The term quantum singularity is used to refer to many different phenomena, which often approximately resemble a gravitational singularity in the scientific sense in that they are massive, localized distortions of space and time. The name invokes one of the most fundamental problems remaining in modern physics: the difficulty in merging Einstein's Theory of Relativity (which includes singularities within its models of black holes) and quantum mechanics. In fact, since singularities are infinitely small according to relativity, they are expected to be quantum mechanical by their nature; a theory of quantum gravity would be required to describe this behavior, and no such theory has yet been completed. On the other hand, only one kind of singularity has ever been observed (black holes), and due to the mass dependent, stable radius of the connected event horizon, it is currently unknown if this kind of singularity actually approaches or even drops below scales relevant to quantum mechanics.
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Star Trek
A quantum singularity is a phenomenon of multiple varieties. One such variety appears in the Star Trek: Voyager episode "Parallax". The singularity creates a mirror image and a temporal distortion. Voyager flies into the singularity after seeing an image of itself inside. To escape, the crew uses a shuttle and fires a tachyon beam at an opening created upon entry. In Voyager episode "Hunters" the Voyager crew discover a Hirogen relay station almost 100,000 years old that is powered by a quantum singularity. The word "tiny" is used to apparently describe the dimensions of the quantum singularity. Specifically, it is stated to be about "a centimeter" in diameter, making it, in fact, ironically and paradoxically enormous, although it is possible that the diameter stated could refer instead to the singularity's event horizon. In episode "Scorpion" Species 8472 and the Borg make use of quantum singularities to travel to and from fluidic space.
Artificial quantum singularities are also used to power Romulan Warbirds as first described in the Star Trek: The Next Generation episode "Timescape". Additionally, in the Star Trek: Deep Space Nine episode "Visionary", the side effects from Quantum Singularities cause one character to shift through time.
Futurama
In the episode of Futurama, "Love and Rocket", the term Quantum Singularity is used after Bender breaks-up with the Planet Express ship, whom he only dated during this episode. The ship takes the break-up pretty hard and then threatens to fly into a giant quasar, thus "the power of 10 billion black holes will smush me and Bender together into a beautiful eternal quantum singularity." Bender gets the crew out of the situation by professing his love for the ship, albeit sarcastically, which distracts it long enough for Fry and Leela to disable the ship's logical processes and restore life support systems.
Megas XLR
In the episode "Battle Royale", the villain Magnanimous threatens to drop Kiva and Jamie into a quantum singularity, which he says is "like a black hole, only portable, and with a cooler name."
Farscape
In the episode "Back and Back and Back to the Future", a scientist belonging to the Ilanic race develops a quantum singularity to be used as an ultimate weapon against their enemies. It was described essentially as a portable black hole.
Stargate SG-1
A gigantic Stargate designed to allow the passage of starships. The Supergate is made up of 90 smaller pieces that are moved through a regular Stargate. Once assembled, a nearby planet is collapsed into a quantum singularity, using a special force field, in order to provide the massive power needed to open a wormhole to the Ori galaxy. Samantha Carter theorizes that the singularity allows a connection to be maintained indefinitely.
The first Ori attempt to create a Supergate in the Milky Way fails when Vala Mal Doran inserts her Tel'tak into the incomplete ring and prevents the segments from completely connecting. The shockwave from the forming singularity then blasts the gate to oblivion. A second Supergate is later built successfully and allows a fleet of Ori motherships into the Milky Way. The SGC eventually blocks the Supergate to the Ori by opening a connection from a Pegasus gate powered by a "natural" black hole.
City of Heroes
In the MMORPG City of Heroes, the quantum singularity is the "pet" power a gravity controller attains at level 32. The singularity takes the form of a human sized ball of light surrounded by waves of coloured energy. The Singularity is portable, and will follow its summoner around. The singularity uses a variety of gravity based attacks.