Quantum-field-theoretic realizability and stability of traversable-wormhole time machines: the open questions of Morris, Thorne, and Yurtsever

Morris, Thorne, and Yurtsever (Phys. Rev. Lett. 61, 1446 (1988)) showed that in classical general relativity a traversable wormhole can be converted into a time machine, provided its throat is supported by stress-energy violating the weak energy condition, and they posed five interlinked questions that must be answered before one can decide whether wormhole-based time machines are physically realizable: (i) does quantum field theory permit the required stress-energy tensors, i.e. are averaged-weak-energy-condition violations allowed in realistic quantum states and material models; (ii) can macroscopic wormholes be created from an initially simply connected universe; (iii) is the Cauchy horizon of the wormhole time machine stable once quantum backreaction and nonlinear dynamics are included, beyond the heuristic $(f/D)B<1$ criterion; (iv) if the horizon is stable, is the extension beyond it unique and the evolution of classical and quantum fields across it well posed; and (v) does a deeper principle - an averaged-energy-condition theorem in quantum field theory, a version of cosmic censorship, or a yet-unknown law of quantum gravity - forbid traversable wormholes or their conversion into time machines?

Background

General relativity permits spacetime metrics with 'handles' - wormholes - connecting otherwise distant regions. A wormhole is traversable if an observer can pass through its throat in a finite proper time and return. Holding a traversable throat open requires 'exotic matter': stress-energy violating the weak energy condition (WEC), the requirement that every physical observer measure a nonnegative local energy density. Classical fields obeying reasonable equations of state satisfy the WEC, so a traversable wormhole is impossible in purely classical general relativity with ordinary matter - but quantum field theory does not respect the WEC (the Casimir effect between conducting plates produces negative energy density). Morris, Thorne, and Yurtsever (MTY) therefore asked whether quantum field theory permits the specific stress-energy tensors a macroscopic traversable wormhole needs, or whether an averaged version of the energy condition - the averaged weak energy condition (AWEC), which integrates the energy density along a complete timelike (or, in null form, null) geodesic and is violated far more reluctantly by quantum fields - is enforced as a theorem.

MTY went further: if the two mouths of a traversable wormhole are moved relative to one another in the ordinary relativistic way, the wormhole becomes a time machine - a spacetime region containing closed timelike curves (CTCs), worldlines along which an observer returns to their own past. The onset of causality violation is a Cauchy horizon, the boundary beyond which the initial data no longer uniquely determine the evolution (the region beyond it is not globally hyperbolic). In earlier model spacetimes, such as Misner space (flat spacetime with points periodically identified along a Lorentz boost, the simplest laboratory for CTCs), blueshifted radiation piles up at this 'chronology horizon' - a Misner-type instability. MTY gave a heuristic classical argument that in the wormhole case this instability is absent: if $(f/D)B<1$, where $f$ is the focal length of the diverging-lens action of the throat on passing radiation, $D$ is the mouth-to-mouth distance along the closed generator, and $B$ is the Doppler boost factor of the moving mouth, then the reduction in wave amplitude dominates over the boost in frequency, leaving the Cauchy horizon immune to this instability; they suspected the horizon is in fact fully stable, which would make it a counterexample to strong cosmic censorship (the conjecture that generic maximal Cauchy developments of initial data are inextendible).

What the letter leaves open is exactly the physics on which all of this rests: whether quantum field theory of realistic matter supplies the needed exotic stress-energy; whether quantum gravity permits macroscopic wormholes to be created from simply connected space at all (for example by enlarging a handle drawn from the 'quantum foam', the hypothesized Planck-scale froth of fluctuating spacetime topology); whether the Cauchy horizon survives the full semiclassical analysis, including the backreaction of quantum fields - the effect of the renormalized expectation value $\langle T_{\mu\nu}\rangle$ of the quantum stress tensor on the metric through the semiclassical Einstein equations; whether evolution across a stable Cauchy horizon is unique and well posed for classical and quantum fields; and whether some deeper principle forbids the whole construction. Three later notions: chronology protection is Hawking's conjecture that the laws of physics prevent the formation of CTCs; a quantum inequality is a Ford-Roman type bound restricting the magnitude and duration of negative energy densities; a Hadamard two-point function is the standard short-distance singularity structure required of physically admissible quantum states on curved spacetime.

Problem Statement

Determine, within semiclassical gravity and ultimately quantum gravity, whether the Morris-Thorne-Yurtsever wormhole time machine is physically realizable, by answering the five interlinked questions the letter poses:

(i) Does quantum field theory permit the specific stress-energy tensors required to support a traversable wormhole throat - in particular, are violations of the averaged weak energy condition allowed in realistic quantum states and realistic material models of the supporting structure (for example, in MTY's illustrative model in which the throat is held open by charged plates, are the plate mass-to-charge-ratio constraints and the requirement that the plate separation $s$ lie below an electron Compton wavelength physically permissible), or does a general theorem forbid them?

(ii) Can macroscopic wormholes be created from an initially simply connected universe by any process allowed in quantum or semiclassical gravity without prohibitive Planck-scale phenomena or violations of cosmic censorship?

(iii) Is the criterion $(f/D)B<1$ sufficient in a full nonlinear analysis - including the backreaction of quantum fields and realistic perturbations - to guarantee the stability of the Cauchy horizon against Misner-type and other instabilities, or do other (classical or quantum) instability mechanisms arise that prevent evolution to the time-machine region?

