  Unitary evolution and projective measurement are fundamental axioms of
quantum mechanics. Even though projective measurement yields one of the
eigenstates of the measured operator as the outcome, there is no theory that
predicts which eigenstate will be observed in which experimental run. There
exists only an ensemble description, which predicts probabilities of various
outcomes over many experimental runs. We propose a dynamical evolution equation
for the projective collapse of the quantum state in individual experimental
runs, which is consistent with the well-established framework of quantum
mechanics. In case of gradual weak measurements, its predictions for ensemble
evolution are different from those of the Born rule. It is an open question
whether or not suitably designed experiments can observe this alternate
evolution.
