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Quantum Mechanics Can Do Anything

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You'd like to give your character supernatural powers but you don't want it to seem too unrealistic? Are you searching a way to explain why the Big Bad can travel through time without ripping the continuum into shreds?
Don't worry. Remember, guys, a well-known Narrative Device is that Quantum Mechanics Can Do Anything. Time-travel? God-mode superpowers? Death rays? Yes, all of that. Expect complex equations, a lot of Techno Babble and explanations of the Schrödinger's Cat experiment and the observer effect that make every conscious being a potential Reality Warper.
It's a lot easier when you don't have to do any research.
This trope applies when quantum physics is exaggerated to explain any kind of bizarre event or to introduce powers and/or improbable technologies which are indistinguishable from magic.
Subtrope of Phlebotinum du Jour and a type of Hand Wave. Can be considered an updated modern version to early-20th-century Lightning Can Do Anything and mid-century Radiation-Induced Superpowers, as a source of implied Magic from Technology in an age where electricity and radioactivity gradually became demystified.
For real info on quantum physics, go to the page of Quantum Physics.
More accurate-to-real-quantum-mechanics forms of this are examples of Minovsky Physics rather than this trope.

Examples
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Dr. Manhattan from Watchmen: a nuclear accident turned him into a Physical God. Doc's body basically suffered 100% matter-to-energy conversion... but because his rather obsessive father trained him as a child to be a watchmaker — thus imbuing him with patience, attention to minute detail, and mechanical understanding — he somehow retained consciousness and "the very first trick [he] figured out was to put [him]self back together". Then he realized he could do it with the rest of reality too.
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The Secret is less philosophical about it than What the #$*! Do We Know!?, but it dabbles in much the same field, using quantum entanglement to explain how the "Law of Attraction" works.
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The Simpsons: Played for Laughs in the episode "Don't Fear The Roofer" when Stephen Hawking explains that Bart didn't see Ray the roofer because of a change in space-time continuum causing a mini black hole that absorbed the light from Ray. It Makes Sense in Context. No, it doesn't.Lisa says this sounds plausible, but it's not: Ray would be blocking the light from behind anyway, so Bart should've seen a black shadow where his stood.
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Wondermark has this strip where one character is annoyed by lazy sci-fi writers using "quantum theory" to justify everything. However, this only annoys him because he uses it to justify his own immoral actions, and they need to "come up with their own shtick!"
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Alice Grove: Alice and other former Super Soldiers like her show off superpowers and abilities that at times seem to break the laws of physics. Near the climax, she reveals that this is because the pre-apocalypse civilization that created them somehow quantum entangled them with black holes, allowing them to shunt their entropy into the singularities. Because of this, she specifically refers to herself and the others as "Maxwell's demons".
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In Power Rangers Time Force, guess the source of the Quantum Ranger's power.
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GN Particles in Mobile Suit Gundam 00 allow a properly equipped Gundam to "quantize" itself, which apparently involves turning the entire machine, pilot included, into GN Particles, teleport, and then reassemble itself. In the series this is only used for short, tactical hops mid-battle, but at the end of the movie, the 00 Qan[T] does this over interstellar distances, effectively inventing FTL travel.
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Aberrants can employ the M-R nodes in their brain to subconsciously manipulate the four elemental forces of quantum physics, and through them channel a number of desired effects attuned to the yadda yadda yadda yadda people with superpowers are awesome.
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Supernatural: Angels are implied several times to be essentially living quantum physics. Castiel describes his existence without a body as "a multi-dimensional waveform of celestial intent", and when the brothers ask why his powers are limited, he says: "Well, the answer to your question can best be expressed as a series of partial differential equations."
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"Because of quantum" is a standard Discworld Hand Wave. The interesting thing is that it's explicitly used in the same way as "magic" is used in Real Life, but on the Discworld, magic is definable, closely studied and quite well understood. (Until it blows up in your face, that is.) But anything that really doesn't make sense and can't be explained, that's probably quantum.note One of the things Death and Ridcully have in common is that they both hate, or at least deeply mistrust, quantum.
