Quotes & Sayings


We, and creation itself, actualize the possibilities of the God who sustains the world, towards becoming in the world in a fuller, more deeper way. - R.E. Slater

There is urgency in coming to see the world as a web of interrelated processes of which we are integral parts, so that all of our choices and actions have [consequential effects upon] the world around us. - Process Metaphysician Alfred North Whitehead

Kurt Gödel's Incompleteness Theorem says (i) all closed systems are unprovable within themselves and, that (ii) all open systems are rightly understood as incomplete. - R.E. Slater

The most true thing about you is what God has said to you in Christ, "You are My Beloved." - Tripp Fuller

The God among us is the God who refuses to be God without us, so great is God's Love. - Tripp Fuller

According to some Christian outlooks we were made for another world. Perhaps, rather, we were made for this world to recreate, reclaim, redeem, and renew unto God's future aspiration by the power of His Spirit. - R.E. Slater

Our eschatological ethos is to love. To stand with those who are oppressed. To stand against those who are oppressing. It is that simple. Love is our only calling and Christian Hope. - R.E. Slater

Secularization theory has been massively falsified. We don't live in an age of secularity. We live in an age of explosive, pervasive religiosity... an age of religious pluralism. - Peter L. Berger

Exploring the edge of life and faith in a post-everything world. - Todd Littleton

I don't need another reason to believe, your love is all around for me to see. – Anon

Thou art our need; and in giving us more of thyself thou givest us all. - Khalil Gibran, Prayer XXIII

Be careful what you pretend to be. You become what you pretend to be. - Kurt Vonnegut

Religious beliefs, far from being primary, are often shaped and adjusted by our social goals. - Jim Forest

We become who we are by what we believe and can justify. - R.E. Slater

People, even more than things, need to be restored, renewed, revived, reclaimed, and redeemed; never throw out anyone. – Anon

Certainly, God's love has made fools of us all. - R.E. Slater

An apocalyptic Christian faith doesn't wait for Jesus to come, but for Jesus to become in our midst. - R.E. Slater

Christian belief in God begins with the cross and resurrection of Jesus, not with rational apologetics. - Eberhard Jüngel, Jürgen Moltmann

Our knowledge of God is through the 'I-Thou' encounter, not in finding God at the end of a syllogism or argument. There is a grave danger in any Christian treatment of God as an object. The God of Jesus Christ and Scripture is irreducibly subject and never made as an object, a force, a power, or a principle that can be manipulated. - Emil Brunner

“Ehyeh Asher Ehyeh” means "I will be that who I have yet to become." - God (Ex 3.14) or, conversely, “I AM who I AM Becoming.”

Our job is to love others without stopping to inquire whether or not they are worthy. - Thomas Merton

The church is God's world-changing social experiment of bringing unlikes and differents to the Eucharist/Communion table to share life with one another as a new kind of family. When this happens, we show to the world what love, justice, peace, reconciliation, and life together is designed by God to be. The church is God's show-and-tell for the world to see how God wants us to live as a blended, global, polypluralistic family united with one will, by one Lord, and baptized by one Spirit. – Anon

The cross that is planted at the heart of the history of the world cannot be uprooted. - Jacques Ellul

The Unity in whose loving presence the universe unfolds is inside each person as a call to welcome the stranger, protect animals and the earth, respect the dignity of each person, think new thoughts, and help bring about ecological civilizations. - John Cobb & Farhan A. Shah

If you board the wrong train it is of no use running along the corridors of the train in the other direction. - Dietrich Bonhoeffer

God's justice is restorative rather than punitive; His discipline is merciful rather than punishing; His power is made perfect in weakness; and His grace is sufficient for all. – Anon

Our little [biblical] systems have their day; they have their day and cease to be. They are but broken lights of Thee, and Thou, O God art more than they. - Alfred Lord Tennyson

We can’t control God; God is uncontrollable. God can’t control us; God’s love is uncontrolling! - Thomas Jay Oord

Life in perspective but always in process... as we are relational beings in process to one another, so life events are in process in relation to each event... as God is to Self, is to world, is to us... like Father, like sons and daughters, like events... life in process yet always in perspective. - R.E. Slater

To promote societal transition to sustainable ways of living and a global society founded on a shared ethical framework which includes respect and care for the community of life, ecological integrity, universal human rights, respect for diversity, economic justice, democracy, and a culture of peace. - The Earth Charter Mission Statement

Christian humanism is the belief that human freedom, individual conscience, and unencumbered rational inquiry are compatible with the practice of Christianity or even intrinsic in its doctrine. It represents a philosophical union of Christian faith and classical humanist principles. - Scott Postma

It is never wise to have a self-appointed religious institution determine a nation's moral code. The opportunities for moral compromise and failure are high; the moral codes and creeds assuredly racist, discriminatory, or subjectively and religiously defined; and the pronouncement of inhumanitarian political objectives quite predictable. - R.E. Slater

God's love must both center and define the Christian faith and all religious or human faiths seeking human and ecological balance in worlds of subtraction, harm, tragedy, and evil. - R.E. Slater

