ENE-2: Superluminal travel requires negative energy

Every L2 and L3 scheme pays in negative energy; positive-energy warp drives cannot be superluminal.

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

The result

Superluminal travel requires negative energy. Olum: any spacetime allowing a signal to arrive earlier than light through flat space must violate the WEC somewhere along the way, given the generic condition. Visser, Bassett and Liberati: perturbatively around flat space, under the NEC every Shapiro time delay is a delay and never an advance, so effective superluminal travel needs NEC violation ("superluminal censorship"). Gao and Wald: under the NEC plus the null generic condition, a fastest null geodesic between distant points cannot pass through a compact region, so there is no gravitational time advance; the NEC can be weakened to Borde's averaged condition

What it forbids or costs

Every L2 and L3 scheme pays in negative energy; positive-energy warp drives cannot be superluminal

Escape hatches

Definitions of "superluminal" that compare against a curved rather than flat background; non-perturbative regimes, which Visser, Bassett and Liberati say their argument does not reach; modified theories of gravity

Who it bites

Physics proposals

• VIOLATES: Alcubierre 1994: the warp drive metric. This is the spacetime Olum's theorem and Visser, Bassett and Liberati's superluminal censorship were written about: a signal arrives earlier than light through flat space, so the WEC and NEC must fail somewhere along the way, and they do, in the wall.
• VIOLATES: Everett and Roman 1997: the superluminal subway. The return leg is a causal path between flat-space points that beats light through flat space, which is Olum's definition; the negative energy the theorem demands is exhibited in the wall.
• VIOLATES: Fell and Heisenberg 2021: positive energy from hidden geometric structure. Superluminal by construction; calls Olum's result a "claimed proof" and offers no way round it; Santiago, Schuster and Visser show the null condition fails for the class
• VIOLATES: Krasnikov 1998: the tube laid on the way out. Olum's theorem is about spacetimes with exactly this property, a causal path between flat-space points that beats light through flat space; the tube's return leg is one, and the weak energy condition fails in the wall as the theorem requires.
• VIOLATES: Lentz 2021: hyper-fast positive-energy solitons. A superluminal bubble that claims to evade Olum by lacking a single fastest causal path; the entry's Visser–Bassett–Liberati and Gao–Wald forms do not need that assumption, and the null energy condition is violated for the whole class
• VIOLATES: Morris, Thorne and Yurtsever: the wormhole time machine (1988). The wormhole is a shortcut relative to flat exterior light, which Olum and Gao–Wald show needs energy-condition violation; the offset trick then turns the shortcut into a loop.
• VIOLATES: Morris–Thorne traversable wormhole (1988). The throat is a shortcut relative to flat exterior light, exactly the time advance Olum and Gao–Wald show requires energy-condition violation; the paper's exotic matter is that violation.
• VIOLATES: Natário 2002: warp drive with zero expansion. Natário cites Visser, Bassett and Liberati and Gao and Wald as the reason all superluminal spacetimes are expected to violate energy conditions, and his theorem is the class-wide confirmation for warp drives.
• VIOLATES: Van Den Broeck 1999: the pocket geometry. The paper opens with Olum's definition of effective superluminal travel and says such spacetimes "will violate at least one of the energy conditions"; this one does, in two places.
• VIOLATES: Visser's thin-shell wormholes (1989). The throat is a shortcut relative to flat exterior light; the paper's mirror argument is a direct instance of the theorem that a time advance needs defocusing and therefore negative energy.
• DODGES: Brane-bulk shortcuts (Chung and Freese 2000, Ishihara 2001, Caldwell and Langlois 2001). Olum's and Gao and Wald's theorems bound time advances within one manifold against its own flat light cone; the shortcut compares a bulk null geodesic with a brane null geodesic on a different manifold, the register's listed escape of a curved rather than flat comparison background, and within the bulk itself no geodesic beats the bulk light cone.
