While the recent measurement of superluminal propagation of muon neutrinos by the OPERA experiment needs independent confirmation, it is still enticing to imagine if it is at all possible to cook up a toy model to explain the faster than light effect, in the context of old ideas from cosmology (Varying Speed of Light (VSL) theories to solve the horizon problem). If indeed muon neutrinos can move faster than light, we will first need to explain why and how neutrinos can "move outside a light cone" without violating the sacred principles that apply for all of the other happy particles that enjoy causality. In other words, if neutrinos are endowed with some new physical super-duper properties, why aren't massless gauge fields (such as photons) or other fermions (such as electrons and quarks) blessed with such superluminal powers? Moreover, since neutrinos are the cousins of charged leptons via weak interactions, shouldn't we expect strange effects in weak induced transitions?
Some colleagues in the community have raised the contention that it is unlikely that neutrinos can propagate faster than the speed of light because it would contradict the arrival time of light emitted from Supernovae 1987. In particular, if the neutrinos were traveling a part in a million faster than light, they would arrive months before the light that was emitted from the Supernovae. The goal of this discussion is to be a theoretical dreamer and assume that we can overcome this contention. Three obvious loopholes are that the supernovae neutrinos were much lower in energy than the terrestrial ones that OPERA observed. Also, the distance scales between the Supernovae were orders of magnitudes apart. Finally, maybe muon neutrinos are different from their electron and tau siblings. Here goes our wish list of ingredients for a model to explain the OPERA effect:
1) OPERA neutrinos at high energies propagate superluminally at short distance scales (I refrain from choosing what this distance scale actually is--let's assume that it's a meter). Low energy propagating neutrinos are screened from this superluminal effect. I'll say more about how this screening can come about.
2) In other words, neutrinos "couple" to space-time in a way such that they can move faster than light.
3) The neutrino superluminality is connected to the fact that neutrinos can undergo flavor oscillations. Therefore, other forms of matter that can't undergo flavor changes (which is mostly everything else) will be excluded from superluminal powers.
Ideally, we would like a mechanism to tie in all these ingredients; something that I'll refrain from in this post (and if I knew, I'd write a paper--hah). Given this wish list, let's see how far we can go with a model. I want to be minimalistic and stay in four dimensions; I love Branes, but expect lots of papers on this perspective.
The first ingredient (superluminality) can be incorporated by using a cosmology idea that was implemented by my collaborator, Joao Magueijo, and I ten years ago (also see work by FQXi's Amelino-Camelia, who has also just posted a paper on the Opera results, and Majid). The basic point was that the universe's space-time was non-commutative (a fundamental uncertainty in the directions of space and time) and filled with radiation, which at low energies propagated at the speed of light. At high energy (early cosmic time), this radiation started to feel the granularity of space-time and the group velocity of the photons deviated from the speed of light. This effect is no different from what is observed in solid state physics with lattice vibrations (whose quanta are phonons). On distance scales larger than the lattice spacing, a phonon's angular frequency (w) of vibration is linearly proportional to the wavevector (k). The phonon's propagation speed will increase on scales proportional to the lattice spacing. Many approaches to quantum gravity (such as Loop Quantum Gravity, Dynamical Triangulations, String Theory) point to some granularity of space-time. However, we expect this "lattization" of space-time to be on the order of the Planck length (or perhaps a millimeter). But let's say by fiat that similarly to the VSL effect, neutrinos speed up because they feel the discrete space-time and their dispersion relations are modified by a lattice effect that builds up coherently as they propagate. Then why don't we see neutrino speed up on cosmological scales? In our model, we'll have to counter this effect with some sort of suppression effect when the lattice looks smooth (we get back a classical space-time). I don't know how to do this, but bear with me for the time being.
Now for the hard part: Why do only neutrinos see the space-time lattice? In this case, since neutrinos are quantum mechanical objects, we can only resort to quantum mechanics to rescue us. We know that symmetries can prevent quantum mechanical processes from happening (such as the selection effect in photon emission due to parity). So, what is special about neutrinos, symmetry wise? Well, their masses are so tiny (compared to the other fermions in nature) that they are helicity eigenstates. So, perhaps, if only neutrinos had helical (chiral) interactions with (discrete/lattice) gravity and were able to superluminally oscillate into each other then this might do the job. We can superselect chiral matter interactions to propagate with superluminal dispersion relations. This implies that gravity should know something about the weak force. A few years ago, Nesti-Percacci, Smolin, and I independently tried to exploit the Chiral nature of gravity by using the self dual Ashtekar-Sen gauge connection variables that break up into two SU(2) copies that commute. It was argued that it is possible to identify one copy to chiral gravity and the other to the weak interaction.
Maybe this, maybe that. This exciting prospect will tantalize theorists to translate their favorite theoretical conundrums into something coherent to explain the potentially ground breaking result that my generation has thirsted for since kindergarten.
Note: I thank Mark Gould for his feedback.