Tuesday, March 30, 2021

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

Nottale's gravitational constant hbargr= GMDm/v0 contains dark mass MD as a parameter. At the surface of Earth MD much smaller than MD and for the planets  one has MD=MSun. It turns out that in the  average sense  MD 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 MD 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 rcr above  which MD=M is true.   Indeed, due to the average MD∝ 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 hgr and the relation between Planck length and CP2 length.

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

Articles and other material related to TGD.

No comments: