The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wavefunction collapse. This implies that all possible outcomes of quantum measurements are physically realized in some "world" or universe. In contrast to some other interpretations, such as the Copenhagen interpretation, the evolution of reality as a whole in MWI is rigidly deterministic. Many-worlds is also referred to as the relative state formulation or the Everett interpretation, after the physicist Hugh Everett who first proposed it in 1957. The formulation was popularized and named many-worlds by Bryce DeWitt in the 1960s and 1970s.
In many-worlds, the subjective appearance of wavefunction collapse is explained by the mechanism of quantum decoherence. Decoherence approaches to interpreting quantum theory have been widely explored and developed since the 1970s, and have become quite popular. MWI is currently considered a mainstream interpretation along with the other decoherence interpretations, collapse theories (including the Copenhagen interpretation), and hidden variable theories such as Bohmian mechanics.
The many-worlds interpretation implies that there is a very large—perhaps infinite—number of universes. It is one of many multiverse hypotheses in physics and philosophy. MWI views time as a many-branched tree, wherein every possible quantum outcome is realised. This is intended to resolve some paradoxes of quantum theory, such as the EPR paradox:462:118 and Schrödinger's cat, since every possible outcome of a quantum event exists in its own universe.
|Part of a series on|
In 1952 Erwin Schrödinger gave a lecture in Dublin in which at one point he jocularly warned his audience that what he was about to say might "seem lunatic". He went on to assert that what the equation that won him a Nobel prize seems to be describing is several different histories, they are "not alternatives but all really happen simultaneously". This is the earliest known reference to the many-worlds.
The idea of MWI originated in Everett's Princeton Ph.D. thesis "The Theory of the Universal Wavefunction", 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"; Everett originally called his approach the "Correlation Interpretation", where "correlation" refers to quantum entanglement). The phrase "many-worlds" is due to Bryce DeWitt, who was responsible for the wider popularisation of Everett's theory, which had been largely ignored for the first decade after publication.
Overview of the interpretation
The key idea of the Many-Worlds interpretation is that unitary quantum mechanics describes the whole universe. In particular, it describes a measurement as an unitary transformation, without using a collapse postulate, and describes observers as ordinary quantum-mechanical systems.:35-38 It stands in sharp contrast to the Copenhagen interpretation, that describes a measurement as a "primitive" concept, not describable by quantum mechanics, divides the universe into a quantum and a classical domain, and makes central use of the collapse postulate.:29-30 MWI's main conclusion is that the universe (or multiverse in this context) is composed of a quantum superposition of an infinite or undefinable:14-17 amount of increasingly divergent, non-communicating parallel universes or quantum worlds.
The Many-Worlds interpretation makes essential use of decoherence to explain the measurement process and the emergence of a quasi-classical world. This has been described by Żurek, one of the pioneers of decoherence theory, as "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.". Żurek, however, emphasizes that his work does not depend on a particular interpretation.[b]
The many-worlds interpretation shares many similarities with the decoherent histories interpretation, that also uses decoherence to explain the process of measurement or wavefunction collapse.:9-11 MWI treats the other histories or worlds as real since it regards the universal wavefunction as the "basic physical entity":455 or "the fundamental entity, obeying at all times a deterministic wave equation".:115 Decoherent histories, on the other hand, needs only one of the histories (or worlds) to be real.:10
Many-worlds is referred to as a theory, rather than just an interpretation, by several authors, including Wheeler, Everett and Deutsch.:328 Everett argued that his theory was the "only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world." Deutsch is dismissive that many-worlds is an "interpretation", saying that calling it an interpretation "is like talking about dinosaurs as an 'interpretation' of fossil records."
This section does not cite any sources. (January 2016) (Learn how and when to remove this template message)
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 well-defined (but time-dependent) 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 spin-state of an electron. Considering a specific axis (say the z-axis) the north pole represents spin "up" and the south pole, spin "down". The superposition states of the system are described by 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 can 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.
This section does not cite any sources. (January 2016) (Learn how and when to remove this template message)
In his 1957 doctoral dissertation, Everett proposed that rather than modeling an isolated quantum system subject to external observation, one could mathematically model an object as well as its observers as purely physical systems within the mathematical framework developed by Paul Dirac, von Neumann and others, discarding altogether the ad hoc mechanism of wave function collapse.
Since Everett's original work, there have appeared a number of similar formalisms in the literature. One such is the relative state formulation. It makes two assumptions: first, 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. Secondly, observation or measurement has no special laws or mechanics, unlike in the Copenhagen interpretation which considers the wavefunction collapse as a special kind of event which occurs as a result of observation. Instead, measurement in the relative state formulation is the consequence of a configuration change in the memory of an observer described by the same basic wave physics as the object being modeled.