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In Let's Build a Zoo, after you buy some double-decker buses, you unlock the quantum accelerator, which bends reality to... add extra seats.
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Quantum mechanics are BioShock Infinite's Applied Phlebotinum, being able to create floating cities, anachronistic technology, elemental powers, multiversal engagement, and a number of other things. The game features heavy themes of the division between constants and variables that define an infinite realm of alternate universes, and while they're heavily exaggerated by the narrative, the theoretical fundamentals are fairly well-researched.
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Age of Wonders: Planetfall is shamelessly soft sci-fi, so the VoidTech Secret Technology takes this trope and runs with it. There's fluff about "entangling probabalistic quantum-realities" and such, but it's really Magic from Technology that frequently nods at popular quantum physics as an excuse to include teleportation and time-manipulation gimmicks.
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Cosmic strings play an important role in Space☆Dandy, as do a sentient gravaton and gravatino.
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Kiln People invents the egolaser, so to speak. ("Just" replace photons with clones.)
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What the #$*! Do We Know!? is based on the idea that we all create our own realities, and that this has somehow mysteriously to do with quantum mechanics. (It could belong to Real Life too because the main financier of this movie, a certain J.Z. Knight a.k.a. Ramtha, has built quite a following on those ideas and sells it as an actual belief/self-help system.)
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In the Marvel Cinematic Universe, a very fictionalized version of quantum physics form the basis of Ant-Man's Sizeshifter powers. In Ant-Man and the Wasp, the premise revolves around trying to rescue a fellow size-changing hero who shrunk down to a quantum level and hasn't been seen for thirty years. When the heroes finally find her, she shows some bizarre side effects, including Psychic Powers and Healing Hands. It's also used to explain the main antagonist's intangibility powers, to turn her back to normal, and what sounds like a throwaway line implies that Time Travel is possible.
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Quantum Leap, of course. The show also establishes that leaping affects Sam's memory — and his own past. This allows the writers to regularly Retcon his skills and personal history.
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This belief apparently exists in the world of Look to the West, although the terminology is different:
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The Quantum Thief: The final book in the trilogy, The Causal Angel, features the discovery on how to use the universe itself as a giant quantum gravity computer and use it to create a new, custom-made universe at will.
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Used liberally in Mass Effect, naturally. In the second game, The Illusive Man communicates with the Normandy II through a device that induces oscillations in a single quantum particle so that they may be observed in an entangled partner on the other end instantaneously, acting as a sort of "Quantum Telegraph". In the Leviathan DLC for the third game, this is also revealed to be how telepathy works. The title aliens somehow evolved the ability to deliberately induce quantum entanglement between electrons in their own nervous systems and those of other creatures, allowing them to communicate with or even control them across the vastness of space through the use of spherical "artifacts" that fill the role of vectors.
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Steam Wars uses this to explain Quantum Dragoon powers specifically how they're able to "teleport" when they're really using Quantum Physics to project themselves in different places at once. Basically, given the setup of the series itself, it's their world's equivalent of the Force.
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Star Trek:
Warp drive is not an example, but the quantum slipstream drive introduced in Star Trek: Voyager is. Star Trek in general treats "quantum" as a one-size-fits-all buzzword to Hand Wave things with. According to some non-canon novels, the transporter works using this trope, handwaving the questions about "creating a copy and killing the original".
Some of the technology also requires an inversion of this, as transporting and replicating things atom by atom and molecule by molecule basically requires "observing" where various subatomic particles in the object in question are and thereby unpredictably altering their course. This is why, for instance, the transporters have something called a "Heisenberg Compensator" to suppress all that quantum unpredictability Heisenberg discovered... somehow. How does the Heisenberg Compensator work, you may ask? It works very well, thank you.
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From The Onion: Sci-Fi Writer Attributes Everything Mysterious to 'Quantum Flux'.
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In Source Code, apparently the quantum effects that power the simulator allow it to change past events by seemingly creating an alternate timeline.
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The Fold cites the observer effect as a key component of transdimensional travel. Also, all human minds have latent telepathic ability building to a critical mass that makes transdimensional breakdown inevitable. Also also, there are monsters coming to eat all humans as soon as that travel becomes possible. The monsters are also Reality Warpers.
