STA-3: Divergence at the chronology horizon

The time-machine step in CAU-3 may be self-destroying.

Kind: constraint · Family: STA (Stability) · Last reviewed: 2026-09-12

The result

Divergence at the chronology horizon: when a wormhole is converted into a time machine, the renormalised stress-energy of quantum fields diverges as one approaches the Cauchy horizon. Kim and Thorne find the divergence extremely weak and propose that quantum gravity cuts it off, which would allow closed timelike curves; Hawking conjectures the opposite

What it forbids or costs

The time-machine step in CAU-3 may be self-destroying

Escape hatches

The Kim and Thorne cutoff, unresolved

Who it bites

Physics proposals

• VIOLATES: Gott's cosmic-string time machine (1991). Grant computes the renormalised stress-energy on the chronology horizon and polarised hypersurfaces of the Gott spacetime and finds it diverges strongly enough for order-one back reaction before the Planck scale; the machine requires that divergence not to matter.
• VIOLATES: Morris, Thorne and Yurtsever: the wormhole time machine (1988). The construction creates a compactly generated chronology horizon at which the renormalised stress-energy of quantum fields diverges (Kim and Thorne); the machine survives only if that divergence is cut off, which the register records as unresolved.
• VIOLATES: Passage through the Kerr interior (Carter 1968). The route runs through a Cauchy horizon at which the classical stress-energy (Poisson–Israel mass inflation) and the renormalised quantum stress-energy (Zilberman et al. 2022) both diverge; this is the same Cauchy-horizon divergence STA-3 records for wormhole time machines, and here there is no proposed cutoff.
• SATISFIES: Gao, Jafferis and Wall: traversable wormholes via a double-trace deformation (2017). No chronology horizon forms because no time machine can be built from this wormhole.
• SATISFIES: Maldacena, Milekhin and Popov: traversable wormholes in four dimensions (2018), and the humanly traversable sequel (2021). No chronology horizon forms because no time machine can be built from a long wormhole.
• SILENT: Alcubierre 1994: the warp drive metric. The chronology-horizon divergence would arise only at the two-bubble time machine of CAU-3, which the letter does not construct; whether the Kim and Thorne cutoff or Hawking's divergence wins there is unsettled and uncomputed for warp bubbles.
• SILENT: Everett and Roman 1997: the superluminal subway. The two-tube machine has a chronology horizon whose semiclassical behaviour the paper does not compute; the Kim and Thorne versus Hawking question is unsettled there.
• SILENT: Krasnikov 1998: the tube laid on the way out. The two-tube time machine would have a chronology horizon; Krasnikov discusses the divergence of the sampled energy density near the Cauchy horizon of a wormhole time machine as a feature to exploit, and whether Hawking's or Kim and Thorne's account holds there is unsettled.
• SILENT: Morris–Thorne traversable wormhole (1988). The 1988 paper predates the time-machine conversion; the chronology-horizon divergence bears once a mouth is moved, and the literature (Kim and Thorne versus Hawking) has not settled whether it destroys the machine.
• SILENT: Natário 2002: warp drive with zero expansion. The chronology horizon would appear only in the two-bubble time machine, which is not constructed here and whose semiclassical fate is unsettled.
• SILENT: Van Den Broeck 1999: the pocket geometry. Only the two-pocket time machine would raise a chronology horizon; not constructed or analysed.
• SILENT: Visser's thin-shell wormholes (1989). The paper names causal constraints as open and does not compute the chronology-horizon divergence; the literature has not settled whether the Kim–Thorne cutoff saves the converted machine.
• SILENT: Warp drives in modified gravity. The two-bubble chronology horizon is neither constructed nor analysed in these theories.

