Quantum Energy Inequalities along stationary worldlines
arXiv:2301.01698 · doi:10.1088/1361-6382/ace233
Abstract
Quantum energy inequalities (QEIs) are lower bounds on the averaged energy density of a quantum field. They have been proved for various field theories in general curved spacetimes but the explicit lower bound is not easily calculated in closed form. In this paper we study QEIs for the massless minimally coupled scalar field in four-dimensional Minkowski spacetime along stationary worldlines - curves whose velocity evolves under a 1-parameter Lorentz subgroup -- and find closed expressions for the QEI bound, in terms of curvature invariants of the worldline. Our general results are illustrated by specific computations for the six protoypical stationary worldlines. When the averaging period is taken to infinity, the QEI bound is consistent with a constant energy density along the worldline. For inertial and uniformly linearly accelerated worldlines, this constant value is attained by the Minkowski and Rindler vacuums respectively. It is an open question as to whether the bounds for other stationary worldlines are attained by other states of interest.
arXiv comment27 pages, 1 figure. v2 29 pages, 1 figure - additional commentary and references added. Final version to appear in Class Q Grav
References in corpus (25)
- The warp drive: hyper-fast travel within general relativity
- The generally covariant locality principle -- A new paradigm for local quantum physics
- Averaged Energy Conditions and Quantum Inequalities
- Energy conditions in general relativity and quantum field theory
- Quantum Field Theory Constrains Traversable Wormhole Geometries
- Bounds on negative energy densities in flat spacetime
- A general worldline quantum inequality
- The unphysical nature of "Warp Drive"
- The Quantum Interest Conjecture
- Interferometric Unruh detectors for Bose-Einstein condensates
- Absolute quantum energy inequalities in curved spacetime
- On wormholes with arbitrarily small quantities of exotic matter
- Bounds on negative energy densities in static space-times
- Local Temperature in Curved Spacetime
- How often does the Unruh-DeWitt detector click beyond four dimensions?
- Energy Inequalities in Quantum Field Theory
- Quantum Energy Inequalities and local covariance I: Globally hyperbolic spacetimes
- Quantum inequalities and `quantum interest' as eigenvalue problems
- Quantum energy inequalities and local covariance II: Categorical formulation
- Quantum inequality in spacetimes with small curvature
- Unruh-like effects: Effective temperatures along stationary worldlines
- Thermal Wightman Functions and Renormalized Stress Tensors in the Rindler Wedge
- A semiclassical singularity theorem
- A quantum energy inequality in the Sine--Gordon model
- Quantum inequality for a scalar field with a background potential