Many-worlds interpretation

Many-worlds interpretation

Overview
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality
Philosophical realism
Contemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....

 of the universal wavefunction
Universal wavefunction
The Universal Wavefunction or Universal Wave Function is a term introduced by Hugh Everett in his Princeton PhD thesis The Theory of the Universal Wave Function, and forms a core concept in the relative state interpretation or many-worlds interpretation of quantum mechanics...

, but denies the actuality of wavefunction collapse
Wavefunction collapse
In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...

. Many-worlds implies that all possible alternative histories and futures are real, each representing an actual "world" (or "universe"). It is also referred to as MWI, the relative state formulation, the Everett interpretation, the theory of the universal wavefunction, many-universes interpretation, or just many-worlds.

The original relative state formulation is due to Hugh Everett in 1957.
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Encyclopedia
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality
Philosophical realism
Contemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....

 of the universal wavefunction
Universal wavefunction
The Universal Wavefunction or Universal Wave Function is a term introduced by Hugh Everett in his Princeton PhD thesis The Theory of the Universal Wave Function, and forms a core concept in the relative state interpretation or many-worlds interpretation of quantum mechanics...

, but denies the actuality of wavefunction collapse
Wavefunction collapse
In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...

. Many-worlds implies that all possible alternative histories and futures are real, each representing an actual "world" (or "universe"). It is also referred to as MWI, the relative state formulation, the Everett interpretation, the theory of the universal wavefunction, many-universes interpretation, or just many-worlds.

The original relative state formulation is due to Hugh Everett in 1957. Later, this formulation was popularized and renamed many-worlds by Bryce Seligman DeWitt in the 1960s and 1970s. The decoherence approaches to interpreting quantum theory have been further explored and developed, becoming quite popular. MWI is one of many multiverse hypotheses in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 and philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

. It is currently considered a mainstream interpretation along with the other decoherence interpretations and the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

.

Prior to many-worlds, reality had always been viewed as a single unfolding history. Many-worlds, however, views reality as a many-branched tree, wherein every possible quantum outcome is realised. Many-worlds claims to reconcile the observation of non-deterministic
Determinism
Determinism is the general philosophical thesis that states that for everything that happens there are conditions such that, given them, nothing else could happen. There are many versions of this thesis. Each of them rests upon various alleged connections, and interdependencies of things and...

 events, such as the random radioactive decay
Radioactive decay
Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles . The emission is spontaneous, in that the atom decays without any physical interaction with another particle from outside the atom...

, with the fully deterministic equations of quantum physics.

In many-worlds, the subjective appearance
Phenomenalism
Phenomenalism is the view that physical objects do not exist as things in themselves but only as perceptual phenomena or sensory stimuli situated in time and in space...

 of wavefunction collapse is explained by the mechanism of quantum decoherence
Quantum decoherence
In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...

, which resolves all of the correlation paradoxes of quantum theory
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, such as the EPR paradox
EPR paradox
The EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...

 and Schrödinger's cat
Schrödinger's cat
Schrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be...

, since every possible
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 outcome of every event defines or exists in its own "history" or "world". In lay terms, there is a very large—perhaps infinite—number of universes, and everything that could possibly have happened in our past, but did not, has occurred in the past of some other universe or universes.

Outline


Although several versions of many-worlds have been proposed since Hugh Everett
Hugh Everett
Hugh Everett III was an American physicist who first proposed the many-worlds interpretation of quantum physics, which he termed his "relative state" formulation....

's original work, they all contain one key idea: the equations of physics that model the time evolution of systems without embedded observers are sufficient for modelling systems which do contain observers; in particular there is no observation-triggered wave function collapse which the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

 proposes. Provided the theory is linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

 with respect to the wavefunction, the exact form of the quantum
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...

 dynamics modelled, be it the non-relativistic Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

, relativistic quantum field theory or some form of quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

 or string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

, does not alter the validity of MWI since MWI is a metatheory
Metatheory
A metatheory or meta-theory is a theory whose subject matter is some other theory. In other words it is a theory about a theory. Statements made in the metatheory about the theory are called metatheorems....

 applicable to all linear quantum theories
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, and there is no experimental evidence for any non-linearity of the wavefunction in physics. MWI's main conclusion is that the universe (or multiverse
Multiverse
The multiverse is the hypothetical set of multiple possible universes that together comprise all of reality.Multiverse may also refer to:-In fiction:* Multiverse , the fictional multiverse used by DC Comics...

 in this context) is composed of a quantum superposition
Quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics. It holds that a physical system exists in all its particular, theoretically possible states simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations.Mathematically, it...

 of very many, possibly even non-denumerably
Uncountable set
In mathematics, an uncountable set is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural numbers.-Characterizations:There...

 infinitely many, increasingly divergent, non-communicating parallel universes or quantum worlds.

The idea of MWI originated in Everett's Princeton
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....

 Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...

 thesis "The Theory of the Universal Wavefunction
Universal wavefunction
The Universal Wavefunction or Universal Wave Function is a term introduced by Hugh Everett in his Princeton PhD thesis The Theory of the Universal Wave Function, and forms a core concept in the relative state interpretation or many-worlds interpretation of quantum mechanics...

", developed under his thesis advisor John Archibald Wheeler
John Archibald Wheeler
John Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...

, 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
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

). The phrase "many-worlds" is due to Bryce DeWitt
Bryce DeWitt
Bryce Seligman DeWitt was a theoretical physicist renowned for advancing gravity and field theories.-Biography:...

