Nuclear and particle physics through Scilab.
Heisenberg Relations
New forms of Uncertainty Relationships in Quantum Mechanics.
ΔE.Δt ~ h
Δp.Δx ~ h
ΔL.Δθ ~ h
* Shouldn’t the constant above be ℏ/2 ? Let us first clear up some air of confusion.
The above relations are kind of vague even though look like canonically powerful ways to represent the formal concepts of the Heisenberg Uncertainty relationships. I have myself confused with these at times … with the added degree of confusion coming from h or h-cross?
But there is nothing to be ashamed of, if one makes such mistakes.
Does ℏ/2 come due to normalization of wave function or discrepancy in definition? eg do they come because variance (ΔE, Δx) and standard deviation (σx , σH ).
Energy-time uncertainty is a distance-time and speed-time uncertainty.
OPERA sees 7.5 km/s fallout which goes above photon-speed. This will be consistent with Relativity if they incurred a larger error on their energy while at the same time keeping their time uncertainty between 1 to 10 nanosecs. SO they need to show us their energy distribution with uncertainties …
The time-energy uncertainty relation.
The time-energy uncertainty 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 we are ourselves making something silly or not.
I have described in two recent articles — will link later, why.
1. One must be careful what energy and what time one is relating to, one just does not take any time and any energy and make a relation, in-fact one can see who is a good physicist from one who is a novice, by seeing 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 Einstein 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 or uncertainties”.
2. Life-times are arbitrary variables as are energies, 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 in 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.