The many-worlds interpretation is DeWitt's popularisation of Everett's work, who had referred to the combined observer–object 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 above. 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.
Under the many-worlds interpretation, the Schrödinger equation, or relativistic analog, holds all the time everywhere. An observation or measurement 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 observer–object's wavefunction to change into a quantum superposition of two or more non-interacting branches, or split into many "worlds". Since many observation-like 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. 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 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.
MWI removes the observer-dependent role in the quantum measurement process by replacing wavefunction collapse with quantum decoherence. Since the role of the observer lies at the heart of most if not all "quantum paradoxes," this automatically resolves a number of problems; see for example the Schrödinger's cat thought experiment, the EPR paradox, von Neumann's "boundary problem", and even wave-particle duality.
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. The MWI was developed with the explicit goal of allowing quantum mechanics to be applied to the universe as a whole, making quantum cosmology possible.
MWI is a realist, deterministic, and local theory. MWI achieves this by removing wavefunction collapse, which is indeterministic and non-local, from the deterministic and local equations of quantum theory.
MWI depends crucially on the linearity of quantum mechanics. If the final theory of everything is non-linear with respect to wavefunctions then many-worlds would be invalid.. While quantum gravity or string theory may be non-linear in this respect there is no evidence to indicate this at the moment.
Interpreting wavefunction collapse
This section needs additional citations for verification. (February 2020) (Learn how and when to remove this template message)
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) are passed through the double slit, a calculation assuming wave-like 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 down onto, or select, just one determinate outcome to "explain" this phenomenon of observation. Wavefunction collapse was widely regarded as artificial and ad hoc, 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 stated 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 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 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 subject–object 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 subject–object 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.[c]) Since the wavefunction merely 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.
In 1985, David Deutsch proposed a variant of the Wigner's friend thought experiment as a test of Many-Worlds versus the Copenhagen interpretation. It consists of an experimenter (Wigner's friend) making a measurement on a quantum system in an isolated laboratory, and another experimenter (Wigner) that 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 it had collapsed into a single branch as predicted by the Copenhagen interpretation. Since then Lockwood (1989), Vaidman and others have made similar proposals. These proposals require placing macroscopic objects in a coherent superposition and interfering them, a task which is currently outside experimental capability.
Probability and the Born rule
Since the inception of the Many-Worlds interpretation physicists have been puzzled about the role of probability in the theory. As put by Wallace, there are two facets to the question: the incoherence problem, which asks why should we assign probabilities at all to outcomes that are certain to occur in some worlds, and the quantitative problem, which asks why should the probabilities be given by the Born rule.
Everett tried to answer these questions in the very paper that introduced Many-Worlds. To address the incoherence problem, he argued that an observer that made a sequence of measurements on a quantum system will in general have an apparently random sequence of results in their memory, which justifies the use of probabilities to describe the measurement process.:69-70 To address the quantitative problem, Everett proposed a derivation of the Born rule based on the properties that a measure on the branches of the wavefunction should have.:70-72 His derivation has been criticized as relying on unmotivated assumptions. Since then several other derivations of the Born rule in the Many-Worlds framework have been proposed. There is no consensus on whether this has been successful.
Derivations of the Born rule based on a frequentist interpretation of probability have been proposed by DeWitt and Graham and Farhi et al., among others. They tried to show that in the limit of infinitely many measurements there would exist no worlds where the relative frequencies didn't match the probabilities given by the Born rule, but these derivations were shown to be mathematically incorrect.
A decision-theoretic derivation of the Born rule was produced by David Deutsch (1999) and refined by Wallace (2002–2009) and Saunders (2004). They consider an agent that takes part in a quantum gamble: the agent makes a measurement on a quantum system, branches as a consequence, and each of the agent's future selves receive a reward that depends on the measurement result. The agent uses decision theory to evaluate the price they would pay to take part in such a gamble, and concludes that the price is given by the utility of the rewards weighted according to the Born rule. Some reviews have been positive, although the status of these arguments remains highly controversial; some theoretical physicists have taken them as supporting the case for parallel universes. For example, a New Scientist story on a 2007 conference about Everettian interpretations quoted physicist Andy Albrecht as saying, "This work will go down as one of the most important developments in the history of science." In contrast, the philosopher Huw Price, also attending the conference, found the Deutsch–Wallace–Saunders approach fundamentally flawed.
Symmetries and invariance
Żurek (2005) has produced a derivation of the Born rule based on the symmetries of entangled states; Schlosshauer and Fine argued that Żurek's derivation is not rigorous, as it does not define what probability is and has several unstated assumptions about how it should behave.
