Fermi Gamma Ray Telescope: Ruling Out Lorentz-Violating Theories

[petergreat]

The almost simultaneous detection of low energy and high energy photons puts tight constraints on models predicting linear dependence of c on E. But it's very far from ruling out quadratic dependence. My question is, why do Lorentz-violating theories commonly predict linear rather than quadratic relation between c and E? A quadratic dependence might arise, for example, if f = Sin[k/k_planck], in which case the group velocity df/dk is a Cos which only shows quadratic deviation from 1 for small angles.

 

[marcus]

My question is, why do Lorentz-violating theories commonly predict linear rather than quadratic relation between c and E?

Peter it is hard to answer without knowing what Lorentz-violating* theories you are thinking of.

The main authority on LQG, for instance, published a review of LQG in May 2008 clearly saying that LQG does not predict Lorentz violation, at least so far.
That is the most up to date source on LQG in the literature (no comprehensive review has appeared since, I regret to say.)

Researchers had tried unsuccessfully to derive a prediction of Lorentz violation in the LQG framework for a couple of years 2005-2007. There was considerable speculation but no one came up with a proof. They wanted to have derived that kind of prediction before Fermi-LAT (then knowns as GLAST) was launched, but were unable to get one.

AFAIK there was never anything saying to expect violation to be first order instead of second order.

*I include here what I would call Lorentz-"bending" as in socalled "deformed special relativity" where there is no preferred frame and the low-energy speed of light c is the same for all observers, but where very high energy photons can travel slower than c.
I think you mean to include that as a kind of Lorentz-violation. So I include it in what I said.

As you point out there are still some kinds of dispersion that might be observed---but the present situation is no-one has a prediction on the table, that I know of. So if that happened it would be of great interest but no one would score any points

The current (May 2008) review article on LQG is here:
http://relativity.livingreviews.org/Articles/lrr-2008-5/
As soon as something more recent comes out I will post it in this updated list of selected QG links:
https://www.physicsforums.com/showthread.php?p=2707406#post2707406
There are some other things there you might find useful, including a few selected 2010 articles, but no more recent survey.

 

[BenTheMan]

The almost simultaneous detection of low energy and high energy photons puts tight constraints on models predicting linear dependence of c on E. But it's very far from ruling out quadratic dependence. My question is, why do Lorentz-violating theories commonly predict linear rather than quadratic relation between c and E? A quadratic dependence might arise, for example, if f = Sin[k/k_planck], in which case the group velocity df/dk is a Cos which only shows quadratic deviation from 1 for small angles.

In physics, we don't know how to do anything except Taylor series and harmonic oscillators. This follows from the idea of an effective field theory, in the Wilsonian sense, which apparently marcus doesn't understand.

I'll give two answers, one short and one longer.

The main idea is that, if some theory DOES predict something crazy like sin(k/k_pl) violations, you can express that as a power series, which converges for all values of the angle.

If you like, take the lagrangian, and add an infinite number of new terms to it, which have increasingly negative powers of mass in front of them:

\mathcal{L} = \mathcal{L}_{MSSM} + \sum_{i=1}^{\infty} \frac{\lambda_i}{M^{i}} \mathcal{O}_{4+i}(\Phi,\partial\Phi)

L_MSSM is the MSSM lagrangian (or SM, if you like), O is some operator (of mass dimension 4+i) consistent with all of the symmetries of the true theory of Nature (described by L), lambda is some c-number, and M is the scale below which this theory is valid. You can derive this type of theory by taking the full lagrangian L and "integrating out" some heavy fields. An example of this is Fermi Theory. Another example is GR. As you can see, this just looks like a Taylor series, and you could engineer a sin by picking lambda appropriately.

As a theorist, it is my job to derive the lambdas and the M, and tell the experimenters what physical processes they should measure. This is what the LQG people did, and they predicted that variations come at first order. Ostensibly, they now back away from this prediction, which shows that their theory is a lot less predictive than some would have you believe.

