# Spacetime is smooth after all?

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1. May 17, 2013

### soothsayer

Just came across this article, which details findings from the Fermi telescope that have an interesting consequence to quantum gravity theories:

www.space.com/19202-einstein-space-time-smooth.html

First, what do you guys think of this finding? Is it legitimate, or flawed? It's obviously just one data point, but the authors seem to think the result is strongly suggestive on its own.

Second, if the results, and the conclusion the authors have drawn from it, WERE correct, what would this mean to current theories of quantum gravity?

Just hoping to put these results in context. Thanks for any input!

2. May 17, 2013

### soothsayer

3. May 17, 2013

### marcus

The finding is generally supportive of current QG.
In May 2008 one of the main leaders in QG, Carlo Rovelli, published an invited review of LQG in which he outlined the theory as it stood at the time and dealt with many issues like that. He stated that LQG did NOT predict an energy dependent speed of light. In particular it would not have predicted dispersion in Gammaray Bursts of the sort tested for.

In 2010 LQG was proven to have a Lorentz covariant formulation. http://arxiv.org/abs/1012.1739

There is a superficial resemblance at verbal level between "space-time foam" which I think was an idea of J.A. Wheeler several decades back---and a mathematical method of calculating transition amplitudes used in LQG called "spin foam". The two things SOUND the same but are different. A "spin foam" is a type of calculation analogous to a Feynman path integral where you truncate the calculation by breaking the path down into linear segments. You do not imagine that the path is MADE of linear segments, merely that you only perform a finite number of measurements on it.

People unfamiliar with QG, including a surprising number of professional astrophysicists, can get confused about this. There were some older LQG papers where it was argued that the theory or some offshoot of it might predict dispersion. However attempts to show this rigorously failed. A 1998 paper by Gambini and Pullin is often cited, presumably for want of anything more recent.

To give a complete answer I would have to go into some less-studied but still important QG theories: CDT and AS (causal dynamical triangulations and asymptotic safety). As far as I know, neither of them predicts dispersion of the type tested for in your paper. They are in that sense "smooth" QG theories. Then there are other less-researched theories I personally don't know much about: the bulk of the research is in those three: LQG, CDT, AS.

Last edited: May 17, 2013
4. May 17, 2013

### soothsayer

That's good to know, Marcus. Thanks. I didn't know that current LQG theories didn't have dispersion. What about String Theory?

5. May 17, 2013

### marcus

there are many possible Superstring theories. I expect most are Lorentz covariant. Howeverr John Ellis is a prominent theorist at CERN, and here's a sample of his work on the subject.

http://arxiv.org/abs/0804.3566
Derivation of a Vacuum Refractive Index in a Stringy Space-Time Foam Model
John Ellis, N. E. Mavromatos, D.V. Nanopoulos
(Submitted on 22 Apr 2008)
It has been suggested that energetic photons propagating in vacuo should experience a non-trivial refractive index due to the foamy structure of space-time induced by quantum-gravitational fluctuations. The sensitivity of recent astrophysical observations, particularly of AGN Mk501 by the MAGIC Collaboration, approaches the Planck scale for a refractive index depending linearly on the photon energy. We present here a new derivation of this quantum-gravitational vacuum refraction index, based on a stringy analogue of the interaction of a photon with internal degrees of freedom in a conventional medium. We model the space-time foam as a gas of D-particles in the bulk space-time of a higher-dimensional cosmology where the observable Universe is a D3-brane. The interaction of an open string representing a photon with a D-particle stretches and excites the string, which subsequently decays and re-emits the photon with a time delay that increases linearly with the photon energy and is related to stringy uncertainty principles. We relate this derivation to other descriptions of the quantum-gravitational refractive index in vacuo.
8 pages, 3 figures.

http://arxiv.org/abs/0901.4052
Probing a Possible Vacuum Refractive Index with Gamma-Ray Telescopes
John Ellis, N.E. Mavromatos, D.V. Nanopoulos
(Submitted on 26 Jan 2009)
We have used a stringy model of quantum space-time foam to suggest that the vacuum may exhibit a non-trivial refractive index depending linearly on gamma-ray energy: ε-1 ~ Egamma/MQG1, where MQG1 is some mass scale typical of quantum gravity that may be ~ 1018 GeV: see Phys. Lett. B 665, 412 (2008) and references therein. The MAGIC, HESS and Fermi gamma-ray telescopes have recently probed the possible existence of such an energy-dependent vacuum refractive index. All find indications of time-lags for higher-energy photons, but cannot exclude the possibility that they are due to intrinsic delays at the sources. However, the MAGIC and HESS observations of time-lags in emissions from AGNs Mkn 501 and PKS 2155-304 are compatible with each other and a refractive index depending linearly on the gamma-ray energy, with MQG1 ~ 1018 GeV. We combine their results to estimate the time-lag Delta t to be expected for the highest-energy photon from GRB 080916c measured by the Fermi telescope, which has an energy ~ 13.2 GeV, assuming the redshift z = 4.2 ≤ 0.3 measured by GROND. In the case of a refractive index depending linearly on the gamma-ray energy we predict Delta t = 25 ± 11 s. This is compatible with the time-lag Delta t ≤ 16.5 s reported by the Fermi Collaboration, whereas the time-lag would be negligible in the case of a refractive index depending quadratically on the gamma-ray energy. We suggest a strategy for future observations that could distinguish between a quantum-gravitational effect and other interpretations of the time-lags observed by the MAGIC, HESS and Fermi gamma-ray telescopes.
6 pages

