Centripetal force on Casimir energies in $\kappa$-deformed rotating frame

TL;DR

This paper explores how a fundamental length scale in $ppa$-space-time affects the centripetal force on a rotating Casimir apparatus, revealing that Casimir energy behaves like mass under rotation.

Contribution

It models the rotating Casimir system in $ppa$-deformed coordinates and demonstrates that Casimir energy experiences centripetal forces similar to mass, confirming mass-energy equivalence in this framework.

Findings

Centripetal force on a single Casimir plate in $ppa$-space-time is derived.

Centripetal force on parallel plates is calculated, including divergent self-energies.

Casimir energy obeys mass-energy equivalence under rotation in $ppa$-space-time.

Abstract

We investigate the implications of a fundamental length scale on the centripetal force on a rotating Casimir apparatus in $\kappa$-space-time. We model the Casimir apparatus rotating with constant angular speed using appropriate $\kappa$-deformed coordinates. We find the $\kappa$-deformed centripetal force on a single plate, as well as for parallel plates. We show that the Casimir energy, including the divergent part (self energies of the plates) experiences centripetal forces like a conventional mass. We also find centripetal force on oriented parallel plates rotating with constant angular speed in $\kappa$-space-time. Results show that the mass-energy equivalence principle holds in the $\kappa$-space-time.