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?
- If the power of gravitational radiation distinguishes between different values of M+m, when G(M+m) is kept constant, the idea is dead. This seems to be the case. The dependence on G(M+m) only leads to contradiction at the limit when M+m approaches zero and G(M+m) is fixed. The reason is that the energy emitted per single period of rotation would be larger than M+m. The natural expectation is that the radiated power per cycle and per mass M+m depends on G(M+m) only as a dimensionless quantity .
- From arXiv one can find an (see article, in which the energy per unit solid angle and frequency radiated ina collision of blackholes is estimated and the outcome is proportional to E2G(M+m)2, where E is the energy of the colliding blackhole.
The result is proportional mass squared measured in units of Planck mass squared as one might indeed naively expect since GM2 is analogous to the total gravitational charge squared measured using Planck mass.
The proportionality to E2 comes from the condition that dimensions come out correctly. Therefore the scaling of G upwards would reduce mass and the power of gravitational radiation would be reduced down like M+m. The power per unit mass depends on G(M+m) only. Gravitational radiation allows to distinguish between two systems with the same Schwartschild radius, although the classical dynamics does not allow this.
- One can express the classical gravitational energy E as gravitational potential energy proportional to GM/R. This gives only dependence on GM as also Equivalence Principle for classical dynamics requires and for the collisions of blackholes R is measured by using GM as a natural unit.
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 article Is the hierarchy of Planck constants behind the reported variation of Newton's constant? or the chapter TGD and astrophysics of "Physics in many-sheeted space-time".
For a summary of earlier postings see Latest progress in TGD.