Editing Multiverse (section)

=== Max Tegmark's four levels ===
{{anchor|Tegmark's classification}}[[Cosmology|Cosmologist]] [[Max Tegmark]] has provided a [[taxonomy (general)|taxonomy]] of universes beyond the familiar [[observable universe]]. The four levels of Tegmark's classification are arranged such that subsequent levels can be understood to encompass and expand upon previous levels. They are briefly described below.<ref>{{cite journal | first=Max| last=Tegmark| journal=Scientific American|date=May 2003| title=Parallel Universes| doi=10.1038/scientificamerican0503-40| volume=288| issue=5| pages=40–51| pmid=12701329| url=https://cds.cern.ch/record/604580|arxiv = astro-ph/0302131 |bibcode = 2003SciAm.288e..40T }}</ref><ref>{{cite book
 | first = Max | last = Tegmark | date = 23 January 2003
 | title = Parallel Universes
 | url = http://space.mit.edu/home/tegmark/multiverse.pdf | access-date=7 February 2006}}</ref>

==== Level I: An extension of our universe ====
A prediction of [[Inflation (cosmology)|cosmic inflation]] is the existence of an infinite [[ergodic hypothesis|ergodic]] universe, which, being infinite, must contain [[Hubble volume]]s realizing all initial conditions.

Accordingly, an infinite universe will contain an infinite number of Hubble volumes, all having the same [[physical law]]s and [[physical constant]]s. In regard to configurations such as the distribution of [[matter]], almost all will differ from our Hubble volume. However, because there are infinitely many, far beyond the [[cosmological horizon]], there will eventually be Hubble volumes with similar, and even identical, configurations. Tegmark estimates that an identical volume to ours should be about [[Double exponential function|10<sup>10<sup>115</sup></sup>]] meters away from us.<ref name="X0302131"/>

Given infinite space, there would be an infinite number of Hubble volumes identical to ours in the universe.<ref name="TegmarkPUstaple">"Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations.", Tegmark, Max, Scientific American. May 2003; 288 (5): 40–51.</ref> This follows directly from the [[cosmological principle]], wherein it is assumed that our Hubble volume is not special or unique.

==== Level II: Universes with different physical constants ====

In the [[eternal inflation]] theory, which is a variant of the [[Inflation (cosmology)|cosmic inflation]] theory, the multiverse or space as a whole is stretching and will continue doing so forever,<ref>{{cite serial |title=[[How the Universe Works#Season 3|How The Universe Works 3]]|episode=First Second of the Big Bang |network=[[Science (TV network)|Discovery Science]] |date=2014}}</ref> but some regions of space stop stretching and form distinct bubbles (like gas pockets in a loaf of rising bread). Such bubbles are embryonic level I multiverses.

Different bubbles may experience different [[spontaneous symmetry breaking]], which results in different properties, such as different [[physical constant]]s.<ref name="TegmarkPUstaple"/>

Level II also includes [[John Archibald Wheeler]]'s [[oscillatory universe]] theory and [[Lee Smolin]]'s [[Cosmological natural selection|fecund universes theory]].

==== Level III: Many-worlds interpretation of quantum mechanics ====
[[File:Schroedingers cat film.svg|thumb|[[Schrödinger's cat]] in the many-worlds interpretation, where a branching of the universe occurs through a superposition of two quantum mechanical states]]
[[Hugh Everett III]]'s [[many-worlds interpretation]] (MWI) is one of several mainstream [[interpretations of quantum mechanics]].

In brief, one aspect of quantum mechanics is that certain observations cannot be predicted absolutely. Instead, there is a range of possible observations, each with a different [[probability]]. According to the MWI, each of these possible observations corresponds to a different "world" within the [[Universal wavefunction]], with each world as real as ours. Suppose a six-sided dice is thrown and that the result of the throw corresponds to [[observable]] quantum mechanics. All six possible ways the dice can fall correspond to six different worlds. In the case of the Schrödinger's cat thought experiment, [[Schrödinger's cat#Many-worlds interpretation and consistent histories|both outcomes would be "real" in at least one "world"]].

