In this paper we bring out a remarkable consistency of theory of Relativity in explaining the anomalous excess of speed of neutrinos observed in the recent baseline experiment of OPERA. The OPERA experiment is performed by shooting neutrinos produced from protons at SPS, CERN to the laboratory at Gran-Sasso where OPERA has placed its neutrino brick detectors. We believe that we have found the reason why this result was misinterpreted to claim superluminal neutrinos..

# OPERA

## 3 anomalies in 3 weeks.

This article tries to put on record exactly why OPERA neutrino anomaly, FLYBY of Galileo anomaly and PIONEER anomalies are not at-all anomalies, based upon my research from late 2011. On 25.11.2013 I sat for couple hours and reviewed the article written from 2011 and added contents. Since I am reading after couple of years I reminded myself exactly why these are not anomalies: and here is why.

Anomaly from OPERA experiment involving neutrino base line:

The mass of elementary particles is equivalent to a proper-time and in another way to the Compton-wavelength. Compton wavelength is defined as $latex \lambda_{Compton} = \frac{h}{mc}&bg=ffcccc&fg=cc00ff&s=1$ where c is the speed-of-light in appropriate units, m is the mass of a given particle, note that h is the Planck’s constant, not the reduced Planck’s constant, usually found in quantum mechanical treatments.

So in case of the OPERA experiment, the neutrino howsoever it challenged the physical validity of the sanctity of proper-time of photon — that proper time of photon is always zero and minimum among all elementary particles, because its a tiny little smurf with hardly any-mass, it could not run faster, because it has mass.

Again the energy uncertainties of the experimental detector would equivalently add mass to the neutrino, a fact completely over-looked by OPERA experiment collaboration.

Photon proper-time is defined to be least, because its mass is zero, hence neutrino must always take more time than photon, for traversing the same distance, but OPERA claimed otherwise. All in all Relativity + Quantum Mechanics restores the anomaly to its nemesis.

Anomaly from FLYBY of Galileo and PIONEER satellites:

For an explanation of the anomalies while equivalence or relativity of mass, momentum, energy, wavelength etc are not needed here, whats simply needed is mass. This mass is a Newtonian concept but rather refined by Einstein’s theory known as Theory of Relativity which branches into two aspects 1. special theory and 2. general theory.

## OPERA anomaly might be out for good.

Quantum mechanics is such a powerful tool it makes all powers fools. You do not have to measure the distance of the CERN – Gran Sasso distance to mm accuracy. This is already measured and inherent in the data-analysis of OPERA. Being an experimental particle physicist I know exactly where.

It is inherent in the 4-vectors they add when they reconstruct these neutrinos from protons and muons or whatever. I know why MINOS didn’t see superluminal neutrinos but OPERA did. MINOS depended on their 4-vectors to set the neutrino mass, which gave them a staggering staggering error of 50 million eVs.

OPERA said we go by the PDG 2 eV upper limit. So they reduced the energy uncertainty on neutrino mass to zero. If they factor in the other energy uncertainty and it turns out that this error is actually smaller than ~0.01 eV, they have found something that will become a PIA for scientists for a good deal of time.

If they make errors larger than this, say even 0.1 eV which still makes the neutrino mass of 2 eV correct but not the inherent kinematic neutrino mass below this level. In this later case we have solved the OPERA neutrino paradox.

My last article gives the mathematical formula that I worked out just this evening which can test OPERA anomaly for it’s worth. Have a good day. Just give me the energy error you have in your neutrino mass or any where. Need be less than 0.01 eV if you still think OPERA is correct. I doubt it.