The Wigner's friend thought experiment can be used to understand non-realism in quantum mechanics. For anyone not familiar, the thought experiment involves two researchers observing an experiment at different times, let's say it's an electron spin. The question is, how should the second researcher to observe the experiment treat the system between his observation and his friend's observation?
In a non-realist interpretation we would say that the second researcher should continue to time evolve the system with the Schrodinger equation until he observes the system himself, but now he must include his friend as part of the quantum system as well. So, the two observers see the collapse of the wavefunctions at different times, which is fine because the time of wavefunction collapse is not given by a linear Hermitian operator so they need not agree about it.
My question concerns what happens if the additional time evolution that the second researcher observes changes the probability. For instance, say there is a 50% probability of spin up when the first researcher observes the experiment. Can this probability change from the second observer's perspective in the time between observations? If it can, how do we explain the fact that if they repeat the experiment 100 times the first researcher would expect to see spin up 50 times and the second researcher would expect to see something else. If it can't, what is the purpose of the additional unitary time evolution that the second researcher uses to describe the situation, couldn't he just use a description where the wavefunction collapses when the first researcher observes the experiment and get the same answer?