Is the hierarchy of Planck constants behind the reported variation of Newton's constant?

It has been known for long time that the measurements of G give differing results with differences between measurements larger than the measurement accuracy (see this and this). 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/hbar_eff, where R replaces Planck length ( l_P= (ℏ G^1/2→ l_P=R) and hbar_eff/h is in the range 10⁶-10⁷.

The spectrum of Newton' constant is consistent with Newton's equations if the scaling of hbar_eff inducing scaling G is accompanied by opposite scaling of M⁴ coordinates in M⁴× 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.

See the article Is the hierarchy of Planck constants behind the reported variation of Newton's constant? or the new chapter About the Nottale's formula for h_gr and the possibility that Planck length l_P and CP₂ length R are identical giving G= R²/ℏ_eff of "Physics in many-sheeted space-time".

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

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