(iv) If the Cauchy horizon is stable, is the extension beyond it unique in a physically meaningful sense for classical and quantum fields, and can well-posed evolution across such nonglobally hyperbolic regions be rigorously demonstrated?

(v) More generally, do deeper principles - for example, an averaged-energy-condition theorem in quantum field theory, a version of cosmic censorship, or a yet-unknown law of quantum gravity - forbid traversable wormholes or their conversion into time machines?

References

1. Robert M. Wald, “Dynamics in nonglobally hyperbolic, static space-times”, Journal of Mathematical Physics 21, 2802-2805 (1980). DOI 10.1063/1.524403, https://doi.org/10.1063/1.524403
2. Michael S. Morris, Kip S. Thorne, Ulvi Yurtsever, “Wormholes, Time Machines, and the Weak Energy Condition”, Physical Review Letters 61, 1446-1449 (1988). DOI 10.1103/PhysRevLett.61.1446, https://doi.org/10.1103/PhysRevLett.61.1446
3. Sung-Won Kim, Kip S. Thorne, “Do vacuum fluctuations prevent the creation of closed timelike curves?”, Physical Review D 43, 3929-3947 (1991). DOI 10.1103/PhysRevD.43.3929, https://doi.org/10.1103/PhysRevD.43.3929
4. S. W. Hawking, “Chronology protection conjecture”, Physical Review D 46, 603-611 (1992). DOI 10.1103/PhysRevD.46.603, https://doi.org/10.1103/PhysRevD.46.603
5. Matt Visser, “From wormhole to time machine: Remarks on Hawking's chronology protection conjecture”, Physical Review D 47, 554-565 (1993). DOI 10.1103/PhysRevD.47.554, https://doi.org/10.1103/PhysRevD.47.554
6. John L. Friedman, Kristin Schleich, Donald M. Witt, “Topological censorship”, Physical Review Letters 71, 1486-1489 (1993). DOI 10.1103/PhysRevLett.71.1486, https://doi.org/10.1103/PhysRevLett.71.1486
7. L. H. Ford, Thomas A. Roman, “Quantum field theory constrains traversable wormhole geometries”, Physical Review D 53, 5496-5507 (1996). DOI 10.1103/PhysRevD.53.5496, https://doi.org/10.1103/PhysRevD.53.5496
8. Éanna E. Flanagan, Robert M. Wald, “Does back reaction enforce the averaged null energy condition in semiclassical gravity?”, Physical Review D 54, 6233-6283 (1996). DOI 10.1103/PhysRevD.54.6233, https://doi.org/10.1103/PhysRevD.54.6233
9. Bernard S. Kay, Marek J. Radzikowski, Robert M. Wald, “Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon”, Communications in Mathematical Physics 183, 533-556 (1997). DOI 10.1007/s002200050042, https://doi.org/10.1007/s002200050042
10. S. V. Krasnikov, “A singularity-free WEC-respecting time machine”, Classical and Quantum Gravity 15, 997-1003 (1998). DOI 10.1088/0264-9381/15/4/020, https://doi.org/10.1088/0264-9381/15/4/020
11. S. Krasnikov, “No time machines in classical general relativity”, Classical and Quantum Gravity 19, 4109-4129 (2002); preprint arXiv:gr-qc/0111054 (2001, revised 2014). DOI 10.1088/0264-9381/19/15/316, https://arxiv.org/abs/gr-qc/0111054
12. John L. Friedman, Atsushi Higuchi, “Topological censorship and chronology protection”, Annalen der Physik 518, 109-128 (2006). DOI 10.1002/andp.200651801-209, https://doi.org/10.1002/andp.200651801-209
13. Noah Graham, Ken D. Olum, “Achronal averaged null energy condition”, Physical Review D 76, 064001 (2007). DOI 10.1103/PhysRevD.76.064001, https://doi.org/10.1103/PhysRevD.76.064001
14. Aron C. Wall, “Proving the achronal averaged null energy condition from the generalized second law”, Physical Review D 81, 024038 (2010). DOI 10.1103/PhysRevD.81.024038, https://doi.org/10.1103/PhysRevD.81.024038
15. Juan Maldacena, Alexey Milekhin, “Humanly traversable wormholes”, Physical Review D 103, 066007 (2021). DOI 10.1103/PhysRevD.103.066007, https://doi.org/10.1103/PhysRevD.103.066007
16. Roberto Emparan, Marija Tomašević, “Quantum backreaction on chronology horizons”, Journal of High Energy Physics 2022(02), 182 (2022). DOI 10.1007/jhep02(2022)182, https://doi.org/10.1007/jhep02(2022)182
17. Juan Maldacena, Alexey Milekhin, Fedor Popov, “Traversable wormholes in four dimensions”, Classical and Quantum Gravity 40, 155016 (2023). DOI 10.1088/1361-6382/acde30, https://doi.org/10.1088/1361-6382/acde30
18. David E. Kaplan, Surjeet Rajendran, Francesco Serra, “Wrong signs are alright”, Journal of High Energy Physics 2025(03), 031 (2025). DOI 10.1007/jhep03(2025)031, https://doi.org/10.1007/jhep03(2025)031