Editing Many-worlds interpretation (section)

== Overview of the interpretation ==
The many-worlds interpretation's key idea is that the [[linear combination|linear]] and [[unitary (physics)|unitary]] dynamics of quantum mechanics applies everywhere and at all times and so describes the whole universe. In particular, it models a measurement as a unitary transformation, a correlation-inducing interaction, between observer and object, without using a [[Wave function collapse|collapse postulate]], and models observers as ordinary quantum-mechanical systems.<ref name=wallace2012/>{{rp|35–38}} This stands in contrast to the [[Copenhagen interpretation]], in which a measurement is a "primitive" concept, not describable by unitary quantum mechanics; using the Copenhagen interpretation the universe is divided into a quantum and a classical domain, and the collapse postulate is central.<ref name=wallace2012/>{{rp|29–30}} In MWI there is no division between classical and quantum: everything is quantum and there is no collapse. MWI's main conclusion is that the universe (or [[multiverse]] in this context) is composed of a [[quantum superposition]] of an uncountable<ref name="Heresy"/> or undefinable<ref name=wallace2010/>{{rp|14–17}} amount or number of increasingly divergent, non-communicating parallel universes or quantum worlds.<ref name=dewitt73/> Sometimes dubbed Everett worlds,<ref name=dewitt73/>{{rp|234}} each is an internally consistent and actualized [[alternative history]] or timeline.

The many-worlds interpretation uses [[decoherence]] to explain the measurement process and the emergence of a quasi-classical world.<ref name=wallace2010/><ref name=saunders2010/> [[Wojciech H. Zurek]], one of decoherence [[theory]]'s pioneers, said: "Under scrutiny of the environment, only [[pointer state]]s remain unchanged. Other states decohere into mixtures of stable pointer states that can persist, and, in this sense, exist: They are einselected."<ref name="ZurekNature2009">{{cite journal | last = Zurek | first = Wojciech | author-link = Wojciech Hubert Zurek | title = Quantum Darwinism | date = March 2009 | arxiv = 0903.5082 |bibcode = 2009NatPh...5..181Z |doi = 10.1038/nphys1202 | volume=5 | issue=3 | journal=Nature Physics | pages=181–188| s2cid = 119205282 }}</ref> Zurek emphasizes that his work does not depend on a particular interpretation.{{efn|"Relative states of Everett come to mind. One could speculate about reality of branches with other outcomes. We abstain from this; our discussion is interpretation-free, and this is a virtue."<ref name=ZurekNature2009/>}}

The many-worlds interpretation shares many similarities with the [[decoherent histories]] interpretation, which also uses decoherence to explain the process of measurement or wave function collapse.<ref name=saunders2010/>{{rp|9–11}} MWI treats the other histories or worlds as real, since it regards the universal wave function as the "basic physical entity"<ref name=everett57/>{{rp|455}} or "the fundamental entity, obeying at all times a deterministic wave equation".<ref name="everett56"/>{{rp|115}} The decoherent histories interpretation, on the other hand, needs only one of the histories (or worlds) to be real.<ref name=saunders2010/>{{rp|10}}

Several authors, including Everett, [[John Archibald Wheeler]] and [[David Deutsch]], call many-worlds a theory or [[metatheory]], rather than just an interpretation.<ref name="Heresy"/><ref name=skyrms1976/>{{rp|328}} Everett argued that it was the "only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world."<ref>{{Citation |last=Everett |first=Hugh |title=Hugh Everett letter to David Raub, 7-April-1980 |date=1980-04-07 |url=https://calisphere.org/item/ark:/81235/d83t9dk9g/ |access-date=2023-08-26}}</ref> Deutsch dismissed the idea that many-worlds is an "interpretation", saying that to call it an interpretation "is like talking about dinosaurs as an 'interpretation' of fossil records".<ref name="MAD"/>{{rp|382}}

=== Formulation ===
In his 1957 doctoral dissertation, Everett proposed that, rather than relying on external observation for analysis of isolated quantum systems, one could mathematically model an object, as well as its observers, as purely physical systems within the mathematical framework developed by [[Paul Dirac]], [[John von Neumann]], and others, discarding altogether the ''ad hoc'' mechanism of [[wave function collapse]].<ref name=everett56/><ref name=dewitt73/>

