Does quantum back-reaction forbid the formation of time machines? · revision history

Revision 1

Accepted · first revision · record

Title

Does quantum back-reaction forbid the formation of time machines?

Plain

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

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.

Settled by

A proof that back-reaction excludes compactly generated chronology horizons under stated assumptions, or an explicit counterexample with sub-Planckian curvature throughout.

Kind

well-posed

Answer type

yes-no

References

(empty)

Literature status

partially-resolved

Status 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.

Posed since

1992