, who was responsible for the wider popularisation of Everett's theory, which had been largely ignored for the first decade after publication. DeWitt's phrase "many-worlds" has become so much more popular than Everett's "Universal Wavefunction
Universal wavefunction
The Universal Wavefunction or Universal Wave Function is a term introduced by Hugh Everett in his Princeton PhD thesis The Theory of the Universal Wave Function, and forms a core concept in the relative state interpretation or many-worlds interpretation of quantum mechanics...

" or Everett-Wheeler's "Relative State Formulation" that many forget that this is only a difference of terminology; the content of both of Everett's papers and DeWitt's popular article is the same.

The many-worlds interpretation shares many similarities with later, other "post-Everett" interpretations of quantum mechanics which also use decoherence to explain the process of measurement or wavefunction collapse. MWI treats the other histories or worlds as real since it regards the universal wavefunction
Universal wavefunction
The Universal Wavefunction or Universal Wave Function is a term introduced by Hugh Everett in his Princeton PhD thesis The Theory of the Universal Wave Function, and forms a core concept in the relative state interpretation or many-worlds interpretation of quantum mechanics...

 as the "basic physical entity" or "the fundamental entity, obeying at all times a deterministic wave equation". The other decoherent interpretations, such as consistent histories
Consistent histories
In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology...

, the Existential Interpretation etc., either regard the extra quantum worlds as metaphorical in some sense, or are agnostic
Agnosticism
Agnosticism is the view that the truth value of certain claims—especially claims about the existence or non-existence of any deity, but also other religious and metaphysical claims—is unknown or unknowable....

 about their reality; it is sometimes hard to distinguish between the different varieties. MWI is distinguished by two qualities: it assumes realism
Philosophical realism
Contemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....

, which it assigns to the wavefunction, and it has the minimal formal structure possible, rejecting any hidden variables
Hidden variables
Hidden variables may refer to:* Hidden variable theories, in physics a class of theories trying to explain away the statistical nature of quantum mechanics* Latent variables, in statistics, variables that are inferred from other observed variables...

, quantum potential
Quantum potential
The quantum potential is a central concept of the de Broglie–Bohm formulation of quantum mechanics, introduced by David Bohm in 1952.Initially presented under the name quantum-mechanical potential, subsequently quantum potential, it was later elaborated upon by Bohm and Basil Hiley in its...

, any form of a collapse postulate (i.e., Copenhagenism
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

) or mental postulates (such as the many-minds interpretation
Many-minds interpretation
The many-minds interpretation of quantum mechanics extends the many-worlds interpretation by proposing that the distinction between worlds should be made at the level of the mind of an individual observer. The concept was first introduced in 1970 by H...

 makes).

Decoherent interpretations of many-worlds use einselection
Einselection
Einselection is short for environment - induced superselection, a nickname coined by Wojciech H. Zurek. Classicality is an emergent property induced in open quantum systems by their environments...

 to explain how a small number of classical pointer states can emerge from the enormous Hilbert space of superpositions have been proposed by Wojciech H. Zurek
Wojciech H. Zurek
Wojciech Hubert Zurek is a well-known physicist and a Laboratory Fellow at Los Alamos National Laboratory. He is a leading authority on quantum theory, especially decoherence. His work also has a lot of potential benefit to the emerging field of quantum computing.Zurek earned his M.Sc. in Kraków,...

. "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." These ideas complement MWI and bring the interpretation in line with our perception of reality.

Many-worlds is often referred to as a theory
Theory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...

, rather than just an interpretation, by those who propose that many-worlds can make testable predictions (such as David Deutsch
David Deutsch
David Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...

) or is falsifiable (such as Everett) or by those who propose that all the other, non-MW interpretations, are inconsistent, illogical or unscientific in their handling of measurements; Hugh Everett
Hugh Everett
Hugh Everett III was an American physicist who first proposed the many-worlds interpretation of quantum physics, which he termed his "relative state" formulation....

 argued that his formulation was a metatheory
Metatheory
A metatheory or meta-theory is a theory whose subject matter is some other theory. In other words it is a theory about a theory. Statements made in the metatheory about the theory are called metatheorems....

, since it made statements about other interpretations of quantum theory; that it was the "only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world." Deutsch is dismissive that many-worlds is an "interpretation", saying that calling it an interpretation "is like talking about dinosaurs as an interpretation of the fossil record."

Interpreting wavefunction collapse


As with the other interpretations of quantum mechanics, the many-worlds interpretation is motivated by behavior that can be illustrated by the double-slit experiment
Double-slit experiment
The double-slit experiment, sometimes called Young's experiment, is a demonstration that matter and energy can display characteristics of both waves and particles...

. When particles of light
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

 (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
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

 of quantum mechanics proposed a process of "collapse
Wavefunction collapse
In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...

" 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 noted that for a composite system – for example a subject (the "observer" or measuring apparatus) observing an object (the "observed" system, such as a particle) – the statement that either the observer or the observed has a well-defined state is meaningless; in modern parlance the observer and the observed have become entangled
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

; 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
Quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics. It holds that a physical system exists in all its particular, theoretically possible states simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations.Mathematically, it...

 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). Since the wavefunction appears to have collapsed then, Everett reasoned, there was no need to actually assume that it had collapsed. And so, invoking Occam's razor
Occam's razor
Occam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae , is a principle that generally recommends from among competing hypotheses selecting the one that makes the fewest new assumptions.-Overview:The principle is often summarized as "simpler explanations...

, he removed the postulate of wavefunction collapse from the theory.

Probability


A consequence of removing wavefunction collapse
Wavefunction collapse
In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...

 from the quantum formalism is that the Born rule
Born rule
The Born rule is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of quantum mechanics...

 requires derivation, since many-worlds claims to derive its interpretation from the formalism. Attempts have been made, by many-world advocates and others, over the years to derive the Born rule
Born rule
The Born rule is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of quantum mechanics...

