Spacetime curvature from ultra rapid measurements of quantum fields

Abstract

We write the curvature of spacetime in terms of the excitation probability of particle detectors ultra-rapidly coupled to a quantum field. More precisely, we provide an expansion for the excitation probability of a smeared UDW detector delta-coupled to a real scalar quantum field in a curved background. Using a short distance expansion for the Wightman function, we express the excitation probability of a detector as the transition probability in Minkowski spacetime plus correction terms written as a function of the curvature tensors and the detector size. Comparing the excitation probability in curved spacetimes with its flat analog, we are able to express the components of the Ricci and Riemann curvature tensors as a function of physically measurable excitation probabilities of different shaped detectors.

7 pages + 3 appendices

References in corpus (10)

• The Unruh effect and its applications
• Quantum Measurement Information as a key to Energy Release from Local Vacuums
• Unruh-DeWitt detector response along static and circular geodesic trajectories for Schwarzschild-AdS black holes
• Non-perturbative analysis of entanglement harvesting from coherent field states
• Long-range entanglement in the Dirac vacuum
• Replacing the Notion of Spacetime Distance by the Notion of Correlation
• Harvesting entanglement from complex scalar and fermionic fields with linearly coupled particle detectors
• The geometry of spacetime from quantum measurements
• General features of the thermalization of particle detectors and the Unruh effect
• Measurements in QFT: Weakly coupled local particle detectors and entanglement harvesting

Cited by in corpus (5)

• Localized non-relativistic quantum systems in curved spacetimes: a general characterization of particle detector models
• Harvesting entanglement from the gravitational vacuum
• Quantum teleportation with relativistic communication from first principles
• Locally detecting UV cutoffs on a sphere with particle detectors
• Holographic reconstruction of asymptotically flat spacetimes