CAU-1: The tachyonic antitelephone

Any FTL signal or vehicle, of any mechanism, unless Lorentz invariance is broken.

Kind: constraint · Family: CAU (Causality) · Last reviewed: 2026-09-12

The result

In special relativity any signal faster than light in one inertial frame travels backwards in time in some other inertial frame. Einstein's 1907 review draws the conclusion from the velocity addition theorem: with a signal speed above c one can always choose a frame in which the effect precedes the cause. Tolman states the same paradox; Benford, Book and Newcomb turn it into the two-signal exchange in which a reply arrives before the question was sent, the tachyonic antitelephone

What it forbids or costs

Any FTL signal or vehicle, of any mechanism, unless Lorentz invariance is broken. This is the constraint every loophole must answer

Escape hatches

A preferred frame (CAU-4); FTL that only works in one direction or between fixed endpoints; accepting closed timelike curves

Who it bites

Physics proposals

• VIOLATES: Alcubierre 1994: the warp drive metric. The bubble delivers a ship between two points in flat space faster than light through that space, which is exactly the signal CAU-1 prices; nothing in the metric breaks Lorentz invariance or picks the exterior rest frame as special, so a second bubble in a boosted frame carries the ship into its own past. The single spacetime is globally hyperbolic, as Alcubierre stresses, but the constraint is about the class of signal, not one instance.
• VIOLATES: Entanglement signalling and the no-communication theorem. An instantaneous signal with no invariant speed is exactly the case CAU-1 covers: in some other inertial frame Bob's reading precedes Alice's choice, and two radios give the Benford, Book and Newcomb antitelephone. No entanglement-radio proposal supplies the Lorentz-breaking that CAU-1 says is the only way out
• VIOLATES: Fell and Heisenberg 2021: positive energy from hidden geometric structure. A central observer at shift 1.26 relative to distant observers, with no frame singled out, is a signal into some observer's past by the entry; the paper's causality section addresses closed curves within one spacetime, not the two-frame argument
• VIOLATES: Gott's cosmic-string time machine (1991). The construction yields observers who visit their own past; a signal round the strings arrives before it was sent, in every frame, which is CAU-1's forbidden outcome by design.
• VIOLATES: Lentz 2021: hyper-fast positive-energy solitons. A timelike payload carried at $v_s > 1$ relative to the fixed stars with no frame singled out is, by the entry, a signal into some observer's past; the paper never mentions causality
• VIOLATES: Meta relativity (Bilaniuk, Deshpande and Sudarshan 1962). A class III signal that is superluminal in one frame goes backward in time in another; the paper's own Fig. 2 shows source and sink exchanging roles, and Benford, Book and Newcomb showed the reinterpretation cannot stop a reply arriving before the question.
• VIOLATES: Morris, Thorne and Yurtsever: the wormhole time machine (1988). The construction yields a traveller who returns before departing, the tachyonic antitelephone realised in curved spacetime with fixed Lorentz invariance.
• VIOLATES: Natário 2002: warp drive with zero expansion. Any member of the class with $v_s > 1$ carries the interior between flat-space points faster than light through that space; nothing in the definition breaks Lorentz invariance or singles out the exterior frame, so a boosted second bubble sends the ship into its own past.
• VIOLATES: Retrocausal signalling proposals. The proposal is retrocausal on its face: Alice's delayed choice would be read by Bob before it was made. That is the antitelephone without needing a second device, and no Lorentz-breaking is offered
• VIOLATES: Tachyons (Feinberg 1967). A Lorentz-invariant tachyon signal is a backward-in-time signal in some inertial frame; Benford, Book and Newcomb built the two-way antitelephone from exactly this proposal, and the reinterpretation principle does not close the loop.
• VIOLATES: The Hartman effect and the Nimtz tunnelling claims. Nimtz's claim is a signal faster than c in the laboratory frame with no preferred frame named, which is the tachyonic antitelephone case CAU-1 describes; Aichmann and Nimtz concede the signals "confront the Einstein causality" and argue only that finite pulse duration blunts the paradox
• VIOLATES: The OPERA superluminal neutrino (2011). The anomaly as claimed was a superluminal signal with no frame picked; in special relativity that is a message to the past in some inertial frame, and the corrected result removes the violation by removing the signal.
• VIOLATES: Van Den Broeck 1999: the pocket geometry. The pocket is carried between flat-space points faster than light through that space by an ordinary Alcubierre exterior, and nothing picks a frame; a boosted second pocket is a message to the past.
• VIOLATES: Warp drives in modified gravity. The metrics are Alcubierre's and Van Den Broeck's unchanged; effective superluminal transport between flat-space points with no preferred frame is exactly the signal CAU-1 prices, and changing the field equations changes nothing about the causal structure.
• DODGES: Bobrick and Martire 2021: physical warp drives. The members the paper calls physical are subluminal Class I shells, so no signal outruns light and the antitelephone never arises; the paper concedes that in Class III the interior observer "will be travelling back in time from the point of view of yet another remote timelike observer" and leaves that class hypothetical, citing Liberati, Sonego and Visser for a Lorentz-breaking way out it does not adopt
