I Find a calculation of Schrödinger's cat experiment?

[vanhees71]

True, but you cannot treat the Geiger counter by solving the Schrödinger wave equation exactly for its $10^{30}$ (or so) constituents, and it is indeed completely sufficient to treat the relevant physics of the Geiger counter in terms of classical physics. It's misleading to write $|\text{decay measured} \rangle$ since the observation that a decay has been registered is not a microscopic but a macrscopic observable. Here lies the key for the understanding that there is no measurement problem, and this was emphasized already by Bohr in the early days of QT.

To understand theoretically, why the classical description of the macroscopic observables of macroscopic systems is a valid approximation of QT, you need quantum statistics or "many-body theory". That's all I'm saying.

 

[Lord Jestocost]

True, but you cannot treat the Geiger counter by solving the Schrödinger wave equation exactly for its $10^{30}$ (or so) constituents, and it is indeed completely sufficient to treat the relevant physics of the Geiger counter in terms of classical physics. It's misleading to write $|\text{decay measured} \rangle$ since the observation that a decay has been registered is not a microscopic but a macrscopic observable. Here lies the key for the understanding that there is no measurement problem, and this was emphasized already by Bohr in the early days of QT.

To understand theoretically, why the classical description of the macroscopic observables of macroscopic systems is a valid approximation of QT, you need quantum statistics or "many-body theory". That's all I'm saying.

There lies no key for the understanding that there is no measurement problem. You are simply making an artificially cut between – whatever you call it – “microscopic” and “macroscopic” observables - quietly and secretly assuming that somewhere a "collapse" or "reduction" occurs.

To say it in terms by Landau and Lifshitz: “Thus quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case, yet at the same time it requires this limiting case for its own formulation.”

 

[vanhees71]

Well, LL is right with that, but I don't consider this as a problem, because QT contains classical mechanics as a limiting case. So there is no contradiction between classical and quantum theory, where the classical approximation is valid. Of course, there is no fundamental "cut". QT is more comprehensive than classical theory, and the better our preparation procedures become, thanks to technological progress, the larger systems can be shown to behave according to QT, e.g., there have been double-slit interference demonstrations by Zeilinger's group for fullerene molecules and as well the demonstration that already a pretty small temperature is enough to destroy the quantum interference due to decoherence because of the emission of just a few thermal photons.

 

[Joe Cool]

True, but you cannot treat the Geiger counter by solving the Schrödinger wave equation exactly for its $10^{30}$ (or so) constituents, and it is indeed completely sufficient to treat the relevant physics of the Geiger counter in terms of classical physics. It's misleading to write $|\text{decay measured} \rangle$ since the observation that a decay has been registered is not a microscopic but a macrscopic observable. Here lies the key for the understanding that there is no measurement problem, and this was emphasized already by Bohr in the early days of QT.

Okay, I now get the idea of taking it as an paradox free macroscopic thing. Before talking with you about the classical limit or black holes I surely need to learn more advanced QT first ...

Thanks everyone for taking so much time to explain it to me in detail!

 

[bhobba]

So there is no contradiction between classical and quantum theory, where the classical approximation is valid.

In fact a careful analysis shows the real basis of classical mechanics is QM - but that is a whole new story and another thread if anyone wants to pursue it either here or on the classical physics sub-forum.

Thank
Bill