Monday, October 17, 2011

Superluminal neutrinos at OPERA. Explained.

I haven't touched this blog for a long while, but now it's time for a new post. Everybody knows by now about those neutrinos flying from Switzerland to Italy with superluminal speeds. Most people bet on some experimental blunder commited by the OPERA collaboration. I bet that OPERA results are correct and I have a simple model, which explains where these missing 60 nanoseconds come from. It is a pity that I cannot attach PDF files here, because I have a 20-page paper with the new theory.

To make a long story short, my theory tells that the actual speed of neutrinos is lower than the speed of light (as it should be for any massive particle). Then why do they arrive in the OPERA detector by 60 ns too early? The idea is that neutrinos start their journey from a point, which is 18 meters closer to Italy than everybody thinks.

The funny thing about neutrinos is that they oscillate between three different flavors. In the case of CERN-OPERA neutrinos, one can ignore the electron neutrinos and think only about muon-tau neutrino oscillations. The thing that's even funnier is that neutrinos can oscillate not only between different flavors, but also between different locations in space. The muon neutrino part of the tandem moves along its own trajectory (with the speed of light) and the tau neutrino part moves along a different parallel trajectory (also with the speed of light). The whole system is switching back and forth between the muon flavor and trajectory and the tau flavor and trajectory. The distance between two trajectories can be huge, e.g., 36 meters. Nothing in the theory forbids that.

It is reassuring to check conservation laws: Indeed, the expectation values for the total momentum and the total energy do not change with time. It is also important that in spite of oscillations, the center of energy of this system moves with a constant velocity (=c) along a straight line. This line is in the middle between the muon and tau neutrino trajectories. This is how the free neutrino system looks like.

Next we need to consider the process of neutrino creation at CERN. This happens in meson decays. For example, a pion decays into a muon and a muon neutrino. Everybody thinks that the muon and the neutrino appear from the same point in space (the decay vertex). However, there is absolutely no reason for this to be the case. Moreover, if the above model of neutrino oscillations is correct, then the muon neutrino simply cannot emerge directly from the interaction vertex. In such a case the law of continuity of the center-of-energy trajectory would be violated. So, we get a situation in which the muon part of the neutrino tandem emerges 18 meters from the decay vertex in the forward direction, and the tau part of the tandem is 18 meters behind. Then the muon neutrino arrives in the OPERA detector by 60 ns earlier than expected, while the tau neutrino (not observed in this experiment) is 60 ns late.

This is, basically, my theory. What about the causality violation? Definitely, we have a superluminal signal propagation: neutrinos are created instantaneously 18 meters away from the decay interaction vertex, while according to special relativity it should take them at least 60 ns to get there. Yes, there is superluminal propagation! No, there is no causality violation! The point is that we have an interacting system, therefore boost transformations of observables do not follow usual Lorentz rule, and the usual logic, which "proves" that "superluminality is not causal" does not work here. You can find more details and examples in my book, where I talk about the causality of action-at-a-distance potentials.

Edit: The text of my preprint is now available at