PlanetPhysics/Quantum Gravity Programs 2

From testwiki
Revision as of 15:54, 4 October 2023 by imported>MathXplore (added Category:Quantum gravity using HotCat)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

Quantum Gravity Programs

There are several distinct [[../SupercomputerArchitercture/|programs]] aimed at developing a [[../SpaceTimeQuantizationInQuantumGravityTheories/|quantum gravity theory]]. These include--but are not limited to-- the following.

  • ∙ The Penrose, twistors programme applied to an open curved [[../SR/|space-time]] (ref. [1]), (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 [[../AntiCommutationRelations/|fermion]] of spin-3/2 of undefined [[../Mass/|mass]] and unitary `homogeneity' (which has not been observed so far);
  • ∙ The Weinberg, [[../AntiCommutationRelations/|supergravity]] theory, which is consistent with [[../AntiCommutationRelations/|supersymmetry]] and [[../MathematicalFoundationsOfQuantumTheories/|superalgebra]], and utilizes graded [[../BilinearMap/|Lie algebras]] and matter-coupled [[../HamiltonianAlgebroid3/|superfields]] in the presence of weak gravitational [[../CosmologicalConstant/|fields]];
  • ∙ The programs of Hawking and Penrose [1]) in quantum cosmology, concerned with singularities, such as black and `white' holes; S. W. Hawking combines, joins, or `glues' an initially flat Euclidean [[../MetricTensor/|metric]] with convex [[../LebesgueMeasure/|Lorentzian]] metrics in the expanding, and then contracting, space-times with a very small value of [[../AlbertEinstein/|Einstein's]] [[../CosmologicalConstant/|cosmological `constant]]'. Such `Hawking', double-pear shaped, space-times also have an initial Weyl [[../Tensor/|tensor]] value close to zero and, ultimately, a largely fluctuating Weyl tensor during the `final crunch' of our [[../MultiVerses/|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;
  • ∙ The [[../NonAbelianQuantumAlgebraicTopology3/|TQFT/]] approach that aims at finding the `[[../ModuleAlgebraic/|topological' invariants]] of a [[../NoncommutativeGeometry4/|manifold]] embedded in an abstract [[../NormInducedByInnerProduct/|vector space]] related to the [[../ThermodynamicLaws/|statistical mechanics]] problem of defining extensions of the partition [[../Bijective/|function]] for many-particle quantum [[../GenericityInOpenSystems/|systems]];
  • ∙ The string and [[../10DBrane/|superstring]] theories/M-theory that `live' in higher dimensional spaces (e.g., n≥6, preferred n−dim=11), and can be considered to be [[../CoIntersections/|topological]] [[../CategoricalGroupRepresentation/|representations]] of physical entities that vibrate, are quantized, interact, and that might also be able to 'predict' fundamental masses relevant to [[../QuantumParticle/|quantum 'particles';]]
  • ∙ The Baez `[[../Cod/|categorification]]' programme ([2], [3]) that aims to deal with [[../CosmologicalConstant/|quantum field]] and [[../SUSY2/|QG]] problems at the abstract level of [[../Cod/|categories]] and [[../TrivialGroupoid/|functors]] in what seems to be mostly a global approach;
  • ∙ The `monoidal category' and valuation approach initiated by Isham (ref. [4]) to the [[../CosmologicalConstant2/|quantum measurement]] problem and its possible solution through local-to-global, finite constructions in [[../SmallCategory/|small categories]].

Most of the quantum gravity programs are consistent with the Big-Bang theory, or the theory of a rapidly [[../ExpandingUniverse/|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 [[../BlackHoles/|black holes]] `without hair', evaporating black holes and naked singularities.

All Sources

[2] [3] [5] [6] [7] [8] [9] [1] [10] [11] [12] [13] [14] [15] [16] [17]

References

  1. ↑ 1.0 1.1 1.2 S. W. Hawking and R. Penrose. 2000. The Nature of Space and Time . Princeton and Oxford: Princeton University Press.
  2. ↑ 2.0 2.1 J. Baez. 2004. Quantum quandaries : a category theory perspective, in Structural Foundations of Quantum Gravity , (ed. S. French et al.) Oxford Univ. Press.
  3. ↑ 3.0 3.1 J. Baez. 2002. Categorified Gauge Theory. in Proceedings of the Pacific Northwest Geometry Seminar Cascade Topology Seminar,Spring Meeting--May 11 and 12, 2002. University of Washington, Seattle, WA.
  4. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Isham1
  5. ↑ I.C. Baianu, James Glazebrook, G. Georgescu and Ronald Brown. 2008."Generalized `Topos' Representations of Quantum Space--Time: Linking Quantum N--Valued Logics with Categories and Higher Dimensional Algebra.", (Preprint )
  6. ↑ J. Butterfield and C. J. Isham : A topos perspective on the Kochen--Specker theorem I - IV, Int. J. Theor. Phys , 37 (1998) No 11., 2669--2733 38 (1999) No 3., 827--859, 39 (2000) No 6., 1413--1436, 41 (2002) No 4., 613--639.
  7. ↑ J. Butterfield and C. J. Isham : Some possible roles for topos theory in quantum theory and quantum gravity, Foundations of Physics .
  8. ↑ F.M. Fernandez and E. A. Castro. 1996. (Lie) Algebraic Methods in Quantum Chemistry and Physics. , Boca Raton: CRC Press, Inc.
  9. ↑ Feynman, R. P., 1948, "Space--Time Approach to Non--Relativistic Quantum Mechanics", Reviews of Modern Physics , 20: 367--387. [It is reprinted in (Schwinger 1958).]
  10. ↑ R. J. Plymen and P. L. Robinson: Spinors in Hilbert Space. Cambridge Tracts in Math. 114 , \emph{Cambridge Univ. Press} 1994.
  11. ↑ I. Raptis : Algebraic quantisation of causal sets, \emph{Int. Jour. Theor. Phys.} 39 (2000), 1233.
  12. ↑ I. Raptis : Quantum space-time as a quantum causal set, arXiv:gr−qc/0201004.
  13. ↑ J. E. Roberts : More lectures on algebraic quantum field theory (in A. Connes, et al. (Non--commutative Geometry ), Springer (2004).
  14. ↑ C. Rovelli : Loop quantum gravity (1997), arXiv:gr−−qc/9710008.
  15. ↑ Jan Smit. 2002. Quantum Field Theory on a Lattice .
  16. ↑ S. Weinberg.1995--2000. The Quantum Theory of Fields . Cambridge, New York and Madrid: Cambridge University Press, Vols. 1 to 3.
  17. ↑ Wess and Bagger. 2000. Supergravity. (Weinberg)

Template:CourseCat

Retrieved from "https://en.wikiversity.beta.math.wmflabs.org/w/index.php?title=PlanetPhysics/Quantum_Gravity_Programs_2&oldid=2243"