 

[marcus]

Smolin's January 2005 paper is, in a sense, the exception that proves the rule. It made a handwaving "prediction" that was not derived from the actual LQG framework.
Rovelli, Ashtekar, Freidel and the other main people did not go along with it.
Several researchers made a sustained effort during 2005-2007 to actually derive that prediction from LQG, but were unable to.

Smolin's paper avoids saying that it is about 4D LQG. It gives an argument which he says is "generic and independent of dimension".
It applies not to any specific QG but to a kind of "semiclassical approximation" which he argues would apply to any and all QG generically, but which people like Kowalski-Glikman, who did the follow-up work during 2005-2007, could not get to work rigorously.

Therefore the argument is not specific to LQG or any concrete example of a QG that I know of. Maybe someone wants to look at the January 2005 paper and see: http://arxiv.org/abs/hep-th/0501091

I don't know of any people in the LQG research community who have "backed away" from predicting dispersion. Maybe someone here can think of someone. The main people I can think of never subscribed to such a prediction. And Smolin himself (who has not done much with LQG since 2006 or so) has not given up on the idea of first or second-order or some kind of generic dispersion!
He has a recent paper with a couple of co-authors (not specifically LQG people but well-known) where he says "look, dispersion hasn't been ruled out" and other things.

In fact, I guess, it has not been ruled out. And if it is ever observed that will be a demerit to the present LQG framework, because LQG as it stands was never able to rigorously predict dispersion (or the contrary!). Observing dispersion would force LQG to be revised. Further revised, it is being re-worked currently to get more consistency between Hamiltonian and path integral formulations.

Rovelli has a 2003 paper proving that strict Lorentz invariance is consistent with the salient LQG feature that the area and volume operators have discrete spectra. That's a signpost to where the core LQG opinion has been, at least that far back. But consistency is not implication.

 

[tom.stoer]

By "predicting second order violations ..." you certainly mean "predicting vanishing first order but non-vanishing second order violations ...".

As there are no derivations of that kind at all, it seems a little bit irrelevant.

Afaik there are some ideas like vector-condensates and such strange things, but from the "mainstream QG approaches" like strings, LQG, asymptotic safety I have not heard anything else but local Lorentz invariance w/o breaking or deformation.

What about non-commutative geometry?

 

[BenTheMan]

As there are no derivations of that kind at all, it seems a little bit irrelevant.

Pun intended or not :)

There's no reason, a priori, to expect the first order variation to vanish. One would have to come up with some symmetry argument about why they shouldn't be there.

In general, those effective operators are there. The fact that they aren't observed provides a non-trivial constraint about the fundamental theory.

 

[tom.stoer]

Afaik the LQG guys used weave states or something like that to solve for photon propagation. So Lorentz violation was an artefact of a wrong approx. for the states; I guess weave states do not solve H|weave> = 0.

Why do you think that already the basic Lagrangian should contain symmetry-violating terms?

 

[BenTheMan]

Why do you think that already the basic Lagrangian should contain symmetry-violating terms?

I _said_ the lagrangian _should_ have those terms unless some symmetry forbids them.

What I wrote down was the most general operator, O, which was consistent with the gauge symmetries of the low energy theory, and which was suppressed by powers of M. You should (or someone should) be able to explain why that dimension 5 operator is not there, or why the coefficient in front of the operator is small.

This is the operator which is being constrained by the Fermi measurements, right?

 

[tom.stoer]

Violation of Lorentz invariance is forbidden by exakt local Lorentz (or Poincare) gauge symmetry in most QG approaches

 

[petergreat]

By "predicting second order violations ..." you certainly mean "predicting vanishing first order but non-vanishing second order violations ...".

As there are no derivations of that kind at all, it seems a little bit irrelevant.

I haven't studied LQG, but I remember that for a 1D chain of oscillators connected by springs, the dispersion relation for the normal modes is f = Sin[k/k_max], therefore the variation of phonon speed is quadratic for small k. That's the only analogous physics I've studied, so my natural reaction to the news that Fermi has ruled out linear variation is "why not 2nd-order?". Of course, I know LQG is not a naive spacetime lattice model, so what I'm saying may be very irrelevant.

