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The multiverse (or meta-universe) is the hypothetical set of finite and infinite possible universes, including the universe in which we live. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, and the physical laws and constants that describe them.
The various universes within the multiverse are called "parallel universes", "other universes" or "alternate universes."
- 1 Origin of the concept
- 2 Explanation
- 3 Search for evidence
- 4 Proponents and skeptics
- 5 Arguments against multiverse theories
- 6 Classification schemes
- 7 M-theory
- 8 Black-hole cosmology
- 9 Anthropic principle
- 10 Occam's Razor
- 11 Modal realism
- 12 Trans-world identity
- 13 See also
- 14 References
- 15 Bibliography
- 16 External links
Origin of the concept
In Dublin in 1952, Erwin Schrödinger gave a lecture in which he jocularly warned his audience that what he was about to say might "seem lunatic." He said that, when his Nobel equations seemed to describe several different histories, these were "not alternatives, but all really happen simultaneously." This is the earliest known reference to the multiverse.
The structure of the multiverse, the nature of each universe within it, and the relationships among these universes differ from one multiverse hypothesis to another.
Multiple universes have been hypothesized in cosmology, physics, astronomy, religion, philosophy, transpersonal psychology, and literature, particularly in science fiction and fantasy. In these contexts, parallel universes are also called "alternate universes", "quantum universes", "interpenetrating dimensions", "parallel dimensions", "parallel worlds", "alternate realities", "alternate timelines", and "dimensional planes".
The physics community continues to debate the multiverse hypothesis. Prominent physicists disagree about whether the multiverse exists.
Some physicists say the multiverse is not a legitimate topic of scientific inquiry. Concerns have been raised about whether attempts to exempt the multiverse from experimental verification could erode public confidence in science and ultimately damage the study of fundamental physics. Some have argued that the multiverse is a philosophical rather than a scientific hypothesis because it cannot be falsified. The ability to disprove a theory by means of scientific experiment has always been part of the accepted scientific method. Paul Steinhardt has famously argued that no experiment can rule out a theory if the theory provides for all possible outcomes.
In 2007, Nobel laureate Steven Weinberg suggested that if the multiverse existed, "the hope of finding a rational explanation for the precise values of quark masses and other constants of the standard model that we observe in our Big Bang is doomed, for their values would be an accident of the particular part of the multiverse in which we live."
Search for evidence
Around 2010, scientists such as Stephen M. Feeney analyzed Wilkinson Microwave Anisotropy Probe (WMAP) data and claimed to find evidence suggesting that our universe collided with other (parallel) universes in the distant past.[unreliable source?] However, a more thorough analysis of data from the WMAP and from the Planck satellite, which has a resolution 3 times higher than WMAP, did not reveal any statistically significant evidence of such a bubble universe collision. In addition, there was no evidence of any gravitational pull of other universes on ours.
Proponents and skeptics
Proponents of one of the multiverse hypotheses include Stephen Hawking, Brian Greene, Max Tegmark, Alan Guth, Andrei Linde, Michio Kaku, David Deutsch, Leonard Susskind, Alexander Vilenkin, Yasunori Nomura, Raj Pathria, Laura Mersini-Houghton, Neil deGrasse Tyson, and Sean Carroll.
Scientists who are generally skeptical of the multiverse hypothesis include: Nobel laureate Steven Weinberg, Nobel laureate David Gross, Paul Steinhardt, Neil Turok, Viatcheslav Mukhanov, Michael S. Turner, Roger Penrose, George Ellis, Joe Silk, Adam Frank, Marcelo Gleiser, Jim Baggott, and Paul Davies.
