Sunday, 9 October 2011

Faster than light neutrinos, A possible solution

I've been a few weeks late to comment on CERN's OPERA experiment's paradigm breaking result, that neutrinos travel faster than light (nature), (orignal paper). Initial skeptism has not lead to any resolution of the result via mis-measurement. The excess is in speed measured is small, three thousandth of a percent, the muon neutrinos, crossing the 732 kilometers from the CERN lab where there created to the OPERA neutrino detector in Italy, some 60 nanoseconds earlier than the light would have done. OPERA quote a 6 sigma statistical significance and the results do match with earlier measurement at the MINOS experement at Fermilab. The quoted speed at OPERA is (v − c)/c = [+2.48 ± 0.28(stat) ± 0.3(syst)] × 10−5.

Standard Special Relativity does allow for particles that travel faster than light, know as tachyons, they obey the standard equations of relativity except they have negative squared mass, another words imaginary mass in the sense of complex numbers. Allowing Tachyons however cause quantum field theory to be unstable, describing a vacuum that would decay. More over the OPERA results do not fit standard tachyons, the tachyon mass of the neutrino would be i*120MeV in gross contrast to the measured neutrino mass, and also tachyons travel slower with increasing energy, nearer the speed of light from above at infinite energy, and traveling infinity fast when the have zero energy. OPERA in fact notice a constant speed for neutrinos across a doubling of energy from 17 to 35 Gev. While vacuum stability might be saved by the handedness (chirality) of neutrinos, empty space emitting a back to back pair of an neutrino and an anti-neutrino would violate spin conservation by one unit, due to the neutrino being left handed while the anti-neutrino is right handed. Thus a field theory of tachyonic chiral neutrino might be stable while it would be unstable for normal particles. However such a theory still would not fit the OPERA results.

Moreover neutrinos in empty space do not apear to be superluminal. When the supernova SN1987A exploded in the large Magellanic could the neutrinos where detect to arrive some 3 hours before the light. This might seem superluminally however the light is delayed by traveling though the stars core. If the neutrinos traveled at the OPERA speed, they would have arrived some 4.5 years earlier.

In order to achieve a resolution of the OPERA result compatible with both quantum field theory and the light speed measurement of the supernova neutrinos. It is necessary to find a theory where the speed of propagation of neutrinos is faster than light only in the presence of a matter field. In fact quantum field theory can vary the speed of light depending on the energy density of the QED vacuum, a result found in 1994 by Latorre, Pascual and Tarrach. Given a vacuum energy density of ρ. The speed of light is modified to.

$$ v = 1 - {44/135} α^2 {ρ/m_e^4} $$

In unit where c=hbar =1.

In keeping with our axial force, the same formula should carry over to the speed of axi-photons and the maximum speed of neutrinos (approached as the neutrino speed became very much greater than there rest mass time c squared). The electron mass in the formula would replaced with the mass of the lightest neutrino, and alpha with the axial coupling constant, which we predicted was some 60 times smaller the than alpha in QED.

$$ α_ν =~ {1/137} * {1/60} =~ 0.121*10^{-4}$$

The mass of the lightness neutrino is unknown, but we estimated to be 0.14 milli-electron volts in order to produced dark energy. This would lead to a negative energy density of

$$ ρ = -2*10^{-12} (eV)^4 = -2 (meV)^4 $$

Interestingly this is in the same region as the observed figure of dark energy density in cosmology about 3 (meV)^4, however dark energy is still a positive energy density, only the pressure need be negative, representing a self attracting fluid. The standard speed of supernova neutrinos further would imply that the these is no dark energy in the local region of our galaxy, stellar radiation must blow the region clear of any dark energy. Since no expansion of trapped galactic cluster is observed this is very compatible with cosmology.

In ordinary situations the QED and QAD vacuum energy would be both zero for empty space, and for matter depend quite separately upon the electron density and columb potential and the neutrino density and axial potential. We have already shown that ordinary matter would contain a background sea of neutrinos necessary to cancel the axial charges of the nuclei of atoms, and this background sea would be bound to nuclei with some energy density. From the above we have
around 1 nano eV per cubic nanometer. A binding energy this small, requires a light bosonic particle carrying the axial force, with an rest mass not much larger than the neutrino.

In our paper we have shown that, Neutrino scattering on the the background sea, is strongly suppressed at high energies, falling as $(m_v/E)^2$. The neutrino speed would approach approach the modified speed as $1-(m_v/E)^2$, Thus in the earth between CERN and OPERA, the measured speed would be the modified speed of axi-photons, given the axial binding energy density. An experiment demonstrating the axial force nature of the superluminal speed of neutrino could be produced, by vary the composition of material the neutrinos travel through. The excess speed would vary as bind energy density, which would vary as the atomic number density of the matter passed.

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