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Many-worlds interpretation

 

Many-worlds interpretation

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MWI response: All accepted quantum theories of fundamental physics are linear with respect to the wavefunction. While quantum gravity or string theory may be non-linear in this respect there is no evidence to indicate this at the moment.[15][16]
  • Conservation of energy is grossly violated if at every instant near-infinite amounts of new matter are generated to create the new universes.
MWI response: There are two responses to this objection. First, the law of conservation of energy says that energy is conserved within each universe. Hence, even if "new matter" were being generated to create new universes, this would not violate conservation of energy. Second, conservation of energy is not violated since the energy of each branch has to be weighted by its probability, according to the standard formula for the conservation of energy in quantum theory. This results in the total energy of the multiverse being conserved.[66]
  • Occam's Razor rules against a plethora of unobservable universes – Occam would prefer just one universe; i.e., any non-MWI.
MWI response: Occam's razor actually is a constraint on the complexity of physical theory, not on the number of universes. MWI is a simpler theory since it has fewer postulates.[52] Occams's razor is often cited by MWI adherents as an advantage of MWI.
  • Unphysical universes: If a state is a superposition of two states \Psi_A and \Psi_B, i.e., \Psi = (a \Psi_A + b \Psi_B), i.e., weighted by coefficients a and b, then if b \ll a, what principle allows a universe with vanishingly small probability b to be instantiated on an equal footing with the much more probable one with probability a? This seems to throw away the information in the probability amplitudes. Such a theory makes little sense.
MWI response: The magnitude of the coefficients provides the weighting that makes the branches or universes "unequal", as Everett and others have shown, leading the emergence of the conventional probabilistic rules.[1][4][5][6][7][67]
  • Violation of the principle of locality, which contradicts special relativity: MWI splitting is instant and total: this may conflict with relativity, since an alien in the Andromeda galaxy can't know I collapse an electron over here before she collapses hers there: the relativity of simultaneity says we can't say which electron collapsed first – so which one splits off another universe first? This leads to a hopeless muddle with everyone splitting differently. Note: EPR is not a get-out here, as the alien's and my electrons need never have been part of the same quantum, i.e., entangled.
MWI response: the splitting can be regarded as causal, local and relativistic, spreading at, or below, the speed of light (e.g., we are not split by Schrödinger's cat until we look in the box).[68] For spacelike separated splitting you can't say which occurred first — but this is true of all spacelike separated events, simultaneity is not defined for them. Splitting is no exception; many-worlds is a local theory.[49]

Brief overview

Schematic representation of pair of "smallest possible" quantum mechanical systems prior to interaction: Measured system S and measurement apparatus M. Systems such as S are referred to as 1-qubit systems.

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.

Schematic illustration of splitting as a result of a repeated measurement.

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 (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 six-dimensional space (the reason for the number six is explained in the article on the Bloch sphere). This six-dimensional 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.

Relative state

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 idea is discussed in the next section.

The relative state formulation 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 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 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.
Partial trace as relative state. Light blue rectangle on upper left denotes system in pure state. Trellis shaded rectangle in upper right denotes a (possibly) mixed state. Mixed state from observation is partial trace of a linear superposition of states as shown in lower right-hand corner.
Successive measurements with successive splittings

Under the many-worlds 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 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. 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.

Comparative properties and possible experimental tests

One of the salient properties of the many-worlds interpretation is that it does not require an exceptional method of wave function collapse to explain it. "It seems that there is no experiment distinguishing the MWI from other no-collapse theories such as Bohmian mechanics or other variants of MWI... In most no-collapse interpretations, the evolution of the quantum state of the Universe is the same. Still, one might imagine that there is an experiment distinguishing the MWI from another no-collapse interpretation based on the difference in the correspondence between the formalism and the experience (the results of experiments)."[69]

However, in 1985, David Deutsch published three related thought experiments which could test the theory vs the Copenhagen interpretation.[70] The experiments require macroscopic quantum state preparation and quantum erasure by a hypothetical quantum computer which is currently outside experimental possibility. Since then Lockwood (1989), Vaidman and others have made similar proposals.[69] These proposals also require an advanced technology which is able to place a macroscopic object in a coherent superposition, another task for which it is uncertain whether it will ever be possible. Many other controversial ideas have been put forward though, such as a recent claim that cosmological observations could test the theory,[71] and another claim by Rainer Plaga (1997), published in Foundations of Physics, that communication might be possible between worlds.[72] As of 2010, there are no feasible experiments to test the differences between MWI and other theories.

