- #26

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Pio2001:

eaglelake: The question I was asking is what forces the result to be one of the 2 you mentioned. In my previous posts I explained how I came to the conclusion that other states could result, while _seemingly_ following the basic rules of QM. Evidentially I did break a fundamental rule somewhere in that logic, I just don't see where. I know people have pointed out that the example state I mentioned breaks the symmetrization rules and is contrary to the literature which says the state must collapse to one of the two you mentioned, ... but I THINK those things are supposed to follow from the fundamental rules of QM, right? I don't think those things themselves are supposed to be the fundamental QM rules. In the case of the symmetrization requirement Griffths seems to imply that once a system is in an antisymmetric state (like the initial one) the state will automatically remain antisymmetric when evolving under the QM collapse/evolution rules (i.e. symmetrization shouldn't have to be added as a new rule, it should be automatic, a consequence of the more fundamental rules).

One of the postulates of quantum mechanics states that the only possible results of a measurement are the eigenvalues of the observable being measured. The observable is an Hermitian operator. For spin ½, the Pauli spin matrices are the Hermitian operators for each component of the spin. If you solve the eigenvalue equation for any one of the Pauli spin matrices you will get eigenvalues +1 and -1, i.e. spin up and spin down. These are the only values ever obtained in a spin ½ measurement.

Quantum experiments confirm the correctness of this view. As far as I know it has never before been challenged. There is nothing that "forces" this to happen; it simply is a fact. I don't know how else to explain it!