=== Relative state ===
Everett's original work introduced the concept of a ''relative state''. Two (or more) subsystems, after a general interaction, become ''correlated'', or as is now said, [[quantum entanglement|entangled]]. Everett noted that such entangled systems can be expressed as the sum of products of states, where the two or more subsystems are each in a state relative to each other. After a measurement or observation one of the pair (or triple, etc.) is the measured, object or observed system, and one other member is the measuring apparatus (which may include an observer) having recorded the state of the measured system. Each product of subsystem states in the overall superposition evolves over time independently of other products. Once the subsystems interact, their states have become correlated or entangled and can no longer be considered independent. In Everett's terminology, each subsystem state was now ''correlated'' with its ''relative state'', since each subsystem must now be considered relative to the other subsystems with which it has interacted.

In the example of [[Schrödinger's cat]], after the box is opened, the entangled system is the cat, the poison vial and the observer. ''One'' relative triple of states would be the alive cat, the unbroken vial and the observer seeing an alive cat. ''Another'' relative triple of states would be the dead cat, the broken vial and the observer seeing a dead cat.

In the example of a measurement of a continuous variable (e.g., position ''q'') the object-observer system decomposes into a continuum of pairs of relative states: the object system's relative state becomes a [[Dirac delta function]] each centered on a particular value of ''q'' and the corresponding observer relative state representing an observer having recorded the value of ''q''.<ref name="everett56"/>{{rp|57–64}} The states of the pairs of relative states are, post measurement, ''correlated'' with each other.

In Everett's scheme, there is no collapse; instead, the [[Schrödinger equation]], or its [[quantum field theory]], relativistic analog, holds all the time, everywhere. An observation or measurement is modeled by applying the wave equation to the entire system, comprising the object being observed ''and'' the observer. One consequence is that every observation causes the combined observer–object's wavefunction to change into a quantum superposition of two or more non-interacting branches.

Thus the process of measurement or observation, or any correlation-inducing interaction, splits the system into sets of relative states, where each set of relative states, forming a branch of the universal wave function, is consistent within itself, and all future measurements (including by multiple observers) will confirm this consistency.

=== Renamed many-worlds ===
Everett had referred to the combined observer–object system as split by an observation, each split corresponding to the different or multiple possible outcomes of an observation. These splits generate a branching tree, where each branch is a set of all the states relative to each other. [[Bryce DeWitt]] popularized Everett's work with a series of publications calling it the Many Worlds Interpretation. Focusing on the splitting process, DeWitt introduced the term "world" to describe a single branch of that tree, which is a consistent history. All observations or measurements within any branch are consistent within themselves.<ref name=everett56/><ref name=dewitt73/>

Since many observation-like events have happened and are constantly happening, Everett's model implies that there are an enormous and growing number of simultaneously existing states or "worlds".{{efn|"every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth into myriads of copies of itself."<ref name=dewitt71/> DeWitt later softened this extreme view, viewing splitting as decoherence driven and local, in line with other modern commentators.<ref>{{Cite book |url=https://www.degruyter.com/document/doi/10.1515/9781400842742/html |title=The Everett Interpretation of Quantum Mechanics: Collected Works 1955-1980 with Commentary |date=2012-05-20 |publisher=Princeton University Press |isbn=978-1-4008-4274-2 |editor-last=Barrett |editor-first=Jeffrey A. |doi=10.1515/9781400842742 |quote=DeWitt eventually softened his view on the necessity of a splitting universe occurring with every atomic interaction when he broadly embraced the decoherence approaches proposed by Dieter Zeh, Wojciech Zurek, James B. Hartle, Murray Gell-Mann, and others beginning around 1970. |editor-last2=Byrne |editor-first2=Peter}}  </ref>}}

=== Properties ===

MWI removes the observer-dependent role in the [[quantum measurement]] process by replacing [[wave function collapse]] with the established mechanism of [[quantum decoherence]].<ref>{{cite journal|doi=10.1016/j.physrep.2019.10.001 |first=Max |last=Schlosshauer |title=Quantum decoherence |journal=Physics Reports |volume=831 |date=2019-10-25 |pages=1–57 |arxiv=1911.06282|bibcode=2019PhR...831....1S |s2cid=208006050 }}</ref> As the observer's role lies at the heart of all "quantum paradoxes" such as the [[EPR paradox]] and von Neumann's "boundary problem", this provides a clearer and easier approach to their resolution.<ref name=everett57/>

