PlanetPhysics/Quantum Gravity Programs 2

Quantum Gravity Programs
There are several distinct programs aimed at developing a quantum gravity theory. These include--but are not limited to-- the following.


 * $$\bullet$$ The Penrose, twistors programme applied to an open curved space-time (ref. ), (which is presumably a globally hyperbolic, relativistic space-time). This may also include the idea of developing a `sheaf cohomology' for twistors (ref. \cite {Hawking and Penrose}) but still needs to justify the assumption in this approach of a charged, fundamental fermion of spin-3/2 of undefined mass and unitary `homogeneity' (which has not been observed so far);
 * $$\bullet$$ The Weinberg, supergravity theory, which is consistent with supersymmetry and superalgebra, and utilizes graded Lie algebras and matter-coupled superfields in the presence of weak gravitational fields;
 * $$\bullet$$ The programs of Hawking and Penrose ) in quantum cosmology, concerned with singularities, such as black and `white' holes; S. W. Hawking combines, joins, or `glues' an initially flat Euclidean metric with convex Lorentzian metrics in the expanding, and then contracting, space-times with a very small value of Einstein's cosmological `constant'. Such `Hawking', double-pear shaped, space-times also have an initial Weyl tensor value close to zero and, ultimately, a largely fluctuating Weyl tensor during the `final crunch' of our Universe, presumed to determine the irreversible arrow of time; furthermore, an observer will always be able to access through measurements only a limited part of the global space-times in our universe;
 * $$\bullet$$ The TQFT/ approach that aims at finding the `topological' invariants of a manifold embedded in an abstract vector space related to the statistical mechanics problem of defining extensions of the partition function for many-particle quantum systems;
 * $$\bullet$$ The string and superstring theories/M-theory that `live' in higher dimensional spaces (e.g., $$n\geq 6$$, preferred $$n-dim =11$$), and can be considered to be topological representations of physical entities that vibrate, are quantized, interact, and that might also be able to 'predict' fundamental masses relevant to quantum 'particles';
 * $$\bullet$$ The Baez `categorification' programme that aims to deal with quantum field and QG problems at the abstract level of categories and functors in what seems to be mostly a global approach;
 * $$\bullet$$ The `monoidal category' and valuation approach initiated by Isham (ref. ) to the quantum measurement problem and its possible solution through local-to-global, finite constructions in small categories.

Most of the quantum gravity programs are consistent with the Big-Bang theory, or the theory of a rapidly expanding universe, although none `prove' the necessity of its existence. Several competing and conflicting theories were reported that deal with singularities in spacetime, such as black holes `without hair', evaporating black holes and naked singularities.