• DODGES: Brane-bulk shortcuts (Chung and Freese 2000, Ishihara 2001, Caldwell and Langlois 2001). On the brane the signal is superluminal and a boosted brane observer would see it reversed; the bulk geometry singles out the comoving (or local rest) frame in which the advance is fixed, and Ishihara's instruction that "true causality should be defined by the null geodesics in $M$" is the preferred-frame escape CAU-1 names, though none of the three papers says so.
• DODGES: Everett and Roman 1997: the superluminal subway. One tube is superluminal in one direction between two fixed endpoints and returns the traveller at $t_E = D\delta > 0$; CAU-1 names one-directional, fixed-endpoint FTL as an escape hatch and the paper proves the single tube uses it. The paper also proves the hatch closes with a second tube.
• DODGES: Krasnikov 1998: the tube laid on the way out. A single tube gives effective superluminal travel only in one direction along one fixed route and returns the traveller at $t_E = D\delta > 0$, never before departure; CAU-1 lists FTL that works only in one direction or between fixed endpoints as an escape hatch, and this is the cleanest instance of it in the literature. The hatch closes as soon as there are two tubes.
• DODGES: Lorentz-violating frameworks (the Standard-Model Extension and Hořava-Lifshitz gravity). The register's own text says "unless Lorentz invariance is broken", and breaking it is the whole content of these frameworks: a superluminal species moves forward in the preferred frame's time and no boost of a particle changes that ordering.
• DODGES: Morris–Thorne traversable wormhole (1988). A single static wormhole has fixed endpoints in a curved spacetime and no signal reverses order in any frame; the mouths' rest frame is the frame, which is CAU-1's fixed-endpoint escape hatch, and it fails as soon as a mouth moves (CAU-3).
• DODGES: The Scharnhorst effect. A photon faster than c in the plates' rest frame is faster than c in every frame, and CAU-1 would make it a signal to the past unless Lorentz invariance is broken; it is, softly, by the plates, which fix the FTL speed in one frame. This is the escape CAU-1 itself names
• DODGES: Visser's thin-shell wormholes (1989). A single static thin-shell wormhole has fixed mouths and no signal reverses in any frame; the mouths' frame is CAU-1's fixed-endpoint escape, and it fails once a mouth moves.
• SATISFIES: Einstein–Rosen bridge (1935). No signal crosses the bridge (Fuller and Wheeler), so there is no faster-than-light signal to reverse in any frame.
• SATISFIES: ER = EPR (Maldacena and Susskind 2013). No signal crosses the bridge and no local operation on one half of an entangled pair affects the other; there is no faster-than-light signal to reverse in any frame.
• SATISFIES: Fuchs et al. 2024: the constant-velocity physical warp shell. A subluminal shell: nothing outruns light in any frame, so the antitelephone never arises
• SATISFIES: Gain-assisted superluminal light propagation. No signal outruns light: the front moves at c and the information velocity is measured at or below c (Stenner, Gauthier and Neifeld). The authors state the result is not at odds with causality
• SATISFIES: Gao, Jafferis and Wall: traversable wormholes via a double-trace deformation (2017). The signal through the bulk arrives no earlier than the coupled boundary theory allows, and the boundary evolution is unitary and causal; the astronaut emerges long after the coupling was switched on, so no frame sees the effect precede its cause.
• SATISFIES: Kaluza-Klein and the hyperspace reading (Kaluza 1921, Klein 1926, ADD 1998, Randall-Sundrum 1999). The brane's induced light cone is a restriction of the bulk's; no field confined to the brane can outrun brane light, and the frameworks propose no signal that does.
• SATISFIES: Maldacena, Milekhin and Popov: traversable wormholes in four dimensions (2018), and the humanly traversable sequel (2021). The traversal takes longer as seen from outside than the outside path ($\pi\ell > d$), so no signal through the wormhole arrives before a light signal round it, and nothing is reversed in any frame.
• SATISFIES: Passage through the Kerr interior (Carter 1968). Passage to another asymptotic region sends no signal faster than light within any one region; nothing that enters the horizon returns to our exterior, so there is no reversed-order signal for CAU-1 to bite.
• SATISFIES: The relativistic rocket. The ship's worldline is timelike; it arrives after light would in every frame, so no frame sees effect before cause. This is the case CAU-1 leaves untouched
• SATISFIES: Wheeler's geons and quantum foam (1955–1962). Fuller and Wheeler asked exactly this question for the Schwarzschild handle and showed no signal is outpaced; the charged handle hides behind horizons.
• SILENT: Heim theory and the Dröscher-Häuser propulsion proposal (2004 to 2005). The re-entry displacement $nv\Delta T$ is an FTL transport of matter as seen from $\mathbb R^4$ with no frame specified; neither paper mentions causality, and the register's constraint that any such signal is a message to the past in some frame is never addressed.
• SILENT: NASA Eagleworks warp field interferometer. The documents plan a $10c$ craft and a bench bubble and never mention causality
• SILENT: White et al. 2021: the worldline-numerics Casimir pattern. An Alcubierre bubble on a chip is proposed with no velocity and no word on causality; the entry applies to any such bubble that is superluminal

