The “state” of a system that is studied in quantum mechanics is not a property just of the system itself, but rather it is a summary of what is “known” about that system by a class of outside “observers” who do not interact with it in any way between “observations”. (The “observers” don’t actually have to be conscious; anything such as a measurement apparatus that could be changed in some macroscopic way by interaction with the system could play the same role, with the relevant change being identified as “knowledge” so long as different macroscopic states of the “observer” end up associated with different values of whatever property is being “observed”.)

This relative state changes whenever the observer learns something about the system – and when that happens the probabilities of all values other than the one observed become zero (while the value experienced by the observer becomes certain from the observer’s point of view). This change is sometimes called “collapse” – though it should be noted that the total of all the probabilities remains the same, so it might be better to think of the probability distribution being collapsed “sideways” onto the observed value rather than “down” to zero everywhere.

As an example, consider the case of an electron that has just passed through a selector that ensures that its spin in the z-direction is positive (let’s call this “up”). If we think of the spin of the electron as a system in its own right and if we can control the path of the electron without interacting with its spin, then we can represent (what we know about) the spin by a quantum state, and it turns out that if we know the spin is up then we cannot assign any particular value (say left or right) to any horizontal component. All we can say is that if we pass many such electrons through another vertical spin selector they will all measure spin up, but if we measure in any horizontal direction we’ll get positive and negative results with probability 1/2 each. BUT (and here’s the “collapse”) if, on doing that horizontal measurement, we observe spin (say) left, then when we subsequently measure the same horizontal spin we’ll get the same result with certainty and the probability of seeing right will have gone down to zero (while if we go back to measuring the vertical component it will now have equal chances of being up or down – which is another reason for not liking the “collapse” language since what collapses one distribution has spread out another, and in particular has raised the chance of seeing down next time from 0 to 1/2).

Note: Jonathan Joss makes a similar objection to the word “collapse” and suggests that it be called a “rotation” of the state vector (but of course in the relevant Hilbert space rather than physical space).