back to article Warp drives are PLANET KILLERS, Sydney Uni students find

In 1994, a physicist called Miguel Alcubierre proposed a “warp drive” solution resolving the prohibition in Einstein’s special relativity on traveling faster than light. The problem turns out to be that anybody in the path of the incoming space ship gets fried. That’s the conclusion of a group of University of Sydney physics …

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  1. Paul Crawford Silver badge
    Joke

    In a distant galexy...

    ...what we though were GRB due to massive supernova turned out to be the ill-advised warp drive designs of spaceships stopping off at intergalactic fast food place asking "where is the beef?" for the upteenth time.

    1. Wombling_Free
      Alien

      Re: In a distant galexy...

      GRBs were the first thing that went through my mind (actually, they usually are) when I read the headline.

      If GRBs are all pointing towards us, that means... from the edges of the Universe... THEY ARE COMING!

      I for one welcome our our new gamma-ray-emitting alien overlords.

      (hey, shouldn't there be an icon for that, or is it just the alien-grey one?)

  2. montyburns56
    Alien

    Make it so...

    Funnily enough there was a Star Trek: TNG episode called Force Of Nature which was about this theory, so I wonder if rather than having "re-examined the maths of the Alcubierre drive" they really just watched a DVD box set of the show while they were stoned?

    1. Wombling_Free
      Trollface

      Re: Make it so...

      " they really just watched a DVD box set of the show while they were stoned?"

      They are uni students (Sinny Yooni at that), so your point being?

    2. Marty
      Trollface

      Re: Make it so...

      yes, yes,yes,,, whatever.....

      The point is that many of the beings on planet earth dont give a flying f**k at a rolling dohnut about the physics behind "warp" technology as proven by the lack of interest the majority of travellers are regarding the plane they are flying to their holiday destination in, or the car they drive them to work.

      All people are interested in is, "ok, this new plane you build with the star trek engine, how long is it going to take me to fly between New York and Heathrow?" and, "How long are you gonna keep me in the god damned departure lounge/security?"

      Just hurry it up and make it gad damn so !!

      1. illiad

        Re: Make it so,marty??

        hey if they did that, and found it killed all the people in the airport, they would stop it pretty damned quick.... :(

        you dont hear much from the 1900's passengers about possible fatalities due to frost bite and oxygen deprivation...

  3. Kevin 6
    Alien

    So...

    Gene Rodenberry had it right all those years ago?

    If anyone has ever noticed in StarTrek they pretty much didn't exit(or enter unless an emergency) warp drive near a inhabited planet.

    Maybe they should look closer at StarTrek for how to do it too.

    Icon for what Gene Rodenberry really was.

    1. RAMChYLD
      Boffin

      Re: So...

      And so did David Beraben- I think you can't use warp drives until you've moved a sufficient distance away from inhibited planets as well. At least, that's the case in the OOLite clone.

      Anyways, what's wrong with keeping the ship stationary and moving the space around it instead?

      1. Anonymous Coward
        Headmaster

        Re: So...

        Hand in the keys to your Cobra Mk III . Elite uses hyperspace, not warp drive.

        1. Loyal Commenter Silver badge
          Boffin

          Re: So...

          Hyperspace (H key) for inter-system travel, warp (J key) for FTL travel within systems.

          1. perlcat
            Black Helicopters

            Much simpler explanation

            Spacecraft in SF travel 'at the speed of plot'. If travel happened instantaneously from point 'A' on earth to point 'B' on some far-off planet, the travel and the destination wouldn't be all that interesting. (from the perspective of fiction...)

            Like they always say, 'truth is stranger than fiction', and that's because fiction has to follow rules we know -- truth doesn't.

            1. stucs201

              Re: Much simpler explanation

              Well Hamiltons trains through wormholes in the commonwealth books was instant from one planet to another. Made a nice change for the few spaceships to be a novelty because they were mostly redundant, shame he de-emphasised the trains in favour of more standard SF hyperdrives in the second set of books.

              The Silfen paths though, they definately went at the speed of plot.

          2. wheel

            Re: So...

            Well, Jump drive seems to just compress time, to make it seem like it takes less time to reach your destination; that is why you cannot use it when other ships are around (they could blow you out of the sky before you can react). Frontier did away with it altogether, replacing it with various fast forward options (which could be used when other ships were around, though they then tended to blow you out of the sky before you could react).

            Hyperspace drive cannot be used near a planet or star because of their gravity wells, according to the Frontier manual.

            I feel I am revealing the extent of my misspent youth...

    2. AndrueC Silver badge
      Thumb Up

      Re: So...

      That's true in a lot of science fiction. Isaac Asimov's books usually required ships to be a fair distance from a planet before they could enter hyperspace. C.J. Cherryh's books require ships to be most of the way outside the solar system.

      The common theme though tends to be not trying to leave normal space while inside a gravity well. Given the way gravity impacts light it's a reasonable restriction but it's probably more of a device for story telling. Just bouncing from one planet to another at the push of the button makes it sound too easy. Having to first spend a few hours or days travelling in normal space makes it more interesting.

    3. phuzz Silver badge
      Flame

      Re: So...

      The thing with warpdrives/hyperspace/whathaveyou in sci-fi is that if you allow you spaceship to 'enter warpspace' (or whatever) close to a planet, then nothing is ruling out being able to do it from the surface of a planet, in which case, why do you need your big shiny spaceships at all? You could just have a car with an air tight seal, or a shipping container with the warpdrive bolted in the middle.*

      Hence most Scifi doesn't allow warping near planets, so they get to keep their big shiny (not compensating for anything at all honest) starships.

      *(Ken MacLeod did this in Dark Light, strapping a warp drive to a spacestation, to create a slightly unwieldy, but relatively spacious spacecraft)

      1. illiad

        Re: So...

        I think you need to check your startrek schematics for the warp drive size...

        Have you tried fixing a porche engine onto your pushbike????

      2. E 2
        Alien

        Re: So...

        But in Babylon 5, Sheridan opens a hyperspace jump point in the atmosphere of Mars during the attack on EarthGov there, near the end of the Human civil war, and neither was Mars consumed nor the population fried!

        So there!

    4. fLaMePrOoF
      Thumb Up

      Re: So...

      Well, he did postulate the forward deflector as well, a solution to preventing time-locked matter build up at the front of the 'warp field'...

    5. asdf
      FAIL

      Gene was a hack

      Yeah too bad he made every named crew member a super hero at everything (the cameo Yeoman Johnsons of course were there to die for dramatic affect). That's right the ship's doctor unarmed can take down the biggest best Klingon warrior with ease with his WWE double hands clapped like an axe move. Why don't they use that in MMA you ask? Because in MMA they need to actually knock out there opponent instead of break their fingers/hands.

  4. cosymart
    Alien

    Klingons

    No wonder the Klingons were upset if every time the Enterprise turn up it fried half their planets.

  5. James Le Cuirot

    Ban Military Drives!

    Looks like Frontier: Elite II wasn't too far off the mark either.

  6. James Loughner
    Holmes

    Use the energy to produce the bubble

    Start small cycle the bubble on and off use the energy to create a larger bubble etc untill you enclose the ship. There problem solved.

    1. Anonymous Coward
      Anonymous Coward

      Re: Use the energy to produce the bubble

      That is sort of what I was thinking.... Gamma radiation= energy, since we need alot of it, it makes sense to harness this radiation... maybe in the form of a 'catchers mitt' for space craft that converts the gamma radiation into useable energy at the destination... hmmm think about it cannons between stars...

  7. Roger Stenning
    Go

    There's a former company called GDW...

    in the USA, who made the old paper and dice role-playing games; they've folded now, but one such game was called 2300:AD, and used a stutter warp concept - a fast-cycling on/off warp drive that had to be discharged in the gravity well of a star system. Methinks this might have been a tad prophetic - if you cycle it fast enough, you'll get your FTL drive; if it's cycling rapidly enough, there won't be that many particles caught up to produce the harmful radiation and energy at the end of each cycle, thus the frying tonight effect could be minimised. Like I just said: A tad prophetic :-)

    Go, 'cause I wanna walk on Mars before I pop my clogs ;-)

    1. S Watts
      Angel

      Re: There's a former company called GDW...

      The stutter drive of 2300AD used the quantum tunnelling effect to move the vessel forwards by small amounts; each quantum leap taking zero time.

      As an Astrophyics undergrad at the time (mid 80s), it made me curious as to what the effective speed was of a particle when it moved by this method. However, I suspect that the answer would be let down by the lack of a definitive concept of position...

