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.