Manyworlds is an interpretation of quantum mechanics that asserts the objective reality of the wavefunction, but denies the reality of wavefunction collapse. It is also known as MWI, the relative state formulation, theory of the universal wavefunction, parallel universes, manyuniverses interpretation or just many worlds.
The original relative state formulation is due to Hugh Everett ^{[2]}^{[3]} who formulated it in 1957. Later, this formulation was popularized and renamed manyworlds by Bryce Seligman DeWitt in the 1960s and '70s.^{[1]}^{[4]}^{[5]}^{[6]}
Proponents argue that manyworlds reconciles how we can perceive nondeterministic events, such as the random decay of a radioactive atom, with the deterministic equations of quantum physics. Prior to manyworlds, reality had been viewed as a single "worldline". Manyworlds, rather, views reality as a manybranched tree where every possible quantum outcome is realised.
In manyworlds, the subjective appearance of wavefunction collapse is explained by the mechanism of quantum decoherence. By decoherence, manyworlds claims to resolve all of the correlation paradoxes of quantum theory, such as the EPR paradox^{[7]}^{[8]} and Schrödinger's cat,^{[1]} since every possible outcome of every event defines or exists in its own "history" or "world". In layman's terms, there is a very large—perhaps infinite^{[9]}—number of universes, and everything that could possibly have happened in our past, but didn't, has occurred in the past of some other universe or universes.
The decoherence approach to interpreting quantum theory has been further explored and developed^{[10]}^{[11]}^{[12]} becoming quite popular, taken as a class overall. MWI is one of many Multiverse hypotheses in physics and philosophy. It is currently considered a mainstream interpretation along with the other decoherence interpretations and the Copenhagen interpretation.
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Although several versions of manyworlds have been proposed since Hugh Everett's original work,^{[3]} they all contain one key idea: the equations of physics that model the time evolution of systems without embedded observers are sufficient for modelling systems which do contain observers; in particular there is no observationtriggered wavefunction collapse which the Copenhagen interpretation proposes. Provided the theory is linear with respect to the wavefunction, the exact form of the quantum dynamics modelled, be it the nonrelativistic Schrödinger equation, relativistic quantum field theory or some form of quantum gravity or string theory, does not alter the validity of MWI since MWI is a metatheory applicable to all linear quantum theories, and there is no experimental evidence for any nonlinearity of the wavefunction in physics.^{[13]}^{[14 ]} MWI's main conclusion is that the universe (or multiverse in this context) is composed of a quantum superposition of very many, possibly even a nondenumerablely infinitely^{[9]} many, increasingly divergent, noncommunicating parallel universes or quantum worlds.^{[6]}
The idea of MWI originated in Everett's Princeton Ph.D. thesis "The Theory of the Universal Wavefunction",^{[6]} developed under his thesis advisor John Archibald Wheeler, a shorter summary of which was published in 1957 entitled "Relative State Formulation of Quantum Mechanics" (Wheeler contributed the title "relative state";^{[15]} Everett originally called his approach the "Correlation Interpretation", where "correlation" refers to quantum entanglement). The phrase "manyworlds" is due to Bryce DeWitt,^{[6]} who was responsible for the wider popularisation of Everett's theory, which had been largely ignored for the first decade after publication. DeWitt's phrase "manyworlds" has become so much more popular than Everett's "Universal Wavefunction" or EverettWheeler's "Relative State Formulation" that many forget that this is only a difference of terminology; the content of all three papers is the same.
The manyworlds interpretation shares many similarities with later, other "postEverett" interpretations of quantum mechanics which also use decoherence to explain the process of measurement or wavefunction collapse. MWI treats the other histories or worlds as real since it regards the universal wavefunction as the "basic physical entity"^{[16]} or "the fundamental entity, obeying at all times a deterministic wave equation".^{[17]} The other decoherent interpretations, such as many histories, consistent histories, the Existential Interpretation etc, either regard the extra quantum worlds as metaphorical in some sense, or are agnostic about their reality; it is sometimes hard to distinguish between the different varieties. MWI is distinguished by two qualities: it assumes realism,^{[16]}^{[17]} which it assigns to the wavefunction, and it has the minimal formal structure possible, rejecting any hidden variables, quantum potential, any form of a collapse postulate (i.e. Copenhagenism) or mental postulates (such as the manyminds interpretation makes).
