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I was reading a book about the philosophy of science, and in the chapter about QM the author uses a well known example in order to explain quantum entaglement and illustrate the non-separability of individual system in QM. He describes a system composed of two spin-1/2 particles. Said system is in a singlet state:

[tex] \psi_{12} = \frac{1}{\sqrt{2}} (\psi_{1}^{+} \otimes \psi_{2}^{-} - \psi_{2}^{+} \otimes \psi_{1}^{-})[/tex]

The subscripts indicate particle 1 or 2, and the subscipts spin up or down. This is clearly an antysymmetric. Now suppose these two particles are emitted from the same source, but go in different directions. When they are spatially separate, we do an experiment to measure the spin of one electron, and it comes up as plus, and we'd automatically know the spin of the other electron. So far so good. The author then goes on to say that in this case the wavefunction would collapse into:

[tex]

(\psi_{1}^{+} \otimes \psi_{2}^{-})

[/tex]

Which is really weird, because this wavefunction is not antisymmetric. How do you conciliate wavefunction collapse with the antisymmetric requirement of the w.f.?