Uniqueness of the Equation for Quantum State Vector Collapse

The linearity of quantum mechanics leads, under the assumption that the wave function offers a complete description of reality, to grotesque situations famously known as Schrödinger’s cat. Ways out are either adding elements of reality or replacing the linear evolution by a nonlinear one. Models of spontaneous wave function collapses took the latter path. The way such models are constructed leaves the question of whether such models are in some sense unique, i.e., whether the nonlinear equations replacing Schrödinger’s equation are uniquely determined as collapse equations. Various people worked on identifying the class of nonlinear modifications of the Schrödinger equation, compatible with general physical requirements. Here we identify the most general class of continuous wave function evolutions under the assumption of no-faster-than-light signaling.