Copenhagen interpretation

In the Copenhagen interpretation, the mathematics of quantum mechanics allows one to predict probabilities for the occurrence of various events. When an event occurs, it becomes part of the definite reality, and alternative possibilities do not. There is no necessity to say anything definite about what is not observed.

The universe decaying to a new vacuum state

Any event that changes the number of observers in the universe may have experimental consequences.[73] Quantum tunnelling to a 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 favor of many-worlds. In some worlds, quantum tunnelling to a true vacuum state has happened but most other worlds escape this tunneling and remain viable. This can be thought of as a variation on quantum suicide.

Many-minds

The many-minds interpretation is a multi-world interpretation that defines the splitting of reality on the level of the observers' minds. In this, it differs from Everett's many-worlds interpretation, in which there is no special role for the observer's mind.[72]

Reception

There is a wide range of claims that are considered "many-worlds" interpretations. It was often claimed by those who do not believe in MWI[74] that Everett himself was not entirely clear[75] 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, recent biographical sources make it clear that Everett believed in the literal reality of the other quantum worlds.[22] Everett's son reported that Hugh Everett "never wavered in his belief over his many-worlds theory".[76] Also Everett was reported to believe "his many-worlds theory guaranteed him immortality".[77]

One of MWI's strongest advocates is David Deutsch.[78] 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,[79] 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.[56]

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. In fact, Peres not only questioned whether MWI is really an "interpretation", but rather, if any interpretations of quantum mechanics are needed at all. Indeed, an interpretation can be regarded as a purely formal transformation, which adds nothing to the rules of the quantum mechanics. Peres seems to suggest that positing the existence of an infinite number of non-communicating parallel universes is highly suspect per those who interpret it as a violation of Occam's razor, i.e., that it does not minimize the number of hypothesized entities. However, it is understood that the number of elementary particles are not a gross violation of Occam's Razor, one counts the types, not the tokens. Max Tegmark remarks that the alternative to many-worlds is "many words", an allusion to the complexity of von Neumann's collapse postulate. On the other hand, the same derogatory qualification "many words" is often applied to MWI by its critics who see it as a word game which obfuscates rather than clarifies by confounding the von Neumann branching of possible worlds with the Schrödinger parallelism of many worlds in superposition.

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[56] claim MWI is directly testable. Everett regarded MWI as falsifiable since any test that falsifies conventional quantum theory would also falsify MWI.[21]

According to Martin Gardner, the "other" worlds of MWI have two different interpretations: real or unreal; he claims that Stephen Hawking and Steve Weinberg both favour the unreal interpretation.[80] 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,[81] and Martin Gardner reports Hawking saying that MWI is "trivially true".[82] 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."[83] 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."[84] 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.[65]

Polls

Advocates of MWI often cite a poll of 72 "leading cosmologists and other quantum field theorists"[85] conducted by the American political scientist David Raub in 1995 showing 58% agreement with "Yes, I think MWI is true".[86]

The poll is controversial: for example, 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 is 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".[87]

Max Tegmark also reports the result of a "highly unscientific" poll taken at a 1997 quantum mechanics workshop.[88] According to Tegmark, "The many worlds interpretation (MWI) scored second, comfortably ahead of the consistent histories and Bohm interpretations." Such polls have been taken at other conferences, for example, in response to Sean Carroll's observation, "As crazy as it sounds, most working physicists buy into the many-worlds theory"[89] 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?’"[90]

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.[91]

A 2011 poll of 33 participants at an Austrian conference found 6 endorsed MWI, 8 "Information-based/information-theoretical", and 14 Copenhagen;[92] the authors remark that the results are similar to Tegmark's 1998 poll.

Speculative implications

Speculative physics deals with questions which are also discussed in science fiction.

Quantum suicide thought experiment

Quantum suicide, as a thought experiment, was published independently by Hans Moravec in 1987[93][94] and Bruno Marchal in 1988[95][96] and was independently developed further by Max Tegmark in 1998.[97] It attempts to distinguish between the Copenhagen interpretation of quantum mechanics and the Everett 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 regardless of the odds.[98]

