Global versus Local -- Mach's Principle versus the Equivalence Principle

TL;DR

This paper explores the relationship between Mach's principle and the equivalence principle, proposing that quantum effects like Hawking and Unruh radiation reflect a thermal version of Mach's principle, leading to a violation of the equivalence principle.

Contribution

It introduces a novel perspective linking quantum radiation effects to a thermal form of Mach's principle, challenging the universality of the equivalence principle.

Findings

Hawking and Unruh temperatures differ for the same acceleration.

The violation of the equivalence principle depends on proximity to the horizon.

The violation diminishes as the horizon is approached.

Abstract

The equivalence principle is the conceptual basis for general relativity. In contrast Mach's principle, although said to have been influential on Einstein in his formulation of general relativity, has not been shown to be central to the structure of general relativity. In this essay we suggest that the quantum effects of Hawking and Unruh radiation are a manifestation of a {\it thermal} Mach's principle, where the local thermodynamic properties of the system are determined by the non-local structure of the quantum fields which determine the vacuum of a given spacetime. By comparing Hawking and Unruh temperatures for the same local acceleration we find a violation of the Einstein elevator version of the equivalence principle, which vanishes in the limit that the horizon is approached.