Approaches to Quantum Gravity

Prolegomena to any future Quantum Gravity 65causal set theory, causal dynamic triangulations, twistor theory; and attempts toderive S-T structures as emerging from radically different underlying entities, suchas the symmetries of coherent states in quantum information theory (such theoriesare reviewed elsewhere in this volume). It is by no means certain that any of theconservative approaches will lead to a fruitful fusion of quantum theory and GR –indeed, it is even probable that they will not. But until some approach has beendeveloped leading to a consensus in the QG community, every approach deservesto be explored to its limits, if only to draw from the limited successes and ultimatefailure of each such attempt, lessons for the formulation of better alternativeapproaches.AcknowledgementsI thank Mihaela Iftime and Christian Wuthrich [38] for reading an earlier draft ofthis paper and each making several valuable suggestions for improvements adoptedin this version.References[1] A. Ashtekar, Asymptotic Quantization (Naples, Bibliopolis, 1987).[2] A. Ashtekar, J. Lewandowski, “Background independent quantum gravity: a statusreport,” (2004), arXiv:gr-qc/0404018 v1.[3] J. Baez, Quantum quandaries: a category-theoretic perspective, in D. P. Rickles,S. French and J. Saatsi, eds., Structural Foundations of Quantum Gravity (OxfordUniversity Press, 2006), pp. 240–265.[4] P. G. Bergmann and G. Smith, Measurability analysis for the linearized gravitationalfield, General Relativity and Gravitation 14 (1982), 1131–1166.[5] J. Bicák, The role of exact solutions of Einstein’s equations in the development ofGeneral Relativity, (2000), arXiv:gr-qc/0004016 v1.[6] B. S. DeWitt, The quantization of geometry, in Louis Witten (ed.), Gravitation: AnIntroduction to Current Research, New York: J. Wiley and Sons, pp. 266-381 (1962).[7] B. S. DeWitt, The Global Approach to Quantum Field Theory, 2vols.(OxfordClarendon Press, 2003).[8] R. A. D’Inverno, J. Stachel , “Conformal two structure as the gravitational degrees offreedom in General Relativity,” Journal of Mathematical Physics 19 (1978),2447–2460.[9] B. Dittrich, T. Thiemann, “Are the spectra of geometrical operators in LoopQuantum Gravity really discrete?” (2007), arxXiv:0708v2.[10] N. A. Doughty, Lagrangian Interaction/ An Introduction to Relativistic Symmetry inElectrodynamics and Gravitation (Reading, MA/Addison-Wesley, 1990).[11] J. Ehlers, F. A. E. Pirani, A. Schild, “The geometry of free fall and lightpropagation,” in General Relativity/Papers in Honor of J. L. Synge,L. O’Raifeartaigh, ed. (Oxford: Clarendon Press, 1972) pp. 63–85.[12] H. Friedrich, A. Rendall, “The Cauchy problem for the Einstein equations” (2000),arXiv:gr-qc/0002074 v1.