Re:Atomic Spins Evade Heisenberg Uncertainty Principle
by pif on Monday April 03, 2017 @08:30AM
(#14022262)
It's not "imagining the measurements".
The UP is not only: "You can't know position and momentum together." It rather: "Position and measurement _cannot be defined_ together."
In classical mechanics, you can imagine a particle being at a certain position with a certain momentum. In quantum mechanics, you cannot.
Uncertainty Principle refers to the arbitrary precision of two operators. You can measure each operator individually to arbitrary precision. In theory, that is.
If the two operators commute you can get theoretical arbitrary precision on both measurements together. Since their commutator is zero.
If they don't commute, the product of standard deviations of each measurement operator is restricted to no less than half the expectation value of their commutator. (photon-torpedo's comment at the top of this thread gives a better summary).