Fermi (GLAST) almost kills all Lorentz violating theories.

[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
Adrian Cho

"...

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."

 

[Physics Monkey]

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?

 

[marcus]

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
Adrian Cho

"...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.

 

[marcus]

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/E_Planck 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/E_Planck 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?

 

[Nudiustertian]

Not "all"

What Fermi's observational data are actually implying is that in the series expansion of the photon velocity,

v_ph /c = 1 + a₁ (E/E_QG) + a₂ (E/E_QG)² + a₃ (E/E_QG)³ + ...,
​

where E_QG ~ 10¹⁹ GeV, the coefficient a₁ must be << 1 (in relativity all a_i 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 a_i 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/E_QG 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 E_QG. 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.

 

[MTd2]

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

 

[dmtr]

Here is a link to a post by marcus made before the GLAST launch: https://www.physicsforums.com/showthread.php?t=177245 ...seems to be pretty consistent...

 

[MTd2]

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.