Arguments against multiverse theories
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For a start, how is the existence of the other universes to be tested? To be sure, all cosmologists accept that there are some regions of the universe that lie beyond the reach of our telescopes, but somewhere on the slippery slope between that and the idea that there are an infinite number of universes, credibility reaches a limit. As one slips down that slope, more and more must be accepted on faith, and less and less is open to scientific verification. Extreme multiverse explanations are therefore reminiscent of theological discussions. Indeed, invoking an infinity of unseen universes to explain the unusual features of the one we do see is just as ad hoc as invoking an unseen Creator. The multiverse theory may be dressed up in scientific language, but in essence it requires the same leap of faith.— Paul Davies, A Brief History of the Multiverse
Taking cosmic inflation as a popular case in point, George Ellis, writing in August 2011, provided a balanced criticism of not only the science but, as he suggested, the scientific philosophy by which multiverse theories are generally substantiated.
He, like most cosmologists, accepts Tegmark's level-I "domains", even though they lie far beyond the cosmological horizon. Likewise, the multiverse of cosmic inflation is said to exist very far away. It would be so far away, however, that it's very unlikely any evidence of an early interaction will be found. He argues that, for many theorists, the lack of empirical testability or falsifiability is not a major concern.
Many physicists who talk about the multiverse, especially advocates of the string landscape, do not care much about parallel universes per se. For them, objections to the multiverse as a concept are unimportant. Their theories live or die based on internal consistency and, one hopes, eventual laboratory testing.
Although he believes there's little hope that laboratory testing will ever be possible, he grants that the theories on which speculation is based have some scientific merit. He concluded that multiverse theory is a "productive research program":
As skeptical as I am, I think the contemplation of the multiverse is an excellent opportunity to reflect on the nature of science and on the ultimate nature of existence: why we are here.... In looking at this concept, we need an open mind, though not too open. It is a delicate path to tread. Parallel universes may or may not exist; the case is unproved. We are going to have to live with that uncertainty. Nothing is wrong with scientifically based philosophical speculation, which is what multiverse proposals are. But we should name it for what it is.— George Ellis, Scientific American, Does the Multiverse Really Exist?
Max Tegmark's four levels
Cosmologist Max Tegmark has provided a 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.
Level I: Beyond our cosmological horizon
Accordingly, an infinite universe will contain an infinite number of Hubble volumes, all having the same physical laws and physical constants. 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. 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 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.
Level III: Many-worlds interpretation 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 die 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 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 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, 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 Levels I, II, and III are, in fact, the same thing. This hypothesis is referred to as "Multiverse = Quantum Many Worlds".
Level IV: Ultimate ensemble
This level considers all universes to be equally real which can be described by different mathematical structures.
Tegmark writes that:
Abstract mathematics is so general that any 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-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."
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 finite time, although the convergence time itself may not be predictable by a halting program, due to the undecidability of the halting problem. He also explicitly discusses the more restricted ensemble of quickly computable universes.
Brian Greene's nine types
- The quilted multiverse works only in an infinite universe. With an infinite amount of space, every possible event will occur an infinite number of times. However, the speed of light prevents us from being aware of these other identical areas.
- The inflationary multiverse is composed of various pockets in which inflation fields collapse and form new universes.
- The brane multiverse follows from M-theory and states that our universe is a 3-dimensional brane that exists with many others on a higher-dimensional brane or "bulk". Particles are bound to their respective branes except for gravity.
- The cyclic multiverse (via the ekpyrotic scenario) has multiple branes (each a universe) that have collided, causing Big Bangs. The universes bounce back and pass through time until they are pulled back together and again collide, destroying the old contents and creating them anew.
- The landscape multiverse relies on string theory's Calabi–Yau spaces. Quantum fluctuations drop the shapes to a lower energy level, creating a pocket with a set of laws different from that of the surrounding space.
- The quantum multiverse creates a new universe when a diversion in events occurs, as in the many-worlds interpretation of quantum mechanics.
- The holographic multiverse is derived from the theory that the surface area of a space can simulate the volume of the region.
- The simulated multiverse exists on complex computer systems that simulate entire universes.
- The ultimate multiverse contains every mathematically possible universe under different laws of physics.
