On 7/07/2017 10:40 am, Russell Standish wrote:
On Thu, Jul 06, 2017 at 10:22:40PM +1000, Bruce Kellett wrote:
No, position and momentum are dual in the sense I defined. The
observables are not compatible -- position and momentum are not
simultaneously observable.
I know what you mean by "dual", although the conventional term is
"complementary".
Yes, I was avoiding that term because it is sometimes controversial. But
complementarity is a feature of conjugate variables.
Observing S=X+P does not imply simultaneously observing X and P.
As far as I can see, it does. It is not just something you construct by
measuring X then P (or vice versa). X and P are operators in different
spaces, related by a Fourier transform. Unless you mean measuring the
conjugate variables on different members of an ensemble of identically
prepared states?
Prove that I can't observe S, or provide a reference to someone doing
so. It appears rather crucial to your critique.
Again, I do not accept the reversal of the burden of proof. X and P are
conjugate variables so they are not simultaneously measurable.
On your last point, this is not crucial to my critique of your theory.
Well, not unless you are going to rely on this in your proof of
linearity. But as I pointed out a while ago, additivity of operators
does not imply that the state is a vector in a linear space.
Bruce
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