Since the Copenhagen interpretation requires the existence of a classical domain beyond the one described by quantum mechanics, it has been criticized as inadequate for the study of cosmology.<ref name="gell-man1990"/> While there is no evidence that Everett was inspired by issues of cosmology,<ref name="Heresy"/>{{rp|7}} he developed his theory with the explicit goal of allowing quantum mechanics to be applied to the universe as a whole, hoping to stimulate the discovery of new phenomena.<ref name=everett57/> This hope has been realized in the later development of [[quantum cosmology]].<ref>{{Cite book |last1=Gell-Mann |first1=Murray |last2=Hartle |first2=James B. |date=January 1997 |title=Quantum Mechanics in the Light of Quantum Cosmology |url=http://www.worldscientific.com/doi/abs/10.1142/9789812819895_0036 |language=en |publisher=World Scientific |volume=4 |pages=347–369 |doi=10.1142/9789812819895_0036 |isbn=978-981-02-2844-6}}</ref>

MWI is a [[philosophical realism|realist]], [[deterministic]] and [[principle of locality|local]] theory. It achieves this by removing wave function collapse, which is indeterministic and nonlocal, from the deterministic and local equations of quantum theory.<ref name="DeterminismLocal"/>

MWI (like other, broader multiverse theories) provides a context for the [[anthropic principle]], which may provide an explanation for the [[fine-tuned universe]].<ref>[[Paul C.W. Davies|Paul C. W. Davies]], ''Other Worlds'', chapters 8 & 9 ''The Anthropic Principle'' & ''Is the Universe an accident?'', (1980) {{ISBN|0-460-04400-1}}.</ref><ref>[[Paul C.W. Davies|Paul C. W. Davies]], ''The Accidental Universe'', (1982) {{ISBN|0-521-28692-1}}.</ref>

MWI depends crucially on the [[linear combination|linearity]] of quantum mechanics, which underpins the [[quantum superposition|superposition principle]]. If the final [[theory of everything]] is non-linear with respect to wavefunctions, then many-worlds is invalid.<ref name="dewitt71"/><ref name="dewitt73"/><ref name="everett57"/><ref name="dewitt67"/><ref name="dewitt72"/> All [[quantum field theory|quantum field theories]] are linear and compatible with the MWI, a point Everett emphasized as a motivation for the MWI.<ref name="everett57"/> While quantum gravity or [[string theory]] may be non-linear in this respect,<ref name="penrose"/> there is as yet no evidence of this.<ref name="weinberglinearitydoft">[[Steven Weinberg]], ''Dreams of a Final Theory: The Search for the Fundamental Laws of Nature'' (1993), {{ISBN|0-09-922391-0}}, pp. 68–69.</ref><ref name="weinberglinearityannalsop">[[Steven Weinberg]]. ''Testing Quantum Mechanics'', Annals of Physics Vol. 194, #2 (1989), pp. 336–386.</ref>

Weingarten<ref>{{cite journal|first1=Don|last1=Weingarten|title=Macroscopic Reality from Quantum Complexity|url=https://link.springer.com/article/10.1007/s10701-022-00554-0|journal=Foundations of Physics|date=5 April 2022|issn=1572-9516|pages=45|volume=52|issue=2|doi=10.1007/s10701-022-00554-0|arxiv=2105.04545}}</ref> and Taylor & McCulloch<ref>{{cite journal|first1=Jordan|last1=Taylor|first2=Ian|last2=McCulloch|title=Wavefunction branching: when you can’t tell pure states from mixed states|url=https://quantum-journal.org/papers/q-2025-03-25-1670/|journal=Quantum|date=25 March 2025|issn=2521-327X|pages=1670|volume=9|doi=10.22331/q-2025-03-25-1670|arxiv=2308.04494}}</ref> have made separate proposals for how to define wavefunction branches in terms of quantum circuit [[Quantum_complexity_theory|complexity]].

=== Alternative to wavefunction collapse ===
As with the other interpretations of quantum mechanics, the many-worlds interpretation is motivated by behavior that can be illustrated by the [[double-slit experiment]]. When [[photon|particles of light]] (or anything else) pass through the double slit, a calculation assuming wavelike behavior of light can be used to identify where the particles are likely to be observed. Yet when the particles are observed in this experiment, they appear as particles (i.e., at definite places) and not as non-localized waves.

