Mach's relativity of rotation in light of contemporary physics

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.