Schrodinger Equation; Concepts and Problems in Quantum Mechanics. Reply

A long and technical discourse on Quantum Wave Function.

A 64 slide presentation styled discourse on the Quantum Wave Function. It consists of detailed solution of 5 important and interesting problems, apart from a threadbare discussion of the concepts.

Does Quantum Mechanics Apply to our life’s tiniest moorings? Reply

The correspondence Principle. This guy which gets talked a lot has a simpler form at times. Again this principle is a specific or corollary of O = A*B with the understanding that even if one of the variable say A can be insignificant it still depends on the sequence of other variables which decides how significant the total outcome would be. Therefore given that B can be significant enough to over ride A’s insignificance the outcome O can be significant. In other words an event might correspond from a scale of insignificance to a scale of significance. Often a scale of insignificance can be the micro or nano scale and the scale of significance is reached because it is not insignificant. So there is a bridge between two scales, one of insignificance and one of significance. One of micro and one that is not micro but lies close. In all totality this is the reason why Quantum Mechanical effects can be carried to the Classical scale and this is known as correspondence Principle. More…

The time-energy uncertainty relation … 4

Updated this diagram on 28-02-2012


This article **and one more I posted before this** is the answer why OPERA was capable to measure the neutrinos pacing beyond the photons. The answer is Quantum Mechanical energy-time uncertainty principle, present errors/uncertainties on neutrino mass even allow in prinicple a time measurement to the precision of 10^ -22 seconds, OPERA did just 10^ -9 seconds. Nature says **I am quoting, attention please**: “the limits I have imposed on theory and experiments by human beings is good enough for them to track down the photon, and anything else by using neutrinos, to the 10^22 th of a second. ”

The time-energy uncertainity relation is a blessing in disguise which comes in handy to check various values that are quoted so as to see if something is inconsistent or not. It’s very powerful in guiding to check if you are yourself making something silly or not.

I have described in two articles (on recent, link will later) why

1. one must be careful what energy and what time one is relating to, you just do not take any time an any energy and make a relation, in-fact you cn see who is a good physicist from one who is a novice by seeng how this relation is used by him. This was joked by Landau: I can measure the energy and then look at my watch, time is just a parameter. But Eisntein and Niels Bohr argued during a very short time interval one must be careful what energy is allowed and what is not, there is a constraint on the windows of errors/uncertainties

2. life-times are arbitrary variables as are energy, their means are not necessarily linked inversely as in case of the uncertainty relation itself, the latter gives a relation between the error-window which are linked inversely. SO watch out how much inconsistent description is given in an average article eg in wikipedia and even our text-books. These are training the future physicists very wrongly. One needs experience of solving good problems, one is to work in experiments of highest standard and understand them. Then this practice makes the case easy for you. Feynman said “it is safe to say no one understands quantum mechanics” I say ” … that + practice makes it easy to have a better control over inconsistency we make in applying quantum mechanics, problem and only problem, solving them, can give you the feel for what is being talked about” SO have a good training in quantum mechanics (course-work in undergrad, grad school) solve real-life problems and learn from good sources.

Why is no one telling you photon can’t have a zero mass as per quantum mechanical uncertainty principle? Possibly no one thought (well those who are competitive physicists, in some way or other they know this, they may not think explicitly, taht is why I am mentioning)

Photon really can’t have an absolute zero mass but an extremely small mass is allowed so as to allow a corresponding error on time. eg I wrote one article yesterday where photon mass is experimentally found to be between 10^(-27) eV to 10^(-7) eV. Now if you take that to be the width on mass/energy it is essentially 10^(-7) because the other factor is zero compared to this.

SO delE x delT >= h (4.136 x 10 ^ -15 eV.s)
delE = 10^(-7) eV, this gives a delT of 0.4136 nano-seconds. In other-words this is not the life time of the photon but it is saying photon at-least lives for this time if we are to measure it’s energy of 10^(-7) eV, **0.4136 nano-seconds or more, and we quote an infinitely large number for it’s actual life-time which is a mean, this is infered from a detailed measurement, here I am positing on the basic idea**.

Since we have that capability of time precision we have been able to measure photon mass to much smaller limits. **present best value of photon mass is 10 ^ -18 eV, hence we alllow corresponding large error on time, this is what I had described in the article: why scientists think photon is massless ?, the GHz frequency measurement of photon mass entailed a large error on photon mass of 10^-7 eV, note that GHz is inverse of a nano-second. ha ha ha**

Now the OPERA neutrino measured a nano-second time, hence it actually allowed a 10^-7 eV energy-uncertainty. that is this measurement of OPERA with the inherent methods of the experiment could not have dealt with a situation if the neutrinos were to have an energy-uncertainty less than 10^-7 eV. That would have meant a better time measurement than nano-second. **In actuality they possibly had a better time resolution, but given that neutrino mixing meant a far worse energy-uncertainty the time need not have been more accurate to make a precise and accurate experiment, the good statistics made the experiment a discovery and the good control over the systematics made it a robust and valid measurement. The other issues of anomaly or not and everything is free from errors or not will be performed again, by them or by others and it is needed**

But it is clear that an error as much as a MeV in the neutrino mass makes the measurement sensitive to a time of 10,000th of an attosecond (10^-22s) in theory. How precise clocks you have and how much dispersion of time resolution occurs in your experimental set-up is a problem of technology and research but nature is kind to far below attosecond level even with MeV errors on rest-mass of the particle. The good point of OPERA as is not understood by me in the beginning and now I see I have friends in the blogo-sphere who are affectedby such a syndrome is: it is just a speed measurement, hence make a baseline, let the two participants run along the baseline and measure your time to a desired level of accuracy by allowing yourself a desired level of uncertainty on the energy. Once the speed has been measured we have proved our point beyond any doubt and uncertainty. As is cusomary the next thing in line is “anomaly”. The anomaly has to be addressed by various new techniques of the measurement or external independent experiments. But this is a very clever measurement an example of how experiments are carried out in the best traditions of scientific practice.