  A theory of electron spin is developed here based on the extended least
action principle and assumptions of intrinsic angular momentum of an electron
with random orientations. By incorporating appropriate relative entropy for the
random orientations of intrinsic angular momentum in the extended least action
principle, the theory recovers the quantum formulation of electron spin. The
two-level quantization of spin measurement is a natural mathematical
consequence. The formulation of measurement probability when a second
Stern-Gerlach apparatus is rotated relative to the first Stern-Gerlach
apparatus, and the Schr\"{o}dinger-Pauli equation, are also derived
successfully. Furthermore, we provide an intuitive physical model and
formulation to explain the entanglement phenomenon between two electron spins.
In this model, spin entanglement is the consequence of correlation between the
random orientations of the intrinsic angular momenta of the two electrons.
Since the orientation is an intrinsic local property of electron, the
correlation of orientations can be preserved even when the two electrons are
remotely separated. Such a correlation can be manifested without causal effect.
Owing to this orientation correlation, the Bell-CHSH inequality is shown to be
violated in a Bell test. A potential experiment is proposed to test the
validity of the present theory. In a typical Bell test that confirms the
violation of Bell-CHSH inequality, the present theory suggests that by adding a
sufficiently large time delay before Bob's measurement, the Bell-CHSH
inequality can become non-violated. Limitations of the theory are also
discussed to inspire further investigations on a more rigorous physical model
of electron spin.
