ENE-7: Topological censorship, no wormhole shortcuts

The modern form of ENE-2 for L3: a wormhole may be traversable, but it cannot be a shortcut.

Kind: constraint · Family: ENE (Energy) · Last reviewed: 2026-09-12

The result

Topological censorship and the achronal averaged null energy condition. Friedman, Schleich and Witt: in an asymptotically flat spacetime obeying the averaged null energy condition, every causal curve from past to future null infinity can be deformed to one that stays outside any topology, so no traversable wormhole shortcut is visible from outside. Graham and Olum: quantum fields can violate the ANEC on chronal null geodesics, but the achronal version, on complete null geodesics that are the fastest path between their points, survives, and that is the version the censorship theorem needs. Wall derives the achronal ANEC from the generalized second law of horizon thermodynamics in semiclassical gravity; Hartman, Kundu and Tajdini prove the ANEC from microcausality of quantum field theory in flat space, for interacting theories in more than two dimensions

What it forbids or costs

The modern form of ENE-2 for L3: a wormhole may be traversable, but it cannot be a shortcut. Any traversal that beats the outside route needs achronal ANEC violation, which no known quantum field supplies

Escape hatches

Wormholes that are traversable but slower than the outside path (the Gao, Jafferis and Wall and the Maldacena, Milekhin and Popov constructions do exactly this); spacetimes that are not asymptotically flat

Who it bites

Physics proposals

• VIOLATES: Morris, Thorne and Yurtsever: the wormhole time machine (1988). The time machine needs a short wormhole, one whose traversal beats the outside route, since a long one cannot be offset into a loop; that is exactly the achronal ANEC violation the theorem forbids. The 2007 to 2017 achronal ANEC proofs close the loophole the 1988 abstract left open for short wormholes.
• VIOLATES: Morris–Thorne traversable wormhole (1988). An asymptotically flat spacetime with a handle whose throat length is far less than the outside distance between the mouths: the very causal curve the theorem says must be deformable to the exterior, and here it is not. The exotic matter the paper asks for must therefore violate the ANEC on the achronal null geodesics through the throat, which no known quantum field supplies. The 1988 paper predates the theorem and could not have addressed it.
• VIOLATES: Visser's thin-shell wormholes (1989). Two copies of Minkowski space with a region cut out and the boundaries identified: an asymptotically flat spacetime with a handle, and a throat that is a shortcut relative to the outside. Friedman, Schleich and Witt say that curve must be deformable to the exterior under the ANEC, so the edge stress-energy must violate the achronal version, a stronger failure than the pointwise one Visser exhibits and one no quantum field is known to supply.
• DODGES: Brane-bulk shortcuts (Chung and Freese 2000, Ishihara 2001, Caldwell and Langlois 2001). The route is not a handle in one asymptotically flat four-dimensional spacetime but a null geodesic of a warped anti-de Sitter bulk that leaves and rejoins the brane; the bulk is neither asymptotically flat nor of changed topology, so neither hypothesis of Friedman, Schleich and Witt holds, and the achronal ANEC is never tested because the bulk light cone is respected throughout.
• DODGES: Gott's cosmic-string time machine (1991). Two moving strings in a spacetime that is topologically Minkowski and flat off the strings: no handle, so no topology for the theorem to censor, and the total momentum of the pair is spacelike, so the spacetime is not asymptotically flat in the sense the theorem needs. The closed curves evade Friedman, Schleich and Witt the way they evade ENE-2, by falling outside the hypotheses rather than by violating the achronal ANEC.
• DODGES: Heim theory and the Dröscher-Häuser propulsion proposal (2004 to 2005). The transit through a parallel space is not a handle in an asymptotically flat spacetime of general relativity; it lives in a different theory of gravity with extra dimensions of its own, which puts it outside the theorem's hypotheses. As with ENE-2 the escape is asserted, not shown: no equations are supplied in which the achronal ANEC could be checked.
• DODGES: Passage through the Kerr interior (Carter 1968). The passage does not return to the future null infinity it started from: it leaves our asymptotic region through the Cauchy horizon into another, so it is not a causal curve from past to future null infinity of one asymptotically flat end and the theorem's premise is not met. Mass inflation then seals the door anyway, so nothing here beats an outside route because there is no outside route to beat.
• SATISFIES: Einstein–Rosen bridge (1935). The bridge is the object the theorem describes: an asymptotically flat vacuum spacetime with a handle, and vacuum obeys the ANEC on every null geodesic. Its verdict is the theorem's: no causal curve from one exterior's past infinity reaches the other exterior, the throat pinches off first, and nothing beats the outside route.
• SATISFIES: ER = EPR (Maldacena and Susskind 2013). The conjecture takes non-traversability as its own premise: Maldacena and Susskind assume the bridge stays closed in the quantum theory and say the identification would be wrong otherwise. The setting is anti-de Sitter rather than asymptotically flat, so the theorem applies in its holographic form, and the outcome is the same: no signal from one exterior to the other, so nothing beats the outside route.
• SATISFIES: Gao, Jafferis and Wall: traversable wormholes via a double-trace deformation (2017). This is the register's named escape hatch. The negative averaged null energy sits on the horizon generators, which stop being achronal once the boundaries are coupled, so the achronal ANEC survives, and a signal through the bulk arrives no sooner than the direct boundary coupling allows: traversable, not a shortcut. The setting is anti-de Sitter, but the paper obeys the theorem's content rather than escaping its hypotheses.
• SATISFIES: Maldacena, Milekhin and Popov: traversable wormholes in four dimensions (2018), and the humanly traversable sequel (2021). The paper's own words: a long wormhole, one that takes longer to go through than the ambient space, and short wormholes are forbidden by the achronal ANEC, which the authors take as a theorem. The negative Casimir energy sits on null lines wrapping the field-line circles, which are not achronal, so the theorem's hypothesis holds and its conclusion, no shortcut, is met by design. The register lists this construction as the escape hatch.
• SATISFIES: Wheeler's geons and quantum foam (1955–1962). Multiply connected vacuum and electromagnetic solutions obey the ANEC everywhere, so the theorem holds and delivers what Wheeler found: the handles pinch off and no signal beats the outside route. Charge without charge is topology that censorship permits because it is not a shortcut.