 

[BenTheMan]

Violation of Lorentz invariance is forbidden by exakt local Lorentz (or Poincare) gauge symmetry in most QG approaches

As far as I understand, the loop program violates local lorentz invariance. Any theory with a minimum length scale will do the same.

See the linked paper by Smolin.

 

[tom.stoer]

As far as I understand, the loop program violates local lorentz invariance. Any theory with a minimum length scale will do the same.

See the linked paper by Smolin.

I have seen this claim over decades, but this is simply wrong!

LQG preserves local Lorentz (gauge) symmetry. The constraints G (Gauss), D (Diff.) and H (Hamiltonian) together imply that the symmtry is respected on the subspace of physical states.

Roughly speaking the symmetries are implemented via gauge fixing: if you study a two-particle system in QM with V(x,y) = V(x-y) you re-write your Hamitlonian using r (relative) and R (center of mass), separate center of mass motion and use P=0 (as constraint on states) which means R=const. This can be done via unitary transformations and is something like gauge fixing in a quantized theory (you never see this in qm textbooks but you can do that quite easily). In the final theory there is no R and P, the space of physical states does not know anything regarding center of mass momentum; this means that translational invariance has been fixed (not broken).

Something like that is done in LQG as well. The "constraint" P|phys> = 0 introduced by hand is something similar as G(x)|phys> = which is the Gauss law (the Gauss law acts as generator of local Lorentz symmetry in tangent space).

The minimum length is not introduced by hand, it emerges in the spectrum of length, area and volume operators. Compare it with angular momentum in qm. You have an operator algebra forcing you to introduce quantized angular momentum and a minimum l² and m value. Nevertheless rotational invariance is not broken!

 

[BenTheMan]

I have seen this claim over decades, but this is simply wrong!

If Lorentz isn't broken, then what is the source of the claims of Lorentz violations coming from Quantum Gravity?

Am I not free to think of Loop Quantum Gravity in terms of a Lagrangian?

In other words, if what you say is right, AND the 2005 paper already linked above is right, do you see the contradiction? If LQG preserves Lorentz Invariance, and it truly is a fundamental symmetry of the theory, then how can one ever expect to find Lorentz Violations in nature?

 

[tom.stoer]

The results from 2005 are due to approximations; unfortunately no exact solutions are known, so every approximation (spin network state) may violate certain symmetries.

According to the ideas from 2005 the theory has DSR (doubly-special relativity) as long-distance limit; here Lorentz symmetry is realized non-linearly; this deformation is different from breaking.

(if you are interested you should read more about DSR; but afaik as of today nobody claims that DSR is the non-listance limit of LQG)

 

[marcus]

In other words, if what you say is right, AND the 2005 paper already linked above is right, do you see the contradiction? ...

heh heh
The 2005 paper you linked to is not about LQG. It doesn't even mention LQG as far as I can see.
It is kind of bizarre how you keep harping on this one 2005 paper, which is basically about DSR.
Here's the link, if anyone wants to see what Ben keeps referring to http://arxiv.org/abs/hep-th/0501091

During 2005-2007 a major effort was made to connect (4d) LQG to DSR as a flat or semiclassical limit. It failed.

It seems to me that you, Ben, have been told repeatedly over several years that (in 4d at least) LQG is consistent with Lorentz invariance and does not predict any deformation of special relativity, as yet.

But you keep harping on that 2005 paper about DSR that does not even connect with LQG.

It is strange.

It is as if, instead of wanting to understand, you wanted to confuse or discredit by repeating an untrue rumor over and over again.

BTW it is true that in 2005 Freidel and Livine were able to prove in the 3d case that the type of spinfoam LQG they were using DID have a semiclassical limit and that it DID conform to some type of DSR. This is what raised people's hopes that something similar could be shown in 4d. Considerable effort went into trying to show that---a central person in that research was Kowalski-Glikman. By 2007 he gave up. I don't know the details---those are just the broad outlines.

