  In this work we consider some consequences of the Bohr-Sommerfeld-Hansson
(Old or quasi-classical) quantum theory of the Newtonian gravity, i.e. of the
"gravitational atom". We prove that in this case (for gravitational central
force and quantized angular momentum) centrifugal acceleration becomes
formally-theoretically dependent (proportional to fourth degree) of the mass of
"gravitational electron" rotating around "gravitational nucleus" for any
quantum number (state). It seemingly leads toward a paradoxical breaking of the
relativistic equivalence principle which contradicts to real experimental data.
We demonstrate that this equivalence principle breaking does not really appear
in the (quasi classical) quantum theory, but that it necessary appears only in
a hypothetical extension of the quantum theory that needs a classical like
interpretation of the Bohr-Sommerfeld angular momentum quantization postulate.
It is, in some sense, similar to Bell-Aspect analysis that points out that a
hypothetical deterministic extension of the quantum mechanics, in distinction
to usual quantum mechanics, can reproduce experimental data if and only if it
is non-local (superluminal) in contradiction with relativistic locality
(luminality) principle.