Fictional drives

• SILENT: 2001: A Space Odyssey (1968): the Star Gate. A gate visible from outside on Japetus that leads elsewhere is the handle topological censorship forbids under the averaged null energy condition; the work does not address the theorem.
• SILENT: Andromeda: the slipstream. The strings connect fixed masses like handles would, and if they were tunnels in our spacetime topological censorship would apply; the show places them in another dimension and never says which, so the row is neither answered nor excluded.
• SILENT: Banks's Culture: the energy grid, infraspace and ultraspace (1987 onward). Displacement is a wormhole shortcut in our spacetime and topological censorship says such a shortcut needs achronal ANEC violation; the novels give a failure rate and no energy.
• SILENT: Battlestar Galactica: the FTL jump (2004 series). A jump is a shortcut visible from outside in flat space; topological censorship is never touched.
• SILENT: Commonwealth: CST wormholes with trains through them (Hamilton 2004). Gateways are shortcuts visible from outside in flat space; topological censorship is never touched.
• SILENT: Contact: the Machine and the tunnel system (Sagan 1985, Zemeckis 1997). Topological censorship says a wormhole shortcut visible from outside needs the achronal ANEC to fail; the tunnels are exactly such a shortcut and the theorem, published in 1993, postdates the novel and is never touched by the film.
• SILENT: Cowboy Bebop (1998): the astral gates. A ring in open space leading to another ring is the handle topological censorship forbids under the averaged null energy condition; unaddressed.
• SILENT: Dune: the Guild navigators and folding space (Herbert 1965). If folding space means a shortcut visible from outside, topological censorship applies; the work has nothing to say about it.
• SILENT: Elite Dangerous: the frame shift drive (Frontier Developments, 2014). If the jump is read as a wormhole, as the community wiki reads it, topological censorship forbids the shortcut without achronal ANEC violation; the game never addresses it.
• SILENT: EVE Online: the warp drive (CCP Games, 2003). Stargates are traversable shortcuts through flat asymptotics, which topological censorship forbids without achronal ANEC violation; the lore says it cannot explain the gates and stops.
• SILENT: Event Horizon (1997): the gravity drive. Topological censorship is exactly the theorem that says no shortcut through a handle is visible from outside under the averaged null energy condition; the gateway is such a handle and the film never touches the question.
• SILENT: Farscape (1999): wormholes, and starburst as a separate thing. A wormhole mouth visible in open space that leads elsewhere is the handle topological censorship forbids under the averaged null energy condition; the show does not address it.
• SILENT: FTL: Faster Than Light, the jump drive as a game mechanic. Beacon links behave like fixed connections between points in space, and if they were handles topological censorship would bear on them; the game says nothing about what a link is, so the row is neither answered nor excluded.
• SILENT: Guardians of the Galaxy Vol. 2 (2017): jump points. A portal visible from outside that leads elsewhere is the handle topological censorship forbids under the averaged null energy condition; unaddressed.
• SILENT: Homeworld: hyperspace cores and the Far Jumpers. The sequel's gates are fixed pairs of ends in the world, the handles topological censorship applies to; the games say nothing about them that answers or excludes the row.
• SILENT: Hyperion: the farcasters (Simmons 1989). A farcaster is a shortcut visible from outside in flat space; topological censorship is never touched.
• SILENT: Interstellar: the wormhole near Saturn (2014). The wormhole is a shortcut visible from outside in an asymptotically flat region near Saturn, which topological censorship forbids under the achronal ANEC; the film does not touch the theorem.