These theories require the presence of 10 or 11 spacetime dimensions respectively. The extra 6 or 7 dimensions may either be compactified on a very small scale, or our universe may simply be localized on a dynamical (3+1)-dimensional object, a D3-brane. This opens up the possibility that there are other branes which could support other universes. This is unlike the universes in the quantum multiverse, but both concepts can operate at the same time.
A black-hole cosmology is a cosmological model in which the observable universe is the interior of a black hole existing as one of possibly many universes inside a larger universe. This includes the theory of white holes, which are on the opposite side of space-time.
While a black hole sucks everything in, including light, a white hole releases matter and light. Hence the name "white hole".
If there were a large (possibly infinite) number of universes, each with possibly different physical laws (or different fundamental physical constants), then some of these universes (even if very few) would have the combination of laws and fundamental parameters that are suitable for the development of matter, astronomical structures, elemental diversity, stars, and planets that can exist long enough for life to emerge and evolve.
The weak anthropic principle could then be applied to conclude that we (as conscious beings) would only exist in one of those few universes that happened to be finely tuned, permitting the existence of life with developed consciousness. Thus, while the probability might be extremely small that any particular universe would have the requisite conditions for life (as we understand life), those conditions do not require intelligent design as an explanation for the conditions in the Universe that promote our existence in it.
An early form of this reasoning is evident in Arthur Schopenhauer's 1844 work "Von die Neidigkeit und dem Leiden des Lebens", where he argues that our world must be the worst of all possible worlds, because if it were significantly worse in any respect it could not continue to exist.
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Proponents and critics disagree about how to apply Occam's Razor. Critics argue that to postulate an almost infinite number of unobservable universes, just to explain our own universe, seems contrary to Occam's Razor. But proponents argue that, in terms of Kolmogorov complexity, the proposed multiverse is simpler than a single idiosyncratic universe.
For example, multiverse proponent Max Tegmark argues:
[A]n entire ensemble is often much simpler than one of its members. This principle can be stated more formally using the notion of algorithmic information content. The algorithmic information content in a number is, roughly speaking, the length of the shortest computer program that will produce that number as output. For example, consider the set of all integers. Which is simpler, the whole set or just one number? Naively, you might think that a single number is simpler, but the entire set can be generated by quite a trivial computer program, whereas a single number can be hugely long. Therefore, the whole set is actually simpler... (Similarly), the higher-level multiverses are simpler. Going from our universe to the Level I multiverse eliminates the need to specify initial conditions, upgrading to Level II eliminates the need to specify physical constants, and the Level IV multiverse eliminates the need to specify anything at all.... A common feature of all four multiverse levels is that the simplest and arguably most elegant theory involves parallel universes by default. To deny the existence of those universes, one needs to complicate the theory by adding experimentally unsupported processes and ad hoc postulates: finite space, wave function collapse and ontological asymmetry. Our judgment therefore comes down to which we find more wasteful and inelegant: many worlds or many words. Perhaps we will gradually get used to the weird ways of our cosmos and find its strangeness to be part of its charm.
A pervasive idea in fundamental physics and cosmology that should be retired: the notion that we live in a multiverse in which the laws of physics and the properties of the cosmos vary randomly from one patch of space to another. According to this view, the laws and properties within our observable universe cannot be explained or predicted because they are set by chance. Different regions of space too distant to ever be observed have different laws and properties, according to this picture. Over the entire multiverse, there are infinitely many distinct patches. Among these patches, in the words of Alan Guth, "anything that can happen will happen—and it will happen infinitely many times". Hence, I refer to this concept as a Theory of Anything. Any observation or combination of observations is consistent with a Theory of Anything. No observation or combination of observations can disprove it. Proponents seem to revel in the fact that the Theory cannot be falsified. The rest of the scientific community should be up in arms since an unfalsifiable idea lies beyond the bounds of normal science. Yet, except for a few voices, there has been surprising complacency and, in some cases, grudging acceptance of a Theory of Anything as a logical possibility. The scientific journals are full of papers treating the Theory of Anything seriously. What is going on?— Paul Steinhardt, "Theories of Anything" edge.com
Steinhardt claims that multiverse theories have gained currency mostly because too much has been invested in theories that have failed (e.g., inflation theory and string theory). He sees in them an attempt to redefine the values of science, to which he objects even more strongly:
A Theory of Anything is useless because it does not rule out any possibility and worthless because it submits to no do-or-die tests. (Many papers discuss potential observable consequences, but these are only possibilities, not certainties, so the Theory is never really put at risk.)— Paul Steinhardt, "Theories of Anything" edge.com
Possible worlds are a way of explaining probability and hypothetical statements. Some philosophers, such as David Lewis, believe that all possible worlds exist and that they are just as real as the world we live in (a position known as modal realism).
