Could the Opera result be interpreted as some kind of hint to a discrete spacetime that is only seen for high enough energy neutrinos?
I think I've read (some time ago) something like this in a popular article where among other things tests of quantum gravity theories, that assume a discrete spacetime, are explained.
Looking around in blogs and other places in the web, I notice that this is disussed seldom or not at all... ``
Searching on Google there is nothing new . Considering the plethora of arxiv papers coming out with theoretical comments on the superluminal result I would think that if the LQG model had something to say, it would have said it, particularly if it were vindicated.
So the answer is "no" . For the nonce.
Because if one reads the wiki article there exists the cryptic:
led Lee Smolin and others to suggest that spin network states must break Lorentz invariance. Lee Smolin and Joao Magueijo then went on to study doubly special relativity, in which not only there is a constant velocity c but also a constant distance l. They showed that there are nonlinear representations of the Lorentz lie algebra with these properties (the usual Lorentz group being obtained from a linear representation). Doubly special relativity predicts deviations from the special relativity dispersion relation at large energies (corresponding to small wavelengths of the order of the constant length l in the doubly special theory)
It may be that LQG might be able to accommodate the OPERA result, though again, from not having jumped at the opportunity I would not hold my breath.
p.s. I am an experimentalist and am treating theories statistically :).
In several theories, space itself is discrete, somewhat in relation to the Planck length, $$l_p = \sqrt{\frac{\hbar G}{c^3}} \simeq 1.616199 \times 10^{-35}\quad m$$ .
More specifically in loop quantum gravity, Carlo Rovelli's 1998 overview paper states the following:
The spin-networks picture of space–time is mathematically precise and physically compelling: nodes of spin networks represent elementary grains of space, and their volume is given by a quantum number that is associated with the node in units of the elementary Planck volume $$V = \left( \frac{\hbar G}{c^3} \right)^{3/2}$$
So, from what I understand of LQG, space has always been discrete. However, mathematically, space being discrete does not imply that time also is (which would mean that spacetime is discrete). A counter example in 2D would be the floor and ceiling functions.
Concerning the OPERA results, let's keep in mind that several explanations have been published which don't allow for supralumnial neutrinos, cf this Universe Today article or this Bad Astronomy article.
I am relatively new here, and I might not have fully answered your question, so feel free to post comments or even modify my answer to improve it. Thanks!
ve read a number of different possible explanaitions of Opera or reason why is possibly wrong too. But Im just curious what Carlo Rovelly for example and these guys would say about it if it were right ...
$\endgroup$
Generically, we expect big deviations from the predictions of SR to occur at energies comparable to the Planck energy. At lower energies, there would probably be smaller deviations, which might be detectable in high-precision experiments. However, the OPERA neutrinos are at an energy that is extremely small compared to the Planck energy, and the effect claimed is rather large -- about $10^{-5}$. This argues strongly against interpreting it as a quantum gravity effect. A possible exception is that in theories with large extra dimensions, the Planck energy can be the same as the electroweak unification energy -- in fact, this is the aesthetic motivation for these theories. (In these theories, the apparent value of G differs from its value when you get down to the scale at which the extra dimensions are rolled up.) But LHC data don't seem to support large extra dimensions: http://arxiv.org/abs/1012.3375