The mirror universe is a fictional parallel universe in which the plots of several Star Trek television episodes take place. It is named for "Mirror, Mirror", the original series episode in which it first appeared.
In the mirror universe the patterns of events move in similar manners to that of the "regular universe", but the intentions and characterizations are different, often showing "evil" characteristic in place of "good" and visa versa. The mirror universe shares a similar history to that of the regular universe"and many of the same people exist in this reality, but they and the world they live in are skewed versions of their "normal" counterparts.
The mirror universe, like all parallel universes, is believed to lie parallel to "our" universe on another dimensional plane in a six-dimensional continuum: three dimensions of space, and three of time. The dimensions of space (height, width, and depth) are familiar. The linear motion of time (past-present-future) can be considered one "dimension" of time. Time's other dimensions are made up of probability fields that are the "height" and "width" of time. In essence, these temporal dimensions encompass every possible past, present, and future that could exist, and does, "elsewhere" in the continuum.
A potentially infinite number of timelines lie in these higher temporal dimensions, running parallel to "our" universe. The amount of divergence between universes - essentially the difference between their quantum signatures - determines how "far apart" they are in temporal terms. The mirror universe lies quite "close" to "our" universe in a dimensional sense, one of the reasons it was the first parallel dimension encountered by visitors from "our" universe.
Everything in a particular timeline resonates on the subatomic level with a unique "signature," a particular sort of vibration that can be measured on the quantum level, and cannot be changed by any means known to Federation science. The quantum resonance signature is a sort of blueprint, or script, of its entire universe; the movements of each and every one of its particles in every moment of its time. This quantum signature is normally of little interest, since it is common to everything in the universe. However, objects from outside the universe have a different quantum signature. This includes people and objects from a parallel universe. A quantum scan can determine whether or not something is from the same universe as the scanner. If the quantum signature of the subject's home universe is known, then it can also be identified.
The mirror universe is unusual, even for a parallel universe. Most parallel universes known to Federation science are what might be termed alternate histories. They diverge from known Federation history at a particular place in space-time, known as the divergence point. From that moment on, they follow their own history, but before the divergence, they are identical to "our" universe, save for a difference in quantum signature.
Some parallels appear to have diverged from "our" universe's history so long ago that it is difficult to determine the divergence point. These parallels are quite different from "our" universe, up to and including vastly different lifeforms evolving on Earth, Vulcan, and other planets of the galaxy. The further the divergence point is from "our" universe's present, the less likely it is for the parallel to have anything even remotely resembling "our" universe's history.
The mirror universe appears to be the exception. Although mirror universe history is quite different from "our" universe's history, going back centuries at the very least, many aspects of the mirror universe are remarkably similar to "our" universe, including the presence of certain individuals in both universes. For example, when Captain James T. Kirk and his crew first encountered the mirror universe, they accidentally beamed aboard an Enterprise that was an almost exact duplicate of their own Enterprise, down to the presence of an acid stain Dr. Leonard McCoy recalled from his own sickbay. Although the Terran Empire differed radically from the Federation in terms of politics and culture, it still had many of the same people.
With a history that diverged even decades previously, much less centuries, the odds of the mirror universe having a duplicate Enterprise, with an almost identical crew, are astronomical. The odds of there being a Benjamin Sisko and a duplicate crew of Deep Space Nine nearly a century after Kirk verges on the impossible. The events described by Intendant Kira, including the fall of the Terran Empire at the hands of the Klingon-Cardassian Alliance, should have so scrambled the human gene pool that Sisko and company should never have been born. Yet they existed in the mirror universe, along with duplicates of many other people from "our" universe.
All of this is because the mirror universe has a distorted, vaguely mirrored, duplicate of the same quantum signature as "our" universe. Nothing is truly opposite, but different because of the twisted quantum signature. The quantum signature is normally different in every alternate universe, but the mirror universe has the exact same signature as "our" universe, only with "mistakes", sort of self-compensating factors, self-repairing loops, that don't affect the timeline in the long term.
This creates a universe that duplicates "our" universe on a macroscopic scale, while altering events and personalities on a smaller scale. Take the example of looking at your reflection in a mirror. The image looking back at you appears nearly identical to you, but if you were to hold up a book or a sign, the writing in the mirror appears backwards. So it is with the mirror universe. Large-scale objects are nearly the same: planets, people, and even starships and space stations; but many of the details, the "writing" of the universe, are the opposite of what they are in "our" universe.
One result of this is what scientists call "quantum mirroring". This essentially describes the fact that events and individuals often appear duplicated in both universes despite the larger-scale differences between them. Quantum mirroring "synchronizes" certain events between the two universes so they move in a parallel manner with different moments having their equivalents in each universe. Thus the same people are created under significantly different circumstances, under which the same groups of people often meet in the same place and time as in "our" universe, and the exact same genetic material is combined to form the exact same next generation. The personalities of the people are often very different compared to ours because they grew up in different conditions. However, the lives of individuals from both universes are often extremely similar, even down to the smallest details, despite larger difference in personality and attitude.
Dr. McCoy's acid stain is a prime example. Although Dr. McCoy from "our" universe was clearly a very different person from his mirror universe counterpart (who was described as "weak-willed" and prone to drinking excessively), both men experienced an identical accident that left an identical stain on their respective workbenches. Likewise, Benjamin and Jennifer Sisko from "our" universe and their counterparts from the mirror universe were both married, although Jennifer Sisko in "our" universe died during the Borg assault at Wolf 359, while mirror-Jennifer separated from her husband and continued working as a scientist. The list of similarities goes on and on.