When an observer causes the wave function of a particle to collapse, how can we know that the wave function was not collapsed already before the measurement?
Suppose we measure the z-component of the spin of an electron. After the measurement, it is entirely aligned along the measured direction, e.g. the +z-direction. Before the measurement we need to assume that a probability distribution proportional to $|\Psi|^2$ of the two allowed directions is present.
If we repeat the measurement with many identically prepared electrons, we should see such a distribution finally. For example, we could measure 40% spin-down and 60% spin-up.
However, it seems we could also assume that all of these particles have a defined spin-direction before we measure them.
What is an intuitive (being aware that quantum phenomena as such are rarely intuitive) explanation for why we cannot simply assume that the spin was already aligned completely in that measured direction?
With regards to the suggestion that this two-year old question is a duplicate of the one asked yesterday, I would like to point out that my question isn't limited to entanglement, but asks about a very fundamental principle in quantum mechanics, and as such is not a duplicate.
Answer
Quantum mechanics was developed in order to match experimental data. The seemingly very weird idea that some observables do not have a definite value before their measurement is not something physicists have been actively promoting, it is something that theoretical considerations followed by many actual experiments have forced them to admit.
I don't think there is an intuitive explanation for this. It is closely linked to the notion of superposition. The basic idea is that we do indirectly observe the effects of interference between superposed quantum states, but upon actual measurement we never see superposed states, only classical, definite values. If we suppose these values where there all along, then why would we have any interference? The whole framework of QM would be pointless.
In other words, a quantum state is what it is (whatever that is) precisely because it is in contrast to a classical state: crucially, it only describes a probability distribution for observables values, not actual, permanent values for these observables.
A wavefunction that would always be collapsed would just be a classical state. Now why (and does?) a measurement "collapse" anything at all is an open question, the measurement problem.
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