Large fluctuations of time and change of space-time signature

Abstract

We consider five-dimensional cylindric spacetime $V^5$ with foliation of codimension ~1. The leaves of this foliation are four-dimensional &#34;parallel&#34; universes. The metric of five-dimensional spacetime and induced metrics of four-dimensional universes are flat. The &#34;large&#34; fluctuations of the 5-metric are studied. These fluctuations depend only on the coordinate $x^0$, and under these fluctuations the curvature of $V^5$ is not zero. The contribution of the fluctuations in the Feynman path integral over five-dimensional trajectories doesn&#39;t change the amplitude of the probability of the real physical four-dimensional universe. Moreover the large fluctuations of 5-metric $G_{AB}$ are large fluctuations for physical four-dimensional universe $V^4$ and change signature of $V^4$. The change of the signature from $<+--->$ to $<---->$ and inversely occurs in the all 3-dimensional space simultaneously (in absolute time) and can take arbitrarily large period of time.