  The quantum hydrodynamic-like equations for two real variables (i.e., the
phase and the amplitude of the wave function) of the relativistic Klein-Gordon
equation are derived in the present paper. The paper also shows that in
classical limit the hydrodynamic Klein-Gordon equations lead to the Madelung
pseudo-potential [1] as well as to the quantum pseudo potential for a charged
particle given by Janossy [2] and by Bialynicki et al [3]. The origin of the
non-local interactions of quantum mechanics in the hydrodynamic model are
discussed both for free and charged particles.
