Does the quantal gravitational force vanish below critical radius in average sense?

Nottale’s gravitational constant hbar_gr= GM_Dm/v₀ contains dark mass M_D as a parameter. At the surface of Earth M_D much smaller than M_D and for the planets  one has M_D=M_Sun. It turns out that in the  average sense  M_D must grow to M.   This is  required by  the condition that  Bohr radii correspond to the classical radii in the average sense. The actual dependence of M_D on r  is expected to  be a staircase like function.

At the quantum level, this   effectively eliminates  the average  gravitational force in the scales below the critical radius r_cr above  which M_D=M is true.   Indeed, due to the average M_D∝ r dependence,  gravitational potential would be constant on the average. 

 Could one regard this   effective elimination of  the gravitational force as a kind of    Quantum Equivalence Principle or   as an analog of asymptotic freedom?

See the article Two alternative generalizations of Nottale’s hypothesis or the chapter About the Nottale’s formula for h_gr and the relation between Planck length and CP₂ length.

For a summary of earlier postings see Latest progress in TGD.

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