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The Many-Worlds Interpretation (MWI) of quantum mechanics holds thatthere are many worlds which exist in parallel at the same space andtime as our own. The existence of the other worlds makes it possibleto remove randomness and action at a distance from quantum theory andthus from all physics. The MWI provides a solution to the measurement problem of quantum mechanics.

The fundamental idea of the MWI, going back to Everett 1957, is thatthere are myriads of worlds in the Universe in addition to the worldwe are aware of. In particular, every time a quantum experiment withdifferent possible outcomes is performed, all outcomes are obtained,each in a different newly created world, even if we are only aware ofthe world with the outcome we have seen. The reader can split theworld right now using this interactive quantum world splitter. The creation of worlds takes place everywhere, not just in physicslaboratories, for example, the explosion of a star during asupernova.

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There are two aspects of the measure of existence of a world. First,it quantifies the ability of the world to interfere with other worldsin a gedanken experiment, as expounded at the end of this section.Second, the measure of existence is the basis for introducing anillusion of probability in the MWI as described in the nextchapter. The measure of existence is the parallel of the probabilitymeasure discussed in Everett 1957 and pictorially described inLockwood 1989 (p. 230).

The probability in the MWI cannot be introduced in a simple way as inquantum theory with collapse. However, even if there is no probabilityin the MWI, it is possible to explain our illusion of apparentprobabilistic events. Due to the identity of the mathematicalcounterparts of worlds, we should not expect any difference betweenour experience in a particular world of the MWI and the experience ina single-world universe with collapse at every quantummeasurement.

Sebens and Carroll 2018 provided a proof of the Probability Postulatebased on symmetry considerations in the framework of the self-locationuncertainty of Vaidman 1998. However Kent 2015 and McQueen and Vaidman2019 argued that their proof fails because it starts with ameaningless question. The proof considers a situation as in a sleepingpill experiment presented above: I was asleep during a quantummeasurement, but unlike the original proposal, there was not any changein my state. I was not moved to different rooms according to theresults of the experiment. Still, the question is asked: What is theprobability for me to be in a world with a particular outcome? Whetherthat question can be meaningfully asked depends on whether I havebranched. The critics argue that, although there are separate worlds,I have not yet branched and thus the question is not meaningful (atthis stage, I am in both worlds). The Sebens and Carroll proof mightget off the ground if the program of diverging worlds Saunders 2010,forthcoming-b succeeds. Note also that Dawid and Friederich 2020 criticiseSebens and Carroll 2018 on other grounds.

A popular criticism of the MWI in the past, see Belinfante 1975, whichwas repeated by Putnam 2005, is based on the naive derivation of theprobability of an outcome of a quantum experiment as beingproportional to the number of worlds with this outcome. Such aderivation leads to the wrong predictions, but accepting the idea ofprobability being proportional to the measure of existence of a worldresolves this problem. Although this involves adding a postulate, wedo not complicate the mathematical part (i) of the theory since we donot change the ontology, namely, the wave function. It is a postulatebelonging to part (ii), the connection to our experience, and it is avery natural postulate: differences in the mathematical descriptionsof worlds are manifest in our experience, see Saunders 1998.

There are claims that a believer in the MWI will behave in anirrational way. One claim is based on the naive argument described inthe previous section: a believer who assigns equal probabilities toall different worlds will make equal bets for the outcomes of quantumexperiments that have unequal probabilities.

Another claim, Lewis 2000, is related to the strategy of a believer inthe MWI who is offered to play a quantum Russian roulettegame. The argument is that I, who would not accept an offer to play aclassical Russian roulette game, should agree to play the roulette anynumber of times if the triggering occurs according to the outcome of aquantum experiment. Indeed, at the end, there will be one world inwhich Lev is a multi-millionaire and in all other worlds there will beno Lev Vaidman alive. Thus, in the future, Lev will be a rich andpresumably happy man.

However, adopting the Probability Postulate leads all believers in theMWI to behave according to the Behavior Principle and with thisprinciple our behavior is similar to the behavior of a believer in thecollapse theory who cares about possible future worlds according tothe probability of their occurrence. I should not agree to playquantum Russian roulette because the measure of existence of worldswith Lev dead will be much larger than the measure of existence of theworlds with a rich and alive Lev. This approach also resolves thepuzzle which Wilson 2017 raises concerning The Quantum DoomsdayArgument.

Albrecht and Phillips 2014 claim that even a toss of a regular coinsplits the world, so there is no need for a quantum splitter,supporting a common view that the splitting of worlds happens veryoften. Surely, there are many splitting events: every Geiger counteror single-photon detector splits the world, but the frequency ofsplitting outside a physics laboratory is a complicated physicsquestion. Not every situation leads to a multitude of worlds: thiswould contradict our ability to predict how our world will look in thenear future.

Vaidman 2001 finds it advantageous to think about all worlds togethereven in analysing a controversial issue of classical probabilitytheory, the Sleeping Beauty problem. Accepting the Probability Postulate reduces the analysis ofprobability to a calculation of the measures of existence of variousworlds. Note, however, that the Quantum Sleeping Beauty problem alsobecame a topic of a hot controversy: Lewis 2007, Papineau andDur-Vil 2009, Groisman et al. 2013, Bradley2011, Wilson 2014, Schwarz 2015.

I thank Michael Ridley for his work on the new edition of this entry.I am grateful to everybody who has borne with me through endlessdiscussions of the MWI via email, Zoom (and face-to-face inpandemic-free parallel worlds). I acknowledge partial support by grant2064/19 of the Israel Science Foundation.

In modern versions of many-worlds, the subjective appearance of wave function collapse is explained by the mechanism of quantum decoherence.[2] Decoherence approaches to interpreting quantum theory have been widely explored and developed since the 1970s.[9][10][11] MWI is considered a mainstream interpretation of quantum mechanics, along with the other decoherence interpretations, the Copenhagen interpretation, and hidden variable theories such as Bohmian mechanics.[12][2]

The many-worlds interpretation uses decoherence to explain the measurement process and the emergence of a quasi-classical world.[15][16] Wojciech H. Zurek, one of decoherence theory's pioneers, said: "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."[17] Zurek emphasizes that his work does not depend on a particular interpretation.[a]

MWI depends crucially on the linearity of quantum mechanics, which underpins the superposition principle. If the final theory of everything is non-linear with respect to wavefunctions, then many-worlds is invalid.[6][1][5][7][8] All quantum field theories are linear and compatible with the MWI, a point Everett emphasized as a motivation for the MWI.[5] While quantum gravity or string theory may be non-linear in this respect,[27] there is as yet no evidence of this.[28][29]

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 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.

In 1985, David Deutsch proposed a variant of the Wigner's friend thought experiment as a test of many-worlds versus the Copenhagen interpretation.[32] 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,[33] which require placing macroscopic objects in a coherent superposition and interfering them, a task currently beyond experimental capability.

Since the many-worlds interpretation's inception, physicists have been puzzled about the role of probability in it. As put by Wallace, there are two facets to the question:[34] the incoherence problem, which asks why we should assign probabilities at all to outcomes that are certain to occur in some worlds, and the quantitative problem, which asks why the probabilities should be given by the Born rule. be457b7860