Sagnac delay in the Kerr-dS space-time: Implications for Mach's principle

TL;DR

This paper investigates how the Sagnac delay in Kerr-de Sitter spacetime relates to Mach's principle, showing that even in the absence of mass and cosmological constant, a non-zero delay indicates an absolute spacetime structure.

Contribution

It provides a novel analysis of the Sagnac delay in Kerr-dS spacetime, highlighting its implications for the existence of an absolute spacetime independent of matter.

Findings

Non-zero Sagnac delay persists in Minkowski limit.

Different behaviors of Sagnac delay for geodesic and non-geodesic observers.

Supports the idea of an absolute spacetime structure.

Abstract

Relativistic twin paradox can have important implications for Mach's principle. It has been recently argued that the behavior of the time asynchrony (different aging of twins) between two flying clocks along closed loops can be attributed to the existence of an absolute spacetime, which makes Mach's principle unfeasible. In this paper, we shall revisit, and support, this argument from a different viewpoint using the Sagnac delay. This is possible since the above time asynchrony is known to be exactly the same as the Sagnac delay between two circumnavigating light rays re-uniting at the orbiting source/receiver. We shall calculate the effect of mass $M$ and cosmological constant $\Lambda$ on the delay in the general case of Kerr-de Sitter spacetime. It follows that, in the independent limits $M\rightarrow 0$, spin $a\rightarrow 0$ and $\Lambda\rightarrow 0$, while the Kerr-dS metric reduces to Minkowski metric, the clocks need not tick in consonance since there will still appear a non-zero observable Sagnac delay. While we do not measure spacetime itself, we do measure the Sagnac effect, which signifies an absolute substantive Minkowski spacetime instead of a void. We shall demonstrate a completely different limiting behavior of Sagnac delay, heretofore unknown, between the case of non-geodesic and geodesic source/observer motion.