ENE-1: The energy conditions

Not itself a no-go, but the currency every other ENE entry is priced in.

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

The result

The energy conditions. Null (NEC): energy density seen along any light ray is non-negative. Weak (WEC): energy density seen by any observer is non-negative. Averaged null (ANEC): the integral along a complete null geodesic is non-negative. All classical matter obeys them; quantum fields violate the pointwise ones and the ANEC only under restrictions

What it forbids or costs

Not itself a no-go, but the currency every other ENE entry is priced in

Escape hatches

Quantum fields (ENE-3, ENE-6)

Who it bites

Physics proposals

VIOLATES: Alcubierre 1994: the warp drive metric. The Eulerian energy density is negative everywhere in the wall by Alcubierre's own equation, so the weak and dominant conditions fail; he states the strong condition fails too, and the null condition fails by the generic theorem of ENE-5.
VIOLATES: Bobrick and Martire 2021: physical warp drives. Every non-trivial metric written down (flattened Alcubierre, Lorentz drive, pocket variant, modified-time and spinning drives) has regions of negative Eulerian density by the paper's equations (12), (15), (17), (19) and (21); the one positive-energy construction reduces to Minkowski space under its own assumptions (Santiago, Schuster and Visser, App. A)
VIOLATES: Everett and Roman 1997: the superluminal subway. The static-observer energy density is negative in a range near the axis by the general argument of section 5 and on the inner wall for the explicit profile; the weak energy condition fails.
VIOLATES: Fell and Heisenberg 2021: positive energy from hidden geometric structure. By the paper's own account the weak, strong and dominant conditions fail in compact regions; only the Eulerian density is positive
VIOLATES: Gao, Jafferis and Wall: traversable wormholes via a double-trace deformation (2017). The averaged null energy along the horizon generators is negative by construction; this is the condition for opening and the paper computes it.
VIOLATES: Krasnikov 1998: the tube laid on the way out. Krasnikov states that creation of a type 1 space machine requires violating the weak energy condition; Everett and Roman compute negative energy density inside the tube wall.
VIOLATES: Lentz 2021: hyper-fast positive-energy solitons. Claims the weak energy condition; Celmaster and Rubin find negative Eulerian density in the published geometry, and Santiago, Schuster and Visser show a positive Eulerian density would not have been enough in any case
VIOLATES: Maldacena, Milekhin and Popov: traversable wormholes in four dimensions (2018), and the humanly traversable sequel (2021). The Casimir-like stress tensor of the lowest-Landau-level fermions has negative null-null components along the field-line circles; the null energy condition fails there, and this is the mechanism.
VIOLATES: Morris, Thorne and Yurtsever: the wormhole time machine (1988). The throat needs $\tau_0 > \rho_0 c^2$; the paper itself sharpens the requirement to violation of the averaged weak energy condition along null geodesics through the throat.
VIOLATES: Morris–Thorne traversable wormhole (1988). At the throat $\tau_0 > \rho_0 c^2$, so $T_{\mu\nu}k^\mu k^\nu < 0$ for radial null $k$: the null condition fails, and therefore the weak and every stronger pointwise condition.
VIOLATES: NASA Eagleworks warp field interferometer. Alcubierre's metric, which the 2011 paper says violates the strong, weak and dominant conditions; the test article's energy is positive, so the programme needs the conditions to fail somewhere it has no source for
VIOLATES: Natário 2002: warp drive with zero expansion. Theorem 1.7 proves every non-flat warp drive spacetime violates the weak or the strong condition, and the zero-expansion example has $\rho \leq 0$ everywhere; Santiago, Schuster and Visser add the null condition.
VIOLATES: Tachyons (Feinberg 1967). The classical field with $m^2 < 0$ has a potential unbounded below, so its energy density $\tfrac12\dot\phi^2 + \tfrac12(\nabla\phi)^2 - \tfrac12\mu^2\phi^2$ can be negative for any observer; this is the instability, and the energy conditions are the currency in which it shows.
VIOLATES: The Scharnhorst effect. The Casimir vacuum violates the pointwise energy conditions, and the effect exists precisely because it does: the velocity shift is proportional to a negative energy density. The violation is the quantum, static, tiny one ENE-1 already allows for
