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The actual energy errors OPERA team is making

December 3, 2011

Mohan, mdashf

The actual energy errors OPERA team is making: 3.4062 x 10 (-2) eV,

OPERA has to show their energy uncertainty distribution, they need it below: 3.4062 x 10 (-2) eV if they are to make a claim on superlumial neutrinos, showing just the time uncertainty of 10 ns would not do, since Uncertainty reln is an inequality and higher energy errors could give you a higher distance error at the same time error.

QM >= 6.582×10^-7 eV for 1-nanosec time accuracy,{OPERA ideal}

QM >= 6.582×10^-8 eV for 10-nanosec time accuracy,{OPERA syst. and stat.}

QM >= 6.582×10^-9 eV for 100-nanosec time accuracy {irrelevant}

You can see that the time accuracy is really not playing a role here: perhaps I need to factor in the distance inaccuracy first to see something more interesting as I described in my preciding article. But why is the experiment making a larger error than the uncertainity relation minimum given above? what are the experimental factors? Is it only distance error? I will try to excavate more.

I did a laborious calculation that tells me the OPERA excess you see of del_beta=0.000025 {25 ppm they say, I find 7.5 km/s excess, remember beta~1, ultra-ultra-relativistic} corresponds to a 3.4062 x 10^-2 eV energy uncertainity {using beta to 10th order} Quantum Mechanics uncertainity with 10 nanosec error makes you make energy inaccurate to 6.582 x 10^-8 eV, 1 nanosec >> 6.582×10^-7 eV. {100 nanosec would make this 6.582 x 10^-9 eV, so time error does not really make the situation difficult except we need to see 60 nanosec excess which has a meaning if we keep time-error to say 10 nanosec} The only catch is the beta’s to the 10th order is achived from binomial expansion, which forces 0<=beta<=1, so going a little above beta=1, how harmful is it? we went 25 ppm above which should be fine for the binomial convergence? Then this analysis says you are safe from quantum mechanics yet you are disobeying Relativity. SO relativity might have to give up on a sharp c=1 idea or it has to allow itself to be modified, in case even OPERA turns out to be incorrect, theoretically we see how Qmech and Relativity are not completely consistent with each other. {anyway you are even if you do not use beta you can see it just from uncertainity relation, I am just the first person outside OPERA team who computed  exactly how much error you are making on energy given you see 7.5 km/s excess.}

If you read my last article, I did not yet find exactly how aberration could explain this if it does. But given the fact that there is quantum mechanics we may not have to.

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