Three Kinds of Special Relativity via Inverse Wick Rotation

TL;DR

This paper explores three types of special relativity derived from inverse Wick rotations of different 4-dimensional spaces, linking them to de Sitter, Minkowski, and anti-de Sitter geometries and proposing an instanton tunneling scenario related to the cosmological constant and multiverse.

Contribution

It introduces a unified perspective on special relativity through inverse Wick rotations of various 4D spaces, highlighting their physical significance and potential cosmological implications.

Findings

Identification of three kinds of special relativity in different spacetime geometries.

Proposal of an instanton tunneling scenario explaining positive cosmological constant.

Linking the inverse Wick rotation framework to multiverse theories.

Abstract

Since the special relativity can be viewed as the physics in an inverse Wick rotation of 4-d Euclid space, which is at almost equal footing with the 4-d Riemann/Lobachevski space, there should be important physics in the inverse Wick rotation of 4-d Riemann/Lobachevski space. Thus, there are three kinds of special relativity in de Sitter/Minkowski/anti-de Sitter space at almost equal footing, respectively. There is an instanton tunnelling scenario in the Riemann-de Sitter case that may explain why $\La$ be positive and link with the multiverse.