UPDATE; 10 Dec 2011:
There is an update to this analysis which will change the results, but is much more stringent on anomaly as reported by OPERA-experiment. So the following should be taken as a partial attempt. Check here for latest result: Bad news for OPERA.
update to this article: (No Superluminal Neutrinos)
EXCERPTS from last article:
” I reviewed and the gammas do not really turn out to be very large numbers, in fact to 20th power of beta gammas go to order of 5.002, in the right units everything fits in so well we will get a very exact number for minimum energy uncertainty in the order of eV, most likely ~4 eV.
So OPERA must come clean on total energy uncertainties below say 4 eV to claim superluminal neutrinos, at their quoted levels of uncertainty on time.
This is also in line with an article I wrote on 31/October/2011 .
In that article: citing Weinberg’s results from his text book, Weinberg’s results were for uncertainty on proper-time of neutrino in the same order we findour speed-uncertainty to be, which only means the 7.5 km/second quoted by OPERA-experiment will be washed away by as little as 4 eV uncertainty onenergy.
This is also most likely, and I seriously think IT IS, that MINOS-experiment does NOT see any speed excess consistent with their significance as they had kinematically and combinatorially factored-in their neutrino mass, to be in the order of ~50 MeV.
It is NOT the uncertainty-in-energy or uncertainty-in-time howsoever small or large they may be that is causing such excesses to be meaningful or meaningless. It is the uncertainty relations of energy-time, speed-time or (proper-time)-time that is in the order of h-cross, which is good enough to void or invalidate any claims of superluminal attributes neutrinos were thought to have. “
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.
My incorrect binomial factors had led to a 6% error on my earlier claim on minimum speed uncertainty, which was 1.98 km/second but now (stands corrected at) 2.21 km/second.