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While Qualia the Purple is actually accurate in its explanation of physics concepts, as a science fiction, it abuses physics, and in particular quantum mechanics, to quite some extent.
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Again when reviewing WALL•E, when it turns out that the spaceship doesn't have a sophisticated recycling system and so they must make new stuff by "erm, quantum".
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In Falling Skies, Karen tells Ben that the Overlords are able to predict future events, including what the rebels will do next, through their superior understanding of quantum mechanics. Ben points out that they currently have the Overlord held captive, and she admits that sometimes their calculations need adjustment.
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Rascal Does Not Dream of Bunny Girl Senpai: The primary plot-driver, Adolescence Syndrome, happens as a result of adolescent angst being mashed up with various quantum physics concepts to produce strange phenomena, such as child actor Mai Sakurajima taking a break from her career due to burnout, and then gradually becoming Ret-Gone because she is no longer being observed by the public.
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Futurama includes this in one of Professor Farnsworth's entirely scientific explanations:
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Oh boy, Noein. Listing every bit of techno-magic they call "quantum" something-or-other would take too long. Even the story itself can largely be explained using Schrödinger's Cat as an allegory (which one of the characters actually does partway through). The characters from the "future"? They can time-travel/dimension hop because they are "quantum existences". They constantly talk about making sure their "existence is established", because an "uncertain existence" leads to possibly being erased from reality. The future and the past are also not on the same timeline (of which there are infinite), but can still influence each other, and... um... wibbly-wobbly quantumey-wantumey...
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In Anathem, quantum effects are used to build a "Saunt Grod's machine", a nondeterministic Turing machine; at least as theorized uses go, this would suggest that BQP contains NP, a mathematical open question generally thought to be false.
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Canada's Worst Handyman: Season 1 contestant Keith attempts to use "quantum physics" as an Insane Troll Logic explanation for why he didn't bother measuring before digging fence post holes.
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In Deus Ex: Human Revolution, the armor piercing mod for the pistol involves quantum tunneling.
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In Endless Space, a lot of end game stuff is based on the idea that a firm enough handle on quantum mechanics can make physics go sit in the corner. In reality, QM and physics largely "agree" unless a very specific set of circumstances occur.
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One issue of The Incredible Hercules centering around Amadeus Cho involves a town where things only exist if you're looking at them and willpower can alter reality, all "justified" by Schrödinger's Cat.
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In Illium and Olympos, Quantum-based technology allows for the simulation of godlike magical powers. "Quantum teleportation" can be used to travel through space, time and into other dimensions. Basically, the word "quantum" is dropped into any explanation of how nearly anything works in the setting.
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Eclipse Phase uses quantum cryptography realistically, and attempts to insert some realism in a Subspace Ansible that uses quantum entanglement by having each byte break the connection between a pair of entangled particles. However it also speculates that psi creates quantum fields in the brain enabling quantum computation, though it does acknowledge that doesn't explain telepathy, just the lower-level mental augmentation slights like grok or pattern recognition.
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Doctor Who has the Weeping Angels, which turn to stone whenever anything is looking at them because they are "quantum locked". While this still falls under Artistic License – Physics or Artistic License – Biology, it's also an unusually deliberate allusion to the observer effect.
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The song "Kingdom of Heaven" in the album Design Your Universe by Epica has these verses:
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In Evolve, as her title suggests, Quantum Caira uses quantum for her abilities.
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An episode of The Cape introduces Dice, a woman capable of predicting events with an eerie accuracy, which is explained by her being able to see everything down to the quantum level. The Big Bad Chess studies her ability and manages to turn it into a software product that can do things like predict stock market trends (let's ignore the obvious result of completely destroying the idea of a stock market by turning everyone into an insider trader). For some strange reason, the only person she can't predict or even account for is Vince (a possible explanation is that she doesn't know his true identity, who is supposed to be dead anyway, resulting in an anomaly).
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In Andromeda, slipstream navigation relies on "the ability of organic observers to collapse wave functions". Later, Harper and Technical Director Hohne develop a working teleporter that Harper explains via the use of "quantum entanglement", pointing out that it allows them to disregard the Heisenberg Uncertainty Principle. The teleporter even allows Time Travel, although it can only function in the vicinity of a black hole.