Charles Sebens and Sean M. Carroll, building on work by Lev Vaidman, proposed a similar approach based on self-locating uncertainty. In this approach, decoherence creates multiple identical copies of observers, who can assign credences to being on different branches using the Born rule. The Sebens–Carroll approach has been criticized by Adrian Kent, and Vaidman himself does not find it satisfactory.
The preferred basis problem
As originally formulated by Everett and DeWitt, the Many-Worlds interpretation had a privileged role for measurements: they determined which basis of a quantum system would give rise to the eponymous worlds. Without this the theory was ambiguous, as a quantum state can be equally well be described (e.g.) as having a well-defined position, or as being a superposition of two delocalised states. The assumption that the preferred basis to use is the one coming from a measurement of position results in worlds having objects in well-defined positions, instead of worlds with delocalised objects (which would be grossly incompatible with experiment). 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. This is known today as the preferred basis problem.
The preferred basis problem has been solved, according to Saunders and Wallace, among others, with the incorporation of decoherence in the Many-Worlds theory. 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 do not play a special role anymore, but 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 to decide whether a pair of worlds have split or not. 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. 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.
This approach to deriving the preferred basis has been criticized as creating a 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. Wallace contends that decoherence theory does not depend on probability, but only on the notion that one is allowed to do approximations in physics.:253-254
The initial reception of the MWI interpretation was overwhelmingly negative, with the notable exception of Bryce DeWitt. Wheeler made considerable efforts to formulate the theory in a way that would be palatable to Bohr, visited Copenhagen in 1956 to discuss and him, and convinced Everett to visit as well, which happened in 1959. Nevertheless, Bohr and his collaborators completely rejected the theory.[d] Everett left academia in 1956, never to return, and Wheeler eventually disowned the theory.
One of MWI's strongest advocates is David Deutsch. 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, 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 then MWI will be testable (at least against "naive" Copenhagenism) via the reversible observation of spin.
Asher Peres was an outspoken critic of MWI. For example, a section in his 1993 textbook had the title Everett's interpretation and other bizarre theories. Peres argued that all of the varieties of many-worlds interpretations merely shifted the arbitrariness or vagueness of the collapse postulate to the question of when "worlds" can be regarded as separate, and that no objective criterion for that separation can actually be formulated.
MWI is considered by some to be unfalsifiable and hence unscientific because the multiple parallel universes are non-communicating, in the sense that no information can be passed between them. Others claim MWI is directly testable.
Victor J. Stenger remarks that Murray Gell-Mann's published work explicitly rejects the existence of simultaneous parallel universes. Collaborating with James Hartle, Gell-Mann had been, before his death, working toward the development a more "palatable" post-Everett quantum mechanics. Stenger thinks it's fair to say that most physicists dismiss the many-world interpretation as too extreme, while noting it "has merit in finding a place for the observer inside the system being analyzed and doing away with the troublesome notion of wave function collapse".[e]
Max Tegmark reports the result of a "highly unscientific" poll taken at a 1997 quantum mechanics workshop. According to Tegmark, "The many worlds interpretation (MWI) scored second, comfortably ahead of the consistent histories and Bohm interpretations."
In response to Sean Carroll's statement, "As crazy as it sounds, most working physicists buy into the many-worlds theory", Michael Nielsen counters: "at a quantum computing conference at Cambridge in 1998, a many-worlder surveyed the audience of approximately 200 people... Many-worlds did just fine, garnering support on a level comparable to, but somewhat below, Copenhagen and decoherence." However, Nielsen notes that it seemed most attendees found it to be a waste of time: Asher Peres "got a huge and sustained round of applause… when he got up at the end of the polling and asked 'And who here believes the laws of physics are decided by a democratic vote?'"
A 2005 poll of fewer than 40 students and researchers taken after a course on the Interpretation of Quantum Mechanics at the Institute for Quantum Computing University of Waterloo found "Many Worlds (and decoherence)" to be the least favored.
A 2011 poll of 33 participants at an Austrian conference found 6 endorsed MWI, 8 "Information-based/information-theoretical", and 14 Copenhagen; the authors remark that MWI received a similar percentage of votes as in Tegmark's 1997 poll.