, rather than just conventionally assume it, so as to reproduce all the required statistical behaviour associated with quantum mechanics. There is no consensus on whether this has been successful.

Everett, Gleason and Hartle


Everett (1957) briefly derived the Born rule
Born rule
The Born rule is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of quantum mechanics...

 by showing that the Born rule was the only possible rule, and that its derivation was as justified as the procedure for defining probability in classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

. Everett stopped doing research in theoretical physics shortly after obtaining his Ph.D., but his work on probability has been extended by a number of people. Andrew Gleason
Andrew Gleason
Andrew Mattei Gleason was an American mathematician and the eponym of Gleason's theorem and the Greenwood–Gleason graph. After briefly attending Berkeley High School he graduated from Roosevelt High School in Yonkers, then Yale University in 1942, where he became a Putnam Fellow...

 (1957) and James Hartle
James Hartle
James Burkett Hartle is an American physicist. He has been a professor of physics at the University of California, Santa Barbara since 1966, and he is currently a member of the external faculty of the Santa Fe Institute...

 (1965) independently reproduced Everett's work, known as Gleason's theorem
Gleason's theorem
Gleason's theorem, named after Andrew Gleason, is a mathematical result of particular importance for quantum logic. It proves that the Born rule for the probability of obtaining specific results to a given measurement, follows naturally from the structure formed by the lattice of events in a real...

 which was later extended.

De Witt and Graham


Bryce De Witt and his doctoral student R. Neill Graham later provided alternative (and longer) derivations to Everett's derivation of the Born rule
Born rule
The Born rule is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of quantum mechanics...

. They demonstrated that the norm
Normed vector space
In mathematics, with 2- or 3-dimensional vectors with real-valued entries, the idea of the "length" of a vector is intuitive and can easily be extended to any real vector space Rn. The following properties of "vector length" are crucial....

 of the worlds where the usual statistical rules of quantum theory broke down vanished, in the limit where the number of measurements went to infinity.

Deutsch et al.


An information-theoretic
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

 derivation of the Born rule from Everettarian assumptions, was produced by David Deutsch
David Deutsch
David Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...

 (1999) and refined by Wallace (2002–2009) and Saunders (2004). Deutsch's derivation is a two-stage proof: first he shows that the number of orthonormal
Orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for inner product space V with finite dimension is a basis for V whose vectors are orthonormal. For example, the standard basis for a Euclidean space Rn is an orthonormal basis, where the relevant inner product is the dot product of...

 Everett-worlds after a branching is proportional to the conventional probability density
Probability density
Probability density may refer to:* Probability density function in probability theory* The product of the probability amplitude with its complex conjugate in quantum mechanics...

. Then he uses game theory to show that these are all equally likely to be observed. The last step in particular has been criticised for circularity
Circular definition
A circular definition is one that uses the term being defined as a part of the definition or assumes a prior understanding of the term being defined. Either the audience must already know the meaning of the key term, or the definition is deficient in including the term to be defined in the...

. Other 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. In the New Scientist
New Scientist
New Scientist is a weekly non-peer-reviewed English-language international science magazine, which since 1996 has also run a website, covering recent developments in science and technology for a general audience. Founded in 1956, it is published by Reed Business Information Ltd, a subsidiary of...

 article, reviewing their presentation at a September 2007 conference, Andy Albrecht, a physicist at the University of California at Davis, is quoted as saying "This work will go down as one of the most important developments in the history of science."

Wojciech H. Zurek
Wojciech H. Zurek
Wojciech Hubert Zurek is a well-known physicist and a Laboratory Fellow at Los Alamos National Laboratory. He is a leading authority on quantum theory, especially decoherence. His work also has a lot of potential benefit to the emerging field of quantum computing.Zurek earned his M.Sc. in Kraków,...

 (2005) has produced a derivation of the Born rule, where decoherence has replaced Deutsch's informatic assumptions. Lutz Polley (2000) has produced Born rule derivations where the informatic assumptions are replaced by symmetry arguments.

The Born rule and the collapse of the wave function have been obtained in the framework of the relative-state formulation of quantum mechanics by Armando V.D.B. Assis. He has proved that the Born rule and the collapse of the wave function follow from a game-theoretical strategy, namely the Nash equilibrium
Nash equilibrium
In game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...

 within a von Neumann zero-sum game between nature and observer.

Properties of the theory

  • MWI removes the observer-dependent role in the quantum measurement process by replacing wavefunction collapse
    Wavefunction collapse
    In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...

     with quantum decoherence
    Quantum decoherence
    In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...

    . 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 Schrödinger's cat
    Schrödinger's cat
    Schrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be...

     thought-experiment, the EPR paradox
    EPR paradox
    The EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...

    , von Neumann
    John von Neumann
    John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...

    's "boundary problem" and even wave-particle duality. Quantum cosmology
    Quantum cosmology
    In theoretical physics, quantum cosmology is a field attempting to study the effect of quantum mechanics on the formation of the universe, or its early evolution, especially just after the Big Bang...

     also becomes intelligible, since there is no need anymore for an observer outside of the universe.
  • MWI is realist
    Philosophical realism
    Contemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....

    , deterministic, local theory, akin to classical physics
    Classical physics
    What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...

     (including the theory of relativity
    Theory of relativity
    The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

    ), at the expense of losing counterfactual definiteness
    Counterfactual definiteness
    In some interpretations of quantum mechanics, counterfactual definiteness is the ability to speak with meaning of the definiteness of the results of measurements that have not been performed...

