Need to update the floowing article that, after cross checks: I did a small mistake in the above instead of 98.73 nano-meters I approximated it to 100 nano-meters but forgot what is sitting below is 0.3291 femto-sec. SO I used the OPERA time of flight of 71 nano-sec (maximal, from error in quadrature) and see that for this time of flight I obtain a causality violation of 21.3 meters in 71 nanoseconds which is exactly what speed of light is. That is, the causality violation of quantum mechanics is actually in favor of OPERA experiment instead of my earlier claim that we found a constraint. WE see no excess at all from the quantum mechanics causality violation constraints. Apology but don’t ask me how excited I was over the evening that Relativity was restored. Not yet.
Incidentally I spotted the error of mine because I did a smart thing, I tried to cross check the constraint with the electron rest-energy of 0.511 MeV and found a null result. That could never have been the case since it is million times heavier than the neutrino which in the first place was seeing such a constraint because it was billion x billion times heavier than the photon. I browsed through my jumbled up calculations pages, 4 or 5 in number and saw that instead of 98.73 I had made a 100 nano-secs. What if I had thrown these pages? I had to do some mind numbing calculations over and over again before I again saw light. But this time I actually saw neutrino. It is doing something astounding. I don’t want to comment more for now because my analysis gave a null excess over speed of light if indeed quantum mechanics could save Relativity that way.
GO FOR THE ANALYSIS BELOW BUT IT WAS ERRONEOUS FOR A SILLY MISTAKE OF MINE as mentioned above.
new constrainst (old theory); A 2 eV rest-energy neutrino at any energy have to cross photons of 10^-18 eV rest-energy by more than 10129 parts per million of speed of light {3.859/300 = 1.01286 %} to pose serious problems to Theory of Relativity. Such a paradigm may exist at around 100 GeV of energy {and 6-sigma confidently NOT at 17 GeV energy}.
The only formula used for this analysis is from the text-book below: (dx)^2 – (dt)^2 <= (h-cross/m-zero)^2.
Reference: Steven Weinberg, Gravitation and Cosmology, 1972, Wiley India edition, 2009 reprint, page 62, chapter 2, {Temporal Order and antiparticles}, last equation, unnumbered, [[purchased only last week, by a coincidential commuting]]
Physicist Matthew Strassler, Physicist freinds and friends and other people, all of you who have been keeping a close watch on the results of OPERA neutrino results, a very important news: Neutrinos are superluminous as per Relativity as per the OPERA experiment but Quantum Mechanics has come to rescue of Relativity. REF. above using the Weinberg’s text I have made the calculations and see that Quantum Mechanics allows an additional uncertainity over speed of light by 1.01286% percent, that is neutrinos of 2 eV mass or rest energy is allowed to violate causality at this speed barrier (3.03859 x10^8 m/s), if it goes above this limit in the future quantum mechanics cannot rescue Relativity.
At present the OPERA neutrino is breaking causality only at 0.0025 percent above speed of light. this is as I mention below, 2eV neutrino breaks causality to 100 nano-meters and for 0.3291 femto-sec which gives 1.01286% above speed of light. SO for such claims we may have to depend on 0.1 femoto-sec precision and at such precision if neutrinos of 2 eV rest-energy break causality more than 100 nano-meters in a 0.3291 femto-sec precision of time, Relativity will be in serious trouble. Note that we may need more than 0.1 fs time-precision for a confident claim and upto a 1 atto-sec precision does not take us more than 100 eV fuzziness in our energy calculations. OR with present time precision we may need 10129 ppm speed above speed of light at any energy which seems plausible/possible scene at around or above 10000 GeV = 10 TeV energy. (considering no additional energy loss scenario/channel is blocking such a paradigm, also my energy loss diagram will show a better estimate of needed energy since I just multiplied the order of magnitude here but my diagram is a good fit for available ppm excess from experiments)
You may consider the matter of OPERA controversy is rested for good for the time being. This is the power of simple and basic calculations of Physics. Again this was possible because I purchased the famous text book of Weinberg’s Gravity (General Relativity) and cosmology very recently, only a week ago and was browsing a little ahead than what I had already finished.
Ofcourse OPERA experiment may have to repeat it’s experiment at much larger energy and/or other experiments at atto-sec precision may be needed. But at present time precsion of OPERA it will not make the case at 17 GeV energy. This is also in line with my earlier energy loss calculations although things were not as clear. (you can see how the energy loss of photon was increasing really really fast at higher energy)
0.0025% of c is 750 km/s and 1.01286 % is 3859 km/s above speed of light.
The essence of the calculation: Quantum mechanics allows a photon to break it’s own causality, that is, a photon of rest energy 10^-18 eV can move a spacelike distance of 1.97×10^8 kms or it can move into a such a space-like distance for 658 seconds but a 2eV rest-energy neutrino can only move into a spacelike distance for a mere 100 nano-meters and this occurs only for 1/3rd of a femoto-second (0.3291 x 10^-15 sec).
{note that the self consistency of above is in line with zero rest energy of photon which gives a huge value for causality violation in terms of time, because if you use photons to prove their inconsistency in uphelding Lorentz invariance you will need to go above a breaking of 658 seconds if you are to use photons as a measurement parameter}
That is Neutrinos are allowed to break the photon-on-the-shell barrier for a 100 nano-meter or ~1/3rd of a femto-second. SO one needs time sensitivity of an attosecond (10^-18 sec) *preferably*, 1/10th of femto-sec will do, to throw Relativity into dustbin for ever. {If you are very strict about such a remark I am only saying in such a hypothetical scenario one need not use these old calculations any more but need a new-physics definitely) In this other scenario since 1/10th of a femto-sec allows necessarily an energy uncertainity of order of 1 eV only and 1 attosecond will restrict you to have a 100 eV only error, that is so small given that you know the photon mass of 10^-18 eV (already) and neutrino mass of 2 eV (you may need additional perfect* measurements) allowing yourself only 100 eV energy errors in your measurement. (which we do all the time in particle physics experiment, 100 eV errors in particle masses, check for mass errors on your favorite meson on PDG) WE can say for ever and confidently how exactly Relativity is valid in such a hypothetical Lorentz breaking.
But I have made the calculations using these causality breaking already known from quantum mechanics and this is saying clearly OPERA neutrino results are far below the allowed causality breaking. OPERA is breaking the causality by 0.0025% of speed of light but Quantum mechanics allows upto 1.01286% within speed of light. Such a causality breaking is available perhaps for energies of the order 10 TeV.
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