Is the formation of gravitational bound states impossible in superstring models?
I decided to take here from a previous posting an argument allowing to conclude that super string models are unable to describe macroscopic gravitation involving formation of gravitationally bound states. Therefore superstrings models cannot have desired macroscopic limit and are simply wrong. This is of course reflected also by the landscape catastrophe meaning that the theory ceases to be a theory in macroscopic scales. The failure is not only at the level of superstring models: it is at the level of quantum theory itself. Instead of single value of Planck constant one must allow a hierarchy of Planck constants predicted by TGD. My sincere hope is that this message could gradually leak through the iron curtain to the ears of the super string gurus.
Superstring action has bosonic part proportional to string area. The proportionality constant is string tension proportional
to 1/hbar G and is gigantic. One expects only strings of length of order Planck length be of significance.
It is now clear that also in TGD the action in Minkowskian regions contains a string area. In Minkowskian regions of
space-time strings dominate the dynamics in an excellent approximation and the naive expectation is that string theory should give an excellent description of the situation.
String tension would be proportional to 1/hbar G and this however raises a grave classical counter argument. In string model massless particles are regarded as strings, which have contracted to a point in excellent approximation and cannot have length longer than Planck length. How this can be consistent with the formation of gravitationally bound states is however not understood since the required non-perturbative formulation of string model required by the large valued of the coupling parameter GMm is not known.
In TGD framework strings would connect even objects with macroscopic distance and would obviously serve as correlates for the formation of bound states in quantum level description. The classical energy of string connecting say the two wormhole contacts defining elementary particle is gigantic for the ordinary value of hbar so that something goes wrong.
I have however proposed that gravitons - at least those mediating interaction between dark matter have large value of Planck constant. I talk about gravitational Planck constant and one has heff= hgr=GMm/v0, where v0/c<1 (v0 has dimensions of velocity). This makes possible perturbative approach to quantum gravity in the case of bound states having mass larger than Planck mass so that the parameter GMm analogous to coupling constant is very large. The velocity parameter v0/c becomes the dimensionless coupling parameter. This reduces the string tension so that for string world sheets connecting macroscopic objects one would have T ∝ v0/G2Mm. For v0= GMm/hbar, which remains below unity for Mm/mPl2 one would have hgr/h=1. Hence the action remains small and its imaginary exponent does not fluctuate wildly to make the bound state forming part of gravitational interaction short ranged. This is expected to hold true for ordinary matter in elementary particle scales. The objects with size scale of large neutron (100 μm in the density of water) - probably not an accident - would have mass above Planck mass so that dark gravitons and also life would emerge as massive enough gravitational bound states are formed. hgr=heff hypothesis is indeed central in TGD based view about living matter.
To conclude, it seems that superstring theory with single value of Planck constant cannot give rise to macroscopic gravitationally bound matter and would be therefore simply wrong much better than to be not-even-wrong.
See the chapter Recent View about Kähler Geometry and Spin Structure of "World of Classical Worlds" of "Quantum TGD as Infinite-Dimensional Spinor Geometry" .