    . MWI achieves this by removing wavefunction collapse
    Wavefunction collapse
    In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...

    , which is indeterministic and non-local, from the deterministic and local equations of quantum theory
    Quantum theory
    Quantum theory may mean:In science:*Quantum mechanics: a subset of quantum physics explaining the physical behaviours at atomic and sub-atomic levels*Old quantum theory under the Bohr model...

    .
  • MWI (or other, broader multiverse
    Multiverse (science)
    The multiverse is the hypothetical set of multiple possible universes that together comprise everything that exists and can exist: the entirety of space, time, matter, and energy as well as the physical laws and constants that describe them...

     considerations) provides a context for the anthropic principle
    Anthropic principle
    In astrophysics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental...

     which may provide an explanation for the fine-tuned universe
    Fine-tuned universe
    The fine-tuned universe is the proposition that the conditions that allow life in the Universe can only occur when certain universal fundamental physical constants lie within a very narrow range, so that if any of several fundamental constants were only slightly different the universe would be...

    .
  • MWI, being a decoherent
    Quantum decoherence
    In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...

     formulation, is axiomatically more streamlined than the Copenhagen
    Copenhagen interpretation
    The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

     and other collapse
    Wavefunction collapse
    In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...

     interpretations; and thus favoured under certain interpretations of Occam's razor
    Occam's razor
    Occam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae , is a principle that generally recommends from among competing hypotheses selecting the one that makes the fewest new assumptions.-Overview:The principle is often summarized as "simpler explanations...

    . Of course there are other decoherent interpretations that also possess this advantage with respect to the collapse interpretations.

Common objections and misconceptions

  • The many-worlds interpretation is very vague about the ways to determine when splitting happens, and nowadays usually the criterion is that the two branches have decohered
    Quantum decoherence
    In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...

    . However, present day understanding of decoherence does not allow a completely precise, self contained way to say when the two branches have decohered/"do not interact", and hence many-worlds interpretation remains arbitrary. This is the main objection opponents of this interpretation raise, saying that it is not clear what is precisely meant by branching, and point to the lack of self contained criteria specifying branching.
MWI response: the decoherence or "splitting" or "branching" is complete when the measurement is complete. In Dirac notation
Bra-ket notation
Bra-ket notation is a standard notation for describing quantum states in the theory of quantum mechanics composed of angle brackets and vertical bars. It can also be used to denote abstract vectors and linear functionals in mathematics...

 a measurement is complete when:
where represents the observer having detected the object system in the i-th state. Before the measurement has started the observer states are identical; after the measurement is complete the observer states are orthonormal
Orthonormality
In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and both of unit length. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length...

. Thus a measurement defines the branching process: the branching is as well- or ill- defined as the measurement is; the branching is as complete as the measurement is complete - which is to say that the delta function above represents an idealised measurement. Although true "for all practical purposes" in reality the measurement, and hence the branching, is never fully complete, since delta functions are unphysical,
Since the role of the observer and measurement per se plays no special role in MWI (measurements are handled as all other interactions are) there is no need for a precise definition of what an observer or a measurement is — just as in Newtonian physics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

 no precise definition of either an observer or a measurement was required or expected. In all circumstances the universal wavefunction
Universal wavefunction
The Universal Wavefunction or Universal Wave Function is a term introduced by Hugh Everett in his Princeton PhD thesis The Theory of the Universal Wave Function, and forms a core concept in the relative state interpretation or many-worlds interpretation of quantum mechanics...

 is still available to give a complete description of reality.
Also, it is a common misconception to think that branches are completely separate. In Everett's formulation, they may in principle quantum interfere (i.e., "merge" instead of "splitting") with each other in the future, although this requires all "memory" of the earlier branching event to be lost, so no observer ever sees two branches of reality.
  • MWI states that there is no special role nor need for precise definition of measurement in MWI, yet Everett uses the word "measurement" repeatedly throughout its exposition.
MWI response: "measurements" are treated as a subclass of interactions, which induce subject-object correlations in the combined wavefunction. There is nothing special about measurements (such as the ability to trigger a wave function collapse), that cannot be dealt with by the usual unitary
Unitarity (physics)
In quantum physics, unitarity is a restriction on the allowed evolution of quantum systems that insures the sum of probabilities of all possible outcomes of any event is always 1....

 time development process. This is why there is no precise definition of measurement in Everett's formulation, although some other formulations emphasise that measurements must be effectively irreversible or create classical information.
  • The splitting of worlds forward in time, but not backwards in time (i.e. i.e. merging worlds), is time asymmetric and incompatible with the time symmetric nature of Schrödinger's equation, or CPT invariance in general.
MWI response: The splitting is time asymmetric; this observed temporal asymmetry is due to the boundary conditions imposed by the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

  • There is circularity in Everett's measurement theory. Under the assumptions made by Everett, there are no 'good observations' as defined by him, and since his analysis of the observational process depends on the latter, it is void of any meaning. The concept of a 'good observation' is the projection
    Projection (linear algebra)
    In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that P2 = P. It leaves its image unchanged....

     postulate in disguise and Everett's analysis simply derives this postulate by having assumed it, without any discussion.

MWI response: Everett's treatment of observations / measurements covers both idealised good measurements and the more general bad or approximate cases. Thus it is legitimate to analyse probability in terms of measurement; no circularity is present.

  • Talk of probability in Everett presumes the existence of a preferred basis to identify measurement outcomes for the probabilities to range over. But the existence of a preferred basis can only be established by the process of decoherence, which is itself probabilistic or arbitrary.
MWI response: Everett analysed branching using what we now call the "measurement basis
Basis (linear algebra)
In linear algebra, a basis is a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space or free module, or, more simply put, which define a "coordinate system"...

