The birth of the Universe as a result of the change of the metric signature
arXiv:2207.02689 · doi:10.3390/physics4010012
Abstract
In this paper, I discuss the idea that the birth of our Universe may be a result of a quantum transition from a physical continuum with the Euclidean signature to a Lorentzian spacetime. A similar idea was expressed by Andrei D. Sakharov. At the classical level, the idea was studied by George F. R. Ellis and his collaborators, who explored if solutions to the classical Einstein equation exist which admit a change of metric signature. The present paper aims at examining possible realizations of this idea at the level of quantum gravity, in the framework of the Wheeler - DeWitt theory and in the extended phase space approach to quantization of gravity. I intend to answer the questions: Does the Hartle - Hawking wave function imply such a realization? How can this idea be realized in the extended phase space approach to quantum gravity, where the change of signature is described by imposing special conditions on -component of the metric in different regions of the physical continuum? The conclusion is that the idea can be realized from a formal mathematical point of view, but it can hardly help in understanding how spacetime structure and time itself appeared from a timeless continuum.
arXiv comment15 pages, 1 figure; the paper was written for the Special Issue titled "Light on Dark Worlds - A Themed Issue in Honor of Professor Maxim Yu. Khlopov on the Occasion of His 70th Birthday"
References in corpus (16)
- Open Inflation Without False Vacua
- Quantum Creation of an Open Inflationary Universe
- Dynamical Origin of the Lorentzian Signature of Spacetime
- Why is Spacetime Lorentzian?
- The strange equation of quantum gravity
- Is the Wheeler -- DeWitt equation more fundamental than the Schrödinger equation?
- No Time for Time from No-Time
- Loop quantum gravity, signature change, and the no-boundary proposal
- Quantum geometrodynamics of the Bianchi IX model in extended phase space
- Dynamical Generation of Spacetime Signature by Massive Quantum Fields on a Topologically Non-Trivial Background
- The exact cosmological solution to the dynamical equations for the Bianchi IX model
- On the meaning of the wave function of the Universe
- Quantum geometrodynamics in extended phase space - I. Physical problems of interpretation and mathematical problems of gauge invariance
- Alternative route towards the change of metric signature
- Is the Copenhagen interpretation inapplicable to Quantum Cosmology?
- On A. D. Sakharov's hypothesis of cosmological transitions with changes in the signature of the metric