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Ghostbusters (1984):
Word for word, each one of them is carrying an unlicensed nuclear accelerator on their back. Looks like Quantum Mechanics can bust ghosts!
Also, when Egon warns the others to avoid crossing the streams, Ray makes a comment about "total protonic reversal". Quantum Mechanics can even destroy the Universe thanks to a Ghostbuster's equipment.
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String Theory (2009): The protagonist uses this explanation to Hand Wave how children can be genetically engineered with abilities like Psychic Powers and Reality Warping.
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In the Buffy the Vampire Slayer episode "Out of Mind, Out of Sight", Giles gives a simplified explanation of quantum mechanics (or what he calls it, anyway) as a theory of how Marcie Ross became invisible: everyone in Sunnydale High ignored Marcie and made her feel invisible, and with a little help from the Hellmouth, her perception of herself became reality.
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The 21st century reincarnation of The Authority's Jenny Sparks is Jenny Quantum, a Reality Warper who, so far, can teleport, time travel, cross dimensions, create dimensions, and manipulate "quantum energy", in addition to more mundane superpowers like flight, and these are just the abilities she's manifested in her first decade. As a century baby, she still has nine more decades to develop her powers further.
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Rough Draft: In Final Draft, the superhuman abilities of the functionals are explained away using quantum mechanics. In one case, the protagonist has to take a test to enter a functional building, which involves drinking acid. He ends up realizing that, in some alternate reality, there is a version of him that drinks acid for breakfast (literally) and incorporates that into himself. The only ones besides the original functionals who understand this stuff are the people from a "faraway" parallel world who have used the same knowledge to seal their reality away from all others.
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Timeline uses liberal quantum technobabble to explain its "Not-really-Time-Travel Time Travel". The technology started as an attempt to build a teleporter after a company built the first quantum computer, which was capable of storing the position and state (thus breaking the Heisenberg Uncertainty Principle) of every atom in an object. Instead of teleporting though the machine sends objects to Alternate Universes. Things started getting really quantum mechanic-ey when it's revealed that they have no idea how to turn that data back into a real object. So every time the machine is used the person or object sent must therefore arrive from yet another different universe than the one it was originally sent from, where they have the ability to turn data back into reality.
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Warp drive is not an example, but the quantum slipstream drive introduced in Star Trek: Voyager is. Star Trek in general treats "quantum" as a one-size-fits-all buzzword to Hand Wave things with. According to some non-canon novels, the transporter works using this trope, handwaving the questions about "creating a copy and killing the original".
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Yu-Gi-Oh!: The advanced technology of the Mecha Phantom Beasts includes quantum-output machines. The decoys created by these machines are nearly indistinguishable from the original on radar and are said to be so efficient at drawing away fire, that as long as a single decoy has been deployed, the original machine cannot be shot down.
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The very title of Quantum Vibe is a shortened version of a fictional field of quantum physics called "quantum vibremonics", which can apparently lead to interdimensional travel.
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Nine Hours, Nine Persons, Nine Doors and its sequel Virtue's Last Reward mainly use this, among other things, to explain the various abilities of the espers, especially the Mental Time Travel.
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The manual for Supreme Commander claims that interstellar teleportation works via quantum tunneling. That's all we get.
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This trope is why Captain Atom is considered the Biggest Billy-Badass in The DCU, even more powerful than Superman and literally capable of doing... well... just about anything he wants. Dr. Manhattan below was an Expy for Captain Atom when DC refused to let Alan Moore kill off all the characters they'd just acquired when they bought out a rival. And then there's Alternate Universe Quantum Superman, who's basically what happens when Clark Kent gets quantum superpowers instead of Nathaniel Adam. During one big event when all Supermen in The Multiverse team up, Quantum Superman is about as badass as the rest put together.
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The following is a list of statements referring to the current page from other pages.

 Quantum Mechanics Can Do Anything
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Speculative Fiction Tropes
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Quantum Mechanics Can Do Anything
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