". It is fundamental theorem of quantum theory that nothing measurable or empirical is changed by adopting a different basis. Everett was therefore free to choose whatever basis he liked. The measurement basis was simply the simplest basis in which to analyse the measurement process.

  • We cannot be sure that the universe is a quantum multiverse until we have a theory of everything
    Theory of everything
    A theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....

     and, in particular, a successful theory of quantum gravity
    Quantum gravity
    Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

    . If the final theory of everything is non-linear
    Linear
    In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

     with respect to wavefunctions then many-worlds would be invalid.

MWI response: All accepted quantum theories
Quantum theory
Quantum theory may mean:In science:*Quantum mechanics: a subset of quantum physics explaining the physical behaviours at atomic and sub-atomic levels*Old quantum theory under the Bohr model...

 of fundamental physics are linear with respect to the wavefunction. While quantum gravity or string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

 may be non-linear in this respect there is no evidence to indicate this at the moment.

  • Conservation of energy
    Conservation of energy
    The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

     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.

  • Occam's Razor
    Occam's razor
    Occam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae , is a principle that generally recommends from among competing hypotheses selecting the one that makes the fewest new assumptions.-Overview:The principle is often summarized as "simpler explanations...

     rules against a plethora of unobservable universes — Occam would prefer just one universe; i.e., any non-MWI interpretation.

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. 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 and , i.e., , i.e., weighted by coefficients a and b, then if , 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
Born rule
The Born rule is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of quantum mechanics...

.

  • Violation of the principle of locality
    Principle of locality
    In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. Experiments have shown that quantum mechanically entangled particles must violate either the principle of locality or the form of philosophical realism known as counterfactual...

    , which contradicts special relativity
    Special relativity
    Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

    : 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
    Simultaneity
    Simultaneity is the property of two events happening at the same time in at least one frame of reference. The word derives from the Latin simul, at the same time plus the suffix -taneous, abstracted from spontaneous .The noun simult means a supernatural coincidence, two or more divinely...

     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
    EPR paradox
    The EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...

     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
Schrödinger's cat
Schrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be...

 until we look in the box). For spacelike separated splitting you can't say which occurred first — but this is true of all spacelike separated events, simultaneity
Simultaneity
Simultaneity is the property of two events happening at the same time in at least one frame of reference. The word derives from the Latin simul, at the same time plus the suffix -taneous, abstracted from spontaneous .The noun simult means a supernatural coincidence, two or more divinely...

 is not defined for them. Splitting is no exception; many-worlds is a local theory.

Brief overview



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 (the surface of) a sphere called the Bloch sphere
Bloch sphere
In quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system , named after the physicist Felix Bloch....

. 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


The goal of the relative-state formalism, as originally proposed by Everett in his 1957 doctoral dissertation, was to interpret the effect of external observation entirely within the mathematical framework developed by Paul Dirac
Paul Dirac
Paul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...

, 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 interpretation makes two assumptions. The first is that the wavefunction is not simply a description of the object's state, but that it actually is entirely equivalent to the object, a claim it has in common with some other interpretations. The second is that observation or measurement has no special role, unlike in the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

 which considers the wavefunction collapse as a special kind of event which occurs as a result of observation.

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
Brownian motion
Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...

.
Under the many-worlds interpretation, the Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

, 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
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

 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 interepretation based on the difference in the correspondence between the formalism and the experience (the results of experiments).”

However, in 1985 David Deutsch published three related thought experiments which could test the theory vs the Copenhagen interpretation. 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. 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, and another claim by Rainer Plaga (1997), published in Foundations of Physics
Foundations of Physics
Foundations of Physics is a monthly journal "devoted to the conceptual bases and fundamental theories of modern physics and cosmology, emphasizing the logical, methodological, and philosophical premises of modern physical theories and procedures"...

, that communication might be possible between worlds. As of 2010, there are no feasible experiments to test the theory.

Copenhagen interpretation


In the Copenhagen interpretation, the mathematics of quantum mechanics allows one to predict probabilities
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 for the occurrence of various events. In the many-worlds interpretation, all these events occur simultaneously. What meaning should be given to these probability calculations? And why do we observe, in our history, that the events with a higher computed probability seem to have occurred more often? One answer to these questions is to say that there is a probability measure
Probability measure
In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity...

 on the space of all possible universes, where a possible universe is a complete path in the tree of branching universes. This is indeed what the calculations seem to give. Then we should expect to find ourselves in a universe with a relatively high probability rather than a relatively low probability: even though all outcomes of an experiment occur, they do not occur in an equal way. As an interpretation which (like other interpretations) is consistent with the equations, it is hard to find testable predictions of MWI.

The universe decaying to a new vacuum state


Any event that changes the number of observers in the universe may have experimental consequences. Quantum tunneling to new vacuum state
Vacuum state
In quantum field theory, the vacuum state is the quantum state with the lowest possible energy. Generally, it contains no physical particles...

 would reduce the number of observers to zero (i.e., kill all life). Some Cosmologists argue that the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

 is in a false vacuum state
False vacuum
In quantum field theory, a false vacuum is a metastable sector of space that appears to be a perturbative vacuum, but is unstable due to instanton effects that may tunnel to a lower energy state. This tunneling can be caused by quantum fluctuations or the creation of high-energy particles...

 and that consequently the universe should have already experienced quantum tunneling to a true vacuum state. This has not happened and is cited as evidence in favor of many-worlds. In some worlds quantum tunneling to a true vacuum state has happened but always other worlds escape this tunneling and remain viable. Which itself is simply another variation on Quantum Suicide
Quantum suicide
In quantum mechanics, quantum suicide is a thought experiment. It was originally published independently by Hans Moravec in 1987 and Bruno Marchal in 1988 and was independently developed further by Max Tegmark in 1998...

 and therefore not testable.

