Of the four types of universes, Level 3 parallel universes have the least to do with string theory directly. A Level 3 parallel universe is a consequence of the many worlds interpretation (MWI) from quantum physics. In this interpretation, every single quantum possibility inherent in the quantum wavefunction becomes a real possibility in some reality.
When the average person (especially a science fiction fan) thinks of a “parallel universe,” he’s probably thinking of Level 3 parallel universes.
The many worlds interpretation was presented by Hugh Everett III to explain the quantum wavefunction, the Schrödinger equation. The Schrödinger equation describes how a quantum system evolves over time through a series of rotations in a Hilbert space (an abstract space with infinite dimensions).
The evolution of the wavefunction is called unitary. (Unitarity basically means that if you add up the probabilities of all possible outcomes, you get 1 as the sum of those probabilities.)
The traditional Copenhagen interpretation of quantum physics assumed that the wavefunction collapsed into a specific state, but the theory presented no mechanism for when or how this collapse takes place. The collapse turned the unitary wavefunction, which contains all possibilities, into a non-unitary system, which ignores the possibilities that never took place.
Everett took a tactic similar to that taken later by string theorists, assuming that each “dimension” predicted mathematically by the wavefunction (an infinite number of them) must be realized in some way in reality. In this theory, all quantum events result in a branching of a universe into multiple universes, so the unitary theory can be treated in a unitary way (no possibilities ever go away).
Level 3 parallel universes are different from the others posed because they take place in the same space and time as our own universe, but you still have no way to access them.
You have never had and will never have contact with any Level 1 or Level 2 universe, but you’re continually in contact with Level 3 universes — every moment of your life, every decision you make, is causing a split of your “now” self into an infinite number of future selves, all of which are unaware of each other.
Though we talk of the universe “splitting,” this isn’t precisely true (under the MWI of quantum physics). From a mathematical standpoint, there’s only one wavefunction, and it evolves over time. The superpositions of different universes all coexist simultaneously in the same infinite-dimensional Hilbert space. These separate, coexisting universes interfere with each other, yielding the bizarre quantum behaviors, such as those of the double slit experiment.
