Wednesday, January 25, 2012

Superluminal neutrinos at OPERA. A new model

As promised in the comments section of the previous post, I've completed work on a new model of neutrino superluminality. This paper is now uploaded at

The idea is that neutrino is not a free particle: it lives in a state of permanent (self-)interaction, which shows up in the form of oscillations between three neutrino types. So, a neutrino should be regarded as a group of three particles, which travel together and periodically change their flavors. Of course, in a relativistically invariant theory the center of energy of this bunch should always move with a constant speed, and for an energetic neutrino this speed should be a bit lower than the speed of light. However, there is no limit on velocities of individual components of the bunch. Positions of these particles can oscillate around the center-of-energy trajectory in concert with the flavor transformation pattern. If averaged over long time, the speed of each component (e.g., mu-neutrino) must be equal to c, but there can be time periods when its speed exceeds the speed of light, and at other times the instantaneous speed can be lower than c.

It is interesting that the amplitude of neutrino position oscillations depends on neutrino masses. For presently known neutrinos with masses around 1 eV/c^2 the magnitude of this effect is estimated to be very small. The suggested solution is to postulate existence of at least one more superheavy neutrino type with the mass of at least 300 MeV/c^2. Then one can easily explain the mu-neutrino position advance of 18 meters observed in the OPERA experiment. This can be seen in the following figure from the paper.

Here L is the neutrino travel distance (in km) and DeltaL is the distance (in meters) between mu-neutrino component and the center-of energy. The curve corresponding to 17 GeV OPERA neutrinos is shown as a broken line. The full line corresponds to MINOS neutrinos with the energy of 3 GeV. From this graph it is clear that MINOS neutrino runs in front of the center-of-energy (i.e., superluminally) up to 1500 km. Then it slows down and runs behind the c.o.e. Beyond 3000 km the neutrino becomes superluminal again, and this pattern is repeated periodically in concert with the mu-tau neutrino oscillation.

SN1987A supernova data (no neutrino superluminality) agree with our predictions quite nicely as well, because neutrino deviations from the light path cannot exceed a few meters, i.e., they are negligible in astronomic observations. The theory also predicts a specific non-linear dependence of the amount of superluminality on neutrino energy and propagation distance. It will be fun to watch how these predictions agree (or disagree) with future neutrino velocity measurements to be performed by the MINOS and OPERA collaborations.

Then what about special relativity, which forbids anything traveling faster than light? This question is answered in the paper as well. As I've said here and here on this blog, simple Lorentz transformations of special relativity are not applicable to interacting systems (such as oscillating neutrinos), so the ban on superluminal velocities does not apply to them.


Blogger M.A.Padmanabha Rao, PhD (AIIMS) said...


M. A. Padmanabha Rao,
Discovery of superluminal velocities of X-rays and Bharat Radiation challenging the validity of Einstein’s formula E= mc^2, IOSR Journal of Applied Physics (IOSR-JAP), .Volume 4, Issue 4 (Sep. - Oct. 2013), PP 08-14, DOI: 10.9790/4861-0440814

Einstein‟s formula can be made useful in proper understanding the physics of a neutrino. The mass of a neutrino has been approximated to be less than one-hundred-thousandth that of an electron [6]. Einstein‟s formula remains unchanged when mass m is simply divided with 100,000 and c2 is multiplied with 100,000 but leads to a better understanding of a fast moving neutrino. The rewritten formula holds the key that in the case of a neutrino, c2 rises by 100,000 times implying that c cannot be finite in Einstein‟s formula. Therefore, if c is replaced with variable velocity v, Einstein‟s formula still holds good in the case of a moving elementary particle such as neutrino. In such a case, neutrino travels nearly 316 times faster than an electron. In nutshell, by virtue of negligibly small mass, neutrino travels faster than electron, as well as X-ray and Bharat radiation photons, which go at superluminal velocities.

Friday, December 27, 2013 at 10:02:00 PM PST  

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