algorithmic complexity in cosmology and quantum gravity算法复杂度在宇宙学和量子引力.pdfVIP

Entropy 2002, 4, 3–31 entropy ISSN 1099-4300 /entropy/ Algorithmic Complexity in Cosmology and Quan- tum Gravity V. Dzhunushaliev1 and D. Singleton2 1. Dept. Phys. and Microel. Engineer., Kyrgyz-Russian Slavic University, Bishkek, Kievskaya Str. 44, 720000, Kyrgyz Republic E-mail: dzhun@hotmail.kg 2. Physics Dept., CSU Fresno, 2345 East San Ramon Ave. M/S 37 Fresno, CA 93740-8031, USA E-mail: dougs@csufresno.ed Received: 13 August 2001 / Accepted: 21 December 2001 / Published: 30 January 2002 Abstract: In this article we use the idea of algorithmic complexity (AC) to study various cosmological scenarios, and as a means of quantizing the gravitational interac- tion. We look at 5D and 7D cosmological models where the Universe begins as a higher dimensional Planck size spacetime which fluctuates between Euclidean and Lorentzian signatures. These fluctuations are governed by the AC of the two different signatures. At some point a transition to a 4D Lorentzian signature Universe occurs, with the extra dimensions becoming “frozen” or non-dynamical. We also apply the idea of algorithmic complexity to study composite wormholes, the entropy of black holes, and the path integral for quantum gravity. Some of the physical consequences of the idea presented here are: the birth of the Universe with a fluctuating metric signature; the transition from a fluctuating metric signature to Lorentzian one; “frozen” extra dimensions as a consequence of this transition; quantum handles in the spacetime foam as regions with multidimensional gravity. Keywords: Algorithmic