Solving the nonlocality riddle by conformal quantum geometrodynamics

A rigorous ab initio derivation of the quantum mechanics of a single particle with spin is presented starting by conformally Weyl-gauge-invariant principle. The particle is described as a relativistic top with six Euler's angles and quantum effects are introduced by assuming that the Weyl's curvature of the particle configuration space acts on it as an external scalar potential. Weyl's conformal covariance is made explicit in all steps of the theory. It is shown that metric of the configuration space accounts for non-quantum relativistic effects, while the affine connections account for quantum relativistic effects. In this way, classical and quantum features acquire well distinguished geometrical origin. A scalar wave function is also introduced to recover the connection with the standard quantum description based on Dirac's four-component spinors. Finally, the case of two entangled spins is considered in the nonrelativistic limit and it is found that the nonlocality rests on the entanglement of the spin internal orientational variables, playing the role of "hidden variables". The theory was carried out in the Minkowski space-time, but it can be easily extended to a space with nonzero Riemann curvature.