The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them. The different universes within the multiverse are called "parallel universes", "other universes", or "alternate universes".
History of the conceptEdit
The concept of multiple universes existed since the middle ages. Notable was the theory of Fakhr al-Din al-Razi of the Islamic Golden Age, who intended to explain the probable existence of the multiverse, based on general principles of the Quran.
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 equations seemed to describe several different histories, these were "not alternatives, but all really happen simultaneously".
The American philosopher and psychologist William James used the term "multiverse" in 1895, but in a different context. The term was first used in fiction and in its current physics context by Michael Moorcock in his 1963 SF Adventures novella The Sundered Worlds.
Multiple universes have been hypothesized in cosmology, physics, astronomy, religion, philosophy, transpersonal psychology, music and all kinds of literature, particularly in science fiction, comic books and fantasy. In these contexts, parallel universes are also called "alternate universes", "quantum universes", "interpenetrating dimensions", "parallel universes", "parallel dimensions", "parallel worlds", "parallel realities", "quantum realities", "alternate realities", "alternate timelines", "alternate dimensions" and "dimensional planes".
The physics community has debated the various multiverse theories over time. Prominent physicists are divided about whether any other universes exist outside of our own.
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 notion rather than a scientific hypothesis because it cannot be empirically 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 evidenceEdit
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. 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 skepticsEdit
Modern proponents of one or more of the multiverse hypotheses include Hugh Everett, Don Page, 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, Sean Carrolland Stephen Hawking.
Scientists who are generally skeptical of the multiverse hypothesis include: David Gross, Paul Steinhardt, Anna Ijjas, Abraham Loeb, David Spergel, Neil Turok, Viatcheslav Mukhanov, Michael S. Turner, Roger Penrose, George Ellis, Joe Silk,Carlo Rovelli, Adam Frank, Marcelo Gleiser, Jim Baggott and Paul Davies.
Arguments against multiverse theoriesEdit
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 is 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, The New York Times, "A Brief History of the Multiverse"
George Ellis, writing in August 2011, provided a criticism of the multiverse, and pointed out that it is not a traditional scientific theory. He accepts that the multiverse is thought to exist far beyond the cosmological horizon. He emphasized that it is theorized to be so far away that it is unlikely any evidence will ever be found. Ellis also explained that some theorists do not believe the lack of empirical testability falsifiability is a major concern, but he is opposed to that line of thinking:
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.
Ellis says that scientists have proposed the idea of the multiverse as a way of explaining the nature of existence. He points out that it ultimately leaves those questions unresolved because it is a metaphysical issue that cannot be resolved by empirical science. He argues that observational testing is at the core of science and should not be abandoned:
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 levelsEdit
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: An extension of our universeEdit
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 constantsEdit
In the eternal inflation theory, which is a variant of the cosmic inflation theory, the multiverse or space 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 mechanicsEdit
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". According to Yasunori Nomura, this quantum multiverse is static, and time is a simple illusion.
Level IV: Ultimate ensembleEdit
This level considers all universes to be equally real which can be described by different mathematical structures.
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 typesEdit
- 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 version postulates that our entire universe exists on a membrane (brane) which floats in a higher dimension or "bulk". In this bulk, there are other membranes with their own universes. These universes can interact with one another, and when they collide, the violence and energy produced is more than enough to give rise to a big bang. The branes float or drift near each other in the bulk, and every few trillion years, attracted by gravity or some other force we do not understand, collide and bang into each other. This repeated contact gives rise to multiple or "cyclic" big bangs. This particular hypothesis falls under the string theory umbrella as it requires extra spatial dimensions.
- The cyclic multiverse has multiple branes 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 encode the contents of 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.
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.
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 der Nichtigkeit 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.
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, is contrary to Occam's razor. However, 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.— Max Tegmark
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).
- John Cooper (1998), "al-Razi, Fakhr al-Din (1149-1209)", Routledge Encyclopedia of Philosophy, Routledge, retrieved 7 March 2010
- Adi Setia (2004), "Fakhr Al-Din Al-Razi on Physics and the Nature of the Physical World: A Preliminary Survey", Islam & Science, 2, retrieved 2 March 2010
- "Erwin Schrödinger and the Quantum Revolution by John Gribbin: review".
- 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?", Int. J. Ethics, 6 (1): 10, doi:10.1086/205378,
Visible nature is all plasticity and indifference, a multiverse, as one might call it, and not a universe.
- 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, Georg; Silk, Joe (16 December 2014). "Scientific Method: Defend the Integrity of Physics". Nature. 516 (7531): 321–323. Bibcode:2014Natur.516..321E. doi:10.1038/516321a. PMID 25519115.
- "Feynman on Scientific Method". YouTube. Retrieved 28 July 2012.
- Steinhardt, Paul (3 June 2014). "Big Bang blunder bursts the Multiverse bubble". Nature. 510 (7503): 9. Bibcode:2014Natur.510....9S. doi:10.1038/510009a. PMID 24899270.
- Weinberg, Steven (20 November 2007). "Physics: What we do and don't know". The New York Review of Books.
- "Astronomers Find First Evidence Of Other Universe". technologyreview.com. 13 December 2010. Retrieved 12 October 2013.
- Max Tegmark; Alexander Vilenkin (19 July 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. 3 August 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 (2015). "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. (20 March 2013). "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.
- The Many Worlds of Hugh Everett, Scientific American
- "Does God exist in the multiverse?". 8 March 2018.
- Greene, Brian (24 January 2011). "A Physicist Explains Why Parallel Universes May Exist". npr.org (Interview). Interviewed by Terry Gross. Archived from the original on 13 September 2014. Retrieved 12 September 2014.
