Dr Narayan Bhadra It is an interesting idea about the quantum gravitation and the consciousness, have you thought to consider the non commutativity and non linearity for this quantum gravitation that we cannot renormalise and quantize. Here are some ideas,
The notion of using skewed lines, if it is deviated from traditional straight geodesics, could possibly emerge in these alternative quantum gravity approaches, especially if they involve discrete or fundamentally different geometric structures at the smallest scales of spacetime. I don t know if it is possible , we need to make experimental observations also for these unconventional geometric structures and the physical framework. in the quest to develop a theory of quantum gravity, the assumption of linearity, particularly in the context of quantum mechanics and its application to gravitational systems, has been a subject of scrutiny and exploration.
The QM operates traditionally in linear framework where the superposition principle combinate the linear combinations , and it is there that the challenges appear for this QG in taken non linear nature of the GR., if we take the GR and the curvature of the spacetime by matter and energy , so it is non linear because the gravitational field influences the geometry of this said spacetime giving curved trajectories for the paticles and the concept of gravitational waves, when we try toi unify this GR and the QM, this non linearity implies the problems that we know, must we modify the linear structures of this QM to converge with the non linear nature of this gravity with the non commutativity, maybe in utilising innovative mathematical formalisms with non linear aspects , but it is not easy because it must be consistent with the observations , a big puzzle.
It is complex all this for the gravity behavior at a foundamental level , if we want to unify this QM and the GR in formulating a gravitational quantum force like the electromagnetism, the weak force and the strong nuclear force, so the challenge is deep because the nature of this gravity is the problem and the non linnearity , the distribution of matter, energy in this spacetime give also variations in potenmtial energy, and so the geodesics is important.
The energy distribution becomes the problem for the linear QM where we must solve these divergences and infinities. Somethings it seems evident myust be modified and the kinetic and potential energies in the hamiltonian and the constraints so are a key at my humble opinion to merge this GR and QM,
It is what I try to do with the spherical topological geometrical algebras that I have invented and the spheres like foundamental objects if we consider the geometry based quantum description and the algebraic structures with operators and properties , so the discrete structures are considered to be the spheres and the volumes and motions are important, The non commutative geometry with specific chosen algebraic structures so become interesting for the deviations from classical mathematics and QM,
the Quantization of the spacetime can be discrete in function of partitions utilised and the mathematical tools so also , so the operators and equations capture the behavior of foudamental objects with specific algebraic framworks , and so the hamiltonian considers the dynamics of these spherical objects towards a QG in trying to solve these divergences, problems of linearity and infinities.
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