• DODGES: Gott's cosmic-string time machine (1991). The Olum and Gao–Wald theorems assume the generic condition, that every causal geodesic meets some curvature; the Gott spacetime is flat off the strings and fails it, which is exactly how positive-energy closed curves evade a theorem that says shortcuts need negative energy.
• DODGES: Heim theory and the Dröscher-Häuser propulsion proposal (2004 to 2005). The parallel-space transit is effective superluminal travel, which the register says requires negative energy in general relativity; the papers place the transit in a different theory of gravity (HQT), which is the register's listed escape, but supply no equations in which the escape could be verified.
• DODGES: Lorentz-violating frameworks (the Standard-Model Extension and Hořava-Lifshitz gravity). Olum, Visser and Gao-Wald assume general relativity with energy conditions and compare with the flat light cone; the SME's FTL sector is a matter-sector property with no geometric time advance and Hořava gravity is a different theory of gravity, the register's listed escape.
• DODGES: Warp drives in modified gravity. ENE-2 lists modified gravity as an escape hatch and this is the hatch. But Olum's and Gao and Wald's theorems are proved from the focusing of null rays, with the energy condition entering as its general-relativistic name, and Santiago, Schuster and Visser note the null convergence condition is violated in any theory; what is dodged is the price tag, not the focusing.
• SATISFIES: Bobrick and Martire 2021: physical warp drives. Agrees with the entry: it states that negative energy is "a general property of any superluminal drive", citing Olum and Visser, Bassett and Liberati, and it confines its positive-energy claim to subluminal shells
• SATISFIES: Einstein–Rosen bridge (1935). Under the null energy condition there is no time advance through the throat; the pinch-off is the concrete instance of the Olum and Gao–Wald result.
• SATISFIES: ER = EPR (Maldacena and Susskind 2013). No time advance is claimed or possible; the paper cites the non-traversability theorems as its own premise.
• SATISFIES: Fuchs et al. 2024: the constant-velocity physical warp shell. Subluminal, and the paper checks the point the entry turns on: the Shapiro delay through the shell is a delay, not an advance
• SATISFIES: Gao, Jafferis and Wall: traversable wormholes via a double-trace deformation (2017). There is no time advance relative to the outside (the boundary), so the Olum and Gao–Wald theorems are not contradicted; the negative energy lives on non-achronal null geodesics, which the achronal theorems do not cover.
• SATISFIES: Maldacena, Milekhin and Popov: traversable wormholes in four dimensions (2018), and the humanly traversable sequel (2021). No time advance relative to the flat exterior: the wormhole is longer than the outside, exactly as the theorems require of a configuration whose negative energy sits only on non-achronal geodesics.
• SATISFIES: NASA Eagleworks warp field interferometer. Accepts that the bubble needs negative energy and says so
• SATISFIES: Passage through the Kerr interior (Carter 1968). No time advance relative to flat exterior light is claimed; the passage leaves our asymptotic region rather than shortening a path within it.
• SATISFIES: The relativistic rocket. The rocket never arrives earlier than light through flat space, so the theorems of Olum, Visser, Bassett and Liberati, and Gao and Wald are respected exactly; they price the schemes that would beat this ship
• SATISFIES: The Scharnhorst effect. Consistent with the theorem's direction: propagation exceeds c only where the effective energy density is negative, and in ordinary vacuum, where the energy conditions hold, the speed is c. No gravitational time advance is claimed
• SATISFIES: Wheeler's geons and quantum foam (1955–1962). With the energy conditions obeyed, the Olum and Gao–Wald theorems forbid a time advance, and the pinch-off and horizons deliver exactly that.
• SATISFIES: White et al. 2021: the worldline-numerics Casimir pattern. Makes no claim to beat the theorem: it accepts that a superluminal bubble needs negative energy and goes looking for some