In Whitehead’s process ontology, we can think of the experiential ground of reality as an eternal pulse whereby what is objectively public in one moment becomes subjectively prehended in the next, and whereby the subject that emerges from its feelings then perishes into public expression as an object (or “superject”) aiming for novelty. There is a rhythm of Being between object and subject, not an ontological division. This rhythm powers the creative growth of the universe from one occasion of experience to the next. This is the Whiteheadian mantra: “The many become one and are increased by one.” - Matthew Segall

Without Love there is no Truth. And True Truth is always Loving. There is no dichotomy between these terms but only seamless integration. This is the premier centering focus of a Processual Theology of Love. - R.E. Slater

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Note: Generally I do not respond to commentary. I may read the comments but wish to reserve my time to write (or write from the comments I read). Instead, I'd like to see our community help one another and in the helping encourage and exhort each of us towards Christian love in Christ Jesus our Lord and Savior. - re slater

Wednesday, January 22, 2025

The Many World's of Quantum Science, Part 1




The Many World's Theory of Quantum Science
Part 1

Below is a vital introduction to Part 2 where I explore Whitehead's process cosmology to quantum science's Many Worlds Theory: Whitehead's Many Worlds Interpretation (WMI) v. Contemporary Scientific Cosmologies, Part 2.

R.E.Slater
January 22, 2025

The Multiverse is REAL - David Deutsch
Alex O'Connor   |   Mar 4, 2024

Within Reason Podcast EpisodesMy new Patreon account: / alexoc
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David Deutsch is a British physicist at the University of Oxford. He is a 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. (Wikipedia.)

David Deutsch's book, The Beginning of Infinity: https://amzn.to/49D3rnR

TIMESTAMPS
00:00 Confidence in the Existence of a Multiverse
05:05 Why People Don’t Agree With David’s View
09:52 How Quantum Mechanics Leads to This Conclusion
20:09 How Science Reacted to the Puzzling Experiment Results
32:14 Why Other Explanations Were Insufficient
40:47 How a Wave Function Test Translates Into a Multiverse
43:47 Visualising the Multiverse
53:21 Is David’s Claim Revolutionary or Obvious?
57:15 Are We Far Off From Quantum Computers?
1:06:30 Philosophical Implications of a Multiverse
1:11:41 Quantum Probability
1:16:39 Does the Multiverse Theory Get Rid of Consequentialism?
1:27:45 How Many Different Universes Are in the Multiverse?

* * * * * * *

Many-worlds interpretation
The quantum-mechanical "Schrödinger's cat" paradox according to the many-worlds interpretation. In this interpretation, every quantum event is a branch point; the cat is both alive and dead, even before the box is opened, but the "alive" and "dead" cats are in different branches of the multiverse, both of which are equally real, but which do not interact with each other.

The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wave function collapse.[1] This implies that all possible outcomes of quantum measurements are physically realized in different "worlds".[2] The evolution of reality as a whole in MWI is rigidly deterministic[1]: 9  and local.[3] Many-worlds is also called the relative state formulation or the Everett interpretation, after physicist Hugh Everett, who first proposed it in 1957.[4][5] Bryce DeWitt popularized the formulation and named it many-worlds in the 1970s.[6][1][7][8]

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

The many-worlds interpretation implies that there are many parallel, non-interacting worlds. It is one of a number of multiverse hypotheses in physics and philosophy. MWI views time as a many-branched tree, wherein every possible quantum outcome is realized. This is intended to resolve the measurement problem and thus some paradoxes of quantum theory, such as Wigner's friend,[4]: 4–6  the EPR paradox[5]: 462 [1]: 118  and Schrödinger's cat,[6] since every possible outcome of a quantum event exists in its own world.

Overview of the interpretation

The many-worlds interpretation's key idea is that the linear and unitary dynamics of quantum mechanics applies everywhere and at all times and so describes the whole universe. In particular, it models a measurement as a unitary transformation, a correlation-inducing interaction, between observer and object, without using a collapse postulate, and models observers as ordinary quantum-mechanical systems.[13]: 35–38  This stands in contrast to the Copenhagen interpretation, in which a measurement is a "primitive" concept, not describable by unitary quantum mechanics; using the Copenhagen interpretation the universe is divided into a quantum and a classical domain, and the collapse postulate is central.[13]: 29–30  In MWI there is no division between classical and quantum: everything is quantum and there is no collapse. MWI's main conclusion is that the universe (or multiverse in this context) is composed of a quantum superposition of an uncountable[14] or undefinable[15]: 14–17  amount or number of increasingly divergent, non-communicating parallel universes or quantum worlds.[1] Sometimes dubbed Everett worlds,[1]: 234  each is an internally consistent and actualized alternative history or timeline.

The many-worlds interpretation uses decoherence to explain the measurement process and the emergence of a quasi-classical world.[15][16] Wojciech H. Zurek, one of decoherence theory's pioneers, said: "Under scrutiny of the environment, only pointer states remain unchanged. Other states decohere into mixtures of stable pointer states that can persist, and, in this sense, exist: They are einselected."[17] Zurek emphasizes that his work does not depend on a particular interpretation.[a]

The many-worlds interpretation shares many similarities with the decoherent histories interpretation, which also uses decoherence to explain the process of measurement or wave function collapse.[16