Mach's Principle in the Acoustic World

TL;DR

This paper explores how coupled bubble oscillations in a cluster relate to Mach's Principle, deriving relations analogous to Eddington and Sciama relations in an acoustic context.

Contribution

It introduces a novel analogy between bubble cluster interactions and Mach's Principle, deriving new relations similar to Eddington and Sciama relations.

Findings

Derived relations analogous to Eddington and Sciama relations

Identified the role of bubble density in cluster dynamics

Established a connection between acoustic interactions and Mach's Principle

Abstract

The aim of this paper is to investigate the coupled oscillations of multiple bubbles within a cluster. The interaction between a bubble and the other bubbles in a cluster produces an additional mass. For a fixed number of bubbles ( ) and uniformly distributed, in case of a certain value of the bubble density, we deduce the relations analogous to the Eddington relation (between the cluster radius and the bubble radius) and the Sciama relation (between the cluster radius and the gravitoacoustic radius) according to Mach's Principle.