Some versions of the Copenhagen interpretation of quantum mechanics proposed a process of "collapse" in which an indeterminate quantum system would probabilistically collapse onto, or select, just one determinate outcome to "explain" this phenomenon of observation. Wave function collapse was widely regarded as artificial and ''[[ad hoc]]'',<ref>{{Cite book |last=Wimmel |first=Hermann |url=https://books.google.com/books?id=I63sCgAAQBAJ |title=Quantum Physics And Observed Reality: A Critical Interpretation Of Quantum Mechanics |date=1992-05-26 |publisher=World Scientific |isbn=978-981-4505-46-8 |pages=45 |language=en}}</ref> so an alternative interpretation in which the behavior of measurement could be understood from more fundamental physical principles was considered desirable.

Everett's PhD work provided such an interpretation. He argued that for a composite system—such as a subject (the "observer" or measuring apparatus) observing an object (the "observed" system, such as a particle)—the claim that either the observer or the observed has a well-defined state is meaningless; in modern parlance, the observer and the observed have become entangled: we can only specify the state of one ''relative'' to the other, i.e., the state of the observer and the observed are correlated ''after'' the observation is made. This led Everett to derive from the unitary, deterministic dynamics alone (i.e., without assuming wave function collapse) the notion of a ''relativity of states''.

Everett noticed that the unitary, deterministic dynamics alone entailed that after an observation is made each element of the [[quantum superposition]] of the combined subject–object wave function contains two "relative states": a "collapsed" object state and an associated observer who has observed the same collapsed outcome; what the observer sees and the state of the object have become correlated by the act of measurement or observation. The subsequent evolution of each pair of relative subject–object states proceeds with complete indifference as to the presence or absence of the other elements, ''as if'' wave function collapse has occurred,<ref name=dewitt73/>{{rp|67,78}} which has the consequence that later observations are always consistent with the earlier observations. Thus the ''appearance'' of the object's wave function's collapse has emerged from the unitary, deterministic theory itself. (This answered Einstein's early criticism of quantum theory: that the theory should define what is observed, not for the observables to define the theory.){{efn|"Whether you can observe a thing or not depends on the theory which you use. It is the theory which decides what can be observed."—[[Albert Einstein]] to [[Werner Heisenberg]], objecting to placing observables at the heart of the new quantum mechanics, during Heisenberg's 1926 lecture at Berlin; related by Heisenberg in 1968.<ref name="einstein26">[[Abdus Salam]], ''Unification of Fundamental Forces'', Cambridge University Press (1990) {{ISBN|0-521-37140-6}}, pp 98–101</ref>}} Since the wave function ''appears'' to have collapsed then, Everett reasoned, there was no need to actually assume that it ''had'' collapsed. And so, invoking [[Occam's razor]], he removed the postulate of wave function collapse from the theory.<ref name=dewitt73/>{{rp|8}}

=== Testability ===

In 1985, [[David Deutsch]] proposed a variant of the [[Wigner's friend]] thought experiment as a test of many-worlds versus the Copenhagen interpretation.<ref name="deutsch1985">{{cite journal|last=Deutsch |first=D. |author-link=David Deutsch |year=1985 |title=Quantum theory as a universal physical theory |journal=[[International Journal of Theoretical Physics]] |volume=24 |number=1 |pages=1–41 |doi=10.1007/BF00670071 |bibcode=1985IJTP...24....1D|s2cid=17530632 }}</ref> It consists of an experimenter (Wigner's friend) making a measurement on a quantum system in an isolated laboratory, and another experimenter (Wigner) who would make a measurement on the first one. According to the many-worlds theory, the first experimenter would end up in a macroscopic superposition of seeing one result of the measurement in one branch, and another result in another branch. The second experimenter could then interfere these two branches in order to test whether it is in fact in a macroscopic superposition or has collapsed into a single branch, as predicted by the Copenhagen interpretation. Since then Lockwood, Vaidman, and others have made similar proposals,<ref name="vaidman_stanfordencyclopedia">{{cite book |last=Vaidman |first=Lev |title=Many-Worlds Interpretation of Quantum Mechanics |url=http://plato.stanford.edu/entries/qm-manyworlds/ |publisher=The Stanford Encyclopedia of Philosophy|year=2018 }}</ref> which require placing macroscopic objects in a coherent superposition and interfering them, a task currently beyond experimental capability.