Fictional drives

• SILENT: 2001: A Space Odyssey (1968): the Star Gate. A passage to another star and back is an FTL signal and neither novel nor film asks in which frame it is instantaneous; the return to Earth is undated in both.
• SILENT: Alien's Nostromo. An FTL freighter of unstated mechanism, ten months for thirty-nine light years, with a distress beacon and a "network" to pick up a lifeboat; no instalment raises the frame or the reply
• SILENT: Asimov's Foundation: the Jump through hyperspace (1942 onward). The antitelephone is never mentioned; hyperwave messages and Jumps are treated as simply fast, in every instalment from 1942 to 1993.
• SILENT: Babylon 5: hyperspace, jump gates and beacons (1993 to 1998). Instant tachyon messages and day-long jumps in one galactic time; no episode asks what a moving observer would see.
• SILENT: Banks's Culture: the energy grid, infraspace and ultraspace (1987 onward). Ships at hundreds of thousands of c and instant Mind-to-Mind talk in one shared time; the antitelephone is never raised in essay or novel.
• SILENT: Battlestar Galactica: the FTL jump (2004 series). Jumps move ships and news faster than light; no episode asks about the frame in which a Raptor's return precedes its departure.
• SILENT: Campbell's Islands of Space (1931): where the word came from. The antitelephone is never raised; the one time puzzle in the book (a system arriving before its own light) is about light travel, not about frames.
• SILENT: Commonwealth: CST wormholes with trains through them (Hamilton 2004). Trains and messages cross hundreds of light years with no transit time; the novel never asks about the frame in which arrival precedes departure.
• SILENT: Contact: the Machine and the tunnel system (Sagan 1985, Zemeckis 1997). The tunnels deliver the Machine from Earth to Vega and the galactic centre faster than light through the space between; no instalment asks about the frame in which the arrival precedes the departure.
• SILENT: Cordwainer Smith: planoforming, Space² and Space³. Skips are instantaneous by Earth's clocks and the ship's alike and no story asks about other observers; "Drunkboat" makes Space³ instantaneous "in relation to our universe" and stops there.
• SILENT: Cowboy Bebop (1998): the astral gates. A gate transit of hours between planets may not beat light at all, and the series never says whether it does; the entry's question is never put in any session.
• SILENT: Dune: the Guild navigators and folding space (Herbert 1965). A heighliner arrives across interstellar distance in no stated time; the novel never asks in which frame it arrived before it left.
• SILENT: Elite Dangerous: the frame shift drive (Frontier Developments, 2014). Supercruise and jumps both beat light through flat space; the game never considers the frame-dependence of arrival order.
• SILENT: Ender's philotic ansible. Ansibles ride the relativistic fleet for decades while another sits on Eros; the two-transmitter antitelephone is the standing configuration of the war and is never mentioned
• SILENT: EVE Online: the warp drive (CCP Games, 2003). Bubbles cross a system faster than light and gates cross between stars instantly; the frame-dependence of arrival order is never raised in lore or mechanics.
• SILENT: Event Horizon (1997): the gravity drive. A jump of light years and back is an FTL signal and the film never asks what frame it is instantaneous in; the seven-year absence is treated as a mystery of where, never of when.
• SILENT: FTL: Faster Than Light, the jump drive as a game mechanic. Jumps are instantaneous and the game has one clock, the fleet's advance; whose clock it is never comes up.
• SILENT: Futurama: the Planet Express ship's dark matter engines (1999 onward). The ship arrives across galaxies in hours and no episode considers the frame-dependence of arrival order; the show's time travel uses other devices.
