How precise is quantum mechanics? In one of my recent calculation of causality violation allowed by quantum mechanics onto Theory of Relativity which only depends on the rest-mass of the participating particle I made a very interesting error. This constraint by quantum mechanics allows a staggering 658 seconds of space-like violation in it’s own causality. This is in line with it’s tiny mass of 10^-18 eV. But a neutrino which is billionxbillion times heavier than the photon comes out to be a mere 0.3291 femto-second or a 98.73 nano-meters only consistent with speed of light and assuming that speed for the neutrino. In other words since neutrino is the next lightest particle after photon (am I correct?) any other heavier particle (next lightest is electron?) will have a far smaller causality violation from present theory.
I approximated the 98.73 nano-meters to a 100 nano-meters. Now we have the related variable of time of .3291 femto-sec is in sight. If we are not to have this variable in sight we would happily go about adjusting our 98.73 nano-meters to a 100 and claim plenty of physics. That is one of the warnings of quantum mechanics, it not only tells us it corresponds to classical mechanics hence it’s laws dictate the phenomena on a large scale but it says these large effects come from very small values. We only need to be very consistent when we are doing such small calculations as prescribed by quantum mechanics to see that what we are seeing on the classical scale is real.
SO my small adjustment which would sound very appropriate to how we teach physics at the elementary level to students many of whom may not be as careful to imbibe a great deal of caution at their formative ages of learning physics is simply to be avoided by having a lot of heuristic skills. (I have a story to recount how somebody had made a fabulous mistake with doppler’s effect, he was an undergrad at Tech)
In result of my erroneous adjustment I did not catch this as soon as I did this. I get a staggering ~3800 km/s of causality violation permitted from theory of quantum mechanics towards the speed of light. That would have immediately washed away any element of surprise from the results of OPERA neutrino publicized a month ago. Has anything else in the recent times has caused as much consternation in the Physics community? Someone knowledgeable please write one article. Irrespective of the correctness of teh OPERA anomaly or result as you will, this was only erroneous on my part.
As soon as I fixed my 100 nano-meters to the correct value of 98.73 nano-meters I see null-amount of causality violation in teh speed of light by neutrino as permitted by quantum mechanics. That is simultaneously, any excess coming from OPERA neutrinos if correct, it perplexes all we know so far, Relativity as well as quantum mechanics. If OPERA result is to be correct one is seeing an experiment that is consistent with Relativity and Quantum Mechanics hence this result is a new physics whose implication will alter Physics for ever hopefully in a way a new theory does to an old theory.
If not correct we will learn a great deal (where and how we make error in the state of the art scientific experiments which bases it’s methods on all that we know so far in essence) It will save the grace of a lot of people that have made counter claims to this experiment, but as scientists this does not augur well for the culture of science since it means most people are not willing to take their pen and paper and make a calculation but prefer the saving dictums of established knowledge a kind of dogmatic response towards science.
(I know many people have crossed their fingers and I also know those who are making boisterous cliams reg. the validity of photon-theory etc are not to be taken as any malicious practice in the contrary of their claim being true, because it is only spontaneous, but I have tried to take my pen and paper and worked through last month in trying to see what it is that we may be missing. Mind it I am not at all trying to prove correctness of OPERA, rather jumped with elation when my yesterday’s mistake landed me to see present theory explaining away the OPERA claim as something that we just overlooked from basic theory. But it hasn’t been as easy so far.)
But the lesson of quantum mechanics is as big a violation of 3800 km/s concerning the modern scenes of Physics must in itself be consistent with as small a precision of 1.27 nano-meters only.Quantum mechanics relates the small to the big as long as there is a correspondence in the process itself. The precision of quantum mechanics therefore is as important to large scale physics as it is to the small.
In my vociferous ways I have also pointed out that this does not mean what OPERA is doing is an eyewash or a hogwash or a plain silly thing. In my opinions it is a brilliant experiment. As long as we are not correctly capable of dispelling the fear that this experiment is posing towards us we must gracefully accept as difficult this experiment is proving by the next day and depending on how long it takes to find it made a mistake somewhere, it will be a sign of how meticulous this experiment might have been itself rather than the traditional dogmatic contrary claims.
Many have grown to believe there might be political angles to it (like they claimed when there was an unexplainable bump found on Higgs energy sector, that may wash away, but it does not make us very smart, because if we are, we would really pinpoint what is the error) It is our responsibility as learned men and as capable physicists to find out the true sources of error if we are to have a competitive interest on it’s merits affecting the future of science.