  Entanglement is the most striking but also most weird property in quantum
mechanics, even though it has been confirmed by many experiments over decades
through the criterion of violating Bell's inequality. However, a fundamental
questions arisen from EPR paradox is still not fully understood, that is, why
and how entanglement emerges in quantum realm but not in classical world. In
this paper, we investigate the quantum dynamics of two photonic modes (or any
two bosonic modes) coupled to each other through a beam splitting. Such a
coupling fails to produce two-mode entanglement. We also start with an
initially separable pure state for the two modes, namely, there are no
entanglement and statistic probability feature to begin with. By solving the
quantum equation of motion exactly without relying on the probabilistic
interpretation, we find that when the initial wave function of one mode is
different from a wave packet obeying the minimum Heisenberg uncertainty (which
corresponds to a well-defined classically particle), the causality in the
time-evolution of each mode is internally broken. It also leads to the
emergence of quantum entanglement between the two modes. The lack of causality
is the nature of statistics. The Bell's theorem only rules out the existence of
local hidden variables in the probabilistic interpretation of quantum
mechanics. It is the breaking of internal causality in the dynamical evolution
of subsystems that induces the probabilistic nature of quantum mechanics, even
though the dynamical evolution of the whole system completely obey the
deterministic Schr\"{o}dinger equation. This conclusion is valid for all
quantum systems. It provides a fundamental origin of the probabilistic feature
within the deterministic framework of quantum mechanics.
