Orthodox Quantization of Einstein’s Gravity: Might Its Unrenormalizability Be Technically Fathomable and Physically Innocuous?

Abstract

Many physical constants related to quantized gravity, e.g., the Planck length, mass, curvature, stressenergy, etc., are nonanalytic in G at G = 0, and thus have expansions in powers of G whose terms are progressively more divergent with increasing order. Since the gravity field’s classical action is inversely proportional to G, the path integral for gravity-field quantum transition amplitudes shows that these depend on G only through the product ħG, and are nonanalytic in G at G = 0 for the same reason that all quantum transition amplitudes are nonanalytic in ħ at ħ = 0, namely their standard oscillatory essential singularity at the classical ‘limit’. Thus perturbation expansions in powers of G of gravity-field transition amplitudes are also progressively more divergent with increasing order, and hence unrenormalizable. While their perturbative treatment is impossible, the exceedingly small value of ħ G makes the semiclassical treatment of these amplitudes extraordinarily accurate, indeed to such an extent that purely classical treatment of the gravity field ought to always be entirely adequate. It should therefore be fruitful to couple classical gravity to other fields which actually need to be quantized: those fields’ ubiquitous, annoying ultraviolet divergences would thereupon undergo drastic self-gravitational red shift, and thus be cut off.