Originally posted by MattMulder
... However, can't one of those theories be wrong, and, therefore, making all of the others collapse in a chain-reaction of cosmic proportions?

Tegmark's classification
Cosmologist Max Tegmark has provided a taxonomy of universes beyond the familiar observable universe. The levels according to Tegmark's classification are briefly described below.


Level I: Beyond our cosmological horizon
A generic prediction of cosmic inflation is an infinite ergodic universe, which, being infinite, must contain Hubble volumes realizing all initial conditions.

An infinite universe should contain an infinite number of Hubble volumes. All will have the same physical laws and physical constants. However, almost all will be different from our Hubble volume regarding configurations such as how matter is distributed in the volume. But since there are an infinite number of such volumes, then some of these will be very similar or even identical to our own. Thus, far beyond our cosmological horizon, there will eventually be a Hubble volume identical to our own. Tegmark estimates that such an identical volume should be about 10118 meters away.


Level II: Universes with different physical constants

"Bubble universes", every disk is a bubble universe (Universe 1 to Universe 6 are different bubbles, they have physical constants that are different from our universe), our universe is just one of the bubbles.In the chaotic inflation theory, a variant of the cosmic inflation theory, the multiverse as a whole is stretching and will continue doing so forever, but some regions of space stop stretching and form distinct bubbles, like gas pockets in a loaf of rising bread. There exists an infinite number of such bubbles which are embryonic level I universes of infinite size. Different bubbles may experience different spontaneous symmetry breaking resulting in different properties such as different physical constants.

This level also include John Archibald Wheeler's oscillatory universe theory and Lee Smolin's fecund universes theory.


Level III: Many-worlds interpretation of quantum mechanics
Hugh Everett's many-worlds interpretation (MWI) is one of several mainstream interpretation of quantum mechanics. In brief, one aspect of quantum mechanics is that certain observations cannot be predicted absolutely. Instead, there is range of possible observations each with a different probability. According to the MWI, each of these possible observations correspond to a different universe. Suppose a die is thrown that contains 6 sides and that the result correspond to a quantum mechanics observable. All 6 possible ways the die can fall correspond to 6 different universes. (More correctly, in MWI there is only a single universe but after the "split" into "many worlds" these cannot in general interact.)

Tegmark argues that a level III multiverse does not contain more possibilities in the Hubble volume than a level I-II multiverse. In effect, all the different "worlds" created by "splits" in a level III multiverse with the same physical constants can be found in some Hubble volume in a level I multiverse. Tegmark writes that "The only difference between Level I and Level III is where your doppelgängers reside. In Level I they live elsewhere in good old three-dimensional space. In Level III they live on another quantum branch in infinite-dimensional Hilbert space." Similarly, all level II bubble universes with different physical constants can in effect be found as "worlds" created by "splits" at the moment of spontaneous symmetry breaking in a level III multiverse.


Level IV: Ultimate Ensemble
The Ultimate Ensemble hypothesis of Tegmark himself. This level considers equally real all universes that can be defined by mathematical structures. This also including those having physical laws different from our observable universe. Tegmark writes that "abstract mathematics is so general that any TOE that is definable in purely formal terms (independent of vague human terminology) is also a mathematical structure. For instance, a TOE involving a set of different types of entities (denoted by words, say) and relations between them (denoted by additional words) is nothing but what mathematicians call a set-theoretical model, and one can generally find a formal system that it is a model of." He argues this "it implies that any conceivable parallel universe theory can be described at Level IV" and "it subsumes all other ensembles, therefore brings closure to the hierarchy of multiverses, and there cannot be say a Level V."

Jürgen Schmidhuber, however, says the "set of mathematical structures" is not even well-defined, and admits only universe representations describable by constructive mathematics, that is, computer programs. He explicitly includes universe representations describable by non-halting programs whose output bits converge after finite time, although the convergence time itself may not be predictable by a halting program, due to Kurt Gödel's limitations.[9][10][11] He also explicitly discusses the more restricted ensemble of quickly computable universes.