  We present a theory of discontinuous motion of particles in continuous
space-time. We show that the simplest nonrelativistic evolution equation of
such motion is just the Schroedinger equation in quantum mechanics. This
strongly implies what quantum mechanics describes is discontinuous motion of
particles. Considering the fact that space-time may be essentially discrete
when considering gravity, we further present a theory of discontinuous motion
of particles in discrete space-time. We show that its evolution may naturally
result in the dynamical collapse process of the wave function, and this
collapse will bring about the appearance of continuous motion of objects in the
macroscopic world.
