Is the Hierarchy of Planck Constants Behind the Reported Variation of Newton's Constant?

Abstract

It has been known for long time that the measurements of G give differing results with differences between measurements larger than the measurement accuracy. This suggests that there might be some new physics involved. In TGD framework the hierarchy of Planck constants h_eff =nh₀, h=6h₀ together with the condition that theory contains CP₂ size scale R as only fundamental length scale, suggest the possibility that Newtons constant is given by G= R²/ℏ_eff, where R replaces Planck length ( l_P= sqrt[ℏ_eff G] à l_P =R) and ℏ_eff /h is in the range 10⁶-10⁷. The spectrum of Newton' constant is consistent with Newton's equations if the scaling of ℏ_eff inducing scaling G is accompanied by opposite scaling of M₄ coordinates in M₄ x CP₂: dark matter hierarchy would correspond to discrete hierarchy of scales given by breaking of scale invariance. In the special case h_eff = h_gr =GMm/v₀ quantum critical dynamics as gravitational fine structure constant v₀/c)/4π as coupling constant and it has no dependence of the value of G or masses M and m. In this article I consider a possible interpretation for the finding of a Chinese research group measuring two different values of G differing by 47 ppm in terms of varying h_eff. Also a model for fountain effect of superfluidity as de-localization of wave function and increase of the maximal height of vertical orbit due to the change of the gravitational acceleration g at surface of Earth induced by a change of h_eff due to super-fluidity is discussed. Also Podkletnov effect is considered. TGD inspired theory of consciousness allows to speculate about levitation experiences possibly induced by the  modification of G_eff at the flux tubes for some part of the magnetic body accompanying biological body in TGD based quantum biology.