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"Do you know that thought experiment with the cat in the box with the poison? Theory requires the cat be both alive and dead until observed. Well, I actually performed the experiment. Dozens of times. The bad news is that reality doesn't exist. The good news is we have a new cat graveyard."
The Schrodinger's Cat thought experiment is increasing in popularity as a Motif in fiction. To elaborate, Erwin Schrödinger's thought experiment involved a cat sealed inside a box with a Geiger counter attached to it. Inside that Geiger counter is a small amount of radioactive substance. The box is set up so that when the radioactive substance decays, a device smashes a vial of toxic gas, killing the cat inside. The thing is, after an hour, until the box is open, there is no way to determine whether the cat inside is alive or dead, thus allowing the cat to be both alive and dead.
The thought experiment was originally a critique of the Copenhagen interpretation of Quantum Physics, where the cat can be living and dead at the same time as a superposition of "realities".  The paradox should be obvious. Note that the paradox only exists in the Copenhagen interpretation, the classic interpretation of quantum mechanics. According to the many-worlds interpretation, what actually happens is that the entire world splits into a superposition of worlds where the cat is alive, and those where it is dead.
The reason the experiment is interesting is that in quantum mechanics, things like subatomic particles routinely exist in superpositions of states, and correct predictions of the outcomes of certain experiments can only be made by taking these effects into account. The experiment posits that if we can accept that small particles (like the radioactive trigger) can be in these kinds of states, then we have to accept that large objects (like the cat) can also be in these kinds of states, raising the question of why we don't routinely observe that.
This thought experiment immediately became popular as a metaphor for uncertainty of the truth, fate, Quantum Physics, how quantum physics can do anything, and whatever the hell is inside that box. Ironically though, the original experiment was used to show how stupid the idea of superposition was.
To elaborate further, we're dealing with radioactive nuclei; a nucleus is at the centre of an atom, and some nuclei are radioactive, so they do something called "radioactive decay". Heisenberg's Uncertainty Principle shows that it's impossible to directly observe this decay because it involves particles so small that any equipment we have to monitor them—even the smallest, like photons and electrons—would interfere with what they're doing, so we can't get reliable results about an electron's both momentum and position—one or the other, but not both. Therefore, any particular radioactive nucleus may, at any moment, be either decayed, or undecayed. That much isn't controversial.
The Copenhagen interpretation says that, because of this, each particle is 50% decayed and 50% undecayed. Schrödinger thought that this idea was Insane Troll Logic, so he extended it to show: if the decay of a radioactive nucleus will set off a device which will release toxic gas into a box that contains a cat, and if (as per the Copenhagen interpretation) the nucleus is 50% decayed and 50% undecayed, the device is 50% triggered and 50% untriggered, so the cat is simultaneously 50% killed and 50% still alive.
Here's a video that explains the principle in question.
- Schrodinger's Butterfly: The story is both real and All Just a Dream simultaneously.
- Schrodinger's Cast: A character is both alive and dead simultaneously, in different versions of the story.
- Schrodinger's Gun: The location and nature of the plot device are undetermined until you look for it.
- Schrodinger's Player Character: The cast of the story is undetermined until the player chooses his or her role.
- Schrodinger's Question: In a role-playing game, the correct answer to the question is undetermined until the player gives the answer.
- Schrodinger's Suggestion Box: In a role-playing game, some rules are undetermined until a player asks if their bright idea is permitted.
Schrödinger's Cat may or may not exist in these works, you'll have to check to know for sure:
Anime & Manga
- To Aru Majutsu no Index uses Schrödinger's Cat in order to explain the Esper abilities: the state of the "cat" outside of their mind is whatever the user's mind deems it to be, allowing the manifestation of the abilities.
- Misaka Imouto tries to name her cat Schrödinger, but Touma shoots that idea down. That name is taboo for cats.
- Umineko no Naku Koro ni has this as a recurring motif, and is used to explain the fantasy scenes as something that could have happened but not necessarily did happen.
- Similarly, Higurashi no Naku Koro ni uses the cat; most notably, Frederica Bernkastel uses it in one of her poems. In that poem, the cat dies, referring to the end of Minagoroshi-hen, as well as the fate Rika encounters a few nights after the Watanagashi.
- Done a couple of times in Yu-Gi-Oh! GX. Bastion Misawa has it as a formula on his wall (dub only) and a character uses a card which uses Schrödinger's Cat as a basis.
- Sayonara, Zetsubou-sensei has a whole episode about the concept which discusses it in detail.
- Hellsing actually has a character named Schrödinger, and he has a power to be 'everywhere and nowhere' -- allowing him to always be in all plot relevant spots at once, as well as to Retcon any damage he suffers. And he's a Catboy.
- In Animal Man, the final issue of the Peter Milligan-penned Alternate Universe arc referred to Schrödinger's cat, and was titled "Schrodinger's Pizza."
- In All-Star Superman, the Ultrasphinx traps Lois Lane in a state of quantum uncertainty, between life and death, unless someone can answer its riddle. Superman answers it and saves her.
- In one The Mighty Thor story, Donald Blake references Schrödinger's cat in describing the Odinsleep, saying the sleeper is in a state between life and death.
- Played with in The Incredible Hercules, where Amadeus Cho finds himself playing a deadly Role-Playing Game (itself a Schrodinger's Butterfly of a sort), in which his character, Mastermind Excello, encounters a box containing a cat that is literally both dead and alive in the lair of a Mad Scientist.
- Done wonderfully in the glee fanfic "Magical Thinking", which can be read here 
- In Academy Blues, Laura develops a spell called "Schrodinger", which places her in a state between life a death, and allows her to literally be anywhere within a large radius. The spell is somewhat unstable, and she tends to fade in and out in different locations at random times. The spell encloses her body at the location she initiated the spell in a box of light.
- The 2001 short film The Heisenberg Principle, directed by Cris Jones, explores this is in a mystical/artistic way.
- Dirk Gentlys Holistic Detective Agency saw Dirk begin to explain Schrödinger's cat normally, before talking about how he intervened in the experiment to save the cat's life.
- The Salmon of Doubt features half of a cat. Not a cat chopped in half and lying still, the very lively and normal-acting rear part of a cat, which just kind of ends midway along. The cat's name is Gusty Winds, and near the end of what Douglas Adams had written before he died, Dirk comes across a road sign that says "Gusty winds may exist."
- In the Discworld novels, Death does not understand how this would work. A pretty thing would come to pass if he couldn't tell if a cat was dead or not.
- Pratchett makes multiple references to this. In The Unadulturated Cat, the theory is used to explain the ability of Offscreen Teleportation that all cats seem to have (apparently, the cat was so distressed by being locked in a box with radioactive materials, it became an instant expert in teleportation)
- In Lords and Ladies the motif is spoofed once again, when the cat locked in the box turns out to be Greebo.
Technically, a cat locked in a box may be alive or it may be dead. You never know until you look. In fact, the mere act of opening the box will determine the state of the cat, although in this case there were three determinate states the cat could be in: these being Alive, Dead, and Bloody Furious.
- An incarnation of Schrödinger's Cat appears in Wyrm. It looks and acts a lot like the Cheshire Cat from Alice in Wonderland. But it's actually an avatar of Wyrm.
- In Crushed by Laura and Tom Mc Neal, this becomes a critical plot point after Wickham reveals his past to Audrey.
Live Action TV
- In Stargate SG-1, Carter explains why her cat is called Schrödinger to a scientifically advanced alien. (Season 1, episode 17, "Enigma".)
- Amusingly, the alien agrees with Schrodinger when she finishes, anyone who thinks that might be true has misunderstood the laws of physics.
- Flash Forward lets us know that Simon is a scientist because he explains it when we first meet him.
- On The Big Bang Theory, Sheldon uses it as a metaphor about whether or not Penny and Leonard's date will be successful or not.
- The third season premiere of Six Feet Under opens with Nate trapped in a Mental World with recurring references to Schrödinger's Cat, highlighting the fact that he's in an in-between state while undergoing risky brain surgery and won't know where he is until he actually takes a risk and "opens the box."
- Digital Devil Saga literally has a cat named Schrödinger. Its role in the plot is mostly to confuse you.
- Though it makes a lot more sense when you realise it's an aspect of Seraph that achieved enlightenment.
- In Nethack a monster known as the Quantum Mechanic will sometimes drop a box when it dies. When you open the box either a living cat will jump out or a cat corpse will be found inside. What's more, examining the code shows that which will be found is undetermined until you check -- as opposed to every other container in the game, the contents of which are determined when the box is spawned.
- Ghost Trick has a rather... literal interpretation of the trope. To be exact, by the end of the game, Sissel is de-facto a dead-immortal cat.
- In a supplemental Portal comic:
GLaDOS: Do you know that thought experiment with the cat in the box with the poison? Theory requires the cat be both alive and dead until observed. Well, I actually performed the experiment. Dozens of times. The bad news is that reality doesn't exist. The good news is we have a new cat graveyard.
- The same comic later compares Chell to the cat, surviving in stasis but with no guarantee she'll ever be woken up.
- There was an achievement in Portal 2 called Schrödinger's Catch, which involved catching a box before it hit the ground. Obviously a reference to the cat, and likely also a reference to the comic.
- Also mentioned by the Fact Core:
Fact Core: The Schrödinger's Cat paradox outlines a situation in which a cat in a box must be considered, for all intents and purposes, simultaneously alive and dead. Schrödinger created this paradox as a justification for killing cats.
- One of Ratman's dens early in the game has a diagram of a cat apparently jumping out of a box, with quantum physics equations scribbled all over it.
- Selected randomly as a gambling device in the Money-Making Game in Kingdom of Loathing, where the winner is decided by one player guessing whether the cat is alive or dead. Of course, you don't actually get to choose.
- This Xkcd strip is a Schrödinger's comic.
- Well, maybe. It would be in the strictest sense if absolutely nobody-- including the author-- knew what the last panel was before it was read. Then again, since humor is heavily subjective, until each individual person has read it they have no idea whether it'll be funny to them or not, so the quantum mechanics does work in that way.
- Checkerboard Nightmare featured a minor character named Schrödinger the Cat. He could see all possible realities simultaneously and as a result he's completely insane.
- This strip of Irregular Webcomic references Schrödinger's thought experiment in the punchline, but you'll notice that the explanatory note below the comic starts off talking about Heisenberg. As DMM points out in the final paragraph, the punchline of the comic existed in a state of flux while he was writing The Rant.
- Later, Jamie and Adam remove the "thought" from "thought experiment" and actually set up Schrödinger's Cat with an actual box and an actual cat. Next MythBusters strip, after Jamie says there's no way to determine whether the cat is alive or dead without opening the box and observing the cat, Adam kicks it and makes it yowl.
(Commentary) Technically, in the experimental sense, this is actually "observing" the cat. Quantum mechanics isn't quite that perverse.
- Luke Surl explains why the cat is dead.
- In an earlier strip, he drew some interesting parallels with classic literature.
- A classroom lecture on Schrödinger's Cat is given in this page of Spy6teen
- This early Dresden Codak comic.
"Somewhere, Niels Bohr walks among us, unobserved and immortal."
- Doug Rattman, at the end of Portal 2: Lab Rat (comic that ties the two Portal games together), considers Chell to be like a Schrödinger's Cat.
"Both alive and dead, until someone opens the box."
- Referenced in this Cyanide and Happiness comic.
- Scenes From A Multiverse has fun with this in this strip, which briefly presents an entire civilization based on the uncertainty theory, including universal ownership of celebratory "cat boxes".
- Captain SNES has a cat named Schrödinger, whose state in Videoland cannot be determined by the residents, as it is from the real world, and it generally proceeds to make fools of everyone it meets.
- Linkara criticises the experiment in one of his reviews. In his top 11 mistakes, he admits he missed the point somewhat.
- Cecil Adams (of The Straight Dope) explains the concept in rhyme.
- Used as a joke in a Futurama episode. The cops catch Erwin Schrödinger speeding with a box containing a cat, he's not clear whether it's alive or dead (until Fry opens the box and the cat claws his face), and there's also drugs in there.
- A famous quote by Stephen Hawking is the following: "When I hear about Schrödinger's cat, I reach for my gun." I'll allow About.com to explain this:
This represents the thoughts of many physicists, because there are several aspects the thought experiment that bring up issues. The biggest problem with the analogy is that quantum physics typically only operates on the microscopic scale of atoms and subatomic particles, not on the macroscopic scale of cats and poison vials.
- It's either that or a crippling fear of zombie cats.
- Radioactive zombie cats.
- How does he reach for his gun anyway?
- Also, physicists such as John Gribbin (author of In Search of Schrödinger's Cat and Schrödinger's Kittens) wonder at what point particles go from being "quantum" to "ordinary". How big do you have to be to be normal? How small do you have to be to be in two places at once?
- It's either that or a crippling fear of zombie cats.
- According to the Copenhagen equation, the cat is 50% alive and 50% dead.
- A classical example is the double-slit experiment for electrons where the resulting interference pattern is only expected if you assume the electron is in a superposition of states