Editing Many-worlds interpretation (section)

== Preferred basis problem ==

As originally formulated by Everett and DeWitt, the many-worlds interpretation had a privileged role for measurements: they determined which [[Basis (linear algebra)|basis]] of a quantum system would give rise to the eponymous worlds. Without this the theory was ambiguous, as a quantum state can equally well be described (e.g.) as having a well-defined position or as being a superposition of two delocalized states. The assumption is that the preferred basis to use is the one which assigns a unique measurement outcome to each world. This special role for measurements is problematic for the theory, as it contradicts Everett and DeWitt's goal of having a reductionist theory and undermines their criticism of the ill-defined measurement postulate of the Copenhagen interpretation.<ref name="skyrms1976">{{cite journal |author1=Skyrms |first=Brian |author-link1=Brian Skyrms |date=1976 |title=Possible Worlds, Physics and Metaphysics |journal=Philosophical Studies |volume=30 |issue=5 |pages=323–332 |doi=10.1007/BF00357930 |s2cid=170852547}}</ref><ref name=ballentine1973/> This is known today as the ''preferred basis problem''.

The preferred basis problem has been solved, according to Saunders and Wallace, among others,<ref name="saunders2010">{{Cite book |last1=Saunders |first1=Simon |url=http://users.ox.ac.uk/~lina0174/introduction.pdf |title=Many Worlds? Everett, Quantum Theory and Reality |publisher=Oxford University Press |year=2010 |editor=Saunders |editor-first=S. |chapter=Many Worlds? An Introduction |author-link=Simon Saunders |editor2=Barrett |editor-first2=J. |editor3=Kent |editor-first3=A. |editor4=Wallace |editor-first4=D.}}</ref> by incorporating decoherence into the many-worlds theory.<ref name="gell-man1990">{{Cite book |last1=Gell-Mann |first1=M. |title=Complexity, Entropy, and the Physics of Information |last2=Hartle |first2=J. B. |publisher=Addison-Wesley |year=1990 |editor=Zurek |editor-first=W. H. |chapter=Quantum mechanics in the light of quantum cosmology |arxiv=1803.04605}}</ref><ref>{{cite journal |author1=Saunders |first=Simon |date=1993 |title=Decoherence, relative states, and evolutionary adaptation |journal=Foundations of Physics |volume=23 |issue=12 |pages=1553–1585 |bibcode=1993FoPh...23.1553S |doi=10.1007/BF00732365 |s2cid=119754481}}</ref><ref>{{cite journal |author1=Saunders |first=Simon |date=1995 |title=Time, quantum mechanics, and decoherence |url=http://philsci-archive.pitt.edu/463/1/part1.pdf |journal=Synthese |volume=102 |issue=2 |pages=235–266 |doi=10.1007/BF01089802 |s2cid=14550985}}</ref><ref>{{cite journal |author1=Hartle |first=James B. |date=2011 |title=The quasiclassical realms of this quantum universe |journal=Foundations of Physics |volume=41 |issue=6 |pages=982–1006 |arxiv=0806.3776 |bibcode=2011FoPh...41..982H |doi=10.1007/s10701-010-9460-0 |s2cid=118469123}}</ref> In this approach, the preferred basis does not have to be postulated, but rather is identified as the basis stable under environmental decoherence. In this way measurements no longer play a special role; rather, any interaction that causes decoherence causes the world to split. Since decoherence is never complete, there will always remain some infinitesimal overlap between two worlds, making it arbitrary whether a pair of worlds has split or not.<ref name = stappbasis>{{cite journal | last1 = Stapp | first1 = Henry | year = 2002 | title = The basis problem in many-world theories | url = http://www-physics.lbl.gov/~stapp/bp.PDF | journal = Canadian Journal of Physics | volume = 80 | issue = 9 | pages = 1043–1052 | doi=10.1139/p02-068|arxiv = quant-ph/0110148 |bibcode = 2002CaJPh..80.1043S | s2cid = 18634782 }}</ref> Wallace argues that this is not problematic: it only shows that worlds are not a part of the fundamental ontology, but rather of the ''emergent'' ontology, where these approximate, effective descriptions are routine in the physical sciences.<ref>{{cite journal |author1=Wallace |first=David |date=2003 |title=Everett and structure |journal=Studies in History and Philosophy of Science |volume=34 |issue=1 |pages=87–105 |arxiv=quant-ph/0107144 |bibcode=2003SHPMP..34...87W |doi=10.1016/S1355-2198(02)00085-0 |s2cid=15222560}}</ref><ref name="wallace2010">{{Cite book |author1=Wallace |first=David |title=Many Worlds? Everett, Quantum Theory and Reality |publisher=Oxford University Press |year=2010 |editor=Saunders |editor-first=S. |chapter=Decoherence and Ontology, or: How I Learned To Stop Worrying And Love FAPP |editor2=Barrett |editor-first2=J. |editor3=Kent |editor-first3=A. |editor4=Wallace |editor-first4=D. |arxiv=1111.2189}}</ref> Since in this approach the worlds are derived, it follows that they must be present in any other interpretation of quantum mechanics that does not have a collapse mechanism, such as Bohmian mechanics.<ref name=BrownWallace>{{cite journal | last1 = Brown | first1 = Harvey R | author-link = Harvey Brown (philosopher) | last2 = Wallace | first2 = David | year = 2005 | title = Solving the measurement problem: de Broglie–Bohm loses out to Everett | url = http://philsci-archive.pitt.edu/archive/00001659/01/Cushing.pdf | journal = Foundations of Physics | volume = 35 | issue = 4 | pages = 517–540 | doi=10.1007/s10701-004-2009-3|arxiv = quant-ph/0403094 |bibcode = 2005FoPh...35..517B | s2cid = 412240 }}</ref>

This approach to deriving the preferred basis has been criticized as creating circularity with derivations of probability in the many-worlds interpretation, as decoherence theory depends on probability and probability depends on the ontology derived from decoherence.<ref name=kent2009/><ref name=zurek2005/><ref name="baker">{{cite journal |author=Baker |first=David J. |year=2007 |title=Measurement outcomes and probability in Everettian quantum mechanics |url=http://philsci-archive.pitt.edu/2717/1/OutcomeProbEverett.pdf |journal=Studies in History and Philosophy of Science |volume=38 |issue=1 |pages=153–169 |bibcode=2007SHPMP..38..153B |doi=10.1016/j.shpsb.2006.05.003}}</ref> Wallace contends that decoherence theory depends not on probability but only on the notion that one is allowed to do approximations in physics.<ref name=wallace2012/>{{rp|253–254}}