  We investigate the meaning of the wave function by analyzing the mass and
charge density distribution of a quantum system. According to protective
measurement, a charged quantum system has mass and charge density proportional
to the modulus square of its wave function. It is shown that the mass and
charge density is not real but effective, and it is formed by the ergodic
motion of a localized particle with the total mass and charge of the system.
Moreover, it is argued that the ergodic motion is not continuous but
discontinuous and random. This result suggests a new interpretation of the wave
function, according to which the wave function is a description of random
discontinuous motion of particles, and the modulus square of the wave function
gives the probability density of the particles being in certain locations. It
is shown that the suggested interpretation of the wave function disfavors the
de Broglie-Bohm theory and the many-worlds interpretation but favors the
dynamical collapse theories, and the random discontinuous motion of particles
may provide an appropriate random source to collapse the wave function.