VIOLATES: Van Den Broeck 1999: the pocket geometry. The paper states the geometry violates the strong, dominant and "especially" the weak energy condition, and computes negative Eulerian energy density in both the wall and the neck.
VIOLATES: Visser's thin-shell wormholes (1989). Surface energy density $\sigma < 0$ on every convex part of the throat; the paper proves violation of the weak and averaged weak conditions by the focusing theorem.
VIOLATES: White et al. 2021: the worldline-numerics Casimir pattern. The bubble sought is Alcubierre's, which needs negative energy density by the very formula the paper reproduces; the paper embraces that need and offers Casimir energy to meet it
DODGES: The Mach effect thruster. The wormhole term makes the transient rest mass negative, a violation of the weak energy condition by construction, but this is reached through a theory of gravity that is not general relativity, which is the escape ENE-1 does not cover. For the thruster alone the energy conditions are respected
DODGES: Warp drives in modified gravity. The matter stress-energy is made to satisfy the weak and null conditions (Einstein-Cartan) or the weak and strong conditions (conformal gravity) by assigning the negative part to torsion or Bach-tensor terms; Capozziello, Lobo and Mimoso show this is what energy conditions mean in extended theories. The register's conditions are on matter, and matter now obeys them; the effective source does not.
SATISFIES: Brane-bulk shortcuts (Chung and Freese 2000, Ishihara 2001, Caldwell and Langlois 2001). Ishihara's shortcut requires $T_{ab}k^ak^b > 0$ on the brane, which is the null energy condition holding, not failing; the bulk is anti-de Sitter vacuum, whose negative cosmological constant saturates the NEC.
SATISFIES: Einstein–Rosen bridge (1935). Vacuum (or an electromagnetic field in the charged case) obeys the null, weak and averaged null conditions everywhere.
SATISFIES: ER = EPR (Maldacena and Susskind 2013). The eternal black hole is a vacuum solution; the conjecture assumes the integrated null energy condition holds well enough to keep the bridge closed.
SATISFIES: Fuchs et al. 2024: the constant-velocity physical warp shell. Null, weak, strong and dominant conditions evaluated numerically over sampled null and timelike observers at every grid point, with no violation above the $10^{34}$ J m$^{-3}$ numerical floor against values of order $10^{39}$
SATISFIES: Gott's cosmic-string time machine (1991). Cosmic strings satisfy the weak energy condition, as Carroll et al. note; no negative energy appears anywhere in the solution.
SATISFIES: Kaluza-Klein and the hyperspace reading (Kaluza 1921, Klein 1926, ADD 1998, Randall-Sundrum 1999). Kaluza-Klein vacuum, ADD's flat torus and the single-brane Randall-Sundrum model obey the energy conditions (anti-de Sitter saturates the NEC); the two-brane model's visible brane has negative tension and violates the WEC there, which is a cost of the hierarchy mechanism rather than of any FTL claim.
SATISFIES: Passage through the Kerr interior (Carter 1968). Kerr is a vacuum solution; the perturbations that drive mass inflation are ordinary radiation obeying the energy conditions.
SATISFIES: The relativistic rocket. Fuel, ship, exhaust and interstellar gas all obey the null and weak energy conditions; the energy density seen by every observer is positive
SATISFIES: Wheeler's geons and quantum foam (1955–1962). Electromagnetic radiation and vacuum obey the null and weak energy conditions everywhere in these solutions.
SILENT: Heim theory and the Dröscher-Häuser propulsion proposal (2004 to 2005). The kinetic energy of the craft is said to come from the vacuum with zero net extraction; no stress-energy tensor is written for the gravitophoton field, so whether any energy condition is violated cannot be checked from the papers.
SILENT: Lorentz-violating frameworks (the Standard-Model Extension and Hořava-Lifshitz gravity). Kostelecký and Lehnert find energy positivity can fail in some observer frames at high energy without a completion; that is a statement about the Hamiltonian of quanta, not the curvature-sourcing energy conditions, and neither framework addresses the NEC or WEC of its own background fields.
SILENT: Meta relativity (Bilaniuk, Deshpande and Sudarshan 1962). The paper never writes a stress-energy tensor; the reinterpretation principle makes every particle's energy positive by relabelling, but whether a gas of class III particles satisfies the weak energy condition for every observer is not addressed here and is rarely treated in the literature.

