Since the announcement of the OPERA result there have been numerous theory papers written about the Faster Than Light neutrinos and posted to arXiv and even viXra. For next Friday the CERN theory group have organised a three hour seminar to discuss various theories. The rule of engagement is that nobody is allowed to talk about the result being wrong. They just have to imagine that it has been robustly confirmed and consider how they would explain it. It is a great idea and a pity that they are too shy to webcast it.
In any such discussion I think the first thing to remember is that the measurement was a purely classical one so you have to first address the classical (non-quantum) implications. This can go two ways. Either the Lorentz transforms are (locally) valid or not. In the experiment, protons were fired at a fixed target to generate pions and kaons that decay to provide a beam of neutrinos. If we want to keep the principles of special relativity intact in our explanation then we have to face the fact that the experiment can be transformed to one where a fast-moving target is smashed into stationary protons as seen by someone moving in the reference frame of the protons. This is enough of a Lorentz boost to transform the neutrino worldlines so that they would become anti-neutrinos that began life at the OPERA detector and headed towards CERN to meet the pions. This means they would have to anticipate the experiment so causality is dramatically violated. You can’t escape this result if you want to keep the Lorentz transformations. It does not matter whether the neutrinos are acting like classical tachyons with imaginary mass or if they are passing through a stargate buried underground that teleports them closer to the detector. The fact is that if Lorentz invariance holds then you can use the experiment to send information back in time. Some imaginative people may be able to dream up theories in which time-travel is acceptable due to branching timelines or whatever, but you might as well believe in Dr Who.
The second alternative is to consider violations of Lorentz invariance and this is what most theorists would do. It remains true that the size of the violations is large and classical in nature. This is not some subtle quantum gravity effect that only reveals itself at the Plank scale. It has to be something that is only hidden because of the difficulty is detecting neutrinos. Lorentz violation justifies the headlines that “Einstein was wrong” but not just at scales where spacetime structure is expected to break down. This is being seen at velocity scales accessible to a modest particle accelerator.
The measurements tell us that the superluminal velocity of neutrinos does not vary much with energy. They don’t seem to approach the speed of light as the energy increases as classical tachyons would. In fact the lack of dispersion observed suggests a fixed speed for neutrinos at least over the range of energies produced in the experiment. Other observations of cosmic neutrinos tells us that much lower energy neutrinos seem to travel at the speed of light. You can consider variations on the possible behavior but I think it is difficult to escape one of two possible conclusions. Either the speed of light a few kilometers underground where the neutrinos passed is faster than the speed of light above ground, or there is a second fixed speed everywhere that high energy neutrinos adhere to.
In the first case you could drill a deep hole and send down an atomic clock, when you bring it back up you will find that time has passed more quickly. This would have to be a much bigger effect than the known GR effects. I can’t see how such an effect would not have been seen in some other observation so I wont consider it further.
The remaining possibility is that there are two (or more) constant speeds everywhere in nature. This is not something you can attribute to violations of Lorentz invariance. It simply implies that Lorentz invariance is completely wrong, but wait. Einstein replaced special relativity with general relativity where the spacetime metric is just a dynamical field associated with gravity. In GR the Lorentz transformation is just a subset of a more general transformation that locally preserves the metric. Suppose there were two metric fields that both transform according to the rules of general relativity but one of them is only coupled to neutrinos and other weakly interacting matter. This I think is the best hope for a classical theory that could explain the superluminal neutrinos without causality violations.
However, with two metrics on spacetime you can combine them to define a preferred reference frame. E.g you can multiply one metric by the inverse of the other and construct the eigenvectors of the result to define vector fields that define a stationary frame. Effectively you have created an aether theory, but at least one where the aether filed is dynamical and nearly invisible. I think this is the least radical way to explain the OPERA result if it stands up.
What about the extra dimensional theories that some people are getting excited about? They don’t escape the classical arguments I have given and I suspect that these arguments can be made more robust if someone believes the OPERA result strongly enough to try it. You will either have to accept strong causality violations or an aether field that determines the frame for a second fixed speed. Any such arguments will make assumptions but violating those assumptions would require a paradigm shift to something so radical that we can’t really anticipate it.
Of course the much simpler explanation is that the experiment has neglected some systematic error, but that is too boring.