keepit said:
i hope I'm not being annoying here but since i haven't taken enough math, i don't see a mechanism here. I was trained in mechanisms.
You are right to see a gap. This gap (an undiscovered mechanism by which geometry can guide matter and matter can, in turn, bend geometry) fascinates and attracts researchers to QG.
One wants to find out how, at their roots, matter and geometry are related, so it will seem natural that they interact.
As an inexpert bystander just watching the ongoing research in quantum geometry/gravity I would say that Einstein 1915 GR is merely DESCRIPTIVE of the manner in which matter and geometry interact. The reason people are drawn into QG research is they want to understand the mechanism of that interaction.
The LHS of 1915 GR equation is purely geometric, a package of numbers describing curvature.
The RHS of the equation is about matter a package of numbers describing energy and momentum.
So it is saying that, at any given point, LHS = RHS, meaning that matter is determining how the geometry is bending/changing.
And by definition the geometry determines the geodesics, the shortest distance paths, along which matter tries to flow.
So it is DESCRIBING the interaction that we see occurring in reality. We see matter and geometry behaving like that. But the equation is not saying why they interact like that.
So the quantum relativists, or quantum gravitists if you prefer, seem to be expecting that if they can delve down into the quantum roots of geometry, they will be able to find a connection between the quantum description of matter and that of geometry. A way to put BOTH into the same Feynman path integral, or if you like both into the same Lagrangian (a mathematical machine that physicists customarily use to describe dynamics). That would be lovely! quantum matter and geometry working together in the same mathematical machine which is cranking out combined TRANSITION AMPLITUDES between initial and final combined quantum states of geometry and matter! (You can see how this would excite and motivate some researchers.)
I don't want to overstate this, but I think you are pointing out an interesting and attractive gap in the current picture that people have.
There is also the thing of people wanting to understand how geometry and matter behave at extremely high energy density---what could have been happening around start of expansion? could there have been a bounce when the energy density was very high?
And I gather some people would like to be able to compute scattering amplitudes for head-on or nearly head-on particle collisions where the energy is not high enough to form a miniature black hole but is nevertheless high enough that ordinary QFT doesn't work because geometry does get involved. So there's a bunch of other motivations, things people are curious about besides what you suggested.