Debate if the other worlds are real
According to Martin Gardner, the "other" worlds of MWI have two different interpretations: real or unreal; he claimed that Stephen Hawking and Steven Weinberg both favour the unreal interpretation. Gardner also claims that the nonreal interpretation is favoured by the majority of physicists, whereas the "realist" view is only supported by MWI experts such as Deutsch and Bryce DeWitt. Hawking has said that "according to Feynman's idea", all the other histories are as "equally real" as our own, [f] and Martin Gardner reports Hawking saying that MWI is "trivially true". In a 1983 interview, Hawking also said he regarded the MWI as "self-evidently correct" but was dismissive towards questions about the interpretation of quantum mechanics, saying, "When I hear of Schrödinger's cat, I reach for my gun." In the same interview, he also said, "But, look: All that one does, really, is to calculate conditional probabilities—in other words, the probability of A happening, given B. I think that that's all the many worlds interpretation is. Some people overlay it with a lot of mysticism about the wave function splitting into different parts. But all that you're calculating is conditional probabilities." Elsewhere Hawking contrasted his attitude towards the "reality" of physical theories with that of his colleague Roger Penrose, saying, "He's a Platonist and I'm a positivist. He's worried that Schrödinger's cat is in a quantum state, where it is half alive and half dead. He feels that can't correspond to reality. But that doesn't bother me. I don't demand that a theory correspond to reality because I don't know what it is. Reality is not a quality you can test with litmus paper. All I'm concerned with is that the theory should predict the results of measurements. Quantum theory does this very successfully." For his own part, 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.
Quantum suicide thought experiment
Quantum suicide is a thought experiment in quantum mechanics and the philosophy of physics. Purportedly, it can distinguish between the Copenhagen interpretation of quantum mechanics and the many-worlds interpretation by means of a variation of the Schrödinger's cat thought experiment, from the cat's point of view. Quantum immortality refers to the subjective experience of surviving quantum suicide.
Most experts believe that the experiment would not work in the real world, because the world with the surviving experimenter has a lower "measure" than the world prior to the experiment, making it less likely that the experimenter will go on to experience their survival.:371
Absurdly improbable timelines
DeWitt has stated that "[Everett, Wheeler and Graham] do not in the end exclude any element of the superposition. All the worlds are there, even those in which everything goes wrong and all the statistical laws break down."
Max Tegmark has affirmed that absurd or highly unlikely events are inevitable but rare under the MWI interpretation. To quote Tegmark, "Things inconsistent with the laws of physics will never happen - everything else will ... it's important to keep track of the statistics, since even if everything conceivable happens somewhere, really freak events happen only exponentially rarely."
- "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."
- 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.
- "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.
- Everett recounted his meeting with Bohr as "that was a hell... doomed from the beginning". Léon Rosenfeld, a close collaborator of Bohr, said "With regard to Everett neither I nor even Niels Bohr could have any patience with him, when he visited us in Copenhagen more than 12 years ago in order to sell the hopelessly wrong ideas he had been encouraged, most unwisely, by Wheeler to develop. He was undescribably stupid and could not understand the simplest things in quantum mechanics.":113
- Gell-Mann and collaborator James Hartle, along with a score of others, have been working to develop a more palatable interpretation of quantum mechanics that is free of the problems that plague all the interpretations we have considered so far. This new interpretation is called, in its various incarnations, post-Everett quantum mechanics, alternate histories, consistent histories, or decoherent histories. I will not be overly concerned with the detailed differences between these characterizations and will use the terms more or less interchangeably.:176
- In response to Ken Campbell's question "all these trillions of Universes of the Multiverse, are they as real as this one seems to be to me?" Hawking states, "Yes.... According to Feynman's idea, every possible history (of Ken) is equally real."
- Bryce S. DeWitt (1970). "Quantum mechanics and reality". Physics Today. 23 (9): 30. doi:10.1063/1.3022331. See also Leslie E. Ballentine; Philip Pearle; Evan Harris Walker; Mendel Sachs; Toyoki Koga; Joseph Gerver; Bryce DeWitt (1971). "Quantum‐mechanics debate". Physics Today. 24 (4): 36. doi:10.1063/1.3022676.
- Everett, Hugh; Wheeler, J. A.; DeWitt, B. S.; Cooper, L. N.; Van Vechten, D.; Graham, N. (1973). DeWitt, Bryce; Graham, R. Neill (eds.). The Many-Worlds Interpretation of Quantum Mechanics. Princeton Series in Physics. Princeton, NJ: Princeton University Press. p. v. ISBN 0-691-08131-X.
- Tegmark, Max (1997). "The Interpretation of Quantum Mechanics: Many Worlds or Many Words?". Fortschritte der Physik. 46 (6–8): 855–862. arXiv:quant-ph/9709032. doi:10.1002/(SICI)1521-3978(199811)46:6/8<855::AID-PROP855>3.0.CO;2-Q.
