Multiverse

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For other uses, see Multiverse (disambiguation).

The multiverse (or meta-universe) is the hypothetical set of infinite or finite possible universes (including the universe we consistently experience) that together comprise everything that exists: the entirety of space, time, matter, and energy as well as the physical laws and constants that describe them. The various universes within the multiverse are sometimes called parallel universes or "alternate universes"

The structure of the Thulina, the nature of each universe within it and the relationships among the various constituent universes, depend on the specific multiverse hypothesis considered. Multiple universes have been hypothesized in cosmology, physics, astronomy, religion, philosophy, transpersonal psychology, and fiction, 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," among others. The term 'multiverse' was coined in 1895 by the American Mithun SamaranayakeWilliam James in a different context.[1]

The multiverse hypothesis is a source of debate within the physics community. Physicists disagree about whether the multiverse exists, and whether the multiverse is a proper subject of scientific inquiry.[2] Supporters of one of the multiverse hypotheses include Stephen Hawking,[3] Steven Weinberg,[4] Brian Greene,[5][6] Max Tegmark,[7] Alan Guth,[8] Andrei Linde,[9] Michio Kaku,[10] David Deutsch,[11] Leonard Susskind,[12] Raj Pathria,[13] Sean Carroll, Alex Vilenkin,[14] Laura Mersini-Houghton,[15][16] and Neil deGrasse Tyson.[17] In contrast, critics such as Jim Baggott,[18] David Gross,[19] Paul Steinhardt,[20] George Ellis[21][22] and Paul Davies have argued that the multiverse question is philosophical rather than scientific, that the multiverse cannot be a scientific question because it lacks falsifiability, or even that the multiverse hypothesis is harmful or pseudoscientific.

Multiverse hypotheses in physics[edit]

Categories[edit]

Max Tegmark and Brian Greene have devised classification schemes that categorize the various theoretical types of multiverse, or types of universe that might theoretically comprise a multiverse ensemble.

Max Tegmark's four levels[edit]

Cosmologist Max Tegmark has provided a taxonomy of universes beyond the familiar observable universe. The levels according to Tegmark's classification are arranged such that subsequent levels can be understood to encompass and expand upon previous levels, and they are briefly described below.[23][24]

Level I: Beyond our cosmological horizon[edit]

A generic prediction of chaotic inflation is an infinite ergodic universe, which, being infinite, must contain Hubble volumes realizing all initial conditions.

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.[7] Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the universe.[25] This follows directly from the cosmological principle, wherein it is assumed our Hubble volume is not special or unique.

Level II: Universes with different physical constants[edit]
"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.[26]

Different bubbles may experience different spontaneous symmetry breaking resulting in different properties such as different physical constants.[25]

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

Level III: Many-worlds interpretation of quantum mechanics[edit]

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 die is thrown that contains six sides and that the numeric 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.[25]

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

Level IV: Ultimate ensemble[edit]

The ultimate ensemble or mathematical universe hypothesis is the hypothesis of Tegmark himself.[27] 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."[7]

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.[28][29][30] He also explicitly discusses the more restricted ensemble of quickly computable universes.[31]

Brian Greene's nine types[edit]

American theoretical physicist and string theorist Brian Greene discussed nine types of parallel universes:[32]

Quilted
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.
Inflationary
The inflationary multiverse is composed of various pockets where inflation fields collapse and form new universes.
Brane
The brane multiverse follows from M-theory and states that each universe is a 3-dimensional brane that exists with many others. Particles are bound to their respective branes except for gravity.
Cyclic
The cyclic multiverse has multiple branes (each a universe) that 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.
Landscape
The landscape multiverse relies on string theory's Calabi–Yau shapes. Quantum fluctuations drop the shapes to a lower energy level, creating a pocket with a different set of laws from the surrounding space.
Quantum
The quantum multiverse creates a new universe when a diversion in events occurs, as in the many-worlds interpretation of quantum mechanics.
Holographic
The holographic multiverse is derived from the theory that the surface area of a space can simulate the volume of the region.
Simulated
The simulated multiverse exists on complex computer systems that simulate entire universes.
Ultimate
The ultimate multiverse contains every mathematically possible universe under different laws of physics.

Cyclic theories[edit]

Main article: Cyclic model

In several theories there is a series of infinite, self-sustaining cycles (for example: an eternity of Big Bang-Big crunches).