Decoherent interpretations of manyworlds use einselection to explain how a small number of classical pointer states can emerge from the enormous Hilbert space of superpositions have been proposed by Wojciech H. Zurek. "Under scrutiny of the environment, only pointer states remain unchanged. Other states decohere into mixtures of stable pointer states that can persist, and, in this sense, exist: They are einselected."^{[18]} These ideas complement MWI and bring the interpretation in line with our perception of reality.
Manyworlds is often referred to as a theory, rather than just an interpretation, by those who propose that manyworlds can make testable predictions (such as David Deutsch) or is falsifiable (such as Everett) or that all the other, nonMWI, are inconsistent, illogical or unscientific in their handling of measurements; Hugh Everett argued that his formulation was a metatheory, since it made statements about other interpretations of quantum theory; that it was the "only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world."^{[19]}
As with the other interpretations of quantum mechanics, the manyworlds interpretation is motivated by behavior that can be illustrated by the doubleslit experiment. When particles of light (or anything else) are passed 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 nonlocalized waves.
Some versions of the Copenhagen interpretation of quantum mechanics proposed a process of "collapse" in which an indeterminate quantum system would probabilistically collapse down onto, or select, just one determinate outcome to "explain" this phenomenon of observation. Wavefunction collapse was widely regarded as artificial and adhoc, so an alternative interpretation in which the behavior of measurement could be understood from more fundamental physical principles was considered desirable.
Everett's Ph.D. work provided such an alternative interpretation. Everett noted that for a composite system – for example a subject (the "observer" or measuring apparatus) observing an object (the "observed" system, such as a particle) – the statement that either the observer or the observed has a welldefined 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 wavefunction collapse) the notion of a relativity of states.
Everett noticed that the unitary, deterministic dynamics alone decreed that after an observation is made each element of the quantum superposition of the combined subjectobject wavefunction 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 subjectobject states proceeds with complete indifference as to the presence or absence of the other elements, as if wavefunction collapse has occurred, which has the consequence that later observations are always consistent with the earlier observations. Thus the appearance of the object's wavefunction'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).^{[20]} Since the wavefunction 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 wavefunction collapse from the theory.
A consequence of removing wavefunction collapse from the quantum formalism is that the Born rule requires derivation, since manyworlds claims to derive its interpretation from the formalism. Attempts have been made, by manyworld advocates and others, over the years to derive the Born rule, rather than just conventionally assume it, so as to reproduce all the required statistical behaviour associated with quantum mechanics. There is no consensus on whether this has been successful.^{[21]}^{[22]}^{[23]}
Everett (1957) briefly derived the Born rule by showing that the Born rule was the only possible rule, and that its derivation was as justified as the procedure for defining probability in classical mechanics. Everett stopped doing research in theoretical physics shortly after obtaining his Ph.D., but his work on probability has been extended by a number of people. Andrew Gleason (1957) and James Hartle (1965) independently reproduced Everett's work, known as Gleason's theorem^{[24]}^{[25]} which was later extended.^{[26]}^{[27]}
Bryce De Witt and his doctoral student R. Neill Graham later provided alternative (and longer) derivations to Everett's derivation of the Born rule. They demonstrated that the norm of the worlds where the usual statistical rules of quantum theory broke down vanished, in the limit where the number of measurements went to infinity.
