ពហុចក្រវាល: បួនជាន់របស់មែខ្ស-ថិហ្កម៉ាខ

បួនជាន់របស់មែខ្ស-ថិហ្កម៉ាខ 

លោកធាតុវិទូ លោកមែខ្ស-ថេហ្កម៉ាខបានផ្ដល់នូវវគ្គីករណសាស្ត្រមួយអំពីពួកចក្រវាលក្រៅពីចក្រវាលដែលយើងសង្កេតឃើញធ្លាប់ស្គាល់រួចមកហើយ។ ជាន់នានាអាស្រ័យទៅតាមចំណាត់ថ្នាក់របស់ថេហ្កម៉ាខត្រូវរៀបជាជាន់ៗបន្តគ្នាអាចយល់បានដោយគូរជារង្វង់ និង ពាសពីលើជាន់មុនៗគេ ហើយជាន់អស់ទាំងនោះត្រូវបានពណ៌នាដោយខ្លីៗខាងក្រោម។

 ជាន់ទី១: ឯនាយដែនលោកធាតុរបស់យើង 
ការព្យាករណ៍តាមពួកនៃរំប៉ោងកលិយុគគឺជាចក្រវាលព្រឹត្តាសទភាព ដែលជាសភាពអនន្ត ត្រូវតែមានមាឌហាប៊លជាច្រើនដែលដឹងលក្ខណៈដើមទាំងអស់។

ដោយហេតុនោះហើយ ចក្រវាលអនន្តមួយនឹងមានចំនួនមាឌហាប៊លអនន្តមួយដែរ ទាំងអស់នឹងមានច្បាប់រូបវិទ្យា និង លំនឹងរូបវិទ្យាដូចគ្នា។  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 1010115 meters away from us. Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the Universe."Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations.", Tegmark M., Sci Am. 2003 May;288(5):40–51. This follows directly from the cosmological principle, wherein it is assumed our Hubble volume is not special or unique.

 ជាន់ទី២: ពួកចក្រវាលដែលមានលំនឹងរូបវិទ្យាផ្សេងគ្នា 
thumb|"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. Such bubbles are embryonic level I multiverses. Linde and Vanchurin calculated the number of these universes to be on the scale of 101010,000,000.Zyga, Lisa "Physicists Calculate Number of Parallel Universes", PhysOrg, 16 October 2009.

Different bubbles may experience different spontaneous symmetry breaking resulting in different properties such as different physical constants.

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

 ជាន់ទី៣ : បំណកស្រាយពហុ-លោកនៃយន្តសាស្ត្របមាណតា 
Hugh Everett'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 universe. Suppose a six-sided  is thrown and that the result of the throw corresponds to a quantum mechanics observable. All six possible ways the die can fall correspond to six different universes.

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. According to Yasunori Nomura and Raphael Bousso and Leonard Susskind, this is because global spacetime appearing in the (eternally) inflating multiverse is a redundant concept. This implies that the multiverses of Level I, II, and III are, in fact, the same thing. This hypothesis is referred to as "Multiverse = Quantum Many Worlds".

Related to the many-worlds idea are Richard Feynman's multiple histories interpretation and H. Dieter Zeh's many-minds interpretation.

 ជានទី៤: សរុបអវសាន 
The ultimate ensemble or mathematical universe hypothesis is the hypothesis of Tegmark himself. This level considers equally real all universes that can be described by different mathematical structures. Tegmark writes that "abstract mathematics is so general that any Theory Of Everything (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 "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."

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.J. Schmidhuber (1997): A Computer Scientist's View of Life, the Universe, and Everything. Lecture Notes in Computer Science, pp. 201–208, Springer: IDSIA – Dalle Molle Institute for Artificial IntelligenceJ. 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 IDSIA – Dalle Molle Institute for Artificial Intelligence He also explicitly discusses the more restricted ensemble of quickly computable universes.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: IDSIA – Dalle Molle Institute for Artificial Intelligence