  In this paper we consider generalization of classical and quantum mechanics
that directly follows from the causality principle and topology of a system
state space. In generalized mechanics, the Hamiltonian/Schrodinger equations
remain the same, but the Hamiltonian may depend on the action and its
canonically conjugated variables as additional dynamical variables. This
extension of quantum mechanics indicates that the quantization of matter could
be an evolutionary process, and in the distant future, even massive bodies may
become entirely quantum objects without well-defined trajectories and shapes.
In the classical limit, the first approximation of the Hamiltonian with respect
to the action explains the accelerated expansion of the Universe, Hubble law,
formation of spiral galaxies with a non-Kepler curve of rotation velocity, and
asymmetry between distributions of matter and antimatter. This theory predicts
that our open universe could have extended pre-history and be preceded by a
long set of closed precursor universes.
