It had to happen. New Scientist managed to find a physicist willing to describe the OPERA result as “evidence for string theory”:

So if OPERA’s results hold up, they could provide support for the existence of sterile neutrinos, extra dimensions and perhaps string theory. Such theories could also explain why gravity is so weak compared with the other fundamental forces. The theoretical particles that mediate gravity, known as gravitons, may also be closed loops of string that leak off into the bulk. “If, in the end, nobody sees anything wrong and other people reproduce OPERA’s results, then I think it’s evidence for string theory, in that string theory is what makes extra dimensions credible in the first place,” Weiler says.

**Update**: hep-ph is chock-a-block with papers purporting to explain the OPERA results, using theoretical models of varying degrees of absurdity. There is however one much more sensible paper this evening, from Cohen and Glashow, which points out that superluminal neutrinos would produce electron-positron pairs via bremsstrahlung, and lose energy, which is not observed. This is also incompatible with Super-Kamionkande and IceCube data. No matter what sort of extra dimensions you introduce for the neutrinos to travel in, the OPERA claim seems to be in violent disagreement with other observations.

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http://muon.wordpress.com/2011/10/01/theories-about-superluminal-neutrinos/

A list of theories about OPERA results.

J mentioned: http://arxiv.org/abs/1109.6160

The story seems to be that a portable atomic clock was synchronized with the OPERA clock, and then transported to CERN, and used to measure the offset with the clock there. There are obviously all kinds of problems – special and general relativistic effects would make that measurement useless.

Fortunately, the “Portable Time Transfer Device” that was used does not such thing. OPERA used highly accurate GPS based clock synchronization. The common view time transfer mode is explained here:

http://tf.nist.gov/time/commonviewgps.htm

The one problem is to measure accurately the offset between the GPS signal and the local clock, and the “Portable Time Transfer Device” enables the use of exactly the same device at both CERN and OPERA, so that uncertainties introduced by the use of different devices is eliminated.

The Cohen and Glashow paper does not prove the OPERA result wrong, but instead suggest a way to reconcile OPERA with the 1987 supernova observations.

OPERA showed that the average velocity of the neutrinos over their first 730km of travel was higher than c. C&G suggests that neutrinos can slow down to c via pair production. Therefore their average velocity from the supernova to Earth can remain very close to c even if their initial velocity was higher.

This deceleration might also explain why OPERA observes neutrinos with different energies to have average velocities that differ only slightly.

ZZZ, OPERA reports seeing neutrinos of 42.9 GeV or higher. Cohen and Glashow say that if neutrinos are superluminal, even travelling over just 730 kilometers, they shed energy so rapidly that whatever their initial energy, few if any should have reached OPERA with energies greater than 12.5 GeV. “The observation of neutrinos with energies in excess of 12.5 GeV cannot be reconciled with the claimed superluminal neutrino velocity measurement.” If C&G are correct, OPERA is wrong.

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Bob,

First I’m not any reasonable statistician, I’m in fact a quite unreasonable one, who is more of an extremely diligent probability theorist disguised as a statistician.

What it comes down to is very simple, they fit a flawed statistical model. The attractively simple model of a linear time shift, assumes a prior that any and every time shift is possible. All the 6-sigma indicates is that there is good convergence in the MLE, not that the finding is correct. Bluntly MLEs do not test hypotheses.

Another possible attack they could have used is to propose a model with a parameter controlling the lower bound of time shifts allowed, and that limits toward the simple linear shift model. Then fit the MLEs of each model and use the likelihood ratio test to compare the two models.

I bet that in the coming weeks, the assumptions behind the derivation of superluminal bremsstrahlung will be a point of contention. There will be a need to return to first principles. For those who want to play, http://arxiv.org/abs/hep-th/0611263 revisits Wigner’s classification of representations of the Poincare group and includes the tachyonic cases…

There’s also a large literature on tachyon physics, like Feinberg’s original paper, and the work of Dawe and Hines, which so far isn’t playing any role in the discussion about OPERA. (Dawe and Hines raise the issue of tachyonic bremsstrahlung in their second paper.) So far the model builders are all trying to “save causality”, e.g. with extra dimension models in which the true relativistic speed limit is only realized off our braneworld. But the next step has to be an examination of models in which there are closed timelike curves and retrocausal influences. There have been various attempts to explain quantum mechanics itself as arising from such effects (e.g. http://arxiv.org/abs/gr-qc/0703150) or to employ quantum mechanics in order to neutralize their paradoxical threat (e.g. http://arxiv.org/abs/1005.2219). Hopefully one side effect of OPERA’s announcement will be a closer examination of these issues.