Weak coupling

Another speculation is that the separate worlds remain weakly coupled (e.g., by gravity) permitting "communication between parallel universes". A possible test of this using quantum-optical equipment is described in a 1997 Foundations of Physics article by Rainer Plaga.[72] It involves an isolated ion in an ion trap, a quantum measurement that would yield two parallel worlds (their difference just being in the detection of a single photon), and the excitation of the ion from only one of these worlds. If the excited ion can be detected from the other parallel universe, then this would constitute direct evidence in support of the many-worlds interpretation and would automatically exclude the orthodox, "logical", and "many-histories" interpretations. The reason the ion is isolated is to make it not participate immediately in the decoherence which insulates the parallel world branches, therefore allowing it to act as a gateway between the two worlds, and if the measure apparatus could perform the measurements quickly enough before the gateway ion is decoupled then the test would succeed (with electronic computers the necessary time window between the two worlds would be in a time scale of milliseconds or nanoseconds, and if the measurements are taken by humans then a few seconds would still be enough). R. Plaga shows that macroscopic decoherence timescales are a possibility. The proposed test is based on technical equipment described in a 1993 Physical Review article by Itano et al.[99] and R. Plaga says that this level of technology is enough to realize the proposed inter-world communication experiment. The necessary technology for precision measurements of single ions already exists since the 1970s, and the ion recommended for excitation is 199Hg+. The excitation methodology is described by Itano et al. and the time needed for it is given by the Rabi flopping formula[100]

Such a test as described by R. Plaga would mean that energy transfer is possible between parallel worlds. This does not violate the fundamental principles of physics because these require energy conservation only for the whole universe and not for the single parallel branches.[72] Neither the excitation of the single ion (which is a degree of freedom of the proposed system) leads to decoherence, something which is proven by Welcher Weg detectors which can excite atoms without momentum transfer (which causes the loss of coherence).[101]

The proposed test would allow for low-bandwidth inter-world communication, the limiting factors of bandwidth and time being dependent on the technology of the equipment. Because of the time needed to determine the state of the partially decohered isolated excited ion based on Itano et al.'s methodology, the ion would decohere by the time its state is determined during the experiment, so Plaga's proposal would pass just enough information between the two worlds to confirm their parallel existence and nothing more. The author contemplates that with increased bandwidth, one could even transfer television imagery across the parallel worlds.[72] For example, Itano et al.'s methodology could be improved (by lowering the time needed for state determination of the excited ion) if a more efficient process were found for the detection of fluorescence radiation using 194 nm photons.[72]

A 1991 article by J.Polchinski also supports the view that inter-world communication is a theoretical possibility.[102] Other authors in a 1994 preprint article also contemplated similar ideas.[103]

The reason inter-world communication seems like a possibility is because decoherence which separates the parallel worlds is never fully complete,[104][105] therefore weak influences from one parallel world to another can still pass between them,[104][106] and these should be measurable with advanced technology. Deutsch proposed such an experiment in a 1985 International Journal of Theoretical Physics article,[107] but the technology it requires involves human-level artificial intelligence.[72]

Similarity to modal realism

The many-worlds interpretation has some similarity to modal realism in philosophy, which is the view that the possible worlds used to interpret modal claims exist and are of a kind with the actual world. Unlike the possible worlds of philosophy, however, in quantum mechanics counterfactual alternatives can influence the results of experiments, as in the Elitzur–Vaidman bomb-testing problem or the Quantum Zeno effect. Also, while the worlds of the many-worlds interpretation all share the same physical laws, modal realism postulates a world for every way things could conceivably have been.

Time travel

The many-worlds interpretation could be one possible way to resolve the paradoxes [78] 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 self-consistency principle unnecessary.

Many-worlds in literature and science fiction

A map from Robert Sobel's novel For Want of a Nail, an artistic illustration of how small events – in this example the branching or point of divergence from our timeline's history is in October 1777 – can profoundly alter the course of history. According to the many-worlds interpretation every event, even microscopic, is a branch point; all possible alternative histories actually exist.[1]

The many-worlds 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 information-theoretic 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 many-worlds splittings, which does not involve information flow between paths, or information flow backwards in time considers alternate outcomes of historical events. According to the many-worlds interpretation, all of the historical speculations entertained within the alternate history genre are realized in parallel universes.[1]

The many-worlds interpretation of reality was anticipated with remarkable fidelity in Olaf Stapledon’s 1937 science fiction novel Star Maker, in a paragraph describing one of the many universes created by the Star Maker god of the title. "In one inconceivably complex cosmos, whenever a creature was faced with several possible courses of action, it took them all, thereby creating many distinct temporal dimensions and distinct histories of the cosmos. Since in every evolutionary sequence of the cosmos there were very many creatures, and each was constantly faced with many possible courses, and the combinations of all their courses were innumerable, an infinity of distinct universes exfoliated from every moment of every temporal sequence in this cosmos."

