as another possible way of bridging the gap between quantum gravity at the Planck scale and eﬀective physics at low energies and macroscopic distances...
==endquote==

As they indicate in the conclusions, they haven't yet connected with LQG. But they have connected with, or at least see a way to connect with some LQG "ideas".
==quote page 22==
Further investigations are needed to establish a better link between our initial GFT model, classical solutions and eﬀective ﬁeld theory on the one hand, and a spin foam formulation of the Freidel-Starodubstev classical gravity theory [33] and the particle observable insertions à la Kowalski-Glikman-Starodubtsev [20] on the other, which represent...
==endquote==

It's an exciting prospect!

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atyy
Science 2 April 2010: Vol. 328. no. 5974, p. 27, DOI: 10.1126/science.328.5974.27
Thought Experiment Torpedoes Variable-Speed-of-Light Theories

"..........

The speed variations must be at least 23 orders of magnitude smaller than experimental limits set last year, she says.

"It's incredibly hard to find an observable effect of quantum gravity, so I'm a little bit sorry about the result," says Sabine Hossenfelder of the Nordic Institute for Theoretical Physics in Stockholm. ..........

The debate centers on a decade-old idea known as DSR—for "doubly special relativity" or "deformed special relativity." DSR attempts to reconcile Einstein's theory of special relativity—which says the speed of light is the same for all observers, even if they're moving relative to one another—with the possibility that the speed of light also depends on its wavelength. Such a dependence had been suggested by theories of "noncommutative geometry" and emerges from some theories of "loop quantum gravity"

.......

Developers of DSR aren't ready to concede the point, however. ........ Giovanni Amelino-Camelia ............. Lee Smolin of the Perimeter Institute for Theoretical Physics in Waterloo, Canada, agrees that the effects of quantum spacetime may resolve the paradox and says he's studying the matter."

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Physics Monkey
Homework Helper
There seems to be a lot of confusion on this subject. I would suspect that whatever physics LQG predicts, it has to involve some modification of the notions of distance, time, speed, etc at the Planck scale. Perhaps an energy varying speed of light isn't the right way to think, although again I suspect the speed of light must become less meaningful in some sense at the Planck energy in any theory of quantum gravity. If the modification is more subtle then maybe the cosmic ray experiments can't get at it.

However, there appears to be a more mundane explanation. Namely, if the modification of the speed is second order in one over the Planck energy then the authors of the paper http://www.nature.com/nature/journal/v462/n7271/full/nature08574.html point out that they can't offer any meaningful constraints. I think such a modification is more natural anyway because the quantity $$|\vec{p}|^3 = (p_x^2 + p_y^2 + p_z^2 )^{3/2}$$ isn't nice at $$\vec{p} = 0$$. This is a common observation in condensed matter systems where terms in the low energy effective action like $$| \nabla \phi |^3$$ usually don't appear. I would consider a formula like $$E^2 = p^2 f(p^2 / M^2 )$$ with M of order the Planck mass much more natural, but this formula gives only a second order correction to the speed provided f(x) behaves like 1 + c x + ... generically. And whether or not you like my argument, its remains true that these second order theories are basically unconstrained. That second power of E/M really kills you.

Since the first order models seem highly constrained up to the planck scale, it would be interesting to see what constraints on the mass scale they could put for second order models. In other words, a long standing hope has been that the energy scale of quantum gravity might be much lower than the planck scale, so if we assume a lower energy scale but a second order model how low can the energy scale be?

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marcus
Gold Member
Dearly Missed
Science 2 April 2010: Vol. 328. no. 5974, p. 27, DOI: 10.1126/science.328.5974.27
Thought Experiment Torpedoes Variable-Speed-of-Light Theories

".......The speed variations must be at least 23 orders of magnitude smaller than experimental limits set last year, she says.

"It's incredibly hard to find an observable effect of quantum gravity, so I'm a little bit sorry about the result," says Sabine Hossenfelder of the Nordic Institute for Theoretical Physics in Stockholm. ......

The debate centers on a decade-old idea known as DSR—for "doubly special relativity" or "deformed special relativity." DSR attempts to reconcile Einstein's theory of special relativity—which says the speed of light is the same for all observers, even if they're moving relative to one another—with the possibility that the speed of light also depends on its wavelength. ...

Interesting! The piece in Science was, I gather, based on this:
http://arxiv.org/abs/0912.0090
The Box-Problem in Deformed Special Relativity
20 pages, 3 figures
S. Hossenfelder
(Submitted on 1 Dec 2009)
"We examine the transformation of particle trajectories in models with deformations of Special Relativity that have an energy-dependent and observer-independent speed of light. These transformations necessarily imply that the notion of what constitutes the same space-time event becomes dependent on the observer's inertial frame. To preserve observer-independence, the such arising nonlocality should not be in conflict with our knowledge of particle interactions. This requirement allows us to derive strong bounds on deformations of Special Relativity and rule out a modification to first order in energy over the Planck mass."
Peter Woit included a mention of the Adrian Cho piece in Science.

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marcus
Gold Member
Dearly Missed
To sum up, there has long been a hope (going back well before 2003, I know) that LQG could be connected to DSR. And it was also pointed out early on that DSR does not necessarily have energy dependent photon speed (dispersion). But the hope was that LQG would connect with some version of DSR that DID have dispersion.

So then there would be one possible way to test. (Other potential prospects for testing have now come on the scene, but dispersion used to be the only one people could think of.)

The first paper ( http://arxiv.org/abs/0903.3475 ) by Girelli Livine Oriti shows that they have not yet established a connection between 4d LQG and DSR but there is hope and some researchers are interested in it.

But then the problem remains, even if they got a connection to DSR would that predict a measurable energy-dependence in photon speed?

It seems unlikely, judging from the second paper, by Hossenfelder. If we accept her result, she has ruled out a first-order dependence on the energy.
The term in question is the ratio E/EPlanck where the numerator E is the photon energy and the denominator is the Planck energy.

Given the highest energy gamma rays which have been observed, and the distances traveled, it is only possible to constrain a FIRST ORDER coefficient of dependence. We fall many orders of magnitude short of being able to constrain a second order dependence.

Because in practice E/EPlanck is quite small, so when you square it, the ratio gets even smaller. It is only the very long travel time (on the order of a billion years) that offsets the small ratio and produces a measurable delay. Travel times long enough to offset the ratio squared, and produce a measurable delay, are simply not available.

So it is possible that people like Girelli Livine Oriti will, in fact, eventually prove a connection of 4d LQG to a type of DSR, and that DSR (if it predicted dispersion) might allow a second order dependence of photon speed, which would however not be able to be tested or constrained at least in the way we have seen tried---by measuring Gammaray Burst photon delays.

All still pretty speculative. I haven't followed Hossenfelder's thought experiments through carefully, just provisionally assume her arguments are right. Adrian Cho is a good science journalist, who follows QG. He's the one who broke the Renate Loll 4d CDT story in 2004 (when they first got CDT to work in 4d). The more notice Hossenfelder's paper gets, the more scrutiny by people like Amelino-Camelia, and if it survives intense scrutiny the more likelihood that it's right.

In any case it is certainly not true that the Fermi (GLAST) gammaray observations have "killed all Lorentz violating theories." That is a ridiculous idea. It has not even come within 22 orders of magnitude, one could say.

And it has also not been shown that LQG necessarily bends Lorentz. So if not LQG, what quantum gravity theories are we talking about, exactly?

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Not "all"

What Fermi's observational data are actually implying is that in the series expansion of the photon velocity,
vph /c = 1 + a1 (E/EQG) + a2 (E/EQG)2 + a3 (E/EQG)3 + ...,
where EQG ~ 1019 GeV, the coefficient a1 must be << 1 (in relativity all ai must vanish), i.e., the data are imposing an upper bound on these coefficients.

While these data possibly rule out some LIV theories such as DSR, there may exist theories according to which the coefficients ai are ought to be small. For example, in http://arxiv.org/abs/0906.4282 (in v4 see eqs 21-25) the coefficient a1 is proportional to the constant of refraction of the physical (nontrivial) vacuum and thus is naturally small.

Moreover, according to that theory, the velocity dispersion relation is represented in series w.r.t. not E/EQG but rather E/E0 where E0 is the characteristic vacuum energy. Only in the limit when no strong external fields exist the value of E0 tends to the Planck-scale EQG. In other words, from the point of view of that theory the current astrophysical observations are just imposing an upper bound on the averaged constant of refraction for the physical vacuum which was subjected to the cumulative combination of weak inter- and intragalactic electromagnetic fields, scattering processes, etcetera.

Gold Member
It could be well be that the relation is almost a Heaviside function! :)

Gold Member
http://arxiv.org/abs/1006.2126

Taming nonlocality in theories with deformed Poincare symmetry

Giovanni Amelino-Camelia, Marco Matassa, Flavio Mercati, Giacomo Rosati
(Submitted on 10 Jun 2010)
We here advocate a perspective on recent research investigating possible Planck-scale deformations of relativistic symmetries, which is centered on Einstein's characterization of spacetime points, given exclusively in terms of physical events. We provide the first ever explicit construction of worldlines governed by a Planck-scale deformation of Poincar\'e symmetry. And we show that the emerging physical picture allows a description that is faithful to Einstein's program, but forces the renunciation of the idealization of the coincidence of events. We use this to expose the limitations of the pre-Einsteinian description of spacetime points adopted in some recent related studies. In particular we find that the estimate of nonlocal effects reported in the recent Physical Review Letters 104, 140402 (2010) is incorrect by 29 orders of magnitude.

*****

Bee wrong by 29 orders of magnitude.