• SILENT: Guardians of the Galaxy Vol. 2 (2017): jump points. A jump is an FTL signal between two points and the film never asks in which frame it is instantaneous; seven hundred jumps in a row, and the question is never put.
• SILENT: Halo: slipspace and the Shaw-Fujikawa translight engine (2001 onward). Subjective time in slipspace is stated to be inconsistent between ships, but no work asks what a jump looks like from a moving frame or notices that an FTL arrival is a trip into someone's past.
• SILENT: Homeworld: hyperspace cores and the Far Jumpers. Jumps are effectively instantaneous and the setting has one clock; the antitelephone is never raised.
• SILENT: Hyperion: the farcasters (Simmons 1989). People step between worlds light years apart with no transit time and the fatline sends messages by tachyon; no novel asks in which frame the arrival preceded the departure.
• SILENT: Le Guin's ansible. A fixed ansible plus one aboard a NAFAL ship in relative motion is the two-transmitter antitelephone; the League runs that setup throughout the cycle and no instalment raises the backward-in-time reply. The ch. 9 causal-reversibility joke is the only brush with it
• SILENT: Mass Effect: element zero and the FTL drive (BioWare, 2007). Ships outrun light in flat space between relays; no game raises the frame-dependence of arrival order.
• SILENT: Mass Effect: the mass relays (BioWare 2007 onward). Instantaneous transit between relays thousands of light years apart, and instantaneous messages through comm buoys along the corridors; no Codex entry or line of dialogue asks in which frame the arrival preceded the departure.
• SILENT: Niven's Known Space: the Outsider hyperdrive and the blind spot (1966 onward). Instant hyperwave and three-day light years in one shared time; the antitelephone is never mentioned in the stories, and Niven's time-travel essay does not connect it to the hyperdrive.
• SILENT: No Man's Sky: the hyperdrive, warp cells and range. Warps of any range take the same few seconds and the galaxy shares one real-time clock; the antitelephone is never raised.
• SILENT: Space Battleship Yamato: warp by wave motion engine. The ship and Earth share one countdown across a 296,000-light-year round trip and nobody asks whose year it is; the antitelephone is never raised.
• SILENT: Spaceballs: ludicrous speed (1987). Spaceball One outruns light in flat space; the film's only temporal remark, the overshoot by a week and a half, is a distance joke and does not consider frames.
• SILENT: Star Citizen: quantum drive and jump points. A jump between systems is an FTL signal and no lore piece or in-game text asks in which frame it is instantaneous; the quantum drive is sublight and raises no question.
• SILENT: Star Trek: transwarp, quantum slipstream and the other beyond-warp drives. Every drive here beats light between fixed points in normal space; no episode considers the frame-dependence of the arrival order.
• SILENT: Star Trek: warp drive (1966 onward). Ships outrun light through flat space between stars in every episode; no instalment considers the frame-dependence of arrival order, and stardates are a universal clock by assumption.
• SILENT: Star Wars: hyperspace (1977 onward). Ships and messages cross the galaxy in hours with one shared clock and nobody ever asks what a jump looks like from a moving frame; no film raises the antitelephone.
• SILENT: Starfield (2023): the grav drive. A thirty-light-year jump is an FTL displacement and the game never asks in which frame it is instantaneous; the universal calendar simply does not advance during a jump.
• SILENT: Stargate: the gate network (1994 film, SG-1 1997 onward). A gate delivers a person across interstellar distance in 3.2 seconds ("Insiders"); no episode asks in which frame the arrival preceded the departure. The time travel the show does have is by solar flare, not by boost.