Anyway the 2005 work you keep bringing up is a dead letter. It makes some assumptions concerning the semiclassical limit of a vague generic QG, and argues from those assumptions for some DSR-type dispersion. It was a 2005 conjecture, in effect, that did not work out. Most likely it could not be shown that the LQG semiclassical limit fit those assumptions, the program hit a snag and was put on hold.

Jerzy Kowalski-Glikman is something of a DSR expert. Anyone really interested in the subject should probably check out some of his papers. He sometimes visits here at PF. He and Kris Meissner organized and hosted the Planck Scale conference (XXV Max Born) in 2009. Great conference.

Anyone with a real interest should try to get hold of some recent papers that have something more than a handwave connection to LQG.
Since LQG has been reformulated in 2008-2009 there could be some interesting results in the works that are rigorously based on the new LQG formulation. It is conceivable that some will involve DSR/dispersion, although I haven't seen any signs of this.

Atyy might know some.

 

[marcus]

(if you are interested you should read more about DSR; but afaik as of today nobody claims that DSR is the long-distance limit of LQG)

I think you are right about that. In 4d. There were a couple of papers in 2005 by Freidel Livine that dealt with the 3d case. The results were exciting and raised hopes of getting a testable prediction by that route. Just couldn't be extended, so far, to 4d.

Now it seems the main hope for getting a test of LQG centers on observing the CMB (cosmic microwave background) power spectrum and polarization and a central person in that effort is Aurelien Barrau, who just gave a talk at the ICHEP on testing LQG. Hopefully that initiative will succeed in leading to a test (with luck it might use data from the Planck mission.)

 

[BenTheMan]

heh heh
The 2005 paper you linked to is not about LQG. It doesn't even mention LQG as far as I can see.
It is kind of bizarre how you keep harping on this one 2005 paper, which is basically about DSR.
Here's the link, if anyone wants to see what Ben keeps referring to http://arxiv.org/abs/hep-th/0501091

During 2005-2007 a major effort was made to connect (4d) LQG to DSR as a flat or semiclassical limit. It failed.

It seems to me that you, Ben, have been told repeatedly over several years that (in 4d at least) LQG is consistent with Lorentz invariance and does not predict any deformation of special relativity, as yet.

But you keep harping on that 2005 paper about DSR that does not even connect with LQG.

It is strange.

It is as if, instead of wanting to understand, you wanted to confuse or discredit by repeating an untrue rumor over and over again.

BTW it is true that in 2005 Freidel and Livine were able to prove in the 3d case that the type of spinfoam LQG they were using DID have a semiclassical limit and that it DID conform to some type of DSR. This is what raised people's hopes that something similar could be shown in 4d. Considerable effort went into trying to show that---a central person in that research was Kowalski-Glikman. By 2007 he gave up. I don't know the details---those are just the broad outlines.

Anyway the 2005 work you keep bringing up is a dead letter. It makes some assumptions concerning the semiclassical limit of a vague generic QG, and argues from those assumptions for some DSR-type dispersion. It was a 2005 conjecture, in effect, that did not work out. Most likely it could not be shown that the LQG semiclassical limit fit those assumptions, the program hit a snag and was put on hold.

Jerzy Kowalski-Glikman is something of a DSR expert. Anyone really interested in the subject should probably check out some of his papers. He sometimes visits here at PF. He and Kris Meissner organized and hosted the Planck Scale conference (XXV Max Born) in 2009. Great conference.

Anyone with a real interest should try to get hold of some recent papers that have something more than a handwave connection to LQG.
Since LQG has been reformulated in 2008-2009 there could be some interesting results in the works that are rigorously based on the new LQG formulation. It is conceivable that some will involve DSR/dispersion, although I haven't seen any signs of this.

Atyy might know some.

TLDR

Do you have anything specific to say marcus, or are you just going to cut and paste a bunch of abstracts that you don't understand again?

 

[Haelfix]

"The minimum length is not introduced by hand, it emerges in the spectrum of length, area and volume operators. "

I've seen it both ways before. For instance glancing at Rovelli's quantum gravity paper yesterday, I came across the fact that he claimed that LQG removes the high energy divergences of perturbative gravity by introducing a minimum length cutoff.

