Three alternative generalizations of Nottale's hypothesis in TGD framework

Nottale's gravitational Planc constant ℏ_gr= GMm/v₀ contains  the velocity parameter v₀ as the only parameter. In the perturbative expansion  of  the scattering amplitudes β₀=v₀/c appears  in the role of fine structure constant.    

There is however a problem.

1. The model  for the effects of ELF radiation on vertebrate brain  inspired by  a generalization of Nottale's hypothesis by replacing the total mass M in the case of Earth by M_D≈ 10^-4M_E suggests that in this case the dark particles involved couple only to a part of mass identifiable as dark mass M_D.
2.   Since only GM appears in the basic formulas, the  alternative option is that the value of G is reduced to G_D. This conforms with the fact that in the  TGD framework CP₂ length is the fundamental parameter  G is a prediction of the theory and therefore can vary. 
3. A further option is that the parameter β₀=v₀/c≤ 1 is variable and equals to β₀=1 or to a value not much smaller than 1, say β₀=1/2.

These three options are  critically discussed and compared. The cautious conclusion is that the the third option is the most plausible one.

See the article Three alternative generalizations of Nottale's hypothesis in TGD framework 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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