• SILENT: Mass Effect: the mass relays (BioWare 2007 onward). Relay corridors are shortcuts visible from outside in flat space; topological censorship is never touched.
• SILENT: No Man's Sky: the hyperdrive, warp cells and range. The portals are fixed pairs of ends in the world, exactly the handles topological censorship applies to, and the black holes are one-way throws toward the centre; the game says nothing about either that would answer or exclude the row.
• SILENT: Outer Wilds (2019): Nomai warp cores. Brittle Hollow's black hole leads to a white hole elsewhere in the same system, a handle visible from outside that topological censorship forbids under the averaged null energy condition; the game does not address the theorem.
• SILENT: Star Citizen: quantum drive and jump points. A natural gap in spacetime with a paired exit is the handle topological censorship forbids under the averaged null energy condition; the lore does not address the theorem.
• SILENT: Star Trek: transwarp, quantum slipstream and the other beyond-warp drives. The Borg conduits and the coaxial fold are traversable shortcuts through apparently flat asymptotics, which topological censorship forbids without achronal ANEC violation; never addressed.
• SILENT: Starfield (2023): the grav drive. A jump that connects two systems without crossing the space between is a handle of the kind topological censorship forbids under the averaged null energy condition; unaddressed.
• SILENT: Stargate: the gate network (1994 film, SG-1 1997 onward). A gate is a shortcut visible from outside in a flat region; topological censorship is never touched.
• SILENT: Starman Jones: the congruencies (Heinlein 1953). A fold joining two distant flat regions is a shortcut visible from outside; topological censorship is never touched.
• SILENT: Stellaris: warp, hyperlane and wormhole (Paradox Development Studio, 2016). Wormholes and gateways are traversable shortcuts through flat asymptotics, forbidden by topological censorship without achronal ANEC violation; never addressed.
• SILENT: Super Dimension Fortress Macross (1982): the space fold. A fold that takes a region of space elsewhere is a handle of the kind topological censorship forbids under the averaged null energy condition; unaddressed.
• SILENT: The Alderson drive (Niven and Pournelle 1974). A tramline is a shortcut visible from outside in flat space; topological censorship is never touched.
• SILENT: The Expanse: the ring gates and the slow zone (Corey 2013 onward). The rings are shortcuts visible from outside in flat space; topological censorship is never touched.
• SILENT: The Forever War: collapsar jumps (Haldeman 1974). A collapsar-to-collapsar shortcut is exactly the wormhole topological censorship forbids under the achronal ANEC; the theorem postdates the novel by two decades.
• SILENT: Thor (2011): the Bifrost. A bridge between realms visible from both ends is exactly the handle topological censorship forbids under the averaged null energy condition; unaddressed.
• SILENT: Weber's Honorverse: hyper bands and Warshawski sails (1993 onward). The wormhole junctions are shortcuts in normal space and topological censorship says such a shortcut needs achronal ANEC violation; the novels give transit rules and no energy.
• SILENT: Wing Commander (1990) and the 1999 film: jump points. A natural point in open space leading to another system is the handle topological censorship forbids under the averaged null energy condition; unaddressed.

Sources

• Friedman, Schleich and Witt, Phys. Rev. Lett. 71, 1486 (1993), arXiv:gr-qc/9305017; Graham and Olum, Phys. Rev. D 76, 064001 (2007), arXiv:0705.3193; Wall, Phys. Rev. D 81, 024038 (2010), arXiv:0910.5751; Hartman, Kundu and Tajdini, JHEP 07, 066 (2017), arXiv:1610.05308; Friedman, Schleich and Witt erratum, Phys. Rev. Lett. 75, 1872 (1995), affecting a secondary result only; the "long wormhole" statements in Gao, Jafferis and Wall, JHEP 12, 151 (2017), arXiv:1608.05687, and Maldacena, Milekhin and Popov, arXiv:1807.04726 ✓