• SILENT: Stargate: the ships' hyperdrives. Ships arrive before their own light across intergalactic distances and no episode asks in whose frame; the franchise's time travel is by other means.
• SILENT: Starman Jones: the congruencies (Heinlein 1953). Transitions are instantaneous between stars and reversible; the novel never asks in which frame the return precedes the departure.
• SILENT: Stellaris: warp, hyperlane and wormhole (Paradox Development Studio, 2016). Warp crossed flat space faster than light, hyperlanes and wormholes deliver fleets early; the frame-dependence of arrival order is never raised in any version.
• SILENT: Super Dimension Fortress Macross (1982): the space fold. The Earth-to-Pluto fold is an FTL displacement and the series never asks in which frame it was instantaneous; ship and Earth clocks are simply kept in step for the voyage home.
• SILENT: The Alderson drive (Niven and Pournelle 1974). An instantaneous jump between stars, with return jumps routine, and no question of the frame in which the return precedes the departure.
• SILENT: The Expanse: the ring gates and the slow zone (Corey 2013 onward). Ships and news pass through the gates instantly between systems hundreds of light years apart; no novel or episode asks about the frame in which that is a message into the past.
• SILENT: The Hitchhiker's Guide to the Galaxy: the Infinite Improbability Drive and bistromathics. The ship arrives in a nothingth of a second and nobody asks in whose frame; the antitelephone of CAU-1 is never raised for the drive. The series' time-travel jokes are about grammar, not about FTL ordering.
• SILENT: The Lensman inertialess drive (E. E. Smith, 1934 onward). Free ships and ultra-wave signals both outrun light in flat space; no instalment considers the frame-dependence of their arrival order.
• SILENT: The Orville: quantum drive (2017 onward). Bubbles cross flat space between stars faster than light in every episode; the frame-dependence of arrival order is never considered.
• SILENT: The Skylark of Space (E. E. Smith, 1928). The ship outruns light in flat space, which is exactly the signal CAU-1 prices, and the book never considers that an observer in another frame would see it arrive before it left.
• SILENT: Thor (2011): the Bifrost. Realm-to-realm passage in seconds is an FTL signal and the film never asks which observers see it as instantaneous; clocks on Earth and Asgard simply agree.
• SILENT: Time for the Stars' telepathy. One twin on a torchship at 99 percent of c, one at home, an instantaneous link between them for years: the two-transmitter configuration, with no mention of a reply preceding a question
• SILENT: Vinge's Zones of Thought: FTL only where physics permits it (1992). The antitelephone is never mentioned; the Net's delays are treated as bandwidth, not as frames.
• SILENT: Weber's Honorverse: hyper bands and Warshawski sails (1993 onward). Crossings at thousands of c and in-system FTL messaging in one shared time; the antitelephone is not mentioned in the appendix or the novels.
• SILENT: Wing Commander (1990) and the 1999 film: jump points. A jump is an FTL signal between systems and the film's race to Earth is two such signals compared; in which frame is never asked.
• SILENT: Xenocide: travel through the Outside. The ship arrives instantly and the whole series runs on a single galactic clock, but no passage asks whose "instant" it is; the antitelephone of CAU-1 is never raised for the ansible or the drive.
• ENGAGES: Andromeda: the slipstream. "Angel Dark, Demon Bright" (2000) has the drive deliver the ship into its own past and the crew argue about it; the antitelephone's consequence is shown rather than avoided.
• ENGAGES: Doctor Who: the TARDIS and the time vortex. The whole premise is a vehicle that reaches other observers' pasts, and the show dramatises the consequence rather than avoiding it: "The Aztecs" (1964), "Father's Day" (2005), "The Waters of Mars" (2009). The antitelephone is the ship.