Tegmark argues that a Level III multiverse does not contain more possibilities in the Hubble volume than a Level I or Level 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 [[doppelgänger]]s 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.<ref name="TegmarkPUstaple"/> According to [[Yasunori Nomura]],<ref name="Nomura"/> [[Raphael Bousso]], and [[Leonard Susskind]],<ref name="BoussoSusskind"/> this is because global spacetime appearing in the (eternally) inflating multiverse is a redundant concept. This implies that the multiverses of Levels I, II, and III are, in fact, the same thing. This hypothesis is referred to as "Multiverse = Quantum Many Worlds". According to [[Yasunori Nomura]], this quantum multiverse is static, and time is a simple illusion.<ref>{{Cite journal |arxiv = 1205.5550|doi = 10.1103/PhysRevD.86.083505|title = Static quantum multiverse|journal = Physical Review D|volume = 86|issue = 8|pages = 083505|year = 2012|last1 = Nomura|first1 = Yasunori|last2 = Johnson|first2 = Matthew C.|last3 = Mortlock|first3 = Daniel J.|last4 = Peiris|first4 = Hiranya V.|bibcode = 2012PhRvD..86h3505N|s2cid = 119207079}}</ref>

Another version of the many-worlds idea is [[H. Dieter Zeh]]'s [[many-minds interpretation|''many-minds'' interpretation]].

==== Level IV: Ultimate ensemble ====
The ultimate [[mathematical universe hypothesis]] is Tegmark's own hypothesis.<ref name="Tegmark2014">{{cite book |first=Max |last=Tegmark |date=2014 |title=Our Mathematical Universe: My Quest for the Ultimate Nature of Reality |publisher=Knopf Doubleday Publishing Group |isbn=9780307599803|title-link=Our Mathematical Universe: My Quest for the Ultimate Nature of Reality }}</ref>

This level considers all universes to be equally real which can be described by different mathematical structures.

Tegmark writes: {{quotation|text=[[Abstract mathematics]] is so general that any [[theory of everything|Theory Of Everything (TOE)]] which 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 theory|set-theoretical]] model, and one can generally find a [[formal system]] that it is a model of.}}

He argues that this "implies that any conceivable parallel universe theory can be described at Level IV" and "subsumes all other ensembles, therefore brings closure to the hierarchy of multiverses, and there cannot be, say, a Level V."<ref name="X0302131">{{Cite journal |arxiv=astro-ph/0302131 |bibcode = 2003SciAm.288e..40T |doi = 10.1038/scientificamerican0503-40 |pmid=12701329 |title = Parallel Universes |year = 2003 |last1 = Tegmark |first1 = Max |journal = Scientific American |volume = 288 |issue = 5 |pages = 40–51 }}</ref>

[[Jürgen Schmidhuber]], however, says that the set of mathematical structures is not even [[well-defined]] and that it admits only universe representations describable by [[constructive mathematics]]—that is, [[computer programs]].

Schmidhuber explicitly includes universe representations describable by non-halting programs whose output bits converge after a finite time, although the convergence time itself may not be predictable by a halting program, due to the [[Undecidable problem|undecidability]] of the [[halting problem]].<ref>[[Jürgen Schmidhuber|J. Schmidhuber]] (1997): A Computer Scientist's View of Life, the Universe, and Everything. Lecture Notes in Computer Science, pp. 201–208, Springer: [http://www.idsia.ch/~juergen/everything/ IDSIA – Dalle Molle Institute for Artificial Intelligence].</ref><ref>{{Cite arXiv|eprint=quant-ph/0011122|last1=Schmidhuber|first1=Juergen|title=Algorithmic Theories of Everything|year=2000}}</ref><ref>[[Jürgen Schmidhuber|J. Schmidhuber]] (2002): Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit. ''International Journal of Foundations of Computer Science'' 13 (4): 587–612. [http://www.idsia.ch/~juergen/kolmogorov.html IDSIA – Dalle Molle Institute for Artificial Intelligence].</ref> He also explicitly discusses the more restricted ensemble of quickly computable universes.<ref>[[Jürgen Schmidhuber|J. Schmidhuber]] (2002): The Speed Prior: A New Simplicity Measure Yielding Near-Optimal Computable Predictions. Proc. 15th Annual Conference on Computational Learning Theory (COLT 2002), Sydney, Australia, Lecture Notes in Artificial Intelligence, pp. 216–228. Springer: [http://www.idsia.ch/~juergen/speedprior.html IDSIA – Dalle Molle Institute for Artificial Intelligence].</ref>