- Hugh Everett Theory of the Universal Wavefunction, Thesis, Princeton University, (1956, 1973), pp 1–140
- Everett, Hugh (1957). "Relative State Formulation of Quantum Mechanics". Reviews of Modern Physics. 29 (3): 454–462. Bibcode:1957RvMP...29..454E. doi:10.1103/RevModPhys.29.454. Archived from the original on 2011-10-27. Retrieved 2011-10-24.
- Cecile M. DeWitt, John A. Wheeler eds, The Everett–Wheeler Interpretation of Quantum Mechanics, Battelle Rencontres: 1967 Lectures in Mathematics and Physics (1968)
- Bryce Seligman DeWitt, The Many-Universes Interpretation of Quantum Mechanics, Proceedings of the International School of Physics "Enrico Fermi" Course IL: Foundations of Quantum Mechanics, Academic Press (1972)
- H. Dieter Zeh, On the Interpretation of Measurement in Quantum Theory, Foundations of Physics, vol. 1, pp. 69–76, (1970).
- Wojciech Hubert Zurek, Decoherence and the transition from quantum to classical, Physics Today, vol. 44, issue 10, pp. 36–44, (1991).
- Wojciech Hubert Zurek, Decoherence, einselection, and the quantum origins of the classical, Reviews of Modern Physics, 75, pp 715–775, (2003)
- Osnaghi, Stefano; Freitas, Fabio; Olival Freire, Jr (2009). "The Origin of the Everettian Heresy". Studies in History and Philosophy of Modern Physics. 40 (2): 97–123. Bibcode:2009SHPMP..40...97O. CiteSeerX 10.1.1.397.3933. doi:10.1016/j.shpsb.2008.10.002.
- David Deutsch. The Beginning of infinity. Page 310.
- Blincoe, Nicholas (2012-04-05). "Erwin Schrödinger and the Quantum Revolution by John Gribbin: review". The Telegraph. ISSN 0307-1235. Retrieved 2019-02-10.
- John Archibald Wheeler, Geons, Black Holes & Quantum Foam, ISBN 0-393-31991-1. pp 268–270
- Wallace, David (2012). The Emergent Multiverse: Quantum Theory According to the Everett Interpretation. Oxford University Press. ISBN 978-0-19-954696-1.
- David Wallace (2010). "Decoherence and Ontology, or: How I Learned To Stop Worrying And Love FAPP". In S. Saunders; J. Barrett; A. Kent; D. Wallace (eds.). Many Worlds? Everett, Quantum Theory and Reality. Oxford University Press. arXiv:1111.2189.
- Saunders, Simon (2010). "Many Worlds? An Introduction". In S. Saunders; J. Barrett; A. Kent; D. Wallace (eds.). Many Worlds? Everett, Quantum Theory and Reality (PDF). Oxford University Press.
- Zurek, Wojciech (March 2009). "Quantum Darwinism". Nature Physics. 5 (3): 181–188. arXiv:0903.5082. Bibcode:2009NatPh...5..181Z. doi:10.1038/nphys1202.
- Brian Skyrms (1976). "Possible Worlds, Physics and Metaphysics". Philosophical Studies. 30: 323–332. doi:10.1007/BF00357930.
- Letter from Everett to David Raub, 1980-04-07, avaiable at UCI
- Peter Byrne (2010). The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family. Oxford University Press. ISBN 978-0-19-955227-6.
- M Gell-Mann; J.B. Hartle (1990). "Quantum mechanics in the light of quantum cosmology". In W.H. Zurek (ed.). Complexity, Entropy, and the Physics of Information. Addison-Wesley. arXiv:1803.04605.
- Harvey R. Brown; Christopher G. Timpson (2016). "Bell on Bell's Theorem: The Changing Face of Nonlocality". In Mary Bell; Shan Gao (eds.). Quantum Nonlocality and Reality: 50 years of Bell's theorem. Cambridge University Press. arXiv:1501.03521. doi:10.1017/CBO9781316219393.008.
- Paul C.W. Davies, Other Worlds, chapters 8 & 9 The Anthropic Principle & Is the Universe an accident?, (1980) ISBN 0-460-04400-1
- Paul C.W. Davies, The Accidental Universe, (1982) ISBN 0-521-28692-1
- Penrose, Roger (August 1991). "Roger Penrose Looks Beyond the Classic-Quantum Dichotomy". Sciencewatch. Archived from the original on 2007-10-23. Retrieved 2007-10-21.