An informationtheoretic derivation of the Born rule from Everettarian assumptions, was produced by David Deutsch (1999)^{[28]} and refined by Wallace (20022009)^{[29]}^{[30]}^{[31]}^{[32]} and Saunders (2004).^{[33]}^{[34]} Deutsch's derivation is a twostage proof: first he shows that the number of orthonormal Everettworlds after a branching is proportional to the conventional probability density. Then he uses game theory to shows that these are all equally likely to be observed. The last step in particular has been criticised for circularity.^{[35]}^{[36]} Other reviews have been positive, although the status of these arguments remains highly controversial. It is fair to say that some theoretical physicists have taken them as supporting the case for parallel universes.^{[37]}^{[38]} In the New Scientist article, reviewing their presentation at a September 2007 conference^{[39]}^{[40]}, Andy Albrecht, a physicist at the University of California at Davis, is quoted as saying "This work will go down as one of the most important developments in the history of science."^{[37]}
Wojciech H. Zurek (2005)^{[41]} has produced a derivation of the Born rule, where decoherence has replaced Deutsch's informatic assumptions.^{[42]} Lutz Polley (2000) has produced Born rule derivations where the informatic assumptions are replaced by symmetry arguments.^{[43]}^{[44]}
In Everett's formulation, a measuring apparatus M and an object system S form a composite system, each of which prior to measurement exists in welldefined (but timedependent) states. Measurement is regarded as causing M and S to interact. After S interacts with M, it is no longer possible to describe either system by an independent state. According to Everett, the only meaningful descriptions of each system are relative states: for example the relative state of S given the state of M or the relative state of M given the state of S. In DeWitt's formulation, the state of S after a sequence of measurements is given by a quantum superposition of states, each one corresponding to an alternative measurement history of S.
For example, consider the smallest possible truly quantum system S, as shown in the illustration. This describes for instance, the spinstate of an electron. Considering a specific axis (say the zaxis) the north pole represents spin "up" and the south pole, spin "down". The superposition states of the system are described by (the surface of) a sphere called the Bloch sphere. To perform a measurement on S, it is made to interact with another similar system M. After the interaction, the combined system is described by a state that ranges over a sixdimensional space (the reason for the number six is explained in the article on the Bloch sphere). This sixdimensional object can also be regarded as a quantum superposition of two "alternative histories" of the original system S, one in which "up" was observed and the other in which "down" was observed. Each subsequent binary measurement (that is interaction with a system M) causes a similar split in the history tree. Thus after three measurements, the system can be regarded as a quantum superposition of 8= 2 × 2 × 2 copies of the original system S.
The accepted terminology is somewhat misleading because it is incorrect to regard the universe as splitting at certain times; at any given instant there is one state in one universe.
The goal of the relativestate formalism, as originally proposed by Everett in his 1957 doctoral dissertation, was to interpret the effect of external observation entirely within the mathematical framework developed by Paul Dirac, von Neumann and others, discarding altogether the adhoc mechanism of wave function collapse. Since Everett's original work, there have appeared a number of similar formalisms in the literature. One such idea is discussed in the next section.
The relativestate interpretation makes two assumptions. The first is that the wavefunction is not simply a description of the object's state, but that it actually is entirely equivalent to the object, a claim it has in common with some other interpretations. The second is that observation or measurement has no special role, unlike in the Copenhagen interpretation which considers the wavefunction collapse as a special kind of event which occurs as a result of observation.
The manyworlds interpretation is DeWitt's popularisation of Everett's work, who had referred to the combined observerobject system as being split by an observation, each split corresponding to the different or multiple possible outcomes of an observation. These splits generate a possible tree as shown in the graphic below. Subsequently DeWitt introduced the term "world" to describe a complete measurement history of an observer, which corresponds roughly to a single branch of that tree. Note that "splitting" in this sense, is hardly new or even quantum mechanical. The idea of a space of complete alternative histories had already been used in the theory of probability since the mid 1930s for instance to model Brownian motion.
Under the manyworlds interpretation, the Schrödinger equation, or relativistic analog, holds all the time everywhere. An observation or measurement of an object by an observer is modeled by applying the wave equation to the entire system comprising the observer and the object. One consequence is that every observation can be thought of as causing the combined observerobject's wavefunction to change into a quantum superposition of two or more noninteracting branches, or split into many "worlds". Since many observationlike events have happened, and are constantly happening, there are an enormous and growing number of simultaneously existing states.
If a system is composed of two or more subsystems, the system's state will be a superposition of products of the subsystems' states. Once the subsystems interact, their states are no longer independent. Each product of subsystem states in the overall superposition evolves over time independently of other products. The subsystems states have become correlated or entangled and it is no longer possible to consider them independent of one another. 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.
