Nondifferentiable Dynamic: Two Examples
Abstract
Some nondifferentiable quantities (for example, the metric signature) can be the independent physical degrees of freedom. It is supposed that in quantum gravity these degrees of freedom can fluctuate. Two examples of such quantum fluctuation are considered: a quantum interchange of the sign of two components of the 5D metric and a quantum fluctuation between Euclidean and Lorentzian metrics. The first case leads to a spin-like structure on the throat of composite wormhole and to a possible inner structure of the string. The second case leads to a quantum birth of the non-singular Euclidean Universe with frozen dimension. The probability for such quantum fluctuations is connected with an algorithmical complexity of the Einstein equations.
Cite
@article{arxiv.gr-qc/9912018,
title = {Nondifferentiable Dynamic: Two Examples},
author = {V. Dzhunushaliev},
journal= {arXiv preprint arXiv:gr-qc/9912018},
year = {2015}
}
Comments
essential changes: the initial equations in section III are changed, as the consequence the obtained solution describes the quantum birth of the nonsingular Universe with the matter (electromagnetic field=nondiagonal components of the MD metric)