- Steven Weinberg, Dreams of a Final Theory: The Search for the Fundamental Laws of Nature (1993), ISBN 0-09-922391-0, pg 68–69
- Steven Weinberg Testing Quantum Mechanics, Annals of Physics Vol 194 #2 (1989), pg 336–386
- Wimmel Hermann. Quantum Physics And Observed Reality: A Critical Interpretation Of Quantum Mechanics, p.45, World Scientific, May 26, 1992
- Abdus Salam, Unification of Fundamental Forces, Cambridge University Press (1990) ISBN 0-521-37140-6, pp 98–101
- Deutsch, D. (1985). "Quantum theory as a universal physical theory". International Journal of Theoretical Physics. 24 (1): 1–41. Bibcode:1985IJTP...24....1D. doi:10.1007/BF00670071.
- Vaidman, Lev (2018). Many-Worlds Interpretation of Quantum Mechanics. The Stanford Encyclopedia of Philosophy.
- Wallace, David (2003). "Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation". Stud. Hist. Phil. Mod. Phys. 34 (3): 415–438. arXiv:quant-ph/0303050. Bibcode:2003SHPMP..34..415W. doi:10.1016/S1355-2198(03)00036-4.
- L. E. Ballentine (1973). "Can the statistical postulate of quantum theory be derived?—A critique of the many-universes interpretation". Foundations of Physics. 3: 229–240. doi:10.1007/BF00708440.
- N.P. Landsman, "The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle.", in Compendium of Quantum Physics (eds.) F. Weinert, K. Hentschel, D.Greenberger and B. Falkenburg (Springer, 2008), ISBN 3-540-70622-4
- Kent, Adrian (2010). "One world versus many: The inadequacy of Everettian accounts of evolution, probability, and scientific confirmation". In S. Saunders; J. Barrett; A. Kent; D. Wallace (eds.). Many Worlds? Everett, Quantum Theory and Reality. Oxford University Press. arXiv:0905.0624. Bibcode:2009arXiv0905.0624K.
- Kent, Adrian (1990). "Against Many-Worlds Interpretations". Int. J. Mod. Phys. A. 5 (9): 1745–1762. arXiv:gr-qc/9703089. Bibcode:1990IJMPA...5.1745K. doi:10.1142/S0217751X90000805.
- Edward Farhi; Jeffrey Goldstone; Sam Gutmann (1989). "How probability arises in quantum mechanics". Annals of Physics. 192 (2): 368–382. doi:10.1016/0003-4916(89)90141-3.
- Benioff, Paul (October 1978). "A note on the Everett interpretation of quantum mechanics". Foundations of Physics. 8 (9–10): 709–720. doi:10.1007/BF00717501. ISSN 0015-9018.
- Carlton M. Caves; Rüdiger Schack (2005). "Properties of the frequency operator do not imply the quantum probability postulate". Annals of Physics. 315 (1): 123–146. arXiv:quant-ph/0409144. Bibcode:2005AnPhy.315..123C. doi:10.1016/j.aop.2004.09.009.
- Deutsch, David (1999). "Quantum Theory of Probability and Decisions". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 455 (1988): 3129–3137. arXiv:quant-ph/9906015. Bibcode:1999RSPSA.455.3129D. doi:10.1098/rspa.1999.0443.
- Wallace, David (2002). "Quantum Probability and Decision Theory, Revisited". arXiv:quant-ph/0211104.
- Wallace, David (2003). "Quantum Probability from Subjective Likelihood: Improving on Deutsch's proof of the probability rule". arXiv:quant-ph/0312157.
- Wallace, David (2009). "A formal proof of the Born rule from decision-theoretic assumptions". arXiv:0906.2718 [quant-ph].
- Saunders, Simon (2004). "Derivation of the Born rule from operational assumptions". Proc. Roy. Soc. Lond. A. 460 (2046): 1771–1788. arXiv:quant-ph/0211138. Bibcode:2004RSPSA.460.1771S. doi:10.1098/rspa.2003.1230.
- Saunders, Simon (2004). "What is Probability?". Quo Vadis Quantum Mechanics?. The Frontiers Collection. pp. 209–238. arXiv:quant-ph/0412194. doi:10.1007/3-540-26669-0_12. ISBN 978-3-540-22188-3.
- Merali, Zeeya (2007-09-21). "Parallel universes make quantum sense". New Scientist (2622). Retrieved 2013-11-22. (Summary only).
- Perimeter Institute, Many worlds at 50 conference, September 21–24, 2007Videos
- Price, Huw (2010). "Decisions, Decisions, Decisions: Can Savage Salvage Everettian Probability?". In S. Saunders; J. Barrett; A. Kent; D. Wallace (eds.). Many Worlds? Everett, Quantum Theory and Reality. Oxford University Press. arXiv:0802.1390.