A metaphysical issue which crops up in multiverse theories that posit infinite identical copies of any given universe, is the notion that there can be identical objects in different possible worlds. According to the counterpart theory of David Lewis, the objects should be regarded as similar rather than identical.
- A Universe from Nothing
- Beyond black holes
- Holographic principle
- Hugh Everett
- Impossible world
- Laura Mersini-Houghton
- Martin Rees, Astronomer Royal
- Modal realism
- Multiverse (religion)
- Parallel universe (fiction)
- Philosophy of physics
- Philosophy of space and time
- Roger Penrose
- Simulated reality
- The Fabric of Reality
- Ultimate fate of the universe
- James, William, The Will to Believe, 1895; and earlier in 1895, as cited in OED's new 2003 entry for "multiverse": James, William (October 1895), "Is Life Worth Living?", Internat. Jrnl. Ethics 6: 10, doi:10.1086/205378,
Visible nature is all plasticity and indifference, a multiverse, as one might call it, and not a universe.
- David Deutsch, The Beginning of Infinity, page 310.
- Kragh, H. (2009). "Contemporary History of Cosmology and the Controversy over the Multiverse". Annals of Science 66 (4): 529–551. doi:10.1080/00033790903047725.
- Ellis, George; Silk, Joe (December 16, 2014). "Scientific Method: Defend the Integrity of Physics". Nature 516: 321–323. Bibcode:2014Natur.516..321E. doi:10.1038/516321a.
- "Feynman on Scientific Method". YouTube. Retrieved July 28, 2012.
- Steinhardt, Paul (June 3, 2014). "Big Bang blunder bursts the Multiverse bubble". Nature 510: 9. Bibcode:2014Natur.510....9S. doi:10.1038/510009a.
- Weinberg, Steven (November 20, 2007). "Physics: What we do and don't know". The New York Review of Books.
- Lisa Zyga (December 17, 2010). "Scientists find first evidence that many universes exist". PhysOrg.com. phys.org. Retrieved 12 October 2013.
- "Astronomers Find First Evidence Of Other Universe". technologyreview.com. December 13, 2010. Retrieved 12 October 2013.
- Max Tegmark; Alexander Vilenkin (July 19, 2011). "The Case for Parallel Universes". Retrieved 12 October 2013.
- "Is Our Universe Inside a Bubble? First Observational Test of the 'Multiverse'". Science Daily. sciencedaily.com. Aug 3, 2011. Retrieved 12 October 2013.
- Feeney, Stephen M.; et al. (2011). "First observational tests of eternal inflation: Analysis methods and WMAP 7-year results". Physical Review D 84 (4): 43507. arXiv:1012.3667. Bibcode:2011PhRvD..84d3507F. doi:10.1103/PhysRevD.84.043507.
- Feeney; et al. (2011). "First observational tests of eternal inflation". Physical Review Letters 107 (7): 071301. arXiv:1012.1995. Bibcode:2011PhRvL.107g1301F. doi:10.1103/PhysRevLett.107.071301. PMID 21902380.. Bousso, Raphael; Harlow, Daniel; Senatore, Leonardo (2013). "Inflation after False Vacuum Decay: Observational Prospects after Planck". Physical Review D 91 (8): 083527. arXiv:1309.4060. Bibcode:2015PhRvD..91h3527B. doi:10.1103/PhysRevD.91.083527.
