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

Understand

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.