- Zurek, Wojciech H. (2005). "Probabilities from entanglement, Born's rule from envariance". Phys. Rev. A. 71 (5): 052105. arXiv:quant-ph/0405161. Bibcode:2005PhRvA..71e2105Z. doi:10.1103/physreva.71.052105.
- Schlosshauer, M.; Fine, A. (2005). "On Zurek's derivation of the Born rule". Found. Phys. 35 (2): 197–213. arXiv:quant-ph/0312058. Bibcode:2005FoPh...35..197S. doi:10.1007/s10701-004-1941-6.
- Vaidman, L. "Probability in the Many-Worlds Interpretation of Quantum Mechanics." In: Ben-Menahem, Y., & Hemmo, M. (eds), The Probable and the Improbable: Understanding Probability in Physics, Essays in Memory of Itamar Pitowsky. Springer.
- Sebens, Charles T; Carroll, Sean M (2016). "Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics". The British Journal for the Philosophy of Science. 69 (1): 25–74. arXiv:1405.7577. doi:10.1093/bjps/axw004.
- Kent, Adrian (February 2015). "Does it Make Sense to Speak of Self-Locating Uncertainty in the Universal Wave Function? Remarks on Sebens and Carroll". Foundations of Physics. 45 (2): 211–217. arXiv:1408.1944. doi:10.1007/s10701-014-9862-5. ISSN 0015-9018.
- Vaidman, Lev (2020). "Derivations of the Born Rule". In Meir Hemmo; Orly Shenker (eds.). Quantum, Probability, Logic: Itamar Pitowsky's Work and Influence. Springer Nature Switzerland. PhilSci:15943.
- Simon Saunders (1993). "Decoherence, relative states, and evolutionary adaptation". Foundations of Physics. 23: 1553-1585. doi:10.1007/BF00732365.
- Simon Saunders (1995). "Time, quantum mechanics, and decoherence". Synthese. 102: 235-266. doi:10.1007/BF01089802.
- James B. Hartle (2011). "The quasiclassical realms of this quantum universe". Foundations of Physics. 41: 982-1006. arXiv:0806.3776. doi:10.1007/s10701-010-9460-0.
- Stapp, Henry (2002). "The basis problem in many-world theories" (PDF). Canadian Journal of Physics. 80 (9): 1043–1052. arXiv:quant-ph/0110148. Bibcode:2002CaJPh..80.1043S. doi:10.1139/p02-068.
- David Wallace (2003). "Everett and structure". Studies in History and Philosophy of Science. 34 (1): 87-105. arXiv:quant-ph/0107144. doi:10.1016/S1355-2198(02)00085-0.
- Brown, Harvey R; Wallace, David (2005). "Solving the measurement problem: de Broglie–Bohm loses out to Everett" (PDF). Foundations of Physics. 35 (4): 517–540. arXiv:quant-ph/0403094. Bibcode:2005FoPh...35..517B. doi:10.1007/s10701-004-2009-3.
- David J Baker (2007). "Measurement outcomes and probability in Everettian quantum mechanics" (PDF). Studies in History and Philosophy of Science. 38 (1): 153–169. doi:10.1016/j.shpsb.2006.05.003.
- David Deutsch, The Fabric of Reality: The Science of Parallel Universes And Its Implications, Penguin Books (1998), ISBN 0-14-027541-X
- Deutsch, David (1985). "Quantum theory, the Church–Turing principle and the universal quantum computer". Proceedings of the Royal Society of London A. 400 (1818): 97–117. Bibcode:1985RSPSA.400...97D. CiteSeerX 10.1.1.144.7936. doi:10.1098/rspa.1985.0070.
- Paul C.W. Davies, J.R. Brown, The Ghost in the Atom (1986) ISBN 0-521-31316-3, pp. 34–38: "The Many-Universes Interpretation", pp 83–105 for David Deutsch's test of MWI and reversible quantum memories
- Peres, Asher (1995). Quantum Theory: Concepts and Methods. Kluwer Academic Publishers. p. 374. ISBN 0-7923-2549-4.
- Bunge, M. (2012). "Parallel Universes? Digital Physics?". Evaluating Philosophies. New York: Springer. pp. 152–153. doi:10.1007/978-94-007-4408-0.
- Ellis, G.; Silk, J. (2014). "Scientific method: Defend the integrity of physics". Nature. 516: 321–323. doi:10.1038/516321a. Retrieved 4 July 2019.
- Stenger, V.J. (1995). The Unconscious Quantum: Metaphysics in Modern Physics and Cosmology. Prometheus Books. ISBN 978-1-57392-022-3. LCCN lc95032599.
- Tipler, Frank (1994). The Physics of Immortality. pp. 170–171.
