# Does the Opera result hint to a discrete spacetime?

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... 

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there's a speculation that neutrinos are having a sort of access to higher dimension than our 4 dimensions, through which they can travel space. Without breaking speed limit! –  Vineet Menon Oct 20 '11 at 9:02
@Vineet Menon Yes Ive heard about that short cut thing ;-) ... –  Dilaton Oct 20 '11 at 9:21
Wow guys, it would be nicer if you could express "no-answers" or opinions about why my question is not useful/stupid etc in the form of corresponding answers and comments than by downvotes... Thanks ;-) –  Dilaton Oct 20 '11 at 9:29
Maybe the space is discrete but not by 18 m quanta. ;-) –  Vladimir Kalitvianski Oct 20 '11 at 15:05
If the fat lady sings loud enough, she can shatter space-time. –  Olin Lathrop Aug 31 '13 at 15:53

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 :).

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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!

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Thanks Chris, although this does not yet answer my question, I like the links in it. In the same popular article I mentioned, it was explained that time evolves in discrete steps too in the dynamics of spin networks. Ive read a number of different possible explanaitions of Opera or reason why is possibly wrong too. But I`m just curious what Carlo Rovelly for example and these guys would say about it if it were right ... –  Dilaton Oct 20 '11 at 10:32
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". –  anna v Oct 21 '11 at 5:15
Dear @anna v, maybe You are right... If Your comment were an answer, I would upvote it and after a certain time accept it as a reason why I get no other "positive" answers and they have indeed nothing to say about the Opera result. Howewer, this would be a bit disapointing somehow ... –  Dilaton Oct 21 '11 at 8:32
@ChrisR: The Universe Today and Bad Astronomy articles you linked to refer to a paper by van Elburg, which is completely incorrect. Van Elburg wrote the paper without bother to understand basic facts about the role of relativity in GPS or the coordinate system used in GPS. –  Ben Crowell Nov 27 '11 at 15:18
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