  Under the spin-position decoupling approximation, a vector with a phase in 3D
orientation space endowed with geometric algebra, substitutes the vector-matrix
spin model built on the Pauli spin operator. The standard quantum
operator-state spin formalism is replaced with vectors transforming by proper
and improper rotations in the same 3D space -- isomorphic to the space of Pauli
matrices. In the single spin case the novel spin 1/2 representation: (1) is
Hermitian; (2) shows handedness; (3) yields all the standard results and its
modulus equals the total spin angular momentum S_tot; (4) formalizes
irreversibility in measurement; (5) permits adaptive embedding of the 2D spin
space in 3D. Maximally entangled spin pairs: (1) are in phase and have opposite
handedness; (2) relate by one of the four basic improper rotations in 3D:
plane-reflections for triplets and inversion for singlet; (3) yield the
standard total angular momentum; (4) all standard expectation values for
bipartite and partial observations follow. Depending on whether proper and
improper rotors act one or two sided, the formalism appears in two
complementary forms, the spinor or the vector form, respectively. The proposed
scheme provides a clear geometric picture of spin correlations and
transformations entirely in the 3D physical orientation space.