      2300AD (aka Traveller 2300) is still available through other publishers (Mongoose?). I liked its "hard SF" design and setting. (much abuse of the player's characters by corporate police state in the shadow of the Braziville elevator...)

      1. Anonymous Coward
        Anonymous Coward

        Re: There's a former company called GDW...

        Sci-Fi fiction and games normally places the reasoning that you can't just pop up next to a planet from warp-drive in the hands of gravity wells. Battletech, Renegade Legion, Traveller, 40k and I believe even Star Wars used the caveat and it's pretty much become a paradigm.

        I guess it also gives a reason for space ships to have conventional engines and to look slightly ship-like, rather than simply big sphere-things that just pop between orbits (although that's exactly how fold-space ships in Dune functioned).

        The only mention of FTL radiation woes that I can recall in sci-fi/sci-fi gaming is in Renegade Legion, where ships in T-Space build up radiation, which takes an equal time in normal space0time to dissipate, and will kill the crew if it exceeds a month, rather than killing nearby planets.

  8. heyrick Silver badge

    "every GPS enabled mobile phone contains a relativity corrector"

    Which is only partially correct as while it can pretty much do the lat/long stuff, heights are wildly inaccurate. Walking across a flat field gives me a trace as if I'd hiked across someplace with largish hills. Hell, even standing still has me moving up.

    That said, reality around here is fairly relative anyway...

    1. Chemist

      Re: "every GPS enabled mobile phone contains a relativity corrector"

      If it didn't correct for relativity the lat/long would be way out

      1. Brewster's Angle Grinder Silver badge
        Boffin

        Re: "every GPS enabled mobile phone contains a relativity corrector"

        "If it didn't correct for relativity the lat/long would be way out"

        Yeah, by all of 10m. (It's that order, anyway.)

  9. Thomas 18
    Thumb Up

    Sweet

    Just fly in zigzags stopping every now and then to drop off the beams of energy

    1. Captain Save-a-ho
      Coat

      Re: Sweet

      Is there any other way? This is why Star Wars needed the computer to calculate the hyperspace path.

      The only other option is to finally start looking into infinite improbability. Just sayin'.

      1. Anonymous Coward
        Anonymous Coward

        Re: Sweet

        It is? I thought it was to do with avoiding gravity wells. That's why interdiction ships can pulls ships out of hyperspace: By projecting an artificial gravity well in their path, which the computers will detect and drop the ship out of hyperspace to avoid.

        I'm not a massive SW fan, so I dare say that I'm about to be corrected...

      2. kyza

        Re: Sweet

        No bouncing too close to a supernova...

  10. LaeMing
    Unhappy

    Looks like the funding is about to go balistic for this tech.

    Now there is a military application :-(

    1. LaeMing
      Happy

      Heh Heh. She said 'balistic'

      I see what I did there (though only after clicking 'post').

  11. jubtastic1
    Pint

    Obvious solution

    Don't aim for the place you're going, just nearby, then use boring old Impulse engines for the last leg. Even better, build a great big array to collect all the waste energy from incoming ships, like an orbital power station, and no, 'that's unpossible" isn't a reasonable response to that given we're talking about warp drive.

  12. P. Lee
    Boffin

    We Come In Peace!

    Hey! Where did everyone go?

    1. Anonymous Coward
      Anonymous Coward

      Re: We Come In Peace!

      The only survivor would be Newt Gingrich in his moon base.

      That'll learn 'em.

  13. Derk
    Alien

    re: obvious solution

    Or you could build huge "collectors" in space for all that energy. Every ship would know the co-ordinates to these "collectors" or we could call them gates, or jump gates. The energy collected could be saved and used to return the craft. Some energy could be bleed of to power space stations, we could call the first one B1, etc. Stay clear of any called B5, as strange stuff could go on there.

    1. John G Imrie
      Headmaster

      Re: re: obvious solution

      B1 blue up due to sabotage.

      B2 blue up due to sabotage.

      B3 blue up due to sabotage.

      B4 disappeared into a time warp, and became Valon's base of operations during the previous Shadow war

      B5 got attacked, knocked out of alignment, became a rebel base and the operations centre during the current Shadow war.

      Unless you are called Thomas Jordan, I'd stay clear of the lot of them.

