B Any good lay explanation of the Schrödinger cat duality?

[Nugatory]

Measurement and preparation both imply that uncertainty would change if we could prepare and measure. However, it is no more dependent on our ability to prepare than it is on our ability to measure. The point is that it is not possible to determine with exactness two conjugate variables at a single point in time. No matter how short the time is between the two determinations, assumptions have to be made about what has happened in the intervening interval.
The Born rule (sometimes called the Born Law - but Law it is not) is a matter of probabilities. It is possible, with sufficient information, to determine to a high degree of accuracy the probability of A and B having specific states. But this has nothing to do with determining a single particles position and momentum. Born's rule implies that so long as the standard deviation is other than zero, we have uncertainty.

Can you cite a source for this claim?

 

[Quandry]

Can you cite a source for this claim?

Not sure which of the claims you mean.
Para 1 - I am sure you know many sources for the claim, but it may be that there is something in the way I have expressed it that makes it uncertain.
ΔaΔp ≥ h/ 4π supports the claim but I have chosen not to express it in terms of particle wavelengths.

Para 2 - Once again, I know that you know more about Borns Rule that I do. My claim is that if you do only one measurement Born's rule does not apply, and if you do a statistically meaningful number of measurements resulting in an SD of zero uncertainty does not exist for the case.

 

[vanhees71]

Born's rule applies. It tells you the probability for the outcome of a measurement given the (pure or mixed) state of the system. A single measurement, of course, doesn't tell much about whether these probabilities are correct predictions of not. For that you need an ensemble to get "enough statistics". That's why I think that the minimal statistical interpretation is the only interpretation of QT which makes sense of the formalism as a physical theory. You may add philosophical twists to it (or even to the very "meaning" of probabilities), but in the lab to test a probabilistic prediction you need to repeat an experiment often, i.e., you have to use (large) ensembles.

 

[Quandry]

A single measurement, of course, doesn't tell much about whether these probabilities are correct predictions of not.

You're right of course. My statement was a course way of saying that without sufficient input Borns rule could not provide useful output.

 

[bhobba]

But the real problem - that of measurement in QM (which many will also say is a 'solved' problem - or not even a problem) - hasn't gone away - we've just shifted it about a bit.

Exactly.

Although beyond the level of this thread THE book that explains it is a standard text:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

For the OP start with Feynman:
https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

Once you have done that tell us how you went and we can make further suggestions.

Thanks
Bill