An elegant explanation of the Opera FTL results

Reading the Glashow paper, it looks like Glashow and Cohen actually did use the Standard Model, verbatim, with the caveat that the neutrinos' 4-momenta are spacelike. The decay modes they discuss in that paper would be impossible (kinematically forbidden) if the 4-momenta were timelike, as is easy to see by considering a boost to the initial neutrino's rest frame in the timelike case (no such boost or rest frame would exist in the spacelike case). The Standard Model sums up everything we know to date about the electroweak force, so I don't see what else could be used as a basis for speculation on the matter. I think Glashow's result merely shows that plugging FTL neutrinos into the Standard Model gives results that are inconsistent with existing measurements (as well as presumably violating Relativistic causality).

As for the source you're referencing, I think they're just confirming that taking the "standard" Standard Model and replacing Dirac tachyonic neutrinos with Majorana tachyonic neutrinos still leads to strong disagreement with the experimental results.

 

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Yes.

Yes, technically they aren't using the SM but Majorana's extension to it in their attempt at explaining the "less than unity refraction index for neutrinos traveling inside matter", thus giving theoretical support to the FTL results of the experiment. This is what makes their paper so interesting.

 

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I know nothing much about physics at all, and am sure I am wrong but is it at all possible that neutrinos are not affected by mass/gravity?

 

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Or actually, I misread. They're saying that if you take Glashow's approach but apply it to Majorana neutrinos instead of Dirac neutrinos, then it might explain the OPERA results.

 

The authors show that, by using Majorana's extension to SM, NOT ONLY the Opera result can be explained BUT ALSO SN1987. To my best knowledge this is the only paper that coherently reconciles the Opera results with SN1987 while using the Majorana formalism. BTW, Majorana was a fascinating physicist.

 

That's a really interesting question... My guess is someone has already studied that question by looking at the gravitational lensing effect acting on neutrinos coming to us from distant supernovas and other cosmic sources, and comparing it to the effect one observes for ordinary light. Since the buggers are so hard to produce in controlled bursts, and even harder to detect let alone analyze, I'm not sure we'd have the experimental sensitivity and control to observe the effects of, say, Earth's gravity on a neutrino (there's some nifty experiments which can do that for other particles). Some have indeed proposed that the major sources of dark matter might just be big bunches of neutrinos, which would explain why it doesn't clump together like ordinary matter, although other questions would still be raised.

 

Just for the record, my money's still on the OPERA result being a result of synchronization errors, but in my heart I'm hoping there's something more to it that might actually open up new unexpected avenues of research. A king's ransom to the first supergenius who can produce a working wormhole!

 

Indeed, interesting. The thing is that the lensing effects for photons have moved from measuring the bending effects to measuring the radar effects (as in Shapiro delay, see CM Will monograph). The reason is that the latter are much more precise to measure and easier to set up than the former.
Unfortunately, we cannot perform Shapiro delay tests with neutrinos for obvious reasons.....

 

That would be so cool!

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Thank you Bork. Obviously you knew where I was headed with that. I was just unable to find any data on if they took into account (or even necessary to) the earths gravity on nuetrinos.

 

IF neutrinos had non-zero mass then their path between Cern and Gran' Sasso would be curved instead of following the chord, so their path would be longer resulting into their calculated net speed being lower than measured. So, gravitational effects (IF there are any) do not explain the FTL, quite the opposite, contradict it.

 

Understood. But, what if there are no gravitational affects on neutrinos? I have been trying to find any study that has experimented with this and so far have been unable. If neutrinos are not affected by gravity then perhaps that could be the reason they are arriving seemingly FTL?

 

Then, the neutrinos propagate in a straight line, along the chord, as described in the Opera experiment.

You haven't found any study for reasons I explained in my earlier post, it is very difficult to devise such experiments.

No, see above.

 

Thank you Tach for correcting my questions and being easy on an uninformed mind. Learning all I can, thanks for your input!

 

You are more than welcome!

 

Yes. It would make sense though. If the neutrino does not have a mass, then it would make little, to no sense at all. This is because

\(\bar{\psi}\gamma^{0} (i \hbar \partial_t) \psi - ((\gamma^{i} \cdot \hat{p})c + M_s)\bar{\psi}\psi = \mathcal{L}\)

This makes a nice compact four vector covariant tachyonic neutrino equation. A non-zero mass term would allow you to express the above equation in the following way

\(\gamma^{0} \cdot i\hbar \partial_t(\psi^{\dagger}_L \psi_R + \psi^{\dagger}_R \psi_L) - (\gamma^{i} \cdot \hat{p}c(\psi^{\dagger}_L \psi_R + \psi^{\dagger}_R \psi_L) + M_s(\psi^{\dagger}_L \psi_R + \psi^{\dagger}_R \psi_L)) = \mathcal{L}\)

I have more faith in an nuetrino being it's own antiparticle now than I did a few weeks back. Before this, I believed it was more a Dirac Particle than Majorana particle.

 

Basically rewording bgreen's question, is there any chance that the calculations for the expected time arrival DO include the gravity-induced curve, while the hypothesized gravity-immune neutrinos are following the chord? This could in theory produce the apparent FTL results...making a lot of presumptions about the test and its setup of which I know nothing about. :shrug:

 

This is a question that would have to be put to the OPERA group. From my reading of the paper it was my understanding they were talking about the straight line distance between the point of neutrino generation and the detector. (point of origin is a bit more complex than this suggests, but the straight line distance still holds..., the way I read it.)

It surprises me that Green would even present this kind of speculation in a public manner without checking himself.

I think that it is far more likely that, if the FTL data is overturned, it will be a distance / time issue. At this point it is also likely best to just wait for, at least CERN and MINOS, to ether confirm or refute the existing results.

 

I have claimed that the OPERA results could be a case of a refractive index smaller than 1 inside of rock. This is because the vacuum is less dense inside of rock, as it is between casimir plates which are near one another. It reconciles the results from the supernova SN 1987 A, and it really seems like a fairly intuitive solution to this puzzle. I believe that one problem with this is that someone has already proven that light does not interact with vacuum fluctuations significantly - but the people writing paper in the OP probably have a better grasp of physics than me.

bgreen: this is in fact being investigated http://ptp.ipap.jp/link?PTP/65/1058/ . Unfortunately, I do not think I am able to explain it!

Vacuum fluctuations are supposed to be immensely dense, so why shouldn't they have an effect on light speed? After all, the refractive index of most materials is closely related to its density.

edit: it is also worth noting that there are materials which have high refractive indexes but which do not scatter light significantly!

 

That sounds interesting. It makes me think of the Abraham-Minkowski controversy:

"The result was that the light speed c= 299,792,458m/s in vacuum of Lorentz transformation should be replaced by c/n to describe electrodynamic phenomena in a dielectric medium".

Vacuum is a dielectric medium. Which reminds me of what CptBork said:

I'm a bit surprised about that too, but don't forget that Einstein was wrong! is good publicity.