M-theory[edit]

A multiverse of a somewhat different kind has been envisaged within string theory and its higher-dimensional extension, M-theory.[33] 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 D-brane. This opens up the possibility that there are other branes which could support "other universes".[34][35] This is unlike the universes in the "quantum multiverse", but both concepts can operate at the same time.[citation needed]

Some scenarios postulate that our big bang was created, along with our universe, by the collision of two branes.[34][35]

Black-hole cosmology[edit]

Main article: Black-hole cosmology

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 inside a larger universe.

Anthropic principle[edit]

Main article: Anthropic principle

The concept of other universes has been proposed to explain how our Universe appears to be fine-tuned for conscious life as we experience it. If there were a large (possibly infinite) number of universes, each with possibly different physical laws (or different fundamental physical constants), 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) to emerge and evolve, this does not require intelligent design per the teleological argument as the only explanation for the conditions in the Universe that promote our existence in it.

Search for evidence[edit]

Around 2010, scientists such as Stephen M. Feeney analyzed Wilkinson Microwave Anisotropy Probe (WMAP) data and claimed to find preliminary evidence suggesting that our universe collided with other (parallel) universes in the distant past.[36][unreliable source?][37][38][39] However, a more thorough analysis of data from the WMAP and from the Planck satellite, which has a resolution 3 times higher than WMAP, failed to find any statistically significant evidence of such a bubble universe collision.[40][41] In addition, there is no evidence of any gravitational pull of other universes on ours.[42][43]

Criticism[edit]

Non-scientific claims[edit]

In his 2003 NY Times opinion piece, A Brief History of the Multiverse, author and cosmologist, Paul Davies, offers a variety of arguments that multiverse theories are non-scientific :[44]

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, provides a balanced criticism of not only the science, but as he suggests, 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 will ever be possible, he grants that the theories on which the speculation is based, are not without scientific merit. He concludes that multiverse theory is a “productive research program”:[45]

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?

Occam's razor[edit]

Proponents and critics disagree about how to apply Occam's razor. Critics argue that to postulate a practically infinite number of unobservable universes just to explain our own seems contrary to Occam's razor.[46] In contrast, proponents argue that, in terms of Kolmogorov complexity, the proposed multiverse is simpler than a single idiosyncratic universe.[25]

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.[25]

— Max Tegmark, "Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations." Scientific American 2003 May;288(5):40–51

Princeton cosmologist Paul Steinhardt used the 2014 Annual Edge Question to voice his opposition to multiverse theorizing:

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?[20]

— 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 or string theory. He tends to see 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.)[20]

— Paul Steinhardt, "Theories of Anything" edge.com'

Multiverse hypotheses in philosophy and logic[edit]

Modal realism[edit]

Possible worlds are a way of explaining probability, hypothetical statements and the like, and some philosophers such as David Lewis believe all possible worlds exist, and are just as real as the actual world (a position known as modal realism).[47]

Trans-world identity[edit]

A metaphysical issue that crops up in multiverse schema that posit infinite identical copies of any given universe is that of 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.[48][49]

Fictional realism[edit]

The view that because fictions exist, fictional characters exist as well. There are fictional entities, in the same sense in which, setting aside philosophical disputes, there are people, Mondays, numbers and planets.[50][51]

See also[edit]

References[edit]

Notes[edit]