Fictional drives

SILENT: 2001: A Space Odyssey (1968): the Star Gate. Nothing is said about what the gate is made of beyond "the structure of space itself" in chapter 37, which is not a stress-energy statement.
SILENT: Andromeda: the slipstream. The gravity field generator reduces the ship's mass to open a slippoint, per the setting material, and nothing says what sign of energy that takes; the energy conditions are never mentioned.
SILENT: Asimov's Foundation: the Jump through hyperspace (1942 onward). What a Jump spends is never said; "hyperatomic" is the only word offered for the engine.
SILENT: Babylon 5: hyperspace, jump gates and beacons (1993 to 1998). Opening a jump point is said to be the costly step and the cost is never given a sign or a size.
SILENT: Banks's Culture: the energy grid, infraspace and ultraspace (1987 onward). The grid is named as the energy source and the essay says its author does not know what it is; no sign, no size.
SILENT: Battlestar Galactica: the FTL jump (2004 series). The drive's energy is tylium and its cost is fuel; the currency of a shortcut, negative energy density, is never mentioned.
SILENT: Campbell's Islands of Space (1931): where the word came from. The coils store energy "in the strain in space" and the sign of the density in the altered region is never given.
SILENT: Commonwealth: CST wormholes with trains through them (Hamilton 2004). Generators are described as costly in money and power; the currency of a wormhole, negative energy density, is never named.
SILENT: Cordwainer Smith: planoforming, Space² and Space³. No energy source is ever named for a planoform device; the launching pad of "Drunkboat" is fourteen devices in tandem and nothing is said of what they consume.
SILENT: Cowboy Bebop (1998): the astral gates. Nothing is said about what a gate does to space or what holds it open; no stress-energy statement anywhere.
SILENT: Death's End: curvature propulsion (Liu Cixin, 2010). A subluminal warp shell can satisfy the energy conditions (Fuchs et al. 2024) but the novel never says what the curvature engine is made of or whether its matter is ordinary.
SILENT: Doctor Who: the TARDIS and the time vortex. Energy conditions are never mentioned; the ship's power is the Eye of Harmony, a black hole in the 1996 film, and its sign is never discussed.
SILENT: Dune: the Guild navigators and folding space (Herbert 1965). The Holtzman effect is defined only as the repelling effect of a shield; the novel never says what the drive's energy budget is or in what currency.
SILENT: Elite Dangerous: the frame shift drive (Frontier Developments, 2014). What the drive is made of or fuelled by beyond hydrogen is never stated; the energy conditions are not mentioned.
SILENT: Event Horizon (1997): the gravity drive. Weir's singularity is built from focused gravitons with no statement of the stress-energy required; the energy conditions are never mentioned.
SILENT: Farscape (1999): wormholes, and starburst as a separate thing. Nothing is said about what a wormhole is made of or what the weapon runs on; no stress-energy statement in any episode.
SILENT: FTL: Faster Than Light, the jump drive as a game mechanic. The drive is powered by the reactor through the engines subsystem and fuelled by "fuel"; nothing says what either is or what sign of energy the jump needs.
SILENT: Futurama: the Planet Express ship's dark matter engines (1999 onward). Dark matter is heavy, which is positive energy; what the wall of a moving-universe bubble is made of is never stated.
SILENT: Guardians of the Galaxy Vol. 2 (2017): jump points. Nothing is said about what a jump point is made of; no stress-energy statement anywhere in the franchise.
SILENT: Halo: slipspace and the Shaw-Fujikawa translight engine (2001 onward). The drive's energy is charging time in capacitors; no sign or size is given for what the rupture costs.
SILENT: Homeworld: hyperspace cores and the Far Jumpers. The core's power is never described; in multiplayer a jump costs resource units, which is an economy, not an energy. The energy conditions do not appear.
SILENT: Hyperion: the farcasters (Simmons 1989). The doors are "singularity spheres" and nothing more; the currency of a real shortcut, negative energy density, is never named.
SILENT: Interstellar: the wormhole near Saturn (2014). On screen nothing is said about what holds the wormhole open. The companion book (S2) says exotic negative-energy matter is required and that "they" supplied it, but the film itself never names the currency.
SILENT: Mass Effect: the mass relays (BioWare 2007 onward). The Codex prices everything in element zero and mass reduction; the currency of a real shortcut, negative energy density, is never named for the relays.
SILENT: Niven's Known Space: the Outsider hyperdrive and the blind spot (1966 onward). What the shunt spends is never given a sign or a size.
SILENT: No Man's Sky: the hyperdrive, warp cells and range. The drive burns antimatter in warp cells and the game never says what that means for the energy of the transit; the energy conditions do not appear.
SILENT: Outer Wilds (2019): Nomai warp cores. What a warp core is made of, and what the energy conditions would say about its throat, is never stated; the cores are forged in the Black Hole Forge from unnamed materials.