Mitchell,

The Bekaert/Boulanger paper points out (near the end) that tachyonic unitary irreps cannot have finite-dimensional spin, whereas the neutrino has spin 1/2, which is finite (NB: I look at tachyonic ISO(3,1) myself on page 12 here: http://www.cgoakley.demon.co.uk/qft/RQM.pdf) so in the unlikely event that there is anything superluminal here, Unitary Irreps of the Poincare group are probably going to be an early casualty.

For those entertaining thoughts of using tachyonic representations of the Poincaré group to explain superluminal neutrino propagation, isn’t anyone bother by the fact that the wave equation whose solutions furnish such representations is essentially the Klein-Gordon equation with the sign of the mass term flipped? The reason someone should be bothered by this is that a general theory of hyperbolic PDEs shows that the speed of signal propagation (say as characterized by the support of the retarded Green function) entirely depends on the highest derivative terms, which are unaffected by the sign flip. In other words, the speed of signal propagation by Poincaré invariant “tachyonic” wave equations remains squarely ≤ c.

Igor,

Not following you here. Tachyonic Poincare irreps have E = √((pc)^2-(μc^2)^2), so the dispersion relation of the de Broglie waves is ω=√((kc)^2-(μc^2/hbar)^2) and hence group velocity ∂ω/∂k = kc/√(k^2-(μc/hbar)^2) which is greater than c.

Remarkable paper by Dmitri Nanopoulos and co-author where he gets string to explain stuff going all different speeds in agreement with various observations:

http://arxiv.org/abs/1110.0451

Background Dependent Lorentz Violation from String Theory

I know there are scads of “string theory predicts FTL neutrino” papers, but this could just be a cut above the rest. It explains how they can go FTL thru rock here on earth and yet slower than light out in space between galaxies. It takes the cake.

Chris,

However fast either group or phase velocities are, the information contained in a pulse (be it encoded in a peak or some kind of modulation) cannot outrun the discontinuous edge of the same pulse.

If you model signal propagation with a

retardedsolution of the “tachyonic” wave equationbox φ+(m^2) φ = f, wherefis a source with support in a bounded regionS. Then, interpreting&phias carrying the news about what happened inS, the retarded boundary conditions ensure thatφis exactly zero everywhere outside the domain of influence ofS(the region reached bynullortimelikerays emanating fromS). Hence, the news of what happened inSdoes not reach anywhere faster than light (null rays). This conclusion holds independently of the sign of the(m^2)φterm.If one disallows generation of signals through discontinuous (just non-analytic is enough, actually) processes, then it becomes very difficult to draw the distinction between communication and a priori conspiracy. Then the notion of the speed of a signal becomes significantly muddier.

Ehrlich dismisses Cohen and Glashow’s objection (and some other objections) here: http://arxiv.org/abs/1110.0736v2

Ehrlich argues that the high energy neutrino events logged at OPERA were caused by subluminal neutrinos, and the overall velocity determination is by a mix of super- and sub-luminal neutrinos. Interesting idea, but this would justify Aaron Sheldon’s point on the previous page that speed dispersion needs to be part of the statistical analysis.

A good, old-fashioned clock synchronization problem may the source of the apparent FTL neutrinos according to:

“The OPERA neutrino velocity result and the synchronisation of clocks” by Carlo R. Contaldi

http://arxiv.org/abs/1109.6160

Contaldi wrote: “In an effort to go beyond this accuracy thresh- old, the OPERA experiment employed a travelling Time- Transfer Device (TTD) to calibrate the difference in time signals at each receiver. We assume this device to be a transportable atomic clock of sufficient accuracy.”

Unfortunately his assumption is wrong. The Travelling Time Transfer Device was not a transportable atomic clock. It was yet another portable clock synchronized by GPS and carrying a time difference counter. The TTD was used at CERN and at Gran Sasso to measure an offset between the GPS signal and the local clock. To the extent the TTD remained physically identical at CERN and Gran Sasso, its antenna, antenna cable, electronics delays remained identical, and hence the difference of offsets it measured gives the difference in the two local clocks with high accuracy.

Did anyone predict superluminal particles based on string theory? That would be much more impressive than an after-the-fact rationalisation.

For those interested in a review of relativistic effects in GPS, have a look at this:

* Neil Ashby: “Relativity in the Global Positioning System”, online at “living reviews” here.