{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"834896aa6ae35b0bf3c003ccc8acf2463cc1b82725fff7fe3c2411e85321ab98","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"9f1a6060e3ae5266f98a44f23aed1d86c258a4e81da7320d3838d5b7f345a118","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"grav.qft-curved-backreaction.achronal-anec","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Quantum fields can have negative energy locally, which could in principle hold open wormholes or build time machines. A weaker condition, energy averaged along light rays that never come back to their own past, would exclude these, but it is unproved in curved spacetime.","posed_since":"2007","precise":"The averaged null energy condition, integral of $\\langle T_{ab}\\rangle k^{a} k^{b} d\\lambda \\ge 0$ along complete null geodesics with tangent $k^{a}$ and affine parameter $\\lambda$, is proved for quantum field theory in Minkowski space (Faulkner, Leigh, Parrikar, Wang 2016) but fails on some curved backgrounds. Prove or refute the self-consistent achronal version (Graham and Olum 2007): for every achronal complete null geodesic in a solution of semiclassical gravity, the integral is non-negative. An answer is a proof for a stated class of field theories and spacetimes, or a counterexample that solves the semiclassical equations.","problem_ref":null,"references":"","settled_by":"A proof of the achronal condition for interacting fields on self-consistent semiclassical backgrounds, or an explicit violating solution.","status_note":"Proved in Minkowski space (2016); no curved-spacetime proof as of 2026.","title":"Does the achronal averaged null energy condition hold in curved 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