more than 60years ago, Dirac noted that quantizing curved spacetime operators was difficult...since then quantum gravity has eluded unification with the other forces.
We recently proposed that there is a way to sidestep this problem entirely...transform the operators to linear operators, quantize, restore the nonlinearity of curvature after quantization...
what this means:
a) We recently derived a description of Black-Holes and spacetime with exact coupling, re-obtaining the Hawking current at the event horizon..the theory is a quantum transport NEGF nonequilibrium Green's functions theory
b) We apply this to GEONs or quantum wormholes...these we propose as Wheeler that they are particle-antiparticle pairs...we show that correlation in spacetime introduces self-energy terms that are effectively mass terms and metastable quasiparticle -like lifetimes...
c) We recast special relativistic elliptical equations in parabolic Schroedinger-like form and rederive these very results..we introduce 4D uncertainties, and 4D nonextensivity.
e) We recently derived the nonextensive statistical ensembles Random Matrix Theory ...applicabl;e to quantum chaos, to classical nonlinear regimes and regular regimes outside of complex random systems....the traditional Wigner Gaussian ensembles Random Matrix Theory is ubiquitous in science from nuclear physics to economics...our theory promises to achieve the similar utility. Also as precise description of dnamical statistical correlations are possible, not just a comparison with Gaussian uncorrelated regimes, direct calculation of observables are readily made.