# Quantum Interpretational Philosophy

1. Nov 17, 2005

### kleinwolf

From the Copenhagen Interpretation we learned that the measurement disturbs the syste m in a "fuzzy" way : System=X..Measurement op.=A...End state=Y Y=Eig(A), prob(Y)=|Proj(X,Y)|^2.
Hence after the measurement, the system is Y...
But in my mind, the opposite way is even clearer : The system disturbs the measurement operator...It is even more indicating what a measurement process is : e.g. you put a thermometer, and the thermometer state (operator configuration some kind of, still unknown in QM)..changes...
To recover usual spin QM, let's see this phenomenon in "classical" QM :
the correlation of two observation in A and B is given by the defintion :
$$C(A,B)=<A\otimes B>-<A\otimes\mathbb{I}><\mathbb{I}\otimes B>$$
Then it is clear that the non-averaged operator (we remember : $$<A>=<\Psi|A|\Psi>$$ is then by omitting the $$\textrm{\emph{exterior}}$$ average :
$$K(A,B)=A\otimes B-(A\otimes\mathbb{I})\underbrace{|\Psi\rangle\langle\Psi|}_ {nlin-link}(\mathbb{I}\otimes B)$$
It's clear that this operator K contains a linear term and a non-linear one. THis means that the measurement operator depends on the system it measures...

Does this make any sense ? (There is always a sense, but most of the time the one we wouldn't like, or the one we don't understand).

Last edited: Nov 18, 2005