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

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.

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. :)

How is the Tamburini model reconciled with the Cohen-Glashow paper at arXiv 1109.6562 based on “… pair bremsstrahllung …[which]… proceeds through the neutral current interaction …" ?

Is there some way in which a Tamburini superluminal neutrino avoids emitting neutral current pair bremsstrhllung and the consequent loss of energy going from CERN to Gran Sasso?

Tony

Tommaso, you say that you "see no reason why bremsstrahlung should affect more the superluminal component".

Cohen and Glashow in arXiv 1109.6562 say "... in all cases of superluminal propagation, certain otherwise forbidden processes are kinematically permitted, even in vacuum ...".

I do not see a detailed discussion or reference about that quote from their paper

but

it may be relevant that they do say:

"... The threshold energy for ... pair bremsstrahllung ... is ...

2 m_e / sqrt( v_nu^2 - v_e^2 )

where v_e is the maximal attainable velocity of an electron and m_e its mass ...

we know that v_e = 1 [the speed of light] to a precision of at least 10^(-15) ...".

Maybe Cohen and Glashow are saying that since the electron cannot go faster than light,

neither can the neutrino unless it begins to emit bremsstrahllung electron-positron pairs.

Tony

Lorenz Invariance is already broken when the neutrino is traveling through a medium, the medium is a preferred frame.

The paper however doesn't give any reason why mass term is created in a neutrino traveling through matter.

All these Italians with their faster-than-light neutrinos... nothing more than a big ploy to direct attention away from the economic state of affairs in Italy...

My question is exactly the same as Tony's. I don't see anything that would avoid the energy loss of known electroweak processes (e+ e- emission), something which was not seen in the OPERA final state mean energy distributions?!

Can this "imaginary mass" term somehow effect the *real* kinematics of the neutrinos?

In my own opinion you may not agree with me , so their we go.

Breaking the speed of light is really a not pleasent news and is more like a big mistake that an actual discovery, Why.

1. Speed of ligth on the case of navigation pourpuse is totaly worthless effort, because it used on a real navigation may not only alters the magnetic fields on space causing a distress on it and may change it structure not for future discovery if not for future distruction of ballance. because it will affect only one side of it.

2. to control for example a traveling device at that speed will be very dificult because the universe change every milliseond and what do you see if not what is there.

3. and mos important, Knowing the way we do test and challenge nature today i can,t imagine what may be the result of something that we cant control outside of a laboratory.

So my point is instead o forsing the speed of ligth why not follow it in using natural magnetic fields.

Ill bet this sports for wining novel prices will end on a problem that we may not be able to fix.

like we always do.

If these neutrinos are travelling at superluminal speed, should they not be travelling backwards through time?

If they are travelling backwards through time, how can someone travelling forwards through time observe them for more than an infinitesimally short period of time?

>If these neutrinos are travelling at superluminal speed, should they not be travelling backwards through time?

Only in some reference frames moving relative to the one in which the neutrino's superspeed™ is being measured. Yes that yields trouble, as they will arrive before being sent, so it will look as if the receiver end influences the sender end. Nobody wants that.

The wave length of those energetic neutrinos is so short that it cannot result in collective effects.

The quaternionic Dirac equation runs: (ψ ⇒ψ*)

∇ψ = m ψ*

(No spinors, no α, β, or γ matrices, just quaternions!)

ψ consists of a one dimensional real part and a 3D imaginary part. Here the star means conjugation. It changes the sign of all imaginary base vectors of the quaternion. This action switches the handedness of the field. ψ* is the antiparticle of ψ.

The covariant derivative D delivers

Dψ = m ψ* + A ψ

A derived equation is

∇(ψ ψ) = m (ψ ψ*) = 2 m|ψ|²

Another derived equation is

∇(ψ ψ*) = 2 m Re(ψ ψ)

With the interpretation of (ψ ψ*) as a presence density follows:

∫˯ (ψ ψ*) dV=1

and as a consequence

∫˯∇(ψ ψ) dV =2m

The quaternionic Majorana equation runs: (ψ ⇒ ψˤ)

∇ψ = m ψˤ

In ψˤ two of the imaginary base vectors switch sign. This action DOES NOT switch the handedness. (ψ ψˤ) can no longer be interpreted as presence density. It is not even real!∫˯ (ψ ψˤ) dV is not equal to one. It is not even real. So the factor m in the Majorana equation may be quaternionic rather than real.

For more details see: http://www.crypts-of-physics.eu/Quaternionic_continuity_equation_for_charges.pdf .

Hans, if you've made an equation where the probablities don't sum to one, you've made an equation that can't describe any quantum particle. And its not suprising that the Majorana equation would not work with quaternions, it normally made with a two component weyl spinor, half as many components as a Dirac particle.

There is gap between, "Proton Collision ->Decay to Muons and Muon Neutrinos ->Tau Neutrino ->[gap] tau lepton may travel some tens of microns before decaying back into neutrino and charged tracks." Use the case of Relativistic Muons?

Best,

Superluminal neutrinos is correct.

Is an effect of the existence of 3 basic lengths at the quantum level.

The neutrino breaking the CPT violation, with a nonzero angle theta13, is bounded breaks Lorentz invariance at the quantum level as they move along roads in extra dimensions whose length is less than that corresponding to particles that do not violate CPT

Wouldn't it be cool if people going into extra dimensions and New Physics at the tip of a hat learned to correctly use punctuation marks, spelling, and the basic grammatical structure of English?

Jesus Christ.

Get down that pedestal, you don't look any better there.

T.

http://www.youtube.com/watch?v=JAFQFvSPhQ8

"Only in some reference frames moving relative to the one in which the neutrino's superspeed™ is being measured"

Because movement is relative, does this not mean that every frame of reference that is not the F of R of the neurino could be considered as moving relative to that of the neutrino.

BTW, Tommaso, I applaud your comments about the use of English. I post on a forum or two and struggle with the science, I dread to think what it must be like trying to do that in another language. I have great admiration for those brave people who do.

## Comments