Many-minds



The many-worlds interpretation should not be confused with the similar many-minds
Many-minds interpretation
The many-minds interpretation of quantum mechanics extends the many-worlds interpretation by proposing that the distinction between worlds should be made at the level of the mind of an individual observer. The concept was first introduced in 1970 by H...

 interpretation which defines the split on the level of the observers' minds.

The many-worlds interpretation leads to a deterministic view of nature in which there is no special role for the human mind.

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 that Everett himself was not entirely clear as to what he believed; however MWI adherents (such as DeWitt
Bryce DeWitt
Bryce Seligman DeWitt was a theoretical physicist renowned for advancing gravity and field theories.-Biography:...

, Tegmark
Max Tegmark
Max Tegmark is a Swedish-American cosmologist. Tegmark is a professor at the Massachusetts Institute of Technology and belongs to the scientific directorate of the Foundational Questions Institute.-Early life:...

, Deutsch
David Deutsch
David Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...

 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. Everett's son reported that Hugh Everett "never wavered in his belief over his many-worlds theory". Also Everett was reported to believe "his many-worlds theory guaranteed him immortality".

Advocates of MWI often cite a poll of 72 "leading cosmologists and other quantum field theorists" conducted by the American political scientist David Raub in 1995 showing 58% agreement with "Yes, I think MWI is true"..
The poll is controversial, for example Victor J. Stenger
Victor J. Stenger
Victor John Stenger is an American particle physicist, outspoken atheist, and author, now active in philosophy and popular religious skepticism....

 remarks that Murray Gell-Mann
Murray Gell-Mann
Murray Gell-Mann is an American physicist and linguist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles...

's published work explicitly rejects the existence of simultaneous parallel universes. Collaborating with James Hartle
James Hartle
James Burkett Hartle is an American physicist. He has been a professor of physics at the University of California, Santa Barbara since 1966, and he is currently a member of the external faculty of the Santa Fe Institute...

, Gell-Man 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”.
Max Tegmark
Max Tegmark
Max Tegmark is a Swedish-American cosmologist. Tegmark is a professor at the Massachusetts Institute of Technology and belongs to the scientific directorate of the Foundational Questions Institute.-Early life:...

 also reports the result of a (in his words) '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
Consistent histories
In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology...

 and Bohm interpretations
Bohm interpretation
The de Broglie–Bohm theory, also called the pilot-wave theory, Bohmian mechanics, and the causal interpretation, is an interpretation of quantum theory. In addition to a wavefunction on the space of all possible configurations, it also includes an actual configuration, even in situations where...

." Such polls have been taken at other conferences, for example, in response to Sean Carroll
Sean M. Carroll
Sean Michael Carroll is a senior research associate in the Department of Physics at the California Institute of Technology. He is a theoretical cosmologist specializing in dark energy and general relativity...

's observation, “As crazy as it sounds, most working physicists buy into the many-worlds theory” Michael Nielsen
Michael Nielsen
Michael Aaron Nielsen is a writer living just outside Toronto, Canada. Before, he was an academic in physics. He worked at the Los Alamos National Laboratory, as the Richard Chace Tolman Prize Fellow at Caltech, was Foundation Professor of Quantum Information Science and a Federation Fellow at the...

 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
Asher Peres
Asher Peres was an Israeli physicist, considered a pioneer in quantum information theory. According to his autobiography, he was born in Beaulieu-sur-Dordogne in France, where his father, a Polish electrical engineer, had found work laying down power lines...

 “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.

One of MWI's strongest advocates is David Deutsch
David Deutsch
David Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...

. 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 that MWI will be testable (at least against "naive" Copenhagenism) via the reversible observation of spin.
According to David Deutsch probably less than ten percent of the physicists are talking parallel universes language

Asher Peres
Asher Peres
Asher Peres was an Israeli physicist, considered a pioneer in quantum information theory. According to his autobiography, he was born in Beaulieu-sur-Dordogne in France, where his father, a Polish electrical engineer, had found work laying down power lines...

 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
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

. Peres seems to suggest that positing the existence of an infinite number of non-communicating parallel universes
Multiverse
The multiverse is the hypothetical set of multiple possible universes that together comprise all of reality.Multiverse may also refer to:-In fiction:* Multiverse , the fictional multiverse used by DC Comics...

 is highly suspect per those who interpret it as a violation of Occam's Razor
Occam's razor
Occam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae , is a principle that generally recommends from among competing hypotheses selecting the one that makes the fewest new assumptions.-Overview:The principle is often summarized as "simpler explanations...

, i.e. that it does not minimize the number of hypothesized entities. However, precisely the opposite conclusion is drawn, simply by applying Occam's Razor to the set of assumptions. It's understood the number of elementary particles are not a gross violation of Occam's Razor, one counts the types, not the tokens. Max Tegmark
Max Tegmark
Max Tegmark is a Swedish-American cosmologist. Tegmark is a professor at the Massachusetts Institute of Technology and belongs to the scientific directorate of the Foundational Questions Institute.-Early life:...

 remarks that the alternative to many-worlds is "many words", an allusion
Allusion
An allusion is a figure of speech that makes a reference to, or representation of, people, places, events, literary work, myths, or works of art, either directly or by implication. M. H...

 to the complexity of von Neumann's collapse postulate.
MWI is considered by some to be unfalsifiable and hence unscientific because the multiple parallel universes
Multiverse
The multiverse is the hypothetical set of multiple possible universes that together comprise all of reality.Multiverse may also refer to:-In fiction:* Multiverse , the fictional multiverse used by DC Comics...

 are non-communicating, in the sense that no information can be passed between them. Others claim MWI is directly testable. Everett regarded MWI as falsifiable since any test that falsifies conventional quantum theory
Quantum theory
Quantum theory may mean:In science:*Quantum mechanics: a subset of quantum physics explaining the physical behaviours at atomic and sub-atomic levels*Old quantum theory under the Bohr model...

 would also falsify MWI.