Last edited: May 17, 2013
6. May 18, 2013

### jimgraber

In contrast, http://arxiv.org/abs/1305.2626 is a very recent paper about a very recent GRB which argues for high energy photon delays, and thus possibly some small quantum spacetime structure.

7. May 18, 2013

### atyy

I don't think it is known that current LQG theories don't have dispersion. I believe the answer is simply unknown.

As of August 2011, Rovelli's thoughts in his Zakopane lectures http://arxiv.org/abs/1102.3660 were (Appendix A):

"For completeness, I leave the old problems here, indicating that the progress made, in square parentheses. ...

10. Is there any reason for a breaking or a deformation of local Lorentz invariance, that could lead to observable phenomena such as $\gamma$ ray bursts energy-dependent time of arrival delays, in this theory? [Observation is proceeding fast on this issue. See [1, 139, 140]]."

Last edited: May 18, 2013
8. May 18, 2013

### marcus

I think you misinterpret the question he is asking. The theory as it stands has a Lorentz covariant formulation. One of the "old" problems was Is there any OBSERVATIONAL EVIDENCE reason to modify our form of LQG so as to get some dispersion/delays. This issue is to be decided observationally and the answer emerging is NO. And he cites [1, 139, 140] to that effect. The observational resolution (in the negative) he cautiously suggests is "proceeding fast."

So the suggested response to question 10 is "no, we probably do not have to modify our Lorentz covariant form of LQG to accommodate energy dependent time delays, because these are not being observed"

The Lorentz covariance of the "as is" version was shown here the previous year:
http://arxiv.org/abs/1012.1739
Lorentz covariance of loop quantum gravity
Carlo Rovelli, Simone Speziale
(Submitted on 8 Dec 2010 (v1), last revised 18 Apr 2011 (this version, v3))
The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. ... As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are preciseley in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.
6 pages, 1 figure.

Last edited: May 18, 2013
9. May 18, 2013

### atyy

Sure, but Lorentz covariance of what? You must ensure Lorentz covariance of the classical spacetime. At present it is still unclear if there is even a classical spacetime in the theory. This is why Rovelli indicates that Lorentz covariance of the classical spacetime in the existing Lorentz covariant theory is still open.

10. May 18, 2013

### marcus

Jim, thanks for mentioning this by Amelino-Camelia and a fairly new person on the dispersion-search scene, Dafne Guetta (among others.)
My reading of this is that A-C has a lot invested in the idea and is having to strain both to find evidence and to come up with theory that predicts dispersion. He's talking about small numbers of anomalous photons (like 2 or 3) that could have arrived by chance from somewhere else. Like 2 or 3 photons that his group found recorded in the "extended" Fermi data as having arrived before the GRB trigger started recording the event. And he was also invoking a little-known Non-commutative geometry model which predicts dispersion.

But it's doubtless good to keep an open mind and have people like A-C and Guetta combing the data assiduously. There could really be evidence of a subtle form of dispersion out there and that would be very exciting indeed! Also their hard work probably leads to a better understanding of the source events themselves---what happens when a GRB is produced.

I think Dafne Guetta is one of the upcoming generation and a former collaborator with Tsvi Piran at an Israeli institution. As she is someone who is newer to this line of investigation, but nevertheless expert, I'll be interested to learn her views on it. Your post put her on the radar for me.

11. May 18, 2013

### atyy

Here's another group which thinks the question is not settled in LQG.

http://arxiv.org/abs/1207.0671

Abstract: "... we focus on single modes of the field: the evolution equation is derived from the quantum scalar constraint, and it is shown that the same equation can be obtained from QFT on an "classical" effective geometry. We investigate the dependence of this effective space-time on the wavevector of the mode (which could in principle generate a deformation in local Lorentz-symmetry), focusing our attention on the dispersion relation. ..."

p10-11: "We would like to focus the attention on the issue of Lorentz symmetry, which has not been clarified yet in the complete theory. Our result proves that no violation is present in Bianchi I case (at least when back-reaction can be disregarded), and a linear deviation could be present once the back-reaction is taken into account. However, such findings do not solve the problem. In this search, the tools of “effective metric” and dispersion relation analysis can be used for more realistic cases of matter coupling (such as the electromagnetic field). We hope this work will trigger the question of Lorentz-invariance in LQG, as this approach to quantum gravity does not yet give a definitive statement."

Last edited: May 18, 2013