The recent result by Opera which hints at a possible superluminal motion of neutrinos produced by CERN and shot underground to the Gran Sasso mine in central Italy raised Tamburini's interest. Together with Marco Laveder, a colleague of the Physics Department of Padova University, Tamburini recently wrote an interesting paper where he explains that Einstein's Relativity Theory needs not be put in discussion by the measurement: rather, the fact that neutrinos could exhibit an apparent superluminal motion is inherent in the theory written as far back as 1932 by Ettore Majorana, the talented and mysterious Italian physicist who disappeared shortly thereafter -probably to live in South America under false identity.

Tamburini and Laveder's paper (which you can download from the arxiv) explains how a fictitious "imaginary mass" term in the solution of Majorana equations for neutrino propagation may be responsible for the observed faster-than-light travel of neutrinos in a dense medium.

Specifically, the authors start from the hypothesis that the observed superluminal speed of neutrinos may be caused by matter effects, and they work out the effective imaginary mass which corresponds to each of the experimental measurements.

What I find interesting is that Tamburini and Laveder do not stop at discussing the theoretical interpretation of the alleged superluminal motion, but put their hypothesis to the test by comparing known measurements of neutrino velocity on a graph, where the imaginary mass is computed from the momentum of neutrinos and the distance traveled in a dense medium. The data show a very linear behaviour, which may constitute an explanation of the Opera effect:

## Comments

That would imply a remarkably strong coupling between neutrinos and matter. Neutrinos have a 10^-10 chance to interact with matter directly over the distance of 700 km, but their propagation speed is somehow changed by a factor of 10^-5?

Well, Nameless, while I share your intuition, let's admit that there are holes in your argument and it's far from waterproof. Light isn't basically absorbed in glass either - but it's still slower by 1/3 than it is in the vacuum.

http://motls.blogspot.com/2011/10/majorana-tamburini-laveder-superlumina...

Vladimir, the quantities expressing numerical values of couplings may have various units but "percent" is not among them. Moreover, light works in the same way when it's diluted down to individual photons in which case it's completely analogous to individual neutrinos so your "collective" comments have nothing to do with the actual physics, either. Return to the asylum, please.

Also, these collective phenomena with light in the glass are well "linear" or photon-number independent, to you information. What is valid for one photon, is valid for a beam. Only very high intensity light may cause non-linear effects which are also collective. In other words, photon in the glass is a quasi-particle, like phonon, plasmon, magnon, etc.

I did not get you phrase about asylum. What do you mean with it?

> light works in the same way when it's diluted down to individual photons

I must be in a bad mood today, but holy cow. "diluted down" ... how can people do physics when they don't even have a way to express the situation whereby the photon field only has enough energy to yield a single photon?

If you're not capable of understanding these simple ideas, please realize that the problem is on your side and this problem gives you no right to contaminate the public spaces with your utter stupidity.

Looks like my second comment has disappeared AGAIN, so here's the condensed version of the idea.

Consider a glass prism. When you shoot a photon at the prism, it comes out at an angle to the incident direction. Therefore, even if it's not absorbed, it still interacts with glass. Because glass really couples quite strongly with the EM field. And that is a prerequisite to being able to refract light.

I know that my argument is not waterproof, but it still compares quite positively to Tamburini's argument, which is basically one big hole. :)

This can't be right. Lorentz invariance is a purely geometric effect - there's no interaction term in a Lagrangian that can make a particle propagate superluminally, and the "fictitious" imaginary mass is an effective field theory approximation to some underlying interaction.

You have to get rid of Lorentz invariance to explain this result. Otherwise you get CTCs and grandfather paradoxes.