According to Martin Gardner
Martin Gardner
Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...

, the "other" worlds of MWI have two different interpretations: real or unreal, and claims that Stephen Hawking
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...

 and Steve 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 David Deutsch
David Deutsch
David Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...

 and Bryce DeWitt
Bryce DeWitt
Bryce Seligman DeWitt was a theoretical physicist renowned for advancing gravity and field theories.-Biography:...

. Hawking has said that "according to Feynman's idea", all the other histories are as "equally real" as our own, and Martin Gardner
Martin Gardner
Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...

 reports Hawking saying that MWI is "trivially true", which is an academic way of saying "obviously 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
Schrödinger's cat
Schrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be...

, 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
Roger Penrose
Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...

, saying "He's a Platonist
Platonic realism
Platonic realism is a philosophical term usually used to refer to the idea of realism regarding the existence of universals or abstract objects after the Greek philosopher Plato , a student of Socrates. As universals were considered by Plato to be ideal forms, this stance is confusingly also called...

 and I'm a positivist
Positivism
Positivism is a a view of scientific methods and a philosophical approach, theory, or system based on the view that, in the social as well as natural sciences, sensory experiences and their logical and mathematical treatment are together the exclusive source of all worthwhile information....

. 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
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

 negates the claimed universality of conventional QM.

Speculative implications


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

Quantum suicide thought experiment



It has been claimed that there is a thought experiment that would clearly differentiate between the many-worlds interpretation and other interpretations of quantum mechanics. It involves a quantum suicide
Quantum suicide
In quantum mechanics, quantum suicide is a thought experiment. It was originally published independently by Hans Moravec in 1987 and Bruno Marchal in 1988 and was independently developed further by Max Tegmark in 1998...

 machine and an experimenter willing to risk death. However, at best, this would only decide the issue for the experimenter; bystanders would learn nothing.

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
Foundations of Physics
Foundations of Physics is a monthly journal "devoted to the conceptual bases and fundamental theories of modern physics and cosmology, emphasizing the logical, methodological, and philosophical premises of modern physical theories and procedures"...

article by Rainer Plaga. It involves an isolated ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

 in an ion trap
Ion trap
An ion trap is a combination of electric or magnetic fields that captures ions in a region of a vacuum system or tube. Ion traps have a number of scientific uses such as mass spectrometery and trapping ions while the ion's quantum state is manipulated...

, a quantum measurement that would yield two parallel worlds (their difference just being in the detection of a single photon), and the excitation
Excitation
-Science:* The excited state of an atom* The excitatory postsynaptic potential* The excitation provided with an electrical generator or alternator-Agitation:*Excitement...

 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 millisecond
Millisecond
A millisecond is a thousandth of a second.10 milliseconds are called a centisecond....

s or nanosecond
Nanosecond
A nanosecond is one billionth of a second . One nanosecond is to one second as one second is to 31.7 years.The word nanosecond is formed by the prefix nano and the unit second. Its symbol is ns....

s, 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
Physical Review
Physical Review is an American scientific journal founded in 1893 by Edward Nichols. It publishes original research and scientific and literature reviews on all aspects of physics. It is published by the American Physical Society. The journal is in its third series, and is split in several...

article by Itano et al. 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 Rabbi flopping formula

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. 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).

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. 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.

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

The reason inter-world communication seems like a possibility is because decoherence which separates the parallel worlds is never fully complete, therefore weak influences from one parallel world to another can still pass between them, and these should be measurable with advanced technology. Deutsch proposed such an experiment in a 1985 International Journal of Theoretical Physics
International Journal of Theoretical Physics
The International Journal of Theoretical Physics is a peer-reviewed scientific journal of physics published by Springer Science+Business Media since 1968. According to the Journal Citation Reports, the journal has a 2010 impact factor of 0.670 and publishes both original research and review articles...

article, but the technology it requires involves human-level artificial intelligence
Artificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...

, still not implemented as of 2011.

Similarity to modal realism


The many-worlds interpretation has some similarity to modal realism
Modal realism
Modal realism is the view, notably propounded by David Kellogg Lewis, that all possible worlds are as real as the actual world. It is based on the following tenets: possible worlds exist; possible worlds are not different in kind from the actual world; possible worlds are irreducible entities; the...

 in philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

, which is the view that the possible world
Possible world
In philosophy and logic, the concept of a possible world is used to express modal claims. The concept of possible worlds is common in contemporary philosophical discourse and has also been disputed.- Possibility, necessity, and contingency :...

s used to interpret modal claims actually exist. Unlike 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
Quantum Zeno effect
The quantum Zeno effect is a name coined by George Sudarshan and Baidyanath Misra of the University of Texas in 1977 in their analysis of the situation in which an unstable particle, if observed continuously, will never decay. One can nearly "freeze" the evolution of the system by measuring it...

. Further, the many-worlds interpretation does not postulate that all conceivable worlds (including ones with alternate physical laws) exist, unlike modal realism.

