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

#### Abstract

Nottale's gravitational Planck constant *ħ _{gr}* =

*GMm*/

*v*contains the velocity parameter

_{0}*v*as the only parameter. In the perturbative expansion of the scattering amplitudes

_{0}*β*=

_{0}*v*/

_{0}*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

^{-4}

*M*suggests that in this case the dark particles involved couple only to a part of mass identifiable as dark mass

_{E}*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

*CP*length is the fundamental parameter

_{2}*G*is a prediction of the theory and therefore can vary.

A further option is that the parameter *β _{0}* =

*v*/

_{0}*c*< 1 is variable and equals to

*β*= 1 or to a value not much smaller than 1, say

_{0}*β*=1/2.

_{0}