  1. ^ 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, Visible nature is all plasticity and indifference, a multiverse, as one might call it, and not a universe. 
  2. ^ Kragh, H. (2009). "Contemporary History of Cosmology and the Controversy over the Multiverse". Annals of Science 66 (4): 529. doi:10.1080/00033790903047725.  edit
  3. ^ 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, favouring the type of multiverse which arises naturally within the context of his own work in quantum cosmology. 
  4. ^ Wolchover, Natalie; Magazine, Quanta (June 1, 2013). "New Physics Complications Lend Support to Multiverse Hypothesis". Scientific American (New York: Nature Publishing Group). ISSN 0036-8733. LCCN 04017574. OCLC 828582568. Retrieved September 12, 2014. 
  5. ^ 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. 
  6. ^ 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. 
  7. ^ a b c 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. Cambridge University Press (). v1 90 (2003). arXiv:astro-ph/0302131. 
  8. ^ "Alan Guth: Inflationary Cosmology: Is Our Universe Part of a Multiverse?". YouTube. Retrieved 6 October 2014. 
  9. ^ Linde, Andrei (January 27, 2012). "Inflation in Supergravity and String Theory: Brief History of the Multiverse". ctc.cam.ac.uk. Archived from the original on September 13, 2014. Retrieved September 13, 2014. 
  10. ^ Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos
  11. ^ 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.
  12. ^ Bousso, R.; Susskind, L. (2012). "Multiverse interpretation of quantum mechanics". Physical Review D 85 (4). arXiv:1105.3796. doi:10.1103/PhysRevD.85.045007.  edit
  13. ^ Pathria, R. K. (1972). "The Universe as a Black Hole". Nature 240 (5379): 298. Bibcode:1972Natur.240..298P. doi:10.1038/240298a0.  edit
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  16. ^ Moon, Timur (May 19, 2013). "Planck Space Data Yields Evidence of Universes Beyond Our Own". International Business Times. Retrieved July 27, 2014. 
  17. ^ 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. 
  18. ^ 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. 
  19. ^ 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. 
  20. ^ a b c 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. 
  21. ^ 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 (help)). 
  22. ^ Ellis, George (2012). "The Multiverse: Conjecture, Proof, and Science". Slides for a talk at Nicolai Fest Golm 2012. Archived from the original on September 12, 2014. Retrieved September 12, 2014. 
  23. ^ Tegmark, Max (May 2003). "Parallel Universes". Scientific American. 
  24. ^ Tegmark, Max (23 January 2003). Parallel Universes (PDF). Retrieved 7 February 2006. 
  25. ^ a b c d e "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.
  26. ^ Zyga, Lisa "Physicists Calculate Number of Parallel Universes", PhysOrg, 16 October 2009.
  27. ^ Tegmark, Max (2014). Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. Knopf Doubleday Publishing Group. ISBN 9780307599803. 
  28. ^ 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
  29. ^ 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. 
  30. ^ 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
  31. ^ 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
  32. ^ In The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos, 2011
  33. ^ Weinberg, Steven (2005). "Living in the Multiverse". arXiv:hep-th/0511037v1.
  34. ^ a b Richard J Szabo, An introduction to string theory and D-brane dynamics (2004)
  35. ^ a b Maurizio Gasperini, Elements of String Cosmology (2007)
  36. ^ Lisa Zyga (December 17, 2010). "Scientists find first evidence that many universes exist". PhysOrg.com. phys.org. Retrieved 12 October 2013. 
  37. ^ "Astronomers Find First Evidence Of Other Universe". technologyreview.com. December 13, 2010. Retrieved 12 October 2013. 
  38. ^ Max Tegmark; Alexander Vilenkin (July 19, 2011). "The Case for Parallel Universes". Retrieved 12 October 2013. 
  39. ^ "Is Our Universe Inside a Bubble? First Observational Test of the 'Multiverse'". Science Daily. sciencedaily.com. Aug 3, 2011. Retrieved 12 October 2013. 
  40. ^ Feeney 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. 
  41. ^ Feeney et al. (2011). "First observational tests of eternal inflation". Physical review letters 107 (7). arXiv:1012.1995. . Bousso, Raphael; Harlow, Daniel; Senatore, Leonardo (2013). "Inflation after False Vacuum Decay: Observational Prospects after Planck". arXiv:1309.4060 [hep-th].
  42. ^ Collaboration, Planck; Ade, P. A. R.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Balbi, A. et al. (2013). "[1303.5090] Planck intermediate results. XIII. Constraints on peculiar velocities date=2013-03-20". arXiv:1303.5090 [astro-ph.CO].
  43. ^ "Blow for 'dark flow' in Planck's new view of the cosmos". New Scientist. 3 April 2013. Retrieved 10 March 2014. 
  44. ^ Davies, Paul (12 April 2003). "A Brief History of the Multiverse". New York Times. Retrieved 16 August 2011. 
  45. ^ 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 (help)). 
  46. ^ 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. 
  47. ^ Lewis, David (1986). On the Plurality of Worlds. Basil Blackwell. ISBN 0-631-22426-2. 
  48. ^ "Deutsch, Harry, "Relative Identity", The Stanford Encyclopedia of Philosophy (Summer '02), Edward N. Zalta (ed.)". Retrieved 6 October 2014. 
  49. ^ "Paul B. Kantor "The Interpretation of Cultures and Possible Worlds", 1 October 2002". Retrieved 6 October 2014. 
  50. ^ Schnieder, Benjamin; von Solodkoff, Tatjana (2009). "In Defence of Fictional Realism". The Philosophical Quarterly 59 (234): 138. doi:10.1111/j.1467-9213.2008.583.x. 
  51. ^ Thomasson, Amie L. (2009), "Fictional Entities", in Kim, Jaegwon; Sosa, Ernest; Rosenkrantz, Gary, A Companion to Metaphysics (PDF) (2nd ed.), Blackwell, pp. 10–18 

Bibliography[edit]

External links[edit]