Nature's laws generally exhitbit the maximum amount of symmetry possible. Physical laws are symmetrical in time (same today as yesterday) and in space (same in Moscow as in Washington DC.) The laws also respect other, more abstract symmetries. But there is one situation in which the symmetry is flawed: when physical laws are reflected in a mirror.
Take microscopic particles like electrons, photons, quarks, or neutrinos for instance. They can interact in a number of ways all permitted by the laws of physics. For example, an electron can eject a photon of light that is then absorbed by another electron. A quark can emit a particle called a vector boson, which causes it to become a different kind of quark. Now think of these processes reflected in a mirror. If the governing laws of particle interaction are mirror-symmetric, then every mirror-reflected process could occur in nature.
But in 1956 Chinese-American physicists Tsung Dao Less and Chen Ning Yang discovered that not all mirror-reflected processes do occur. There are some that are never seen in nature. Take the neutrino for example. When it is created, it always corkscrews to the "left" around its direction of travel. No experiment has ever found one corkscrewing to the "right."
Since every experiment before 1956 had shown perfect symmetry within nature, was nature's symmetry flawed, or did it just look that way? Lee and Yang decided that there must exist a "mirror" or "shadow" world, complete with mirror reflected particles. Then both types of neutrino would exist-"left-handed ones in our world, and right handed ones in the mirror world."
Mirror particles would be almost completely identical to their normal counterparts. For example, a mirror electron would have the same mass as a normal electron. Their main difference would be they would interact as mirror images of the way normal particles interact. This back-to-front interaction would usually be the only noticable difference. "Only in rare examples-like the reverse corkscrew of neutrinos-would the difference be marked."
They are different from normal particles in another important feature; they are invisible. Normal particles interact through the exchange of particles. Electromagnetic force for example arises from the endless exchange of photons, a type of "force carrying" particle. Since mirror particles have yet to show up in any experiment, it seems reasonable to believe they do not interact with any known force carrying particle. "This failure to interact with the carriers of electromagnetic force-photons of light-would explain why we do not see mirror matter. A body has to interact with light in order to reflect light into our eyes so we can see it."
Mirror particles do, on the other hand, interact with each other. This means there also exists a set of mirror forces, such as a "mirror electromagnetic force carried by mirror photons." Our ordinary particles ignore these forces as much as their particles ignore ours. Everything in our world would be duplicated there. Mirror protonsand neutrons would form mirror atoms, and molecules. It is perfectly plausible that there are mirror stars and galaxies, or even mirror living organisms. If this is true, it could even prove the existance of so called "dark matter" that is postulated to make up nearly 90% of the universe.
The information in this writeup was derived from:
"The Universe Next Door:The Making of Tomorrow's Science" by Marcus Chown.
The section of his book dedicated to this phenomenon includes plausible evidence for the existence of a mirror world found in both the micro and macroscopic realms. Unfortunately it was too advanced for me to put in my own words, and too long to quote. I highly recommend checking this book out on your own, in order to get a better understanding of this concept.
Another possibly interesting source of information about the subject could be found in John Cramer's "Twistor," a work of science fiction about a mirror earth that occupies the same space as our earth.