I will have to disagree here. My Bible is the Ballentine text book. In
this book it explains in detail, that HUP isn't even about simultaneous
measurements at all.
"Quantum Mechanics, A Modern Development" ISBN981-02-4105-4 - Leslie E.
Ballentine,
Well, Ballentine does have a perspective. Excellent book, though, I suspect.
I think this whole thing may be leading us right into the EPR/Bohr debates,
Bohm's early thinking on what then led to Bell's inequality, John Clauser's
non-definitive experiments to test Bell's at Berkeley, later Aspect's much more
conclusive work, and perhaps leading to the re-unearthing of the many-worlds
viewpoint.
It's my understanding that whether you choose to give up on locality, or the
reality principle, or choose 'many world's as your forte', it's all the same
thing -- 1:1 correspondences, regardless of the insight you choose. The
mathematics may be easier for one problem or other, one choice versus another,
but there is nothing yet to distinguish their predictions. Wheeler may lead you
one way, Everett another, but so far as I'm aware none wins over the other.
More specifically, position and momentum are fundamentally incompatible
observables, in the sense that they do not share a complete orthogonal set of
eigenvectors and therefore cannot be simultaneously measured. If you measure
one, the system goes into some eigenstate. Then measure another, that into yet
another eigenstate. But since they __do not__ commute (observables X and Y have
such a complete set of orthogonal eigenvectors if and only if they commute),
they are fundamentally incompatible and cannot be measured simultaneously. So
what is the meaning, then, of making measurements arbitrarily small? It simply
cannot be done.
That was the question I'd been responding to, when I talked about the viewpoint
of these kinds of dynamic attributes, which are just two faces or facets of some
higher dimensioned volume.
The inequality I mentioned resides at the heart of a debate over interpretation
about the condition of a particle *before* measurement. But there is no way to
measure both position and momentum simultaneously, as they do not commute. One
could say it's a meaningless question and then just rely on the statistical
interpretation. One could suggest that there is a deeper, reality position that
implies more (a path I like to take, at times.) So I think this leads to
cross-purposes types of answers -- and perhaps that is my fault alone. I can't
say, for sure.
Been interesting,
Jon