Here is what I promised for MINOS:
( — in general the energy-time uncertainty relation in particle detectors, in terms of speed-time uncertainties for any particle)
gamma and gamma(c) are NOT 1, but large numbers given by binomial factors.
( — a mistake that, I said previously, gamma=1)
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 find our 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 on energy.
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.
Below you will only have to remove a 2, that I mistakenly put in-front of h-cross. SO the minimum-error is 2.61 mm/second NOT 5.22 mm/second, and so on. BUT other ideas are correct, eg the idea that you have to fit the del(E).del(T) = 0.75 eV-nanosecond might actually be fitted to 0.375 eV-nanosecond. This is because while E, v, p, m, t are all equivalent, mathematically ( — that is as an additional constraint) E = p.p / 2.m = (1 / 2).m.v.v.
( — with a gamma nearly = 1) Do you SEE the 2 now? ( — or will it be further changed?)
Here is an additional note I would make to place a relevant concept as befits the above few lines. ( — wrote today: 26.11.2013) Whats meant by equivalent?
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.
Here those equations are E = p.p / 2.m = (1 / 2).m.v.v. Only such and such forms have been found to be correct and these additional constraints must be applied. Here is a popular mistake committed by the luminaries when they say eg Mass is equivalent to Energy. So in natural units they set them equal; E = m. So-far-so-good this is inconsistent if you are to remember E(squared) = P(squared) + m(squared) in natural units.
— a natural unit is again when c =1, so we set to write E, p, m all as electron-Volts, but in other units one has to be cautioned not to do that.
So when this 2nd equation comes about it reminds us the variable that E is, is NOT only equivalent to m but also equivalent to the variable p. E is therefore equivalent to m and E is equivalent to p. So Energy is not only equivalent to mass but also momentum. Its a catch-22 because in-case of photon you simply can’t say E = m or E = m.c(squared) because that would make all energy equal to zero. YES Photon always be a mass zero, it just does not have that property called mass. Its like Mr Ding just doesn’t know Tagalog or has never studied anthropology.
So a photon does not have guess what a rest-frame or a rest-mass etc. These are all spurious, dubious terms for Physics. One shall only go home with the idea that Photon; all it has is energy and momentum. Which makes photon’s invariant mass to be zero since momentum and energy are exactly equal, a case only when mass is exactly zero all the time.
( — invariant and single photon mass for all you puritans, a point which always explains why all confusion regarding photon can easily be dealt, eg why in medium photons are slower than say electron, because invariant mass of photon is no longer zero, it would explain everything else eg why photon bends under gravity because its invariant mass is no loner zero, a single photon would also bend but for the reason that it has got energy and momentum which have equivalent effect as that fof mass, but don’t say photon has an effective mass, thats hot-water, and perhaps wrong also. One could easily say according to Gravity Theory of Einstein not only mass interacts with mass through gravity but momentum and energy will be equivalently respond to or create gravity)
Given that; one shall always remember the 2nd equation E(squared) = P(squared) + m(squared) as a constraint. So we see immediately that once E = m = 0, (only mass-less particles) the 2nd equation known as Einstein’s relativistic equation or energy-mass-momentum relation gives: E = p. A fact you all know is associated with Photons. All of Photon’s energy ALWAYS comes from its momentum only as it does not have a property called mass, and thats the beginning of Quantum-Mechanics (or wave-particle duality) since its only waves that have momentum and energy but no mass. Voila. Photon bothered the scientists so much that it brings new kind of understanding. If you bother us we will figure you out.
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.
Note that we fit, so any fluctuation in time error reflects in fluctuation in energy error which is why distance becomes erroneous and distance/time = speed is erroneous by that given amount. Just an observation in this order (off the top of mail paper which is freely available in surplus) is sufficient to see that they can not claim superluminal attributes because it leads to the doubt that they may have to do everything more cautiously, when (in actuality) they will make more errors than their claims. This was to be thought-out prior to the performance of the experiment or at-least publication of results if not publicizing of what they have obtained, in mass media. **
** This is the reason why most people shout extraordinary claims require extraordinary evidence. But I think also, it is our responsibility in the name of diligence that we take our pen and paper even if we are countering a claim that we would like to prove bogus. I do not think OPERA did a bogus thing. Although they will later agree that they caused a great ripple around the world for which they might have come with a little more caution. For one thing I did plenty of work in the last 2 months and some of these works are paper quality works (although ArXiv rejected my work on OPERA-anomaly not only once but twice) and I hope will serve in the future for other studies whenever Relativity is concerned. I have already 1 paper that has been written and will be submitted soon. (actually submitted and accepted by many archives, 2 years ago, at the time of these analysis)
I doubt their anomaly will hold any claim since we do not measure energy to this accuracy unless a dedicated measurement is performed with this in mind. Their paper does not mention a single word on this or any error of energy. It just deals with errors on time. This is equivalent to saying the distances were measured to mm accuracy (the least epoch theory of Relativity allows in the vicinity of the surface of earth, so to say, the best one would do) but when the analysis was done it was not kept in mind that errors on distance and energy are correlated, hence allowing an energy error they have actually blown up the distance error in their analysis.
The GPS system is evidently fine as it is safe from how you use and interpret it. The details for non-superluminal claims are shown in the 3 pages I uploaded below. I will upload 1 more when that is ready, but that mainly would deal with MINOS situation, where they can use my analysis and perhaps come with a much more significant yet null excess result.
SO you can go and celebrate that Relativity has not been broken. Also all the money that was going to be spent for redoing all these experiments and all the textbooks that were going to be reviewed and rewritten has been made redundant.