A possible new approach to quantum gravity

Question

It seems nonrenormalization of gravity because renormalization theory is not powerful enough to vanish the infinity. Why not we generalize one of basic method in doing renormalization theory, Ramanujan summation? This is quite bit mathematical rather than physics but both zeta regulazation and Ramanujan summation are weak to sum divergent series. A complete quantum gravity must uses both regulazation theory and renormalization theory, can a possible connection between them be... hypermonstrous moonshine or a new theory ( this is a revolutionized idea ) on non Newtonian calculus and zesors ( similar to tensors but they are quartic mapping ). A theory on quasirenormalization group should be considered. Non newtonian calculus is a possible way to generalize Ramanujan summation. ( There is a good paper about non Newtonian calculus on arxiv, these calculus are nonlinear but Newton-Leibniz calculus is linear)

Comments

What if after successful renormalization of quantum gravity, the calculations results are different from observations? Because first, there is no experiment on quantum character of gravity, and second, GR itself needs additional but still non observed inputs like dark matter and dark energy.

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About that, an elegant solution is quasiregulazation. A quasiregulator would explain why the theory fails. On the other hand, a very powerful test on general relativity is cosmic censhorship hypothesis. A mathematical proof or an experiment on quantum entanglement ( do particles connect by wormhole?) would disprove existence of naked singularities. If true, general relativity must be true, at least in classical limit. And a quantum gravity must be reproduces general relativity ar classical limit. I don t think dark matter and dark energy are problems, if they exist then a fifth fundamental force should be an elegant answer to solve.

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GR is good for weak fields, but is not good for strong ones. There may be many theories, but none may be true - only consistent to some degree with experiment. Fifth or fifty-fifth force is not a solution, but an excuse, to tell the truth.

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On that problem, i think you want to modify general relativity at larger scale. A solution should begin at special relativity, a good one is doubly special relativity but i suggest that not only maxium and minium energy scale and length scale but also entire Planck scales and fundamental constants in physics. Mach s principle must be considered carefully. If true, special relativity is an approximate theory of a general theory.