Time travel


The many-worlds interpretation could be one possible way to resolve the paradoxes that one would expect to arise if time travel
Time travel
Time travel is the concept of moving between different points in time in a manner analogous to moving between different points in space. Time travel could hypothetically involve moving backward in time to a moment earlier than the starting point, or forward to the future of that point without the...

 turns out to be permitted by physics (permitting closed timelike curves and thus violating causality
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....

). 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
Novikov self-consistency principle
The Novikov self-consistency principle, also known as the Novikov self-consistency conjecture, is a principle developed by Russian physicist Igor Dmitriyevich Novikov in the mid-1980s to solve the problem of paradoxes in time travel, which is theoretically permitted in certain solutions of general...

 unnecessary.

Many-worlds in literature and science fiction



The many-worlds interpretation (and the somewhat related concept of possible worlds
Possible Worlds
Possible Worlds may refer to:* Possible worlds, a concept in philosophy* Possible Worlds , by John Mighton** Possible Worlds , by Robert Lepage, based on the Mighton play* Possible Worlds , by Peter Porter...

) has been associated to numerous themes in literature
Literature
Literature is the art of written works, and is not bound to published sources...

, art
Art
Art is the product or process of deliberately arranging items in a way that influences and affects one or more of the senses, emotions, and intellect....

 and science fiction
Science fiction
Science fiction is a genre of fiction dealing with imaginary but more or less plausible content such as future settings, futuristic science and technology, space travel, aliens, and paranormal abilities...

.

Some of these stories or films violate fundamental principles of causality and relativity, and are extremely misleading since the information-theoretic
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

 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.

See also



  • Consistent histories
    Consistent histories
    In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology...

  • EPR paradox
    EPR paradox
    The EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...

  • Fabric of Reality
  • Garden of Forking Paths
  • Interpretation of quantum mechanics
    Interpretation of quantum mechanics
    An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...


  • Many-minds interpretation
    Many-minds interpretation
    The many-minds interpretation of quantum mechanics extends the many-worlds interpretation by proposing that the distinction between worlds should be made at the level of the mind of an individual observer. The concept was first introduced in 1970 by H...

  • Multiverse
    Multiverse (science)
    The multiverse is the hypothetical set of multiple possible universes that together comprise everything that exists and can exist: the entirety of space, time, matter, and energy as well as the physical laws and constants that describe them...

  • Multiple histories
    Multiple histories
    The concept of multiple histories is closely related to the many-worlds interpretation of quantum mechanics. In the same way that the many-worlds interpretation regards possible futures as having a real existence of their own, the theory of multiple histories reverses this in time to regard the...

  • Quantum immortality - a thought experiment.
  • Wave function collapse


Further reading

  • Jeffrey A. Barrett
    Jeffrey A. Barrett
    Jeffrey A. Barrett is Professor of Logic and Philosophy of Science at the University of California, Irvine.-External links:* - Barrett's article on Hugh Everett III's formulation of quantum mechanics in the Stanford Encyclopedia of Philosophy.*...

    , The Quantum Mechanics of Minds and Worlds, Oxford University Press, Oxford, 1999.
  • Julian Brown, Minds, Machines, and the Multiverse, Simon & Schuster, 2000, ISBN 0-684-81481-1
  • The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family by Peter Byrne, ISBN 978-0199552276, Nature review
  • Paul C.W. Davies, Other Worlds, (1980) ISBN 0-460-04400-1
  • James P. Hogan
    James P. Hogan (writer)
    James Patrick Hogan was a British science fiction author.-Biography:Hogan was born in London, England. He was raised in the Portobello Road area on the west side of London...

    , The Proteus Operation (science fiction involving the many-worlds interpretation, time travel and World War 2 history), Baen, Reissue edition (August 1, 1996) ISBN 0671877577
  • Adrian Kent, One world versus many: the inadequacy of Everettian accounts of evolution, probability, and scientific confirmation * Asher Peres
    Asher Peres
    Asher Peres was an Israeli physicist, considered a pioneer in quantum information theory. According to his autobiography, he was born in Beaulieu-sur-Dordogne in France, where his father, a Polish electrical engineer, had found work laying down power lines...

    , Quantum Theory: Concepts and Methods, Kluwer, Dordrecht, 1993.
  • Andrei Linde
    Andrei Linde
    Andrei Dmitriyevich Linde is a Russian-American theoretical physicist and professor of Physics at Stanford University. Dr. Linde is best known for his work on the concept of the inflationary universe. He received his Bachelor of Science degree from Moscow State University. In 1975, Linde was...

     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
    Hugh Everett
    Hugh Everett III was an American physicist who first proposed the many-worlds interpretation of quantum physics, which he termed his "relative state" formulation....

    , John A Wheeler and Niels Bohr
    Niels Bohr
    Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...

     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,
  • David Wallace
    David Wallace
    David Wallace or Dave Wallace may refer to:*David A. Wallace , urban planner and architect*David Euan Wallace , British Conservative member of parliament*David Foster Wallace , American novelist...

    , Harvey R. Brown
    Harvey Brown (philosopher)
    Harvey R. Brown, is a philosopher of physics. He is professor of philosophy at the University of Oxford and a Fellow of Wolfson College, Oxford, as well as a Fellow of the British Academy....

    , Solving the measurement problem: de Broglie-Bohm loses out to Everett, Foundations of Physics,
  • David Wallace, Worlds in the Everett Interpretation, Studies in the History and Philosophy of Modern Physics, 33, (2002), pp. 637–661,
  • John A. Wheeler and Wojciech Hubert Zurek  (eds), Quantum Theory and Measurement, Princeton University Press
    Princeton University Press
    -Further reading:* "". Artforum International, 2005.-External links:* * * * *...

    , (1983), ISBN 0-691-08316-9

External links