Implications of Kleinian relativity

TL;DR

This paper develops a covariant mechanics framework for particles in Kleinian spacetime, revealing novel effects like time contraction and length dilatation, and explores quantum implications and metamaterial analogs.

Contribution

It introduces a new covariant mechanics for Kleinian spacetime, deriving modified relativistic formulas and analyzing quantum and metamaterial analog systems.

Findings

Time contraction and length dilatation effects in Kleinian spacetime

New expressions for relativistic momentum and energy

Metamaterial analog system modeling Klein spacetime

Abstract

Inspired in metamaterials, we present a covariant mechanics for particles in Kleinian spacetime and show some of its effects, such as time contraction and length dilatation. We present the new expressions for relativistic momentum and energy for a point-like particle. To illustrate the new mechanics, we describe the particle motion under a uniform Newtonian gravitational field. We also revisit the free spin-half particle problem in Kleinian spacetime, discuss some quantum implications, like the constraint on the dispersion relation for Weyl fermions, and adapt a metamaterial analog system to Klein spacetime.