- Collaboration, Planck; Ade, P. A. R.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Balbi, A.; Banday, A. J.; Barreiro, R. B.; Battaner, E.; Benabed, K.; Benoit-Levy, A.; Bernard, J. -P.; Bersanelli, M.; Bielewicz, P.; Bikmaev, I.; Bobin, J.; Bock, J. J.; Bonaldi, A.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Burigana, C.; Butler, R. C.; Cabella, P.; Cardoso, J. -F.; Catalano, A.; Chamballu, A.; et al. (2013-03-20). "Planck intermediate results. XIII. Constraints on peculiar velocities". Astronomy & Astrophysics 561: A97. arXiv:1303.5090. Bibcode:2014A&A...561A..97P. doi:10.1051/0004-6361/201321299.
- "Blow for 'dark flow' in Planck's new view of the cosmos". New Scientist. 3 April 2013. Retrieved 10 March 2014.
- Universe or Multiverse. p. 19. ISBN 9780521848411.
Some physicists would prefer to believe that string theory, or M-theory, will answer these questions and uniquely predict the features of the Universe. Others adopt the view that the initial state of the Universe is prescribed by an outside agency, code-named God, or that there are many universes, with ours being picked out by the anthropic principle. Hawking argues that string theory is unlikely to predict the distinctive features of the Universe. But neither is he is an advocate of God. He therefore opts for the last approach, favoring the type of multiverse which arises naturally within the context of his own work in quantum cosmology.
- Greene, Brian (January 24, 2011). A Physicist Explains Why Parallel Universes May Exist. npr.org. Interview with Terry Gross. Archived from the original on September 12, 2014. Retrieved September 12, 2014.
- Greene, Brian (January 24, 2011). Transcript:A Physicist Explains Why Parallel Universes May Exist. npr.org. Interview with Terry Gross. Archived from the original on September 12, 2014. Retrieved September 12, 2014.
- Tegmark, Max (2003). "Parallel Universes". In "Science and Ultimate Reality: from Quantum to Cosmos", honoring John Wheeler's th birthday. J. D. Barrow, P.C.W. Davies, & C.L. Harper eds. v1 (Cambridge University Press). arXiv:astro-ph/0302131. Bibcode:2003SciAm.288e..40T. doi:10.1038/scientificamerican0503-40. "Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations". Scientific American 288: 40–51. May 2003. arXiv:astro-ph/0302131. Bibcode:2003SciAm.288e..40T. doi:10.1038/scientificamerican0503-40. PMID 12701329.
- "Alan Guth: Inflationary Cosmology: Is Our Universe Part of a Multiverse?". YouTube. Retrieved 6 October 2014.
- Linde, Andrei (January 27, 2012). "Inflation in Supergravity and String Theory: Brief History of the Multiverse" (PDF). ctc.cam.ac.uk. Archived (PDF) from the original on September 13, 2014. Retrieved September 13, 2014.
- Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos
- David Deutsch (1997). "The Ends of the Universe". The Fabric of Reality: The Science of Parallel Universes—and Its Implications. London: Penguin Press. ISBN 0-7139-9061-9.
- Bousso, R.; Susskind, L. (2012). "Multiverse interpretation of quantum mechanics". Physical Review D 85 (4). arXiv:1105.3796. Bibcode:2012PhRvD..85d5007B. doi:10.1103/PhysRevD.85.045007.
- Vilenkin, Alex (2007). Many Worlds in One: The Search for Other Universes. ISBN 9780374707149.
- Nomura, Y. (2011). "Physical theories, eternal inflation, and the quantum universe". Journal of High Energy Physics 2011 (11). arXiv:1104.2324. Bibcode:2011JHEP...11..063N. doi:10.1007/JHEP11(2011)063.
