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.

## UPDATE TO: OPERA has lost it’s claim of superluminal neutrino.

A stringent constraint on OPERA speed-excess:

Planck’s constant = 6.6 10^(-7) eV-nanosecond;

A neutrino mass of 2 eV has to be measured to better than 1.15 eV to see any superluminal excess.

— After I fixed mistakes in my binomial-expansion.

At or above this error you see (7.5 + >= 7.5 ) km/second, you can see that this is basic energy-time uncertainty relation. Nothing more. Neutrinos are really not fairy tale.

Method: uncertainty = 1.15 eV x 10 nanosecond x 3,00,000 km/second = 7.5 km/second, minimum you must, is 2.1 km/second corresponding to 0.312 eV, so this does not rule out superluminal neutrinos, you just need to be between (0.312 – 1.15) eV in the OPERA set-up. If you have a 10 MeV total error somewhere, you have to convince the world, that, this is NOT affecting neutrino mass more than 1.15 eV.

## I claim that, OPERA has lost; it’s claim of superluminal neutrino.

My finding was thus, as you see in the equation described in the above analysis (image), if OPERA finds it’s neutrino with energy-error in the order of 1 eV such that its time-error is in the order of 1 nanosecond it will see speed excess (or anomaly) in the order of 7.5 km/second consistent with theory of Relativity and Quantum Mechanics taken together.

In other words OPERA-experiment must fit energy-time uncertainty relation del(E).del(T) = a.h-cross and if it gets a = 0.75 eV-nanosecond, it’s claim of superluminal neutrinos vanish ideally. For a 1 nanosecond time accuracy this means 0.75 eV energy accuracy. All they need to do is see if they have this accuracy in energy, in their experimental detector.

And new INSIGHTS (26.11.2013)

And whats use of saying additional constraint? Theory of Relativity or Einstein’s work centers about whats called the equivalence principle. Here is what its all about. When a contribution to variable A comes from B, C, D, E …, F and so on, we say A is equivalent to all those variables. But it would be mathematically inconsistent to replace the equivalence with a sign of equality. Because only a part of eg B comes into A and we need to know what part, exactly. Or else we would be mathematically inconsistent and therefore Physics: Laws of nature will be wrong or rather incorrect.

The laws of nature or laws of Physics are nothing but a mathematical statement of the constraints on a Physical system. So once we know what exact part of A is contributed by say B, we say (this part of ) A comes exclusively from B. So its only partly A that comes exclusively from B and that part is equal to B with addition of Physics Unit-and-Dimension scheme.

Similarly A is contributed exclusively by C, D and so on. If you add Quantum Mechanics here that would mean there has to be a finite or infinite set of variable that only contribute to the variable A. So whats equivalent is a Physical Attribute that a particular variable contributes to another. But whats equal is a mathematical constraint or equation and when its available for a Physical System we say its a Law of Nature.

## 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.