- Greene, Brian (24 January 2011). "Transcript:A Physicist Explains Why Parallel Universes May Exist". npr.org (Interview). Interviewed by Terry Gross. Archived from the original on 13 September 2014. Retrieved 12 September 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. 288 (5): 40–51. arXiv:astro-ph/0302131. Bibcode:2003SciAm.288e..40T. doi:10.1038/scientificamerican0503-40. PMID 12701329. Tegmark, M (May 2003). "Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations". Scientific American. Vol. 288. pp. 40–51. 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 (27 January 2012). "Inflation in Supergravity and String Theory: Brief History of the Multiverse" (PDF). ctc.cam.ac.uk. Archived (PDF) from the original on 14 July 2014. Retrieved 13 September 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): 045007. 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): 63. 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.
- "How to Find a Multiverse". iai.tv. Retrieved 22 October 2019.
- Catchpole, Heather (24 November 2009). "Weird data suggests something big beyond the edge of the universe". Cosmos. Archived from the original on 14 July 2014. Retrieved 27 July 2014.
- Moon, Timur (19 May 2013). "Planck Space Data Yields Evidence of Universes Beyond Our Own". International Business Times. Retrieved 27 July 2014.
- Freeman, David (4 March 2014). "Why Revive 'Cosmos?' Neil DeGrasse Tyson Says Just About Everything We Know Has Changed". huffingtonpost.com. Archived from the original on 13 September 2014. Retrieved 12 September 2014.
- Sean Carroll (18 October 2011). "Welcome to the Multiverse". Discover. Retrieved 5 May 2015.
- Carr, Bernard (21 June 2007). 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 argued 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.
- 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 (9 March 2014). "Theories of Anything". edge.org. 2014 : WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT?. Archived from the original on 10 March 2014. Retrieved 9 March 2014.
- Ijjas, Anna; Loeb, Abraham; Steinhardt, Paul (February 2017), "Cosmic Inflation Theory Faces Challenges", Scientific American, 316 (2): 32–39, doi:10.1038/scientificamerican0217-32, PMID 28118351
- "Is Nature Simple? 2018 Breakthrough Prize Symposium Panel". YouTube. Retrieved 14 January 2018.
- 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 (9 June 2015). "A Crisis at the (Western) Edge of Physics". Not Even Wrong.
- Woit, Peter (14 June 2015). "CMB @ 50". Not Even Wrong.
- Ellis, George F. R. (1 August 2011). "Does the Multiverse Really Exist?". Scientific American. Vol. 305 no. 2. New York City: Nature Publishing Group. pp. 38–43. Bibcode:2011SciAm.305a..38E. doi:10.1038/scientificamerican0811-38. ISSN 0036-8733. LCCN 04017574. OCLC 828582568. Retrieved 12 September 2014.
- Ellis, George (2012). "The Multiverse: Conjecture, Proof, and Science" (PDF). Slides for a talk at Nicolai Fest Golm 2012. Archived from the original (PDF) on 13 September 2014. Retrieved 12 September 2014.
- Ellis, George; Silk, Joe (16 December 2014), "Scientific Method: Defend the Integrity of Physics", Nature, 516 (7531): 321–323, Bibcode:2014Natur.516..321E, doi:10.1038/516321a, PMID 25519115
- Scoles; Sarah (19 April 2016), "Can Physics Ever Prove the Multiverse is Real", Smithsonian.com
- Frank, Adam; Gleiser, Marcelo (5 June 2015). "A Crisis at the Edge of Physics". The New York Times.
- Baggott, Jim (1 August 2013). Farewell to Reality: How Modern Physics Has Betrayed the Search for Scientific Truth. Pegasus. ISBN 978-1-60598-472-8.
- Davies, Paul (12 April 2003). "A Brief History of the Multiverse". The 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. (1 August 2011). "Does the Multiverse Really Exist?". Scientific American. Vol. 305 no. 2. New York City: Nature Publishing Group. pp. 38–43. Bibcode:2011SciAm.305a..38E. doi:10.1038/scientificamerican0811-38. ISSN 0036-8733. LCCN 04017574. OCLC 828582568. Retrieved 16 August 2011.
- Tegmark, Max (May 2003). "Parallel Universes". Scientific American. Vol. 288. pp. 40–51. arXiv:astro-ph/0302131. Bibcode:2003SciAm.288e..40T. 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.
- Nomura, Yasunori; Johnson, Matthew C.; Mortlock, Daniel J.; Peiris, Hiranya V. (2012). "Static quantum multiverse". Physical Review D. 86 (8): 083505. arXiv:1205.5550. Bibcode:2012PhRvD..86h3505N. doi:10.1103/PhysRevD.86.083505.
- 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, "Die Welt als Wille und 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 978-1-59947-102-0.
- "Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations". Scientific American. Vol. 288 no. 5. May 2003. pp. 40–51. arXiv:astro-ph/0302131. Bibcode:2003SciAm.288e..40T. doi:10.1038/scientificamerican0503-40. PMID 12701329.
- Lewis, David (1986). On the Plurality of Worlds. Basil Blackwell. ISBN 978-0-631-22426-6.
- Carr, Bernard. Universe or Multiverse? (2007 ed.). Cambridge University 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. Bibcode:1985RSPSA.400...97D. CiteSeerX 10.1.1.41.2382. doi:10.1098/rspa.1985.0070. Archived from the original (PDF) on 9 March 2016. Retrieved 15 September 2014.
- 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.
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- 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.
- Multiverse – Radio-discussion on BBC Four with Melvyn Bragg
- Why There Might be Many More Universes Besides Our Own, by Phillip Ball, March 21, 2016, bbc.com.