Machian quantum gravity

This paper presents a theory of quantum gravity incorporating Machian mechanics. Mach's ideas about mechanics are summarized into six principles. Newton's bucket argument is then generalized to relativity to show that the theory lacks a well-defined notion of a rigid rotation. On that account, the Painlevé metric describing a locally rigid rotation is studied and the time dilation effect is found to occur in rotation. Furthermore, the metric is locally Euclidean with a torus topology under Wick rotation. This sets forth the meaning of the imaginary time and facilitates derivation of the rotating Unruh effect with the periodicity trick. To quantize this spacetime, quantum states are reformulated under the Machian considerations. In particular, the vacuum ground state is promoted to a superposition of gravitation with respect to the fixed timeslice. Within this framework, the vierbein formalism of gravity with an extra Lagrange multiplier is adopted to define the rigid rotation, and the variations of the action lead to the Wheeler-DeWitt equation. Its solution represents a graviton induced by the rotation. It shows that the graviton non-thermally contributes to the particle emission rate in the rotating Unruh effect. This subleading correction can locally be measured by the Unruh-Dewitt particle detector.