preprints.org > physical sciences > particle and field physics > doi: 10.20944/preprints202306.1472.v6

Preprint Article Version 6 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 15 June 2023 / Approved: 20 June 2023 / Online: 21 June 2023 (10:01:50 CEST)
Version 2 : Received: 3 October 2023 / Approved: 5 October 2023 / Online: 5 October 2023 (10:51:05 CEST)
Version 3 : Received: 15 October 2023 / Approved: 16 October 2023 / Online: 17 October 2023 (08:00:13 CEST)
Version 4 : Received: 21 November 2023 / Approved: 21 November 2023 / Online: 22 November 2023 (12:12:12 CET)
Version 5 : Received: 25 December 2023 / Approved: 26 December 2023 / Online: 26 December 2023 (09:58:36 CET)
Version 6 : Received: 20 September 2024 / Approved: 23 September 2024 / Online: 23 September 2024 (14:16:15 CEST)

The insuperable obstacle between gravity and quantum mechanics is their spacetimes. Introduction of a (quantum) quadratic form on a state Hilbert space and a (quantum) metric tensor in (3+1)D quantum spacetime solves the problem by providing a common spacetime for both gravity and quantum mechanics which helps further to develop an accurate and generalized form of quantum gravity, i.e., General Quantum Gravity. This formalism yields a (3+1)D pseudo-gravity first order quantum equation, which is technically more accurate than Schr\"odinger equation. A (quantum) Lorentz-like transformation is also possible to be developed in (3+1)D quantum spacetime. Instead of one common Einstein field equation to explain gravitational effects, this formalism yields two individual (quantum) Einstein field equations, namely, one for bosons and another for fermions. In this work, (quantum) metric tensor as well as quantum Riemann tensor, quantum Ricci tensor and quantum Ricci scalar all are found to be the objects of quantization. Apparently, these quantum Riemann tensor, quantum Ricci tensor and quantum Ricci scalar are also found to be multiplicatively renormalizable while all divergences of their higher orders vanish in (3+1)D quantum spacetime. Ultimately, General Quantum Gravity yields that: Quantum Mechanics and Theory of Special and General Relativity are inseparable and naturally inter-expressible for the (quantum) quadratic form and the (quantum) metric tensor in (3+1)D quantum spacetime.

quantum gravity; (quantum) Einstein field equations; renormalization

Physical Sciences, Particle and Field Physics

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