The Mirror Matter Moon theory is one of the most prominent theories on LOST to explain what the island is and why it might behave like it does. Essentially, the island is a moon made of mirror matter. There are two types of matter, the matter we know and love, and the opposite. We can exist in either habitat, but one can not see the other. This is why the island can not be seen until you cross into area around the island – into the mirror matter moon.
LOST might be a multi-layered homage to yin-yang duality (where one side can’t exist without the other). The universe that we live in may have two sides, each invisible (or “dark”) to each the other. Matter operates in the same way on each side, but they are two different universes so stars and planets formed in two different ways. The sides are different according to “mirror reflection symmetry,” meaning that left and right are reversed on the very small scale of particle physics. The particles on our side (Portland) have “left-handed” interactions, and the particles on the other side (Starboardland) have “right-handed” interactions. This right-handed dark matter is known as mirror matter. In the words of Locke in Episode 1: “… Two sides… One is light… One is dark.” Note which hand each stone is in.
Imagine a small, invisible world developed on a dark mirror matter asteroid that crashed into Earth long ago. The island would be a continent on a world “on the other side of Earth,” as the producers have hinted. But this chunk of dark matter also contains exotic material that allows the natural formation of wormholes between the two sides. Thus this dark island connects the two sides of the universe and is a place of epic duality. Mimicking the ebb and flow of yin and yang, dominance over the island continuously shifts between light, faith-based (see Manichaeism), and dark, science-based, factions. When one side becomes too dominant, its power wanes and the other gains strength. Furthermore, the conflict incorporates the yin-yang-like struggle for power between Jacob and Esau. As they can’t exist without each other, for the conflict to end, both sides must perish or the sides must merge.
The light side faction is headed by someone who is born on Earth, moves to the island, and loses his or her father; and the dark side is led by someone who is born on the island and moves to Earth (e.g., Hanso, Aaron). These representatives are symbolic of the dots in the yin-yang. There also seems to be a supernatural force that ensures the balance between factions. That force achieves its ends by communicating through ghosts and ensuring the movement of certain people, like Aaron, back and forth. It’s probably meaningful that 815, the US Army, Juliet [thanks Christine], and possibly Desmond, may have all arrived on an equinox, when light and dark are most balanced.