Fictional drives

• SILENT: 2001: A Space Odyssey (1968): the Star Gate. The gate delivers a time advance over the light path and the negative energy that Olum's theorem requires is never named; the makers' power is unspecified.
• SILENT: Alien's Nostromo. The ship beats light through flat space, which the theorems price in negative energy; the film names no mechanism and pays no bill
• SILENT: Andromeda: the slipstream. A ship reaches M86 in a stream and no episode prices the time advance; Olum's negative energy is never invoked.
• SILENT: Asimov's Foundation: the Jump through hyperspace (1942 onward). A trip that beats light through flat space needs negative energy somewhere; the series prices the Jump in computation and nothing else.
• SILENT: Babylon 5: hyperspace, jump gates and beacons (1993 to 1998). A trip that beats light through flat space needs negative energy somewhere; the show prices jumps in fuel and never in geometry.
• SILENT: Banks's Culture: the energy grid, infraspace and ultraspace (1987 onward). A ship arriving ahead of light through flat space needs negative energy somewhere; the novels draw positive power from the grid and never address the geometry's price.
• SILENT: Battlestar Galactica: the FTL jump (2004 series). That beating light needs negative energy somewhere is never raised.
• SILENT: Campbell's Islands of Space (1931): where the word came from. A ship arriving ahead of light through flat space needs negative energy on the way; the novel spends stored positive energy and never says where the geometry's price is paid.
• SILENT: Commonwealth: CST wormholes with trains through them (Hamilton 2004). That beating light needs negative energy somewhere is never raised.
• SILENT: Contact: the Machine and the tunnel system (Sagan 1985, Zemeckis 1997). That a shortcut faster than light through flat space needs negative energy somewhere along the way is the result Olum proved a decade after the novel; Contact never states the principle, only inherits the tunnels that would require it.
• SILENT: Cordwainer Smith: planoforming, Space² and Space³. A ship arrives fifty light-years away in a flash and no story prices it; Olum's negative energy is never invoked and never denied.
• SILENT: Cowboy Bebop (1998): the astral gates. If the gates deliver a time advance over the light path, the negative energy Olum's theorem requires is never named; if they do not, the entry does not bite, and the show never says which.
• SILENT: Doctor Who: the TARDIS and the time vortex. The ship arrives before light through flat space and no instalment prices it; Olum's theorem would demand negative energy of any geometric account, and the show gives none.
• SILENT: Dune: the Guild navigators and folding space (Herbert 1965). That arriving before light needs negative energy somewhere is never raised.
• SILENT: Elite Dangerous: the frame shift drive (Frontier Developments, 2014). Olum's theorem says supercruise needs negative energy somewhere; the module burns scooped hydrogen.
• SILENT: EVE Online: the warp drive (CCP Games, 2003). Olum's theorem says a bubble that arrives early needs negative energy somewhere; the lore's depleted vacuum is that somewhere, but the connection is never drawn and the quantity is never stated.
• SILENT: Event Horizon (1997): the gravity drive. The film claims a time advance between Earth and Proxima Centauri, which Olum's theorem prices in negative energy, and offers a magnetic field and a graviton beam instead.
• SILENT: Farscape (1999): wormholes, and starburst as a separate thing. Every transit is a time advance over the light path and the negative energy that Olum's theorem requires is never named.
• SILENT: FTL: Faster Than Light, the jump drive as a game mechanic. A ship arrives at a distant beacon before light would, and nothing prices it; Olum's negative energy is never invoked.
• SILENT: Futurama: the Planet Express ship's dark matter engines (1999 onward). Olum's theorem says moving the universe past the ship needs negative energy somewhere; the show's fuel weighs ten thousand pounds a pound and is the wrong sign.
• SILENT: Guardians of the Galaxy Vol. 2 (2017): jump points. Every jump is a time advance over the light path and the negative energy Olum's theorem requires is never named.
• SILENT: Halo: slipspace and the Shaw-Fujikawa translight engine (2001 onward). A trip that beats light through flat space needs negative energy somewhere; the franchise supplies black holes, which are positive mass, and never addresses the sign.
• SILENT: Homeworld: hyperspace cores and the Far Jumpers. Fleets cross the galaxy before their light and nothing prices it; Olum's negative energy is never invoked.
• SILENT: Hyperion: the farcasters (Simmons 1989). That beating light needs negative energy somewhere is never raised.
• SILENT: Interstellar: the wormhole near Saturn (2014). That a shortcut faster than light through flat space needs negative energy somewhere is never stated in the film; Thorne's book states it for the wormhole.
• SILENT: Mass Effect: the mass relays (BioWare 2007 onward). That beating light needs negative energy somewhere is never raised; the Codex's "mass-free corridor" is offered instead.
• SILENT: Niven's Known Space: the Outsider hyperdrive and the blind spot (1966 onward). A trip that beats light through flat space needs negative energy somewhere; the stories price the drive in rate and risk, never in energy.
• SILENT: No Man's Sky: the hyperdrive, warp cells and range. A ship arrives hundreds of light-years away in seconds and nothing prices the time advance; Olum's negative energy is never invoked.
• SILENT: Space Battleship Yamato: warp by wave motion engine. The ship beats light through flat space and nothing prices it; Olum's negative energy is never invoked.
