3.9.6 Quantum Gravity
Quantum gravity is one of the most profound problems of modern physics, which should unite Quantum Mechanics with General Relativity, to be realized as a full Quantum Field Theory. This is all related to the ultimate structure of space-time, whether it is fundamentally continuous or discrete. It is expected that the gravity involves a force mediated by a hypothetical graviton, or may be the force will be a product of a discrete structure of space-time itself, as in Loop Quantum Gravity.
The two serious approaches to this critical problem are Strings theory and Loop Quantum Gravity, described in sections 7 and 8, where Strings Theory tries to develop an effective Quantum Field Theory of gravity at low energies, while Loop Quantum Gravity uses spin networks to obtain granular space that evolves with time, but all these efforts have not been fruitful yet. The essence of the problem is that most of these theories are trying to implement some kind of quantization in a continuous space-time background, which makes any prospective theory of gravity non-re-normalizable.
One of the main consequences of the duality nature of time is that it becomes naturally granular, because the real flow of time in the inner levels has to be interrupted inn order to appear in the outer level, which is what makes time genuinely complex and hyperbolic, thus leading to the three principles of Special and General Relativity all at once. This will allow Quantum Gravity to be expressed in terms of simple Euclidean geometry, without invoking Riemannian manifolds, as it will be discussed in chapter V.