SILENT: Space Battleship Yamato: warp by wave motion engine. The engine's energy is named (wave motion energy, with tachyons in the reference gloss) and its sign never discussed; energy conditions do not appear.
SILENT: Star Trek: transwarp, quantum slipstream and the other beyond-warp drives. Conduits, slipstreams and folds all deliver a ship early through flat space; what sources them is never stated.
SILENT: Star Trek: warp drive (1966 onward). The manual's field layers and coils never say what the field is made of; the energy conditions are not mentioned in any instalment.
SILENT: Star Wars: hyperspace (1977 onward). The energy conditions are the currency of geometric FTL and the films never say what a jump spends beyond fuel names.
SILENT: Starfield (2023): the grav drive. What a grav jump does to space, and what stress-energy it needs, is never stated; the drive's power is a number with no units of physics attached.
SILENT: Stargate: the gate network (1994 film, SG-1 1997 onward). The gate is said to need power to dial and to be held open by a black hole in "A Matter of Time", but the currency of a wormhole, negative energy density, is never named.
SILENT: Stargate: the ships' hyperdrives. The drive's power sources (naquadah, naquadria, ZPMs) are named and their sign is never discussed; energy conditions are not mentioned.
SILENT: Starman Jones: the congruencies (Heinlein 1953). No energy budget for the fold is stated in any currency; the ship's engines are for the approach.
SILENT: Stellaris: warp, hyperlane and wormhole (Paradox Development Studio, 2016). What powers a warp drive, holds a wormhole open or sustains a gateway is never stated beyond "energy" as a resource; the energy conditions are not mentioned.
SILENT: Super Dimension Fortress Macross (1982): the space fold. Nothing is said about what a fold does to space or what it costs; no stress-energy statement anywhere.
SILENT: The Alderson drive (Niven and Pournelle 1974). The drive "uses energy" and no more is said; the currency of a shortcut, negative energy density, is never named.
SILENT: The Expanse: the ring gates and the slow zone (Corey 2013 onward). Nothing is said of what holds a ring open or in what currency; the rings are protomolecule structures and the novels leave it there.
SILENT: The Forever War: collapsar jumps (Haldeman 1974). No energy condition is named; the collapsar is a frozen star and the jump costs nothing beyond the approach speed.
SILENT: The Hitchhiker's Guide to the Galaxy: the Infinite Improbability Drive and bistromathics. The drive's power source is a finite improbability generator and a cup of tea; energy density is never mentioned, and the work is not making a claim that the conditions could price.
SILENT: The Orville: quantum drive (2017 onward). The production names exotic matter (dysonium) as the fuel, which is the energy-condition violation by another name; no episode says what dysonium's energy density is.
SILENT: Thor (2011): the Bifrost. Jane names an Einstein-Rosen bridge, a vacuum solution obeying every energy condition, and the film never says what makes its bridge traversable.
SILENT: Vinge's Zones of Thought: FTL only where physics permits it (1992). What the ultradrive spends is never given a sign or a size.
SILENT: Warhammer 40,000: the Warp (1987 onward). What a warp drive spends to open the rift is never given a size or a sign.
SILENT: Weber's Honorverse: hyper bands and Warshawski sails (1993 onward). Translation and sailing are powered by reactors and by the wave, positive energy by every description; whether the geometry's price has a sign is never asked.
SILENT: Wing Commander (1990) and the 1999 film: jump points. What a jump point is made of is never stated in the game or film; the encyclopaedia's anti-gravitons are not a stress-energy statement and are not in the primary works.
SILENT: Xenocide: travel through the Outside. No energy source is named for the transit; Jane's cost is computational and the ship needs no engine. Energy conditions are never mentioned.
ENGAGES: Contact: the Machine and the tunnel system (Sagan 1985, Zemeckis 1997). By Thorne's account the novel's tunnels are held open by exotic material with negative energy density, attributed to a lost earlier civilisation so that the text need not explain it; this is the reason Morris and Thorne looked for the solutions at all. The engagement is in the book's origin and the paper's §I.C rather than in a passage of the novel this catalogue could quote.
ENGAGES: EVE Online: the warp drive (CCP Games, 2003). The lore article says the bubble is vacuum drained of energy, which is a below-vacuum energy density stated on the page; it does not name the energy conditions but it describes their violation as the drive's working principle.
ENGAGES: Star Citizen: quantum drive and jump points. The developer states that quantum fuel is converted into negative energy density to shape the bubble, which is a stated violation of the energy conditions for the quantum drive; the jump points are given no energy content.

Sources

Hawking and Ellis, The Large Scale Structure of Space-Time (1973), §4.3; Visser, Lorentzian Wormholes (1995), ch. 12; Curiel, "A Primer on Energy Conditions", in Towards a Theory of Spacetime Theories, Einstein Studies 13, pp. 43–104 (2017), arXiv:1405.0403 ✓ (books unverified online)