See also

Notes

  1. ^ a b c d e f g Bryce Seligman DeWitt, Quantum Mechanics and Reality: Could the solution to the dilemma of indeterminism be a universe in which all possible outcomes of an experiment actually occur?, Physics Today, 23(9) pp 30–40 (September 1970) "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." See also Physics Today, letters followup, 24(4), (April 1971), pp 38–44
  2. ^ a b Osnaghi, Stefano; Freitas, Fabio;  
  3. ^ a b Hugh Everett Theory of the Universal Wavefunction, Thesis, Princeton University, (1956, 1973), pp 1–140
  4. ^ a b c d e  
  5. ^ a b c Cecile M. DeWitt, John A. Wheeler eds, The Everett–Wheeler Interpretation of Quantum Mechanics, Battelle Rencontres: 1967 Lectures in Mathematics and Physics (1968)
  6. ^ a b c 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)
  7. ^ a b c d e f g Bryce Seligman DeWitt, R. Neill Graham, eds, The Many-Worlds Interpretation of Quantum Mechanics, Princeton Series in Physics, Princeton University Press (1973), ISBN 0-691-08131-X Contains Everett's thesis: The Theory of the Universal Wavefunction, pp 3–140.
  8. ^ H. Dieter Zeh, On the Interpretation of Measurement in Quantum Theory, Foundation of Physics, vol. 1, pp. 69–76, (1970).
  9. ^ Wojciech Hubert Zurek, Decoherence and the transition from quantum to classical, Physics Today, vol. 44, issue 10, pp. 36–44, (1991).
  10. ^ Wojciech Hubert Zurek, Decoherence, einselection, and the quantum origins of the classical, Reviews of Modern Physics, 75, pp 715–775, (2003)
  11. ^ The Many Worlds Interpretation of Quantum Mechanics
  12. ^ David Deutsch argues that a great deal of fiction is close to a fact somewhere in the so called multiverse, Beginning of Infinity, p. 294
  13. ^ Bryce Seligman DeWitt, R. Neill Graham, eds, The Many-Worlds Interpretation of Quantum Mechanics, Princeton Series in Physics, Princeton University Press (1973), ISBN 0-691-08131-X Contains Everett's thesis: The Theory of the Universal Wavefunction, where the claim to resolves all paradoxes is made on pg 118, 149.
  14. ^ Hugh Everett, Relative State Formulation of Quantum Mechanics, Reviews of Modern Physics vol 29, (July 1957) pp 454–462. The claim to resolve EPR is made on page 462
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  18. ^ a b Everett 1957, section 3, 2nd paragraph, 1st sentence
  19. ^ a b Everett [1956]1973, "Theory of the Universal Wavefunction", chapter 6 (e)
  20. ^  
  21. ^ a b Everett
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  28. ^ James Hartle, Quantum Mechanics of Individual Systems, American Journal of Physics, 1968, vol 36 (#8), pp. 704–712
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  31. ^ Deutsch, D. (1999). Quantum Theory of Probability and Decisions. Proceedings of the Royal Society of London A455, 3129–3137. [1].
  32. ^ David Wallace: Quantum Probability and Decision Theory, Revisited
  33. ^ David Wallace. Everettian Rationality: defending Deutsch’s approach to probability in the Everett interpretation. Stud. Hist. Phil. Mod. Phys. 34 (2003), 415–438.
  34. ^ David Wallace (2003), Quantum Probability from Subjective Likelihood: improving on Deutsch's proof of the probability rule
  35. ^ David Wallace, 2009,A formal proof of the Born rule from decision-theoretic assumptions
  36. ^ Simon Saunders: Derivation of the Born rule from operational assumptions. Proc. Roy. Soc. Lond. A460, 1771–1788 (2004).
  37. ^ Simon Saunders, 2004: What is Probability?
  38. ^ a b David J Baker, Measurement Outcomes and Probability in Everettian Quantum Mechanics, Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, Volume 38, Issue 1, March 2007, Pages 153–169
  39. ^ H. Barnum, C. M. Caves, J. Finkelstein, C. A. Fuchs, R. Schack: Quantum Probability from Decision Theory? Proc. Roy. Soc. Lond. A456, 1175–1182 (2000).
  40. ^ a b Merali, Zeeya (2007-09-21). "Parallel universes make quantum sense". New Scientist (2622). Retrieved 2013-11-22.  (Summary only).
  41. ^ Breitbart.com, Parallel universes exist – study, Sept 23 2007
  42. ^ Perimeter Institute, Seminar overview, Probability in the Everett interpretation: state of play, David Wallace – Oxford University, 21 Sept 2007
  43. ^ Perimeter Institute, Many worlds at 50 conference, September 21–24, 2007
  44. ^ Wojciech H. Zurek: Probabilities from entanglement, Born’s rule from envariance, Phys. Rev. A71, 052105 (2005).
  45. ^ M. Schlosshauer & A. Fine: On Zurek's derivation of the Born rule. Found. Phys. 35, 197–213 (2005).
  46. ^ Lutz Polley, Position eigenstates and the statistical axiom of quantum mechanics, contribution to conference Foundations of Probability and Physics, Vaxjo, Nov 27 – Dec 1, 2000
  47. ^ Lutz Polley, Quantum-mechanical probability from the symmetries of two-state systems
  48. ^ Armando V.D.B. Assis (2011). and the emergence of the Born rule. Annalen der Physik, 2011."\scriptstyle a^{*}_{k}a_{k}"Assis, Armando V.D.B. On the nature of . Annalen der Physik (Berlin) 523: 883–897.  
  49. ^ a b Mark A. Rubin, Locality in the Everett Interpretation of Heisenberg-Picture Quantum Mechanics, Foundations of Physics Letters, 14, (2001) , pp. 301–322, arXiv:quant-ph/0103079
  50. ^ Paul C.W. Davies, Other Worlds, chapters 8 & 9 The Anthropic Principle & Is the Universe an accident?, (1980) ISBN 0-460-04400-1
  51. ^ Paul C.W. Davies, The Accidental Universe, (1982) ISBN 0-521-28692-1
  52. ^ a b Everett FAQ "Does many-worlds violate Ockham's Razor?"
  53. ^ Bryce Seligman DeWitt, Quantum Mechanics and Reality: Could the solution to the dilemma of indeterminism be a universe in which all possible outcomes of an experiment actually occur?, Physics Today, 23(9) pp 30–40 (September 1970); see equation 10
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  55. ^ Tegmark, Max The Interpretation of Quantum Mechanics: Many Worlds or Many Words?, 1998. To quote: "What Everett does NOT postulate: “At certain magic instances, the world undergoes some sort of metaphysical 'split' into two branches that subsequently never interact.” This is not only a misrepresentation of the MWI, but also inconsistent with the Everett postulate, since the subsequent time evolution could in principle make the two terms...interfere. According to the MWI, there is, was and always will be only one wavefunction, and only decoherence calculations, not postulates, can tell us when it is a good approximation to treat two terms as non-interacting."
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Further reading

