I have talked (see this) about the possibility that Planck length lP is actually CP2 length R, which is scaled up by factor of order 103.5 from the standard Planck length. The basic formula for Newton's constant G would be a generalization of the standard formula to give G= R2/ℏeff. There would be only one fundamental scale in TGD as the original idea indeed was. ℏeff at "standard" flux tubes mediating gravitational interaction (gravitons) would be by a factor about n∼ 106-107 times larger than h.
Also other values of heff are possible. The mysterious small variations of G known for a long time could be understood as variations for some factors of n. The fountain effect in super-fluidity could correspond to a value of heff/h0=n larger than standard value at gravitational flux tubes increased by some integer factor. The value of G would be reduced and allow particles to get to higher heights already classically. In Podkletnov effect some factor og n would increase and g would be reduced by few per cent. Larger value of heff would induce also larger delocalization height.
Also smaller values are possible and in fact, in condensed matter scales it is quite possible that n is rather small. Gravitation would be stronger but very difficult to detect in these scales. Neutron in the gravitational field of Earth might provide a possible test. The general rule would be that the smaller the scale of dark matter dynamics, the larger the value of G and maximum value would be Gmax= R2/h0, h=6h0.
Are the blackholes detected by LIGO really so massive?
LIGO (see this) has hitherto observed 3 fusions of black holes giving rise to gravitational waves. For TGD view about the findings of LIGO see this and this. The colliding blackholes were deduced to have unexpectedly larger large masses: something like 10-40 solar masses, which is regarded as something rather strange.
Could it be that the masses were actually of the order of solar mass and G was actually larger by this factor and heff smaller by this factor?! The mass of the colliding blackholes could be of order solar mass and G would larger than its normal value - say by a factor in the range [10,50]. If so, LIGO observations would represent the first evidence for TGD view about quantum gravitation, which is very different from superstring based view. The fourth fusion was for neutron stars rather than black holes and stars had mass of order solar mass.
This idea works if the physics of gravitating system depends only on G(M+m). That classical dynamics depends on G(M+m) only, follows from Equivalence Principle. But is this true also for gravitational radiation?
What about supermassive galactic blacholes?
What about supermassive galactic black holes in the centers of galaxies: are they really super-massive or is G super-large! The mass of Milky Way super-massive blackhole is in the range 105-109 solar masses. Geometric mean is n=107 solar masses and of the order of the standard value of R2/GN=n ∼ 107 . Could one think that this blackhole has actually mass in the range 1-100 solar masses and assignable to an intersection of galactic cosmic string with itself! How galactic blackholes are formed is not well understood. Now this problem would disappear. Galactic blackholes would be there from the beginning!
The general conclusion is that only gravitational radiation allows to distinguish between different masses (M+m) for given G(M+m) in a system consisting of two masses so that classically scaling the opposite scalings of G and M is a symmetry.
See the chapter About the Nottale's formula for hgr and the relation between Planck length and CP2 length R of "Physics in many-sheeted space-time" or the article Is the hierarchy of Planck constants behind the reported variation of Newton's constant?.