Does quantum back-reaction forbid the formation of time machines?
In plain words
General relativity allows spacetimes with closed loops in time, along which one could return to one's own past. Hawking conjectured that quantum effects always destroy such loops as they start to form, but this is shown only in limited cases.
Precise statement
For a spacetime that develops a compactly generated Cauchy horizon (chronology horizon) from regular initial data, the renormalized $\langle T_{ab}\rangle$ of a linear quantum field is not a well-defined distribution at certain base points of the horizon (Kay, Radzikowski, Wald 1997). Determine whether semiclassical or quantum gravitational dynamics generically prevents closed timelike curves from forming, given that the breakdown occurs within a Planck distance of the horizon where the semiclassical approximation itself fails. An answer is a theorem in a controlled approximation, or a model spacetime in which closed timelike curves form with bounded $\langle T_{ab}\rangle$ and curvature below the Planck scale.
What would settle it
A proof that back-reaction excludes compactly generated chronology horizons under stated assumptions, or an explicit counterexample with sub-Planckian curvature throughout.
Status in the literature
Unverified note
The Kay-Radzikowski-Wald theorem (1997) shows that field theory on the fixed background breaks down at the horizon; whether the dynamics prevents the horizon is open as of 2026.