      1. Z-Eden
        Headmaster

        Re: re: obvious solution

        Actually B3 wasn't sabotaged, it simply blew up. B5 would be fine. You'd just have to make sure that any Security Officers of Italian heritage are kept away - they seem to provoke a lot of fights and trouble just seems to flare up when they are around!

      2. TheProf
        Unhappy

        Re: re: obvious solution

        BLEW-UP.

      3. Doug Glass
        Go

        Re: re: obvious solution

        "Blue up"? We're dealing with a whole new kind of spectral shift you're saying?

        1. Tom 13
          Coat

          Re: re: obvious solution

          It's a Farscape thing...

  14. James 100

    Since you'd be going from one solar system to another with this kind of drive, just fly towards their sun - no need to worry about frying inhabitants in it, and another burst of radiation chucked into a colossal fusion explosion is hardly going to matter. Then use plain old impulse drive or whatever to 'taxi' the last few light-minutes to the planet you were aiming for.

    1. Anonymous Coward
      Anonymous Coward

      ...and just remember to look out for pirates and make sure you have your fuel scoops and a docking computer ready.

      1. Audrey S. Thackeray

        Docking computer?

        Pah.

        If you haven't mastered docking by the time you can afford to buy a docking computer you've been wasting your time.

        Fly past, flip and spin was my preferred method - didn't scrape the sides any more often than a docking computer would've.

  15. a_been
    Thumb Up

    A couple of other problems

    As I recall the Alcubierre warp drive had a couple of other technical problems, those being that the access point had a radius smaller than an atom and it required more energy that that contained within the universe, though to be fair the paper i read didn't mention which atom or if it was the whole universe or just the visible universe.

    1. Anonymous Coward
      Anonymous Coward

      Re: A couple of other problems

      A quick skim of the wikipedia article suggests that you need somewhere in the order of 3 solar masses of energy (via E=mc2) to transport "small atoms".

      1. AndrueC Silver badge
        Joke

        Re: A couple of other problems

        So what I'm hearing there is that it's something else that wind turbines can't provide power for.

    2. Michael Wojcik Silver badge

      Re: A couple of other problems

      Yes, and a few other small problems, such as likely requiring exotic matter and possibly creating a naked singularity at the front of the bubble.

      And one big problem, of course, which is that causality is still at risk. That has nothing to do with the waffling over special relativity versus general relativity in the article (and frankly I have no idea what Richard's going on about there).

      If you can send a signal FTL, you can send it outside your light cone. If you can get a signal back[1], then you can arrange a closed time-like curve, and you can get the reply before you send the initial signal. Voila - causality casualty.

      Now, there are hypothetical ways around this, like Novikov consistency (which is basically a formalization of "the universe won't let you break anything"). But this has other issues. For example, if Novikov consistency is correct and can be exploited (which is what we're assuming at this point), then you can solve all formal problems in polynomial time - in other words, P now equals NP.

      That breaks all possible asymmetric-key encryption schemes, and as Ben Franklin once said, those who would give up security for faster-than-light travel deserve neither.

      [1] For example, by having the "signal" be a vehicle that can turn around and come back.

  16. Graham Marsden
    Thumb Up

    Sounds...

    ... infinitely improbable to me.

    (Thumb icon because...)

    1. Anonymous Coward
      Go

      Re: Sounds...

      a sperm whale and a bowl of petunias says you're wrong ;)

  17. Muckminded
    Mushroom

    Two bubbles passing in the night

    Bet there would be a hell of a show if two bubbled vessels got too close, accidentally or otherwise.

  18. Jeremy T
    Pirate

    Fantastic opportunity!

    This is great! We can colonize other planets and not have to worry about nasty alien bugs or creatures hurting our colonists.

    Of course we don't want them to come back.

    1. E 2

      Re: Fantastic opportunity!

      N/P, if the come back, or their relatives show up asking questions we can just stop a star ship in their general vicinity and fry them too! Bwahahahaha!

  19. djs

    every GPS enabled mobile phone contains a relativity corrector

    Shhh! Keep your voice down! If Stephen Fry hears that he'll be postulating that reading email on his Jesus phone is theoretically capable of initiating time travel.

  20. Chemist

    "Einstein's theory of relativity will be 100 years old very soon....."

    So ?