In the "yes" column were Stephen Hawking, Richard Feynman, and Murray Gell-Mann
- Max Tegmark on many-worlds (contains MWI poll)
- Caroll, Sean (1 April 2004). "Preposterous Universe". Archived from the original on 8 September 2004.
- Nielsen, Michael (3 April 2004). "Michael Nielsen: The Interpretation of Quantum Mechanics". Archived from the original on 20 May 2004.
- Survey Results Archived 2010-11-04 at the Wayback Machine
- Schlosshauer, Maximilian; Kofler, Johannes; Zeilinger, Anton (2013). "A Snapshot of Foundational Attitudes Toward Quantum Mechanics". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 44 (3): 222–230. arXiv:1301.1069. Bibcode:2013SHPMP..44..222S. doi:10.1016/j.shpsb.2013.04.004.
- Aldhous, Peter (2007-11-24). "Parallel lives can never touch". New Scientist (2631). Retrieved 2007-11-21.
- A response to Bryce DeWitt, Martin Gardner, May 2002
- TV Series "Reality on the Rocks", episode "Beyond our Ken" (1995)
- Gardner, Martin (2003). Are universes thicker than blackberries?. W.W. Norton. p. 10. ISBN 978-0-393-05742-3.
- Ferris, Timothy (1997). The Whole Shebang. Simon & Schuster. pp. 345. ISBN 978-0-684-81020-1.
- Hawking, Stephen; Roger Penrose (1996). The Nature of Space and Time. Princeton University Press. pp. 121. ISBN 978-0-691-03791-2.
- Tegmark, Max (November 1998). "Quantum immortality". Retrieved 25 October 2010.
- Carroll, Sean (2019). "The Human Side - Living and Thinking in a Quantum Universe". Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime. Penguin. ISBN 9781524743024. At Google Books.
- Deutsch, David (2011). "The Beginning". The Beginning of Infinity. Penguin Group.
- DeWitt, Bryce S. (1970). "Quantum mechanics and reality". Physics Today. 23 (9): 30–35. Bibcode:1970PhT....23i..30D. doi:10.1063/1.3022331.
- Max Tegmark: "Max' multiverse FAQ: frequently asked questions" > "Multiverse philosophy" > "Will I rob a gas station?"
- Jeffrey A. Barrett, The Quantum Mechanics of Minds and Worlds, Oxford University Press, Oxford, 1999.
- Peter Byrne, The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family, Oxford University Press, 2010.
- Jeffrey A. Barrett and Peter Byrne, eds., "The Everett Interpretation of Quantum Mechanics: Collected Works 1955–1980 with Commentary", Princeton University Press, 2012.
- Julian Brown, Minds, Machines, and the Multiverse, Simon & Schuster, 2000, ISBN 0-684-81481-1
- Sean M. Carroll, Something deeply hidden, Penguin Random House, (2019)
- Paul C.W. Davies, Other Worlds, (1980) ISBN 0-460-04400-1
- Osnaghi, Stefano; Freitas, Fabio; Olival Freire, Jr (2009). "The Origin of the Everettian Heresy" (PDF). Studies in History and Philosophy of Modern Physics. 40 (2): 97–123. Bibcode:2009SHPMP..40...97O. CiteSeerX 10.1.1.397.3933. doi:10.1016/j.shpsb.2008.10.002. Archived from the original (PDF) on 2016-05-28. Retrieved 2009-08-07. A study of the painful three-way relationship between Hugh Everett, John A Wheeler and Niels Bohr and how this affected the early development of the many-worlds theory.
- David Wallace, Worlds in the Everett Interpretation, Studies in History and Philosophy of Modern Physics, 33, (2002), pp. 637–661, arXiv:quant-ph/0103092
- John A. Wheeler and Wojciech Hubert Zurek (eds), Quantum Theory and Measurement, Princeton University Press, (1983), ISBN 0-691-08316-9
- "Everettian Interpretations of Quantum Mechanics". Internet Encyclopedia of Philosophy.
- Everett's Relative-State Formulation of Quantum Mechanics – Jeffrey A. Barrett's article on Everett's formulation of quantum mechanics in the Stanford Encyclopedia of Philosophy.
- Many-Worlds Interpretation of Quantum Mechanics – Lev Vaidman's article on the many-worlds interpretation of quantum mechanics in the Stanford Encyclopedia of Philosophy.
- Hugh Everett III Manuscript Archive (UC Irvine) – Jeffrey A. Barrett, Peter Byrne, and James O. Weatherall (eds.).
- Henry Stapp's critique of MWI, focusing on the basis problem Canadian J. Phys. 80,1043–1052 (2002).
- Scientific American report on the Many Worlds 50th anniversary conference at Oxford