Quote by marcus
I don't see how you get this. You mentioned a scattering experiment. I see that as, for instance, a collider experiment. In AsymSafe gravity we have to choose a scale k. Our hunch is it doesn't matter there are various possible choices, Weinberg mentions several including defining k = the momentum transfered in the collision.
So as the energy E goes up, k goes up. G(k) goes to zero.
I would expect the schwarzschild radius R_{s} to be much less than the planck length. But that is just an intuitive guesswe should put in Shaposhnikov's numbers and actually see what happens.
But you say that R_{s} is actually quite large! Much larger than the infrared planck length that we are used to. This is surprising.
It seems to me that you have gone around in a circle. You ramp the collider energy up above Planck energy so you are way way UV. But then you turn around and say the real physical scale is now IR. This is paradoxical. It seems to me that it does not work in the framework of AsymSafe, because it fails to take account of the running of newton's constant.
However you may be right! I realize you know a lot about this. So please explain.

To get r_s>>l_p I'm just using the classical Schwarzschild relation r_s = 2GE where I have equated the centre of mass energy E with the mass. G is something like G= (l_pl)^2 the planck length squared. So if E>>m_pl=1/l_pl therefore r_s/l_pl = 2E/m_pl>>1.
Clearly it doesn't make sense to associate E with k. E is only the centre of mass energy it doesn't say anything about impact parameter b i.e. how "close" the particles come. Something more like k~ E^c b^a would make more sense where a and c are positive constants say c=1 b=2(with some approiate power of G to give it the right dimensions).