Quantum Interpretational Philosophy

[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).

 

[AndyW]

I can understand your perspective on the measurement process and how it relates to the Copenhagen Interpretation. However, I believe it is important to remember that there are multiple interpretations of quantum mechanics and each one offers a different perspective on the measurement process.

The Copenhagen Interpretation does suggest that the measurement disturbs the system in a "fuzzy" way, as you mentioned. This is because the act of measurement causes the system to collapse into one of its possible eigenstates, resulting in a probabilistic outcome. However, this interpretation does not necessarily imply that the system is the one causing the disturbance.

On the other hand, your perspective of the system disturbing the measurement operator is also valid. It highlights the idea that the measurement process is not a one-way street, but rather a complex interaction between the system and the measuring device. This can be seen in experiments such as the double-slit experiment, where the act of measurement can actually alter the behavior of the system.

In terms of your example using the correlation of two observations in classical QM, it is important to note that this is a simplified version and may not fully capture the complexity of quantum measurements. As you mentioned, the non-averaged operator K contains both linear and non-linear terms, which shows that the measurement operator does depend on the system being measured. However, in quantum mechanics, the measurement process is not fully understood and is still an area of active research.

In conclusion, your perspective on the measurement process is valid and adds to the ongoing discussion and exploration of quantum mechanics. As scientists, it is important for us to continue to question and explore different interpretations and perspectives in order to deepen our understanding of the quantum world.