Friday, January 13, 2017

What a burst! A fresh attempt to see space-time foam with gamma ray bursts.

It’s an old story: Quantum fluctuations of space-time might change the travel-time of light. Light of higher frequencies would be a little faster than that of lower frequencies. Or slower, depending on the sign of an unknown constant. Either way, the spectral colors of light would run apart, or ‘disperse’ as they say if they don’t want you to understand what they say.

Such quantum gravitational effects are miniscule, but added up over long distances they can become observable. Gamma ray bursts are therefore ideal to search for evidence of such an energy-dependent speed of light. Indeed, the energy-dependent speed of light has been sought for and not been found, and that could have been the end of the story.

Of course it wasn’t because rather than giving up on the idea, the researchers who’d been working on it made their models for the spectral dispersion increasingly difficult and became more inventive when fitting them to unwilling data. Last thing I saw on the topic was a linear regression with multiple curves of freely chosen offset – sure way to fit any kind of data on straight lines of any slope – and various ad-hoc assumptions to discard data that just didn’t want to fit, such as energy cuts or changes in the slope.

These attempts were so desperate I didn’t even mention them previously because my grandma taught me if you have nothing nice to say, say nothing.

But here’s a new twist to the story, so now I have something to say, and something nice in addition.

On June 25 2016, the Fermi Telescope recorded a truly remarkable burst. The event, GRB160625, had a total duration of 770s and had three separate sub-bursts with the second, and largest, sub-burst lasting 35 seconds (!). This has to be contrasted with the typical burst lasting a few seconds in total.

This gamma ray burst for the first time allowed researchers to clearly quantify the relative delay of the different energy channels. The analysis can be found in this paper
    A New Test of Lorentz Invariance Violation: the Spectral Lag Transition of GRB 160625B
    Jun-Jie Wei, Bin-Bin Zhang, Lang Shao, Xue-Feng Wu, Peter Mészáros
    arXiv:1612.09425 [astro-ph.HE]

Unlike supernovae IIa, which have very regular profiles, gamma ray bursts are one of a kind and they can therefore be compared only to themselves. This makes it very difficult to tell whether or not highly energetic parts of the emission are systematically delayed because one doesn’t know when they were emitted. Until now, the analysis relied on some way of guessing the peaks in three different energy channels and (basically) assuming they were emitted simultaneously. This procedure sometimes relied on as little as one or two photons per peak. Not an analysis you should put a lot of trust in.

But the second sub-burst of GRB160625 was so bright, the researchers could break it down in 38 energy channels – and the counts were still high enough to calculate the cross-correlation from which the (most likely) time-lag can be extracted.

Here are the 38 energy channels for the second sub-burst

Fig 1 from arXiv:1612.09425

For the 38 energy channels they calculate 37 delay-times relative to the lowest energy channel, shown in the figure below. I find it a somewhat confusing convention, but in their nomenclature a positive time-lag corresponds to an earlier arrival time. The figure therefore shows that the photons of higher energy arrive earlier. The trend, however, isn’t monotonically increasing. Instead, it turns around at a few GeV.

Fig 2 from arXiv:1612.09425

The authors then discuss a simple model to fit the data. First, they assume that the emission has an intrinsic energy-dependence due to astrophysical effects which cause a positive lag. They model this with a power-law that has two free parameters: an exponent and an overall pre-factor.

Second, they assume that the effect during propagation – presumably from the space-time foam – causes a negative lag. For the propagation-delay they also make a power-law ansatz which is either linear or quadratic. This ansatz has one free parameter which is an energy scale (expected to be somewhere at the Planck energy).

In total they then have three free parameters, for which they calculate the best-fit values. The fitted curves are also shown in the image above, labeled n=1 (linear) and n=2 (quadratic). At some energy, the propagation-delay becomes more relevant than the intrinsic delay, which leads to the turn-around of the curve.