One of the salient properties of the manyworlds interpretation is that observation does not require an exceptional construct (such as wave function collapse) to explain it. Many physicists, however, dislike the implication that there are infinitely many nonobservable alternate universes.
as of 2006, there are no practical experiments that distinguish between ManyWorlds and Copenhagen. There may be cosmological, observational evidence.
In the Copenhagen interpretation, the mathematics of quantum mechanics allows one to predict probabilities for the occurrence of various events. In the manyworlds interpretation, all these events occur simultaneously. What meaning should be given to these probability calculations? And why do we observe, in our history, that the events with a higher computed probability seem to have occurred more often? One answer to these questions is to say that there is a probability measure on the space of all possible universes, where a possible universe is a complete path in the tree of branching universes. This is indeed what the calculations give. Then we should expect to find ourselves in a universe with a relatively high probability rather than a relatively low probability: even though all outcomes of an experiment occur, they do not occur in an equal way. As an interpretation which (like other interpretations) is consistent with the equations, it is hard to find testable predictions of MWI.
There is a rather more dramatic test than the one outlined above for people prepared to put their lives on the line: use a machine which kills them if a random quantum decay happens. If MWI is true, they will still be alive in the world where the decay didn't happen and would feel no interruption in their stream of consciousness. By repeating this process a number of times, their continued consciousness would be arbitrarily unlikely unless MWI was true, when they would be alive in all the worlds where the random decay was on their side. From their viewpoint they would be immune to this death process. Clearly, if MWI does not hold, they would be dead in the one world. Other people would generally just see them die and would not be able to benefit from the result of this experiment. See Quantum suicide.
Any event that changes the number of observers in the universe may have experimental consequences.^{[62]} Quantum tunnelling to new vacuum state would reduce the number of observers to zero (i.e. kill all life). Some Cosmologists argue that the universe is in a false vacuum state and that consequently the universe should have already experienced quantum tunnelling to a true vacuum state. This has not happened and is cited as evidence in favour of manyworlds.
The manyworlds interpretation should not be confused with the similar manyminds interpretation which defines the split on the level of the observers' minds.
There is a wide range of claims that are considered "manyworlds" interpretations. It is often claimed by those who do not believe in MWI^{[63]} that Everett himself was not entirely clear as to what he believed; however MWI adherents (such as DeWitt, Tegmark, Deutsch and others) believe they fully understand Everett's meaning as implying the literal existence of the other worlds. Additionally Everett's reported belief in quantum immortality, requires belief in the reality of all the manyworlds represented by the components of the uncollapsed universal wavefunction.^{[64]}
"Manyworlds"like interpretations are now considered fairly mainstream within the quantum physics community. For example, a poll of 72 leading physicists conducted by the American researcher David Raub in 1995 and published in the French periodical Sciences et Avenir in January 1998 recorded that nearly 60% thought that the manyworlds interpretation was "true". Max Tegmark also reports the result of a poll taken at a 1997 quantum mechanics workshop.^{[65]} According to Tegmark, "The many worlds interpretation (MWI) scored second, comfortably ahead of the consistent histories and Bohm interpretations." Other such polls have been taken at other conferences: see for instance Michael Nielsen's blog^{[66]} report on one such poll. Nielsen remarks that it appeared most of the conference attendees "thought the poll was a waste of time". MWI sceptics (for instance Asher Peres) argue that polls regarding the acceptance of a particular interpretation within the scientific community, such as those mentioned above, cannot be used as evidence supporting a specific interpretation's validity. However, others note that science is a group activity (for instance, peer review) and that polls are a systematic way of revealing the thinking of the scientific community.
