Abstract
Treatises on Time, the Beginning and the End date back at least twenty-five centuries. Does the flow of time have an objective, universal meaning beyond human perception? Or, is it fundamentally only a convenient, and perhaps merely psychological, notion? Are its properties tied to the specifics of observers such as their location and state of motion? Did the physical universe have a finite beginning, or has it been evolving eternally? Leading thinkers across cultures meditated on these issues and arrived at definite but strikingly different answers. For example, in the sixth century B.C.E., Gautama Buddha taught that ‘a period of time’ is a purely conventional notion; time and space exist only in relation to our experience, and the universe is eternal. In the Christian thought, however, the universe had a finite beginning, and there was debate as to whether time represents ‘movement’ of bodies or whether it flows only in the soul. In the fourth century C.E., St. Augustine held that time itself started with the world.
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References
Ashtekar, A. 1986. New variables for classical and quantum gravity. Phys. Rev. Lett. 57: 2244–2247.
——. 1987. New Hamiltonian formulation of general relativity. Phys. Rev. D36: 1587–1602.
——. 1991. Lectures on non-perturbative canonical gravity. Notes prepared in collaboration with R. S. Tate, chap. 10. Singapore:World Scientific.
——. 2005. Gravity and the quantum. New J. Phys. 7: 198; arXiv:gr-qc/0410054.
Ashtekar, A., Bojowald, M. and Lewandowski, J. 2003. Mathematical structure of loop quantum cosmology. Adv. Theor. Math. Phys. 7: 233–268; gr-qc/0304074.
Ashtekar, A., Bojowald, M. andWillis, J. 2004. Corrections to Friedmann equations induced by quantum geometry, IGPG preprint.
Ashtekar, A. and Lewandowski, J. 1994. Representation theory of analytic holonomy algebras, in Knots and Quantum Gravity, ed J. Baez. Oxford: Oxford University Press.
——. 1995a. Differential geometry on the space of connections using projective techniques. J. Geom. Phys. 17: 191–230.
——. 1995b. Projective techniques and functional integration. J. Math. Phys. 36: 2170–2191.
——. 2004. Background independent quantum gravity: A status report. Class. Quant. Grav. 21: R53–R152; arXiv:gr-qc/0404018.
Ashtekar, A., Pawlowski, T. and Singh, P. 2006a. Quantum nature of the big bang. Phys. Rev. Lett. 96: 141301; arXiv:gr-qc/0602086.
——. 2006b. Quantum nature of the big bang: An analytical and numerical investigation I; arXiv:gr-qc/0604013.
——. 2006c. Quantum nature of the big bang: Improved dynamics; arXiv: gr-qc/0607039.
Ashtekar, A. and Singh, P. 2011. Loop quantum cosmology: A Status Report. Class. Quantum Grav. arXiv:1108.0893 (in preparation).
Baez, J. C. 1994. Generalized measures in gauge theory. Lett. Math. Phys. 31: 213–223.
——. 1996. Spin networks in non-perturbative quantum gravity, in The Interface of Knots and Physics, ed. Kauffman L. Providence: American Mathematical Society, pp. 167–203.
Bojowald, M. 2001. Absence of singularity in loop quantum cosmology. Phys. Rev. Lett. 86: 5227–5230; arXiv:gr-qc/0102069.
——. 2002. Isotropic loop quantum cosmology. Class. Quant. Grav. 19: 2717–2741; arXiv:gr-qc/0202077.
——. 2005. Loop quantum cosmology. Liv. Rev. Rel. 8: 11; arXiv:gr-qc/0601085. ojowald, M., Hernandez, H. H. and Morales-Tecotl, H. A. 2001. Perturbative degrees of freedom in loop quantum gravity: Anisotropies. Class. Quant. Grav. 18: L117–L127; arXiv:gr-qc/0511058.
Fleishchack, C. 2004. Representations of the Weyl algebra in quantum geometry; arXiv:math-ph/0407006.
Gasperini, M. and Veneziano, G. 2003. The pre-big bang scenario in string cosmology. Phys. Rep. 373: 1; arXiv:hep-th/0207130.
Khoury, J., Ovrut, B. A., Steinhardt, P. J. and Turok, N. 2001. The ekpyrotic universe: Colliding branes and the origin of the hot big bang. Phys. Rev. D64, 123522, hep-th/0103239.
Khoury, J., Ovrut, B., Seiberg, N., Steinhardt, P. J. and Turok, N. 2002. From big crunch to big bang. Phys. Rev. D65, 086007, hep-th/0108187.
Lauscher, O. and Reuter, M. 2005. Asymptotic safety in quantum Einstein gravity: nonperturbative renormalizability and fractal spacetime structure; arXiv: hep-th/0511260.
Lewandowski, J., Okolow, A., Sahlmann, H. and Thiemann, T. 2005. Uniqueness of diffeomorphism invariant states on holonomy flux algebras; arXiv: gr-qc/0504147.
Marolf, D. 1995a. Refined algebraic quantization: Systems with a single constraint; arXives:gr-qc/9508015.
——. 1995b. Quantum observables and recollapsing dynamics. Class. Quant. Grav. 12: 1199–1220.
Marolf, D. and Mour˜ao, J. 1995. On the support of the Ashtekar-Lewandowski measure. Commun. Math. Phys. 170: 583–606.
Percacci, R. and Perini, D. 2003. Asymptotic safety of gravity coupled to matter. Phys. Rev. D68: 044018.
Rovelli, C. 2004. Quantum Gravity. Cambridge: Cambridge University Press.
Rovelli, C. and Smolin, L. 1995. Spin networks and quantum gravity. Phys. Rev. D52: 5743–5759.
Thiemann, T. 2003. The Phoenix project: Master constraint program for loop quantum gravity; arXiv:gr-qc/0305080.
——. 2007. Introduction to Modern Canonical Quantum General Relativity. Cambridge: Cambridge University Press.
Willis, J. 2004. On the low energy ramifications and a mathematical extension of loop quantum gravity. Ph.D. dissertation, The Pennsylvania State University, University Park, PA.
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Ashtekar, A. (2012). The Issue of the Beginning in Quantum Gravity. In: Lehner, C., Renn, J., Schemmel, M. (eds) Einstein and the Changing Worldviews of Physics. Einstein Studies, vol 12. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4940-1_18
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