The best-fit value of the quantum gravity energy is 10q GeV with q=15.66 for the linear and q=7.17 for the quadratic case. From this they extract a lower limit on the quantum gravity scale at the 1 sigma confidence level, which is 0.5 x 1016 GeV for the linear and 1.4 x 107 GeV for the quadratic case. As you can see in the above figure, the data in the high energy bins has large error-bars owing to the low total count, so the evidence that there even is a drop isn’t all that great.

I still don’t buy there’s some evidence for space-time foam to find here, but I have to admit that this data finally convinces me that at least there is a systematic lag in the spectrum. That’s the nice thing I have to say.

Now to the not-so-nice. If you want to convince me that some part of the spectral distortion is due to a propagation-effect, you’ll have to show me evidence that its strength depends on the distance to the source. That is, in my opinion, the only way to make sure one doesn’t merely look at delays present already at emission. And even if you’d done that, I still wouldn’t be convinced that it has anything to do with space-time foam.

I’m skeptic of this because the theoretical backing is sketchy. Quantum fluctuations of space-time in any candidate-theory for quantum gravity do not lead to this effect. One can work with phenomenological models, in which such effects are parameterized and incorporated as new physics into the known theories. This is all well and fine. Unfortunately, in this case existing data already constrains the parameters so that the effect on the propagation of light is unmeasurably small. It’s already ruled out. Such models introduce a preferred frame and break Lorentz-invariance and there is loads of data speaking against it.

It has been claimed that the already existing constraints from Lorentz-invariance violation can be circumvented if Lorentz-invariance is not broken but instead deformed. In this case the effective field theory limit supposedly doesn’t apply. This claim is also quoted in the paper above (see end of section 3.) However, if you look at the references in question, you will not find any argument for how one manages to avoid this. Even if one can make such an argument though (I believe it’s possible, not sure why it hasn’t been done), the idea suffers from various other theoretical problems that, to make a very long story very short, make me think the quantum gravity-induced spectral lag is highly implausible.

However, leaving aside my theory-bias, this newly proposed model with two overlaid sources for the energy-dependent time-lag is simple and should be straight-forward to test. Most likely we will soon see another paper evaluating how well the model fits other bursts on record. So stay tuned, something’s happening here.


  1. Pet peeve: " only be compared to themselves" should be "be compared only to themselves". Otherwise it could mean "they could only be compared; they couldn't be eaten nor seen on television".

    In German, this mistake is more difficult to make. If one means "konnten nur mit sich selbst verglichen werden", no-one would say "konnten mit sich selbst nur verglichen werden".

    My other pet peeve are missing dashes in two-word adjectives.

  2. Phillip,

    Thanks, I fixed that. I hope I've distributed all sub-burst, time-lag, propagation-delay-dashes correctly :o)

  3. "if they don’t want you to understand what they say" Vacuum refraction, dispersion, dissipation, dichroism, gyrotropy. Noether's theorems leak angular momentum conservation if vacuum is anisotropic in any way. Dark matter is then Milgrom acceleration re the Tully-Fisher relation. "Such quantum gravitational effects are miniscule, but added up over long distances they can become observable" Both are galactic scale only.

    Alternative: The burst medium is dispersive at short pathlengths, but the intervening path to Earth is inactive. Cf: Optical rotatory dispersion curves and anomalous dispersion.

    Anomalous dispersion (lower refractive index for higher frequencies) suggests a saturated absorption transition.

  4. Nice article Dr. H. You keep me in touch with interesting and very current work in cosmology and you do it in language (I don't mean English) I can understand!

  5. Another informative and interesting article - Thank you

  6. The existence of temporal lags between energy channels of GRBs at KeV+ energies has been known since the mid-1990s and is not controversial. Over 100 GRBs clearly show these usually sub-second lags, and lags have been shown correlated with the intrinsic brightness of the GRB (Norris, Marani & Bonnell ApJ 2000): shorter lags correlate with intrinsically brighter GRBs. Likely, all GRBs would show lags, but many are hidden because either too few photons are available or no clear and separable pulse structures are evident.