A 2005 minor poll on the Interpretation of Quantum Mechanics workshop at the Institute for Quantum Computing University of Waterloo produced contrary results, with the MWI as the least favored.^{[67]}
One of MWI's strongest advocates is David Deutsch.^{[68]} According to Deutsch, the single photon interference pattern observed in the double slit experiment can be explained by interference of photons in multiple universes. Viewed in this way, the single photon interference experiment is indistinguishable from the multiple photon interference experiment. In a more practical vein, in one of the earliest papers on quantum computing,^{[69]} he suggested that parallelism that results from the validity of MWI could lead to "a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it". Deutsch has also proposed that when reversible computers become conscious that MWI will be testable (at least against "naive" Copenhagenism) via the reversible observation of spin.^{[51]}
Asher Peres was an outspoken critic of MWI, for example in a section in his 1993 textbook with the title Everett's interpretation and other bizarre theories. In fact, Peres questioned whether MWI is really an "interpretation" or even if interpretations of quantum mechanics are needed at all. Indeed, the manyworlds interpretation can be regarded as a purely formal transformation, which adds nothing to the instrumentalist (i.e. statistical) rules of the quantum mechanics. Perhaps more significantly, Peres seems to suggest that positing the existence of an infinite number of noncommunicating parallel universes is highly suspect as it violates those interpretations of Occam's Razor that seek to minimize the number of hypothesized entities. Proponents of MWI argue precisely the opposite, by applying Occam's Razor to the set of assumptions rather than multiplicity of universes. In Max Tegmark's formulation, the alternative to manyworlds is the undesirable "many words", an allusion to the complexity of von Neumann's collapse postulate.
MWI is considered by some to be unfalsifiable and hence unscientific because the multiple parallel universes are noncommunicating, in the sense that no information can be passed between them. Others^{[51]} claim MWI is directly testable. Everett regarded MWI as falsifiable since any test that falsifies conventional quantum theory would also falsify MWI.^{[19]}
According to Martin Gardner, MWI has two different interpretations: real or unreal, and claims that Stephen Hawking and Steve Weinberg favour the unreal interpretation.^{[70]} Gardner also claims that the interpretation favoured by the majority of physicists is that the other worlds are not real in the same way as our world is real, whereas the "realist" view is supported by MWI experts David Deutsch and Bryce DeWitt. However Stephen Hawking is on record as a saying that the "other worlds are as real as ours"^{[71]} and Tipler reports Hawking saying that MWI is "trivially true" (scientific jargon for "obviously true") if quantum theory applies to all reality.^{[72]} Roger Penrose agrees with Hawking that QM applied to the universe implies MW, although he considers the current lack of a successful theory of quantum gravity negates the claimed universality of conventional QM.^{[58]}
Speculative physics deals with questions also discussed in science fiction.
It has been claimed that there is a thought experiment that would clearly differentiate between the manyworlds interpretation and other interpretations of quantum mechanics. It involves a quantum suicide machine and an experimenter willing to risk death. However, at best, this would only decide the issue for the experimenter; bystanders would learn nothing. The flip side of quantum suicide is quantum immortality.
Another speculation is that the separate worlds remain weakly coupled (e.g. by gravity) permitting "communication between parallel universes". This requires that gravity be a classical force and not quantized.
The manyworlds interpretation has some similarity to modal realism in philosophy, which is the view that the possible worlds used to interpret modal claims actually exist. Unlike philosophy, however, in quantum mechanics counterfactual alternatives can influence the results of experiments, as in the ElitzurVaidman bombtesting problem or the Quantum Zeno effect.
The manyworlds interpretation could be one possible way to resolve the paradoxes ^{[68]} that one would expect to arise if time travel turns out to be permitted by physics (permitting closed timelike curves and thus violating causality). Entering the past would itself be a quantum event causing branching, and therefore the timeline accessed by the time traveller simply would be another timeline of many. In that sense, it would make the Novikov selfconsistency principle unnecessary.
The manyworlds interpretation (and the somewhat related concept of possible worlds) has been associated to numerous themes in literature, art and science fiction.
Some of these stories or films violate fundamental principles of causality and relativity, and are extremely misleading since the informationtheoretic structure of the path space of multiple universes (that is information flow between different paths) is very likely extraordinarily complex. Also see Michael Clive Price's FAQ referenced in the external links section below where these issues (and other similar ones) are dealt with more decisively.
Another kind of popular illustration of manyworlds splittings, which does not involve information flow between paths, or information flow backwards in time considers alternate outcomes of historical events. According to the manyworlds interpretation, all of the historical speculations entertained within the alternate history genre are realized in parallel universes.^{[1]}