Fictional drives

• SILENT: 2001: A Space Odyssey (1968): the Star Gate. No time machine is constructed, so no chronology horizon; the work does not reach the question.
• SILENT: Commonwealth: CST wormholes with trains through them (Hamilton 2004). No wormhole is turned into a time machine in the text, though the starship's voyages would do it; no chronology horizon is ever in view.
• SILENT: Contact: the Machine and the tunnel system (Sagan 1985, Zemeckis 1997). Divergence at a chronology horizon arises only once a wormhole is made into a time machine; the work never gets that far, so the question never comes up.
• SILENT: Cowboy Bebop (1998): the astral gates. No time machine is constructed, so no chronology horizon; the show does not reach the question.
• SILENT: Event Horizon (1997): the gravity drive. No time machine is constructed, so the chronology-horizon divergence does not arise on screen; the drive's ability to be one is unexamined.
• SILENT: Farscape (1999): wormholes, and starburst as a separate thing. The show builds time machines and never asks whether they destroy themselves; the divergence at a chronology horizon is not in its vocabulary.
• SILENT: Flight of the Navigator (1986). The ship builds a closed loop in David's history, which is where the Cauchy-horizon divergence would sit; the film gives the loop a cost, vaporisation, without a mechanism.
• SILENT: Guardians of the Galaxy Vol. 2 (2017): jump points. No time machine is constructed through the network, so no chronology horizon; the film does not reach the question.
• SILENT: Hyperion: the farcasters (Simmons 1989). No farcaster is turned into a time machine, so no chronology horizon is in view; the entry bears on the class and the work never approaches it.
• SILENT: Interstellar: the wormhole near Saturn (2014). The tesseract loop has a chronology horizon in effect, and nothing in the film asks whether quantum fields diverge there; the loop simply closes.
• SILENT: Mass Effect: the mass relays (BioWare 2007 onward). No relay is turned into a time machine, so no chronology horizon is in view; the entry bears on the class and the work never approaches it.
• SILENT: Outer Wilds (2019): Nomai warp cores. The Nomai build a time machine and never ask whether it destroys itself; the divergence at a chronology horizon is not raised, and the loop runs cleanly for as long as the sun keeps exploding.
• SILENT: Star Citizen: quantum drive and jump points. No time machine is constructed, so no chronology horizon; the lore does not reach the question.
• SILENT: Star Trek: transwarp, quantum slipstream and the other beyond-warp drives. "Timeless" crosses a chronology horizon by transmitter; the divergence at it is not engaged.
• SILENT: Star Trek: warp drive (1966 onward). The slingshot builds chronology horizons that the show crosses without incident; the Kim and Thorne divergence is never engaged.
• SILENT: Starfield (2023): the grav drive. No time machine is constructed, so no chronology horizon; the game does not reach the question.
• SILENT: Stargate: the gate network (1994 film, SG-1 1997 onward). The time loops of "1969" and after create chronology horizons in effect, and no episode asks whether anything diverges there.
• SILENT: Super Dimension Fortress Macross (1982): the space fold. No time machine is constructed, so no chronology horizon; the show does not reach the question.
• SILENT: The Expanse: the ring gates and the slow zone (Corey 2013 onward). No ring is converted into a time machine, so no chronology horizon is ever in view; the entry bears on the class and the work never approaches it.
• SILENT: The Forever War: collapsar jumps (Haldeman 1974). No time machine is built, so no chronology horizon is in view.
• SILENT: Thor (2011): the Bifrost. No time machine is constructed, so no chronology horizon; the film does not reach the question.
• SILENT: Warhammer 40,000: the Warp (1987 onward). The setting has ships arriving before departure and never asks what happens at the boundary of such a loop; the register's divergence at a chronology horizon applies and is untouched.
• SILENT: Wing Commander (1990) and the 1999 film: jump points. No time machine is constructed, so no chronology horizon; the franchise does not reach the question.
• ENGAGES: Doctor Who: the TARDIS and the time vortex. Kim and Thorne's divergence at a chronology horizon has a story counterpart: the vortex energy that destroys anyone who holds it ("The Parting of the Ways", 2005) and the wound that Reapers clean. Whether a time machine self-destroys is the question of the row, and the show's answer is that something intervenes.

Sources

• Kim and Thorne, Phys. Rev. D 43, 3929 (1991); Hawking, Phys. Rev. D 46, 603 (1992) ✓