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Concerning infeasibility of the wave functions of the universe. (English) Zbl 1327.83106

Summary: Difficulties with finding the general exact solutions to the Wheeler-DeWitt equation, i.e. the wave functions of the Universe, are known and well documented. However, the present paper draws attention to a completely different matter, which is rarely if ever discussed in relation to this equation, namely, the time complexity of the Wheeler-DeWitt equation, that is, the time required to exactly solve the equation for a given universe. As it is shown in the paper, whatever generic exact algorithm is used to solve the equation, most likely such an algorithm cannot be faster than brute force, which makes the wave functions of the Universe infeasible.

MSC:

83C45 Quantization of the gravitational field
83F05 Relativistic cosmology
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References:

[1] Ashtekar, A., Reuter, M., Rovelli, C.: From general relativity to quantum gravity. arXiv:1408.4336v1 [gr-qc] (2014)
[2] Kiefer, C.: Quantum gravity: General introduction and recent developments. Ann. Phys. 15, 129148 (2005). arXiv:gr-qc/0508120
[3] Albers, M., Kiefer, C., Reginatto, M.: Measurement analysis and quantum gravity. Phys Rev. D 78, 064051 (2008) · doi:10.1103/PhysRevD.78.064051
[4] Kiefer C.: Conceptual Problems in Quantum Gravity and Quantum Cosmology. ISRN Math. Phys. Volume 2013, Article ID 509316, 17 pages, 2013. arXiv:1401.3578v1 [gr-qc] (2014) · Zbl 1273.83069
[5] Bassi, A., Lochan, K., Satin, S., Singh, T.P, Ulbricht, H.: Models of wave-function collapse, underlying theories, and experimental tests. Rev. Mod. Phys. 85, 471527 (2013) · doi:10.1103/RevModPhys.85.471
[6] Singh, T.: Quantum mechanics without spacetime: a case for noncommutative geometry. arXiv:gr-qc0510042v1 (2005)
[7] Penrose, R.: On the gravitization of quantum mechanics 1: Quantum state reduction. Found. Phys. 445, 557-575 (2014) · Zbl 1311.81009 · doi:10.1007/s10701-013-9770-0
[8] Diósi, L.: Gravity-Related Wave Function Collapse Is Superfluid He Exceptional?. Found. Phys. (2014). doi:10.1007/s10701-013-9767-8 · Zbl 1304.81022
[9] DeWitt, B.: Quantum theory of gravity I. The canonical theory. Phys. Rev 160, 1113 (1967) · Zbl 0158.46504 · doi:10.1103/PhysRev.160.1113
[10] Hartle, J., Hawking, S.: Wave function of the universe. Phys. Rev. D 28, 2960 (1983) · Zbl 1370.83118 · doi:10.1103/PhysRevD.28.2960
[11] Carlip, S.: Quantum gravity: a progress report. arXiv:gr-qc/0108040v1 (2001) · Zbl 1311.81009
[12] Kiefer, C.; Ehlers, J. (ed.); Friedrich, H. (ed.), The Semiclassical Approximation to Quantum Gravity (1994), Berlin
[13] Lucas, A.: Ising formulations of many NP problems. Front. Phys 2(5), 1-15 (2014)
[14] Woeginger, G.: Exact Algorithms for NP-hard Problems: A Survey. Combinatorial Optimization - Eureka, You Shrink! Springer-Verlag, pp. 185-207 (2003) · Zbl 1024.68529
[15] Lokshtanov, D., Marx, D., Saurabh, S.: Lower bounds based on the exponential time hypothesis. Bulletin of the EATCS 84, 41-71 (2011) · Zbl 1258.68068
[16] Vilenkin, A.: Interpretation of the wave function of the universe. Phys. Rev. D 39, 111622 (1989) · doi:10.1103/PhysRevD.39.1116
[17] Kiefer, C.: Wave packets in minisuperspace. Phys. Rev. D 38, 176172 (1988) · doi:10.1103/PhysRevD.38.1761
[18] Calzetta, E., Gonzalez, J.: Chaos and semiclassical limit in quantum cosmology. Phys. Rev. D 51, 68218 (1995)
[19] Cornish, N., Shellard, E.: Chaos in quantum cosmology. Phys. Rev. Lett. 81, 35714 (1998) · doi:10.1103/PhysRevLett.81.3571
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