Generalized Uncertainty Principle for Quantum Fields in Curved Spacetime

Abstract

Quantum fields in curved spacetimes have scattering processes that exhibit decoherence. This is due to the partition of spacetime, and consequentially the Hilbert space, by horizons. The acceleration or gravity normal to these horizons is the determinant of the temperature associated with these horizons. Here we examine the vacuum as measured by an accelerated observer somewhat differently. Thermal creation and annihilation operators act upon pure states to determine thermal distributions of states. The resultant properties of these operators are such that these operators act on a pure state description of a squeezed vacuum to produce increased uncertainty in both conjugate variables. This then demonstrates that the uncertainty relationship of quantum mechanics is more general.