I thought that most members here would be interested in the following facts I've learned while studying the Heisenberg Uncertainty Principle (HUP) which relates the uncertainty between two non-commuting observables, A and B. The general uncertainty principle is expressed as

[tex]\Delta A \Delta B \geq \frac{1}{2}|<\Psi|[A, B]|\Psi>|[/tex]

There are two versions of the HUP:

Version #1: In this version the HUP states that if A and B don't commute, i.e. [A,B] is not zero, then A and B cannot be measured simultaneously in a single measurement, i.e. it applies to single events. In this version uncertainty, [tex]\Delta A[/tex] is defined as the error in the measurement. Some call this the "individual uncertainty principle" (IUP).

Version #2: In this version the HUP states that if A and B don't commute, i.e. [A,B] is not zero, then A and B cannot be measured simultaneously in a single measurement since it applies to a large number of identically prepared systems and measurements. In this version uncertainty, [tex]\Delta A[/tex] is defined as the standard deviation of all of those measurements. In this version both A and B can be measured to arbitrary accuracy and the HUP does

*not* forbid simultaneous measurements.

For more on this please see:

http://statintquant.net/siq/siqse2.htmlStanford has a nice accounting of the uncertainty principle. See

http://plato.stanford.edu/entries/qt-uncertainty/I'd love some input as to what the folks here who are actually skilled in QM give me some feedback on this. That includes ALL of my friends.