- Pathria, R. K. (1972). "The Universe as a Black Hole". Nature 240 (5379): 298–299. Bibcode:1972Natur.240..298P. doi:10.1038/240298a0.
- Catchpole, Heather (November 24, 2009). "Weird data suggests something big beyond the edge of the universe". Cosmos (magazine). Archived from the original on 14 July 2014. Retrieved July 27, 2014.
- Moon, Timur (May 19, 2013). "Planck Space Data Yields Evidence of Universes Beyond Our Own". International Business Times. Retrieved July 27, 2014.
- Freeman, David (March 4, 2014). "Why Revive 'Cosmos?' Neil DeGrasse Tyson Says Just About Everything We Know Has Changed". huffingtonpost.com. Archived from the original on September 12, 2014. Retrieved September 12, 2014.
- Sean Carroll (October 18, 2011). "Welcome to the Multiverse". Discover (magazine). Retrieved May 5, 2015.
- Falk, Dan (March 17, 2015). "Science's Path from Myth to Multiverse". Quanta Magazine (New York: Simons Foundation).
- Davies, Paul (2008). "Many Scientists Hate the Multiverse Idea". The Goldilocks Enigma: Why Is the Universe Just Right for Life?. Houghton Mifflin Harcourt. p. 207. ISBN 9780547348469.
- Steinhardt, Paul (March 9, 2014). "Theories of Anything". edge.org. 2014 : WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT?. Archived from the original on March 9, 2014. Retrieved March 9, 2014.
- Gibbons, G.W.; Turok, Neil (2008). "The Measure Problem in Cosmology". Phys. Rev. D 77 (6): 063516. arXiv:hep-th/0609095. Bibcode:2008PhRvD..77f3516G. doi:10.1103/PhysRevD.77.063516.
- Mukhanov, Viatcheslav (2014). "Inflation without Selfreproduction". Fortschritte der Physik 63 (1): 36–41. arXiv:1409.2335. Bibcode:2015ForPh..63...36M. doi:10.1002/prop.201400074.
- Woit, Peter (June 9, 2015). "A Crisis at the (Western) Edge of Physics". Not Even Wrong.
- Woit, Peter (June 14, 2015). "CMB @ 50". Not Even Wrong.
- Ellis, George F. R. (August 1, 2011). "Does the Multiverse Really Exist?". Scientific American (New York: Nature Publishing Group) 305 (2): 38–43. doi:10.1038/scientificamerican0811-38. ISSN 0036-8733. LCCN 04017574. OCLC 828582568. Retrieved September 12, 2014. (subscription required (. ))
- Ellis, George (2012). "The Multiverse: Conjecture, Proof, and Science" (PDF). Slides for a talk at Nicolai Fest Golm 2012. Archived (PDF) from the original on September 12, 2014. Retrieved September 12, 2014.
- Ellis, George; Silk, Joe (December 16, 2014), "Scientific Method: Defend the Integrity of Physics", Nature 516: 321–323, Bibcode:2014Natur.516..321E, doi:10.1038/516321a
- Frank, Adam; Gleiser, Marcelo (June 5, 2015). "A Crisis at the Edge of Physics". New York Times.
- Baggott, Jim (August 1, 2013). Farewell to Reality: How Modern Physics Has Betrayed the Search for Scientific Truth. Pegasus. ISBN 978-1-60598-472-8. ISBN 978-1-60598-574-9.
- Davies, Paul (April 12, 2003). "A Brief History of the Multiverse". New York Times.
- Davies, Paul (12 April 2003). "A Brief History of the Multiverse". New York Times. Retrieved 16 August 2011.