• ENGAGES: Farscape (1999): wormholes, and starburst as a separate thing. "Unrealized Reality" (4.11): movement through space at speed becomes movement through time, and a wormhole return can arrive before departure. This is the entry's content stated by a character named for its author.
• ENGAGES: Flight of the Navigator (1986). The film's climax is the CAU-1 implication used as plot: the faster-than-light ship carries David to his own past. Not argued from frames, but owned on screen.
• ENGAGES: Interstellar: the wormhole near Saturn (2014). Not through the wormhole but through the tesseract: the film sends data to Murph's past and shows it arriving, then closes the loop. The work accepts that its physics allows signals to earlier times and makes the ending of it.
• ENGAGES: Outer Wilds (2019): Nomai warp cores. High Energy Lab texts: warped Nomai arrive before they depart, by a hundred-thousandth of a second, measured and confirmed. The entry's content is the game's central discovery.
• ENGAGES: Revelation Space lighthuggers. The Nightshade state-four attempt in Redemption Ark erases its victims backwards in time; the Exordium is defined by the author as acausal signalling. The series stages the antitelephone's consequence rather than ignoring it
• ENGAGES: Star Trek subspace radio. "Eye of the Needle" sends a subspace transmission through a micro-wormhole to twenty years in the past and argues the consequences; "Timeless" receives a message from the future; "All Good Things..." names its tachyon loop a paradox. Ordinary subspace radio is never asked the question
• ENGAGES: The Forever War: collapsar jumps (Haldeman 1974). Chapter 1: the jump made physicists "redefine simultaneity" and rebuild general relativity. The text admits that an instantaneous transit is a problem for the time-ordering of special relativity and says so in the sentence that introduces the drive.
• ENGAGES: Timescape's tachyon message. The novel is the antitelephone written by its co-author: a modulated tachyon beam to the past, Tolman's paradox discussed by name in the pub scene, and the message rationed to avoid contradiction
• ENGAGES: Warhammer 40,000: the Warp (1987 onward). The rulebook background states that Warp time and real time disagree unpredictably and that ships have emerged before they departed; the setting admits that FTL and a single consistent timeline cannot both be had, which is the constraint's content, and builds the Imperium's chaos of arrivals on it.
• RULE: Aurora's generation ship. The ship's worldline is timelike at a tenth of c and the author's stated rule excludes FTL; no frame sees effect before cause. Forbidden where it would bite
• RULE: Avatar's Venture Star. The companion's stated profile, 0.7 c and no more, keeps the ship's worldline timelike; the film's five-year cryo is consistent. The companion's entanglement channel would break the rule and is scored under CAU-5
• RULE: Death's End: curvature propulsion (Liu Cixin, 2010). Nothing in the drive exceeds c, by a rule the novel states and keeps; CAU-1 has no signal to price. The trails lower c and cannot raise it.
• RULE: Firefly's Verse. The production's stated rule of no FTL keeps every worldline timelike; on screen the rule is visible only as journeys of hours and days within one system
• RULE: Passengers' Avalon. The stated half light speed keeps the ship's worldline timelike and every message slower than the ship's own light cone allows; no frame sees effect before cause
• RULE: Tau Zero's ramjet. The ship's worldline is timelike throughout; the title is the rule, tau never reaches zero, so no frame sees effect before cause. Forbidden where it would bite

Sources

• Einstein, Jahrbuch der Radioaktivität und Elektronik 4, 411 (1907), §5, pp. 423–424; Tolman, The Theory of the Relativity of Motion (1917), §52, pp. 54–55; Benford, Book and Newcomb, Phys. Rev. D 2, 263 (1970) ✓