• SILENT: Star Trek: transwarp, quantum slipstream and the other beyond-warp drives. Olum's theorem says every one of them needs negative energy somewhere; the episodes supply dilithium, benamite and spores.
• SILENT: Star Trek: warp drive (1966 onward). Olum's theorem says the warp field needs negative energy somewhere; the show's dilithium and antimatter are positive energy, and the shortfall is not raised.
• SILENT: Star Wars: hyperspace (1977 onward). If hyperspace is a different geometry the trip needs negative energy somewhere; no film mentions energy of either sign.
• SILENT: Starfield (2023): the grav drive. Every jump delivers a time advance over the light path and the negative energy Olum's theorem requires is never named; the fuel is helium-3, which is positive energy.
• SILENT: Stargate: the gate network (1994 film, SG-1 1997 onward). That the shortcut requires negative energy somewhere along the way is never stated.
• SILENT: Stargate: the ships' hyperdrives. A ship beats light through flat space and nothing prices it; Olum's negative energy is never invoked.
• SILENT: Starman Jones: the congruencies (Heinlein 1953). That beating light needs negative energy somewhere is never raised.
• SILENT: Stellaris: warp, hyperlane and wormhole (Paradox Development Studio, 2016). Olum's theorem says every mode needs negative energy somewhere; the game's power is a positive number on a budget screen and nobody asks.
• SILENT: Super Dimension Fortress Macross (1982): the space fold. The fold delivers a time advance over the light path and the negative energy Olum's theorem requires is never named.
• SILENT: The Alderson drive (Niven and Pournelle 1974). That beating light needs negative energy somewhere is never raised.
• SILENT: The Expanse: the ring gates and the slow zone (Corey 2013 onward). That a shortcut beating light needs negative energy somewhere is never raised.
• SILENT: The Forever War: collapsar jumps (Haldeman 1974). That beating light needs negative energy somewhere was proved in 1998 and is nowhere in the novel.
• SILENT: The Hitchhiker's Guide to the Galaxy: the Infinite Improbability Drive and bistromathics. The ship beats light through flat space without the text saying what is paid; Olum's theorem would demand negative energy of any geometric mechanism, and the work offers no mechanism.
• SILENT: The Orville: quantum drive (2017 onward). Olum's theorem says the bubble needs negative energy; the show's fuel is described off screen as carrying negative matter and the requirement is never stated on screen.
• SILENT: Thor (2011): the Bifrost. A time advance between realms is claimed on every use and the negative energy Olum's theorem requires is never named; Asgard's power source is unspecified.
• SILENT: Vinge's Zones of Thought: FTL only where physics permits it (1992). A trip that beats light through flat space needs negative energy somewhere; the novel prices the drive in depth and never in energy. The Slow Zone, where the constraint holds outright, is scored under LOR-1.
• SILENT: Warhammer 40,000: the Warp (1987 onward). A trip that beats light through flat space needs negative energy somewhere; the setting prices the trip in souls and never in energy.
• SILENT: Weber's Honorverse: hyper bands and Warshawski sails (1993 onward). A trip that beats light through flat space needs negative energy somewhere; the appendix prices hyper travel in speed lost and shear risked, never in energy conditions.
• SILENT: Wing Commander (1990) and the 1999 film: jump points. Every jump delivers a time advance over the light path and the negative energy Olum's theorem requires is never named.
• SILENT: Xenocide: travel through the Outside. A ship beats light through flat space and nothing prices it; Olum's negative energy is never invoked.
• ENGAGES: Outer Wilds (2019): Nomai warp cores. The game states that the warp's time advance is bought with energy and that the price rises exponentially with the advance; it never names negative energy, but it is the only work in this class that prices the advance at all, and the sign of the price is the register's question.
• RULE: Aurora's generation ship. The stated tenth-of-c ceiling means the ship never arrives before light through flat space; the Olum and Gao and Wald theorems are respected by construction
• RULE: Avatar's Venture Star. Sublight by the companion's stated profile, so no arrival before light through flat space; the theorems are respected by construction
• RULE: Death's End: curvature propulsion (Liu Cixin, 2010). Olum's theorem forbids arriving earlier than light through flat space without negative energy; the ships never arrive earlier than light, by rule, so the theorem is not triggered.
• RULE: Firefly's Verse. Sublight by rule, so no ship arrives before light through flat space; the theorems are respected by construction
• RULE: Passengers' Avalon. Sublight by the stated speed, so no arrival before light through flat space; the theorems are respected by construction
• RULE: Revelation Space lighthuggers. The stated rule that no ship exceeds its relativistic ceiling means no gravitational time advance is ever claimed; the theorems are respected by construction
• RULE: Star Citizen: quantum drive and jump points. The quantum drive is sublight by rule, so it claims no time advance and the entry does not bite on it; the jump points do deliver a time advance and the negative energy they would need is never named.
• RULE: Tau Zero's ramjet. The stated rule that speed only approaches c means the ship never arrives before light through flat space; the Olum and Gao and Wald theorems are respected by construction

Sources

• Olum, Phys. Rev. Lett. 81, 3567 (1998), arXiv:gr-qc/9805003; Visser, Bassett and Liberati, Nucl. Phys. B Proc. Suppl. 88, 267 (2000), arXiv:gr-qc/9810026, with the companion arXiv:gr-qc/9908023; Gao and Wald, Class. Quantum Grav. 17, 4999 (2000), arXiv:gr-qc/0007021 ✓