Three Alternative Generalizations of Nottale's Hypothesis in the TGD framework

Abstract

Nottale's gravitational Planck 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:

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.

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.

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.