- Ellis, George F. R. (August 1, 2011). "Does the Multiverse Really Exist?". Scientific American (New York: Nature Publishing Group) 305 (2): 38–43. doi:10.1038/scientificamerican0811-38. ISSN 0036-8733. LCCN 04017574. OCLC 828582568. Retrieved August 16, 2011. (subscription required (. ))
- Tegmark, Max (May 2003). "Parallel Universes". Scientific American 288: 40–51. doi:10.1038/scientificamerican0503-40. PMID 12701329.
- Tegmark, Max (23 January 2003). Parallel Universes (PDF). Retrieved 7 February 2006.
- "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.
- "First Second of the Big Bang". How The Universe Works 3. 2014. Discovery Science.
- Tegmark, Max (2014). Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. Knopf Doubleday Publishing Group. ISBN 9780307599803.
- 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 Intelligence
- Schmidhuber, Juergen (2000). "Algorithmic Theories of Everything". Sections in: Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit. International Journal of Foundations of Computer Science ():587-612 (2002). Section 6 in: the Speed Prior: A New Simplicity Measure Yielding Near-Optimal Computable Predictions. in J. Kivinen and R. H. Sloan, editors, Proceedings of the 15th Annual Conference on Computational Learning Theory(COLT 2002), Sydney, Australia, Lecture Notes in Artificial Intelligence, pages 216-228. Springer, 2002 13 (4): 1–5. arXiv:quant-ph/0011122. Bibcode:2000quant.ph.11122S.
- 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 IDSIA – Dalle Molle Institute for Artificial Intelligence
- 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
- In The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos, 2011
- Weinberg, Steven (2005). "Living in the Multiverse". arXiv:hep-th/0511037v1.
- Richard J Szabo, An introduction to string theory and D-brane dynamics (2004)
- Maurizio Gasperini, Elements of String Cosmology (2007)
- Arthur Schopenhauer, "De Welt als Wille and Vorstellung," supplement to the 4th book "Von der Nichtigkeit und dem Leiden des Lebens". see also R.B. Haldane and J. Kemp's translation "On the Vanity and Suffering of Life" pp 395-6
- Trinh, Xuan Thuan (2006). Staune, Jean, ed. Science & the Search for Meaning: Perspectives from International Scientists. West Conshohocken, PA: Templeton Foundation. p. 186. ISBN 1-59947-102-7.
- Lewis, David (1986). On the Plurality of Worlds. Basil Blackwell. ISBN 0-631-22426-2.
- Deutsch, Harry (Summer 2002). Edward N. Zalta, ed. "Relative Identity". The Stanford Encyclopedia of Philosophy. Retrieved 6 October 2014.
- "Paul B. Kantor "The Interpretation of Cultures and Possible Worlds", 1 October 2002". Retrieved 6 October 2014.
- Bernard Carr, ed. (2007) Universe or Multiverse? Cambridge Univ. Press.
- Deutsch, David (1985). "Quantum theory, the Church–Turing principle and the universal quantum computer" (PDF). Proceedings of the Royal Society of London A 400 (1818): 97–117. doi:10.1098/rspa.1985.0070.
- Ellis, George F.R.; William R. Stoeger; Stoeger, W. R. (2004). "Multiverses and physical cosmology". Monthly Notices of the Royal Astronomical Society 347 (3): 921–936. arXiv:astro-ph/0305292. Bibcode:2004MNRAS.347..921E. doi:10.1111/j.1365-2966.2004.07261.x.
- Surya-Siddhanta: A Text Book of Hindu Astronomy by Ebenezer Burgess, ed. Phanindralal Gangooly (1989/1997) with a 45-page commentary by P. C. Sengupta (1935).
|Wikiquote has quotations related to: Multiverse|
|Wikimedia Commons has media related to Multiverse.|
- Interview with Tufts cosmologist Alex Vilenkin on his new book, "Many Worlds in One: The Search for Other Universes" on the podcast and public radio interview program ThoughtCast.
- Joseph Pine II about Multiverse, Presentation at Mobile Monday Amsterdam, 2008
- Multiverse – Radio-discussion on BBC Four with Melvyn Bragg