    The term "lag" is somewhat deceiving since what usually occurs is a stretching: a GRB pulse typically starts at the same time in every energy band but the lower energies have the same light curve shape stretched out over a longer time.

    There is some physics -- likely at the GRB source -- causing the positive lags. The Wei et al. (2016) paper reviewed calls these "intrinsic" lags. The paper then posits that different physics -- LIV -- is causing the negative lags. Perhaps. But it seems plausible to me -- as Bee reviewed -- that similar physics -- at the source -- is causing both the positive and negative lags. As Bee points out and is noted in the paper, it has not been proven that the negative lags are created along the long path from the GRB, and this is crucial for this to be a true test of LIV.

    Also, a question that comes to mind is that given that the nature of lags are really stretchings, if the negative lag is caused by LIV then why doesn't it affect the beginning of the pulses?

  7. Anomalous dispersion snuggles with induced transparency (arXiv:1404.5941 and DOI: 10.1126/science.1208066) that could gate a signal versus frequency.

    If doubling the pathlength measurably alters observed anomalous dispersion, observe effect versus distance. Local source dimensions are reasonably random with distance, spacetime foam is in cadence - until failure is curve-fit with a more parameters.

  8. "if Lorentz-invariance is not broken but instead deformed"
    Can you please explain the difference betwen broken Lorentz-invariance and deformed Lorentz-invariance?

  9. Alexey,

    If Lorentz-invariance is broken, you have a preferred frame. If it's deformed, you don't.

  10. Seems to me there is a "preferred frame", the equal momentum imparted to everything by the big bang. We even know what motion "in that frame" is, the motion (through the universe) we would have to have to see the CMB coming equally from all directions, a motion now so routinely calculated that most discussion of the CMB doesn't bother to mention it the as early days

  11. Matthew,

    Yes, there is a preferred frame which is defined by the motion of matter. But there is - in ordinary General Relativity - no preferred fundamental frame (independent of the matter). If (local) Lorentz-invariance is broken, there is one. Best,


  12. Hello Dr. H. "No ... fundamental frame independent of the matter" ok. I get that distinction, thanks. But it still seems to me that the preferred frame "of the matter" still allows us to establish a "standard clock" or "global time". This is the reason why a statement like "the universe is 13.8 billion years old" has any meaning.

  13. Hi Dr. H, I am actually the 2nd author of this paper. Thanks for your nice post and all the discussions on our paper and the relevant topics. I enjoyed reading them very much. P.S., we've another comprehensive study on the same GRB:

  14. Can some GRB expert tell me why we haven't yet seen time-dilation in GRB light curves (similar to that in supernova for example, see

  15. There have been claims of cosmological time dilation in GRBs -- some of which I have been involved with, and some of which I believe (but of course I am therefore biased). The measurement is more difficult than it might seem, though, because the variance is large due to the wide variety in GRB attributes. GRBs can be very different, some being tens of seconds long with multiple peaks, and some being much shorter and simpler. (And visa versa.) Additionally, systematic errors can easily dominate. For example brightness-dependent measurement effects, energy-dependent detector thresholds, and background determinations in a tumultuous sea of changes are all important to understand, to name just three.

    I sometimes think of measuring time dilation in GRBs as analogous to measuring Hubble's constant (Ho) for nearby galaxies. In that case -- why not just measure galaxy distance and redshift for a bunch of galaxies, divide one by the other, and there you have it! But determining Ho has taken decades and there are still potential systematic effects under study. Similarly, why not just measure GRB durations and brightnesses, plot one against the other, and there you have it! But, sometimes, unfortunately, real science takes years of studying the data to understand it well enough to make a reasonable claim. And sometimes, even after all of that study, typically years for GRBs in my experience, a reasonable claim is not guaranteed.

  16. Robert: Thanks for the nice explanation. Can you point me to 1-2 references regarding this?


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