Mach's relativity of rotation in light of contemporary physics

TL;DR

This paper critically examines Mach's relational theory of space, arguing that modern relativity distinguishes between rotating systems and the universe, thus challenging Mach's ideas and showing their limited applicability.

Contribution

The paper refutes Mach's relational notion of space by analyzing its inconsistencies with special and general relativity and clarifies the distinctions between rotating systems and the universe.

Findings

Relativity distinguishes between rotating systems and the universe.

Mach's theory is only applicable at infinitesimal angular velocities.

Modern physics challenges Mach's relational space concept.

Abstract

Mach argued for a relational rather than an absolute notion of space, insisting that centrifugal forces inside a rotating object such as a bucket can be reproduced by keeping the bucket fixed and rotating the universe. In response to a paper of ours denying the validity of Mach's views, Bhadra and Das elaborate on Mach's position. We address several of their arguments and show that Mach's relational notion of space is wrong-headed. Special and general relativity distinguish between a bucket (i.e. any system) rotating in a fixed universe and a bucket fixed in a rotating universe and between a non-rotating bucket in a non-rotating universe and a co-rotating bucket in a rotating universe, distinctions that go against Mach's relational theory of space. Even when taken on its own terms, Mach's theory can apply only to single point-like buckets rotating at infinitesimal angular velocities.