    Thermodynamics have an even longer history. There's no indications that anyone will ever be able to produce a perpetual motion machine.

    1. Ken Hagan Gold badge

      Re: "Einstein's theory of relativity will be 100 years old very soon....."

      Thermodynamics isn't a physical theory. It's a series of logical inferences starting from the premise that everything grinds to a halt (*). Given that starting point, it is hardly surprising that the theory bars perpetual motion machines.

      (* I think the usual language is to assume that there is always an equilibrium state that is reachable from the current state and which, once reached, the system does not leave. It amounts to the same thing.)

      1. Eddie Edwards
        Facepalm

        Re: "Einstein's theory of relativity will be 100 years old very soon....."

        Thermodynamics is an empirical physical theory. Wake me up when you see heat flow from a cold region to a hot region. Then we can talk about perpetual motion machines only being barred because of some flawed logical inferences in the theory.

        1. Ken Hagan Gold badge

          Re: "Einstein's theory of relativity will be 100 years old very soon....."

          Wake *me* up when you have a definition of hot and cold that isn't based on the direction of heat flow.

          1. Anonymous Coward
            Anonymous Coward

            Re: "Einstein's theory of relativity will be 100 years old very soon....."

            "when you have a definition of hot and cold that isn't based on the direction of heat flow"

            Black body radiation ?

            The radiation has a specific spectrum and intensity that depends only on the temperature of the body.

          2. E 2

            Re: "Einstein's theory of relativity will be 100 years old very soon....."

            My theory, derived from L4D Molotov cocktail griefers: "It burns! It burns!"

          3. Chemist

            Re: "Einstein's theory of relativity will be 100 years old very soon....."

            "hot and cold"

            A unit of hot gas has higher pressure than the same amount of colder gas.

        2. Ken Hagan Gold badge

          Re: "Einstein's theory of relativity will be 100 years old very soon....."

          Oh, and read my original quote again. I never said the logical inferences were flawed. I merely pointed out that the premises were self-evidently equivalent to "no perpetual motion".

          You might also consider that some of the best brains in physics over the last 150 years have tried to connect thermodynamics to dynamics. We're still waiting.

  21. bobbles31

    Coming soon to a patent office near you, a phone with a space time field generator that alters the fabric of space time around you in response to voice commands. Occasionally turns into a bird.

    Steve 'Zarniwoop' Jobs isn't dead he is on a cruise in his office.

  22. Evil Auditor Silver badge

    Faster than light travel

    Methinks one needs bloody good eyesight to see oncoming traffic...

  23. hplasm

    Just proves Niven's idea

    That any good space drive also makes a good weapon.

  24. ArkhamNative
    Facepalm

    Epic poor choice of words.

    “The importance of relativity continues to grow - every GPS enabled mobile phone contains a relativity corrector to ensure it takes into account the time difference between the ground and satellite...”

    This is inaccurate and misses the whole mind-blowingly amazing relativistic relevance. What is really happening is that "it takes into account the different rate at which time passes on the satellite and on the ground."

  25. Anonymous Coward
    Anonymous Coward

    Star Trek solution

    Wouldn't a deflector 'solve' this by stopping particles sticking to the windshield?

    1. Johnny Canuck

      Re: Star Trek solution

      That is what I always thought it was for - to push the matter in front of the ship out of the way. The name sort of gives it away.

      1. John 62

        Re: Star Trek solution

        Yeah, but humans hadn't developed deflectors in Star Trek: Enterprise (22nd century). They had barely got hull plating and were zipping around at warp 5.

    2. Anonymous Coward
      Anonymous Coward

      Re: Star Trek solution

      Only in the sense that using "Hollywood physics" solves things. If thats the solution then i choose a TARDIS.

  26. Anonymous Coward
    Anonymous Coward

    Easy solution...

    ... just use the Lagrande Jump Point, then you can fly your Battlemechs in-system via dropship... been reading too many books lately... damn you ebook readers

  27. Brian Miller 1
    Go

    Or....

    Travel in lots of very short pulses such that you never build up an amount that would produce very harmful emissions.

    squirt squirt squirt, each time radiating most of the build up.

    It may take a little longer, but if you can make it interstellar without frying your intended hosts that would be rather more polite...

  28. Destroy All Monsters Silver badge
    Meh

    Nice to demo your math skillz, but relevance to Real World is zero.