  • 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
  • Paul C.W. Davies, Other Worlds, (1980) ISBN 0-460-04400-1
  • James P. Hogan, The Proteus Operation (science fiction involving the many-worlds interpretation, time travel and World War 2 history), Baen, Reissue edition (August 1, 1996) ISBN 0-671-87757-7
  • Adrian Kent, One world versus many: the inadequacy of Everettian accounts of evolution, probability, and scientific confirmation * Asher Peres, Quantum Theory: Concepts and Methods, Kluwer, Dordrecht, 1993.
  • Andrei Linde and Vitaly Vanchurin, How Many Universes are in the Multiverse?
  • Stefano Osnaghi, Fabio Freitas, Olival Freire Jr, The Origin of the Everettian Heresy, Studies in History and Philosophy of Modern Physics 40(2009)97–123. 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.
  • Mark A. Rubin, Locality in the Everett Interpretation of Heisenberg-Picture Quantum Mechanics, Foundations of Physics Letters, 14, (2001), pp. 301–322, arXiv:quant-ph/0103079
  • David Wallace, Harvey R. Brown, Solving the measurement problem: de Broglie–Bohm loses out to Everett, Foundations of Physics, arXiv:quant-ph/0403094
  • David Wallace, Worlds in the Everett Interpretation, Studies in the 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

External links

  • 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.).
  • Michael C Price's Everett FAQ – a clear FAQ-style presentation of the theory.
  • The Many-Worlds Interpretation of Quantum Mechanics – a description for the lay reader with links.
  • Against Many-Worlds Interpretations by Adrian Kent
  • Many-Worlds is a "lost cause" according to R. F. Streater
  • The many worlds of quantum mechanics John Sankey
  • Max Tegmark's web page
  • Henry Stapp's critique of MWI, focusing on the basis problem Canadian J. Phys. 80,1043–1052 (2002).
  • Everett hit count on arxiv.org
  • Many Worlds 50th anniversary conference at Oxford
  • "Many Worlds at 50" conference at Perimeter Institute
  • Scientific American report on the Many Worlds 50th anniversary conference at Oxford
  • Highfield, Roger (September 21, 2007). "Parallel universe proof boosts time travel hopes". The Daily Telegraph. Archived from the original on 2007-10-20. Retrieved 2007-10-26. .
  • HowStuffWorks article
  • Physicists Calculate Number of Parallel Universes Physorg.com October 16, 2009.
  • TED-Education video – How many universes are there?.
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