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The Problem of Time pp 157–179Cite as

Quantum Gravity Programs

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Part of the book series: Fundamental Theories of Physics ((FTPH,volume 190))

Abstract

This chapter introduces the main Quantum Gravity programs to date, with historical inter-connections and various conceptual classifications as follows.

  1. A)

    The covariant, canonical and path integral approach trilemma.

  2. B)

    Spacetime versus space primality.

  3. C)

    Whether or not to alter gravitational theory so as to facilitate its quantization.

  4. D)

    Top-down and bottom-up approaches.

We furthermore outline many of the main programs in the Quantum Gravity literature so far: covariant quantization with its graviton concept, the canonical approaches of geometrodynamics and loop quantum gravity, the gravitational path-integral approach, supergravity, perturbative string theory, and its non-perturbative counterpart: M-theory.

We also continue the Preface’s exposition of the Planck unit regime, and delineate quantum field theory in curved spacetime (QFTiCS) and quantum cosmology’s less extreme regimes. QFTiCS is sufficient setting to consider Hawking and Unruh radiation, and is also an arena in which many quantum field theory concepts and techniques are already limited due to more general forms time and spacetime take here.

This chapter provides significant context for the current book, whose main topics—the Problem of Time and Background Independence underlying this—are major conceptual and foundational topics in Quantum Gravity. Indeed, geometrodynamics, loops, gravitational path integrals, supergravity and M-Theory are all major sites for Background Independent notions and thus exhibition of Problems of Time.

[The Preface and Chaps. 6 and 8 are essential preliminary reading for this chapter, which, in turn, is essential reading for Part III.]

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Notes

  1. 1.

    Since the approximate dates and ancestry of the various Quantum Gravity programs in this Chapter are rather nontrivial, this ‘family tree’ figure may quite often be a useful resource as regards outlining how these programs ‘fit together’ both conceptually and historically.

  2. 2.

    Spin-0 and spin-2 mediators together is also a tenable possibility, as in e.g. Scalar–Tensor Theories of Gravitation.

  3. 3.

    The positive norm notion itself, however, does not require Killing vectors [695].

  4. 4.

    See Appendices Q.9 and U.6 for a conceptual outline of these.

  5. 5.

    Extra spatial dimensions are relatively uncontroversial. However, considering time to have more than one dimension would, carry many technical and conceptual difficulties, starting with the difficulties with ultrahyperbolic PDEs outlined in Sect. 31.3.

  6. 6.

    These actions are named after theoretical physicists Yoichiro Nambu, Tetsuo Goto and Alexander Polyakov.

  7. 7.

    These are named after mathematicians Eugenio Calabi and Shing-Tung Yau. See [673] for an especially accessible presentation of the various layers of structure leading to the definition of these.

  8. 8.

    See Appendix E for a start on what \(E_{8}\) is.

  9. 9.

    This construct is named after early 20th century mathematician Émile Borel; see e.g. [194, 269, 394] for further discussion of this in the context of String Theory.

  10. 10.

    This is named after physicists Fernando Barbero and Giorgio Immirzi. See Sect. 24.9 for the geometrical meaning of this parameter and of the corresponding version of Ashtekar variables.

  11. 11.

    Branes provide further ways of hiding extra dimensions, such as ‘warping’, which are a further large source of phenomenological nonuniqueness.

  12. 12.

    The ‘D’ here stands for Dirichlet boundary-value problem [220], named after 19th century mathematician Gustav Dirichlet.

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  1. DAMTP, Centre for Mathematical Sciences, Cambridge, UK

    Edward Anderson

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Anderson, E. (2017). Quantum Gravity Programs. In: The Problem of Time. Fundamental Theories of Physics, vol 190. Springer, Cham. https://doi.org/10.1007/978-3-319-58848-3_11

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