    “The amount of energy released infront of the ship is unbounded, as we can increase the energy of the released radiation and particles simply by travelling across a larger distance,”

    Oh we can has infinite energy if we just can make this work, then?

    Hell, it's not like the universe forces you to keep your total energy at a constant, right? Yeah, in some parts of the multiverse, Einstein's coffin is being used to spin up Alcubierre Generators.

    1. This post has been deleted by its author

  29. Anonymous Coward
    Anonymous Coward

    "Captain's log, Stardate 7412.6. 1.8 hours from launch. In order to intercept the intruder at the earliest possible time, I must now risk engaging warp drive while still within the solar system."

    Seems Kirk knew it too.

  30. Anonymous Coward
    Mushroom

    Jump drive and weapon all in one?

    It makes you proud to be human.

  31. Anonymous Coward
    Anonymous Coward

    Windscreen

    Once read that Hydrogen atoms hitting the windscreen at near or greater-than light speed would be like driving through a barrage of artillery fire.

    Sad that great inventions also become great weapons.

  32. Vladimir Plouzhnikov

    Obvious application

    Alcubierre cannonballs for interplanetary battleships. Just imagine what a broadside of those will do to a mutinous planet or asteroid!

  33. Anonymous Coward
    Anonymous Coward

    Could this be how a good old blaster could work?

    Just a thought, but if you had a device that could create a small bubble (~5mm across) and have that move down a tube/barrel of a few cm faster than light, and then collapse the bubble at the end.

    Would the result be that all the gas (atmosphere) that was in the barrel at the start becomes a very high powered blast of gamma rays & incredibly fast partclesshooting out the end, along with next to zero recoil.

    And there you have it: a Star Wars style blaster or maybe a B5 PPG.

  34. Robert Ramsay

    Space:1999 had it also...

    http://en.wikipedia.org/wiki/Voyager_One_(Space:_1999)

  35. Dexter
    FAIL

    every GPS enabled mobile phone contains a relativity corrector to ensure it takes into account the time difference between the ground and satellite

    ---------------------------

    This isn't true; the relativistic correction to the clocks is done in the satellites - the clocks are set so as to compensate for relativity, so when they are observed from the ground, they appear to be running at the correct rate.

  36. mad_rocket_scientist

    gamma ray burst?

    The result postulated sure sounds like the observed gamma ray bursts.

  37. Lance 3

    PLAID

    "That’s the conclusion of a group of University of Sydney physics students who have re-examined the maths of the Alcubierre drive, and found that when it decelerated below faster-than-light speeds, it would emit gamma rays sufficient to be seriously unhealthy to anybody waiting in the arrivals lounge."

    The solution is simple. You just go past the destination and then turnaround. Didn't Spaceballs teach us anything. I could careless about Warp drive, I want to go plaid.

  38. dssf

    Nobody's ever plotted a jump this far...

    DO IT, without Baltar's help...

    "You CAN'T PLOT a jump this close -- you could end up inside a mountain or a star..."

    (BTW, why was I thinking of Kookaburra?

    http://en.wikipedia.org/wiki/Kookaburra_%28song%29

    I didn't know/remember that it is of Australian origin, hehehehe....)

    This should be interesting to some:

    http://www.projectrho.com/rocket/spacewardetect.php

    This, too:

    http://www.astronomycafe.net/qadir/qanda.html

    Enjoy!

  39. Joe User

    Re: So...

    RAMChYLD: "Anyways, what's wrong with keeping the ship stationary and moving the space around it instead?"

    Good news, everyone! I've invented the engine for the Planet Express spaceship!

    Professor Farnsworth, "Futurama"

  40. Clive Galway
    Thumb Up

    Sounds useful to me

    An object that travels FTL, then delivers a big bang.

    Sounds like an ideal planet-killing-meteor deflector to me!

  41. Martin Budden Silver badge
    Alien

    This announcement demonstrates why warp drive can't be done.

    All that energy released when you stop... it simply means that you had to put *at least* all that energy in to get moving (because energy can't be created). How much energy are we talking about? Too much to get our mucky hands on (even if we converted our entire Sun into energy for just one flight, it still wouldn't be enough).

    This is why there are no visiting aliens here: warp drive is theoretically possible but so impractical as to be utterly impossible.

    Icon: Sorry, you won't ever see one of these.

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