Newton argued that the concave meniscus of water in a spinning bucket proved rotation relative to an absolute, immaterial space. Mach refuted this by demonstrating that acceleration is only physically meaningful relative to the aggregate cosmic mass distribution. Consequently, a stationary bucket surrounded by a rotating cosmos would produce the identical concave curvature via inductive gravitational forces.

In Machian scalar-tensor frameworks and gravitoelectromagnetic theory, inertia emerges from the cumulative cosmic potential condition satisfying the dimensionless order of magnitude sum of G m_i divided by r_i c squared approaching unity. This cosmological relation indicates that local inertial resistance is an inductive back-reaction mediated by the entire mass within the cosmological horizon.

Einstein formulated General Relativity under the direct philosophical inspiration of Mach, successfully capturing inductive frame dragging and the Lense-Thirring effect. However, General Relativity falls short of being purely Machian because it permits vacuum solutions such as Minkowski and Gödel metrics that possess inertial structures in the total absence of matter.