Well, he can't have it both ways. If you introduce a hard minimum length cutoff, that does implicitly cure the divergences but also automatically guarentees a lorentz invariance violation.

Otoh if you insist that the minimum length scale arises from the discrete spectrum of some sort of position or area operators (and there is another weird haziness in LQG b/c such quantities are not gauge invariant) then it cannot also act like a hard regulator (try this for instance with angular momentum in quantum mechanics to immediately derive contradictions).

 

[marcus]

"The minimum length is not introduced by hand, it emerges in the spectrum of length, area and volume operators. "

I've seen it both ways before. For instance glancing at Rovelli's quantum gravity paper yesterday, I came across the fact that he claimed that LQG removes the high energy divergences of perturbative gravity by introducing a minimum length cutoff.
...

Haelfix, nice to see you addressing detail! Too often one just gets smear and hostility instead of potentially constructive comment.

To save people's having to search thru, who are you quoting? which post? I'd like to see the context of what the person said.

And where in what Rovelli paper? Could you give a link to "Rovelli's QG paper"?
And if the statement is not on page one, could you say which page? Save me trouble scanning thru to try to find the precise statement.

Thx.

 

[JustinLevy]

Well, he can't have it both ways. If you introduce a hard minimum length cutoff, that does implicitly cure the divergences but also automatically guarentees a lorentz invariance violation.

Thank you for your post. The "minimum length" issue always seemed confusing to me since in some arguments LQG starts with continuous spacetime yet finds operators have a discrete spectra, and in others they seem to start with graphs and say continuous spacetime "emerges" from this discrete geometry. Because of discussions here I was getting the impression that these ideas somehow weren't supposed to be contradictory. But I couldn't figure out how lorentz symmetry could possibly fit with all this.

You argument is simple clear, and helps get a handle on why it indeed should sound strange. This doesn't mean their theory can't resolve UV divergences, but it doesn't automatically garauntee that it does. I especially like the angular momentum argument to make it clear one shouldn't treat the discrete operator spectra as if it gives cutoffs.

 

[MTd2]

Why should be UV divergence if there is a minimum length cut off?

 

[BenTheMan]

Too often one just gets smear and hostility instead of potentially constructive comment.

Or, you know, I could just cut and paste the abstracts from a bunch of papers I don't understand, rather than talking about actual physics.

That seems to go over well here.

 

[marcus]

Why should be UV divergence if there is a minimum length cut off?

Exactly! But there is some confusion surrounding the word "cutoff". In LQG the UV divergences are resolved NOT by introducing a min length BY HAND but by the fact that the theory (by itself) supplies minimum positive measurable area and volume. The usual citations are to work by Thiemann in the 1990s.

... The "minimum length" issue always seemed confusing to me since in some arguments LQG starts with continuous spacetime yet finds operators have a discrete spectra, and in others they seem to start with graphs and say continuous spacetime "emerges" from this discrete geometry. Because of discussions here I was getting the impression that these ideas somehow weren't supposed to be contradictory.

That's the right impression, logically there is no contradiction. Quantum operators are about measurement. The area/volume operators can have discrete spectra. (Even though one starts with a continuum.)

This doesn't mean their theory can't resolve UV divergences, but it doesn't automatically guarantee that it does.

That's right! There is definitely something to prove. This gave rise to a series of papers by Thiemann in the 1990s. The theory automatically gives lower bounds on area/volume measurement. Can this be used to prove rigorously the absence of UV divergences? No "cutoff" introduced by hand. After nontrivial work, answer was found to be a tentative yes. (Thiemann's 2007 book is probably the best source on this.)

I especially like the angular momentum argument to make it clear one shouldn't treat the discrete operator spectra as if it gives cutoffs.

I like the angular momentum example too. It doesn't give naive "by hand" cutoffs. As I said there is something that needed to be proved.

"The minimum length is not introduced by hand, it emerges in the spectrum of length, area and volume operators. "

What you quoted here is correct.

For instance glancing at Rovelli's quantum gravity paper yesterday, I came across the fact that he claimed that LQG removes the high energy divergences of perturbative gravity by introducing a minimum length cutoff.

You really should quote exact words. Did R. say "cutoff"? That would suggest something put in by hand, which isn't what happens. What actually did R. say?

Well, he can't have it both ways. If you introduce a hard minimum length cutoff, that does implicitly cure the divergences but also automatically guarentees a lorentz invariance violation.

We've been thru this before. The theory provides discrete spectra for area/vol measurement, not introduced by hand. This is not inconsistent with Lorentz invariance.

 

[marcus]

I found a place where Rovelli uses the word "cutoff"---I think metaphorically since not introduced by hand---in his 2008 review. This is the standard review of the subject.
==quote==
6.9 Matter couplings

The coupling of fermions to the theory [206, 207, 54, 287] works easily. All the important results of the pure GR case survive in the GR + fermions theory. Not surprisingly, fermions can be described as open ends of “open-spin networks”.

The extension of the theory to the Maxwell field [169, 126] and Yang–Mills [290] also works smoothly. Remarkably, the Yang–Mills term in the quantum Hamiltonian constraint can be defined in a rigorous manner, extending the pure gravity methods, and ultraviolet divergences do not appear, strongly supporting the expectation that the natural cutoff introduced by quantum gravity might cure the ultraviolet difficulties of conventional quantum field theory. For an up-to-date account and complete references, see Thiemann’s book [294].
==endquote==

This is easy to find in the review http://relativity.livingreviews.org/Articles/lrr-2008-5/
Just click on section 6.9 in the outline in the lefthand margin.

Haelfix, I am still interested to know the online source and exact quote that you were paraphrasing.

 

[Haelfix]

Page 8 and 9 of his 2004 LQG book or section 5.4 of the living review article, to wit:

"A problem that has been repeatedly tied to quantum gravity, and which loop quantum gravity is able to address, is the problem of the ultraviolet infinities in quantum field theory. The very peculiar nonperturbative short-scale structure of loop quantum gravity introduces a physical cutoff. Since physical spacetime itself comes in quanta in the theory, there is literally no space in the theory for the very high momentum integrations that originate from the ultraviolet divergences. "

Statements like the above are perplexing to a HEP physicist, b/c we know a lot about spacetime cutoffs. A hard cutoff can and will cure the divergence of gravity, however it does necessarily violate LI *unless you fantastically warp the topology of spacetime alla causal sets, or alternatively fine tune all interactions to fantastic accuracy*.

You seem to think that's not the case, (which is my understanding of at least the versions of LQG that I have read as well), however then his statement about curing perturbative divergences most assuredly does not follow.

 

[marcus]

Page 8 and 9 of his 2004 LQG book or section 5.4 of the living review article, to wit:

"A problem that has been repeatedly tied to quantum gravity, and which loop quantum gravity is able to address, is the problem of the ultraviolet infinities in quantum field theory. The very peculiar nonperturbative short-scale structure of loop quantum gravity introduces a physical cutoff. Since physical spacetime itself comes in quanta in the theory, there is literally no space in the theory for the very high momentum integrations that originate from the ultraviolet divergences. "

...

Thanks Haelfix. I looked where this quote is, in section 5.4 of the living review article. I was expecting some reference to papers by Thiemann from around 1995-1998 but there were no references!

Ah! I am glad you mentioned Rovelli's book. Here is a discussion. It starts at the bottom of page 281.
and by the top of page 282 you see "This is how diffeomorphism invariance cures in depth the ultraviolet pathologies of quantum field theory."

Then on page 289 there begins section 7.3 Matter: dynamics and finiteness and at the end of that section, on page 271, he refers to a 1997 paper of Thieman.
This paper is Rovelli's book's reference [201]
http://arxiv.org/abs/gr-qc/9705019
Quantum gravity as the natural regulator of the hamiltonian constraint of matter quantum field theories.