Abstract

In this article we use the idea of algorithmic complexity (AC) to study various cosmological scenarios, and as a means of quantizing the ravitational interaction. 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 overned 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.

Highlights

  • The modern cosmological paradigm is that Universe started from the Big Bang, which was the origin of all matter and energy, and gave rise to the physical laws of Nature: Einstein gravity, Yang-Mills equations, quantum mechanics etc

  • S is an action which has contributions from the fields that occur in the given Universe, and the factor A is connected with the type of physical laws in the Universe

  • In this paper we have considered the possibility that Nature can have changing the physical laws

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Summary

Introduction

The modern cosmological paradigm is that Universe started from the Big Bang, which was the origin of all matter and energy, and gave rise to the physical laws of Nature: Einstein gravity, Yang-Mills equations, quantum mechanics etc. In this article we examine the possibility that the Big Bang was a quantum birth (i.e. a quantum fluctuation) of the Universe from Nothing With this view one can imagine that there could exist other Universes with different physical laws (e.g. non-Einstein gravity). In particular Universes with different physical laws (field equations) are described by different algorithms The length of these algorithms affects the probability that this Universe with a certain set of physical laws will fluctuate into existence. We will give mathematical details to this hypothesis about the connection between algorithmic complexity and the probability for the existence of a given Universe with certain fields and certain physical laws

Kolmogorov’s algorithmic complexity
A toy model for the birth of Minkowski space
Fluctuation of the metric signature
The 5D Fluctuating Universe
The 7D Fluctuating Universe
Regular Universe
Non-singular birth of the Universe
Algorithmic complexity applied to non-cosmological systems
A composite 5D wormhole as the sum of Holographic principle and the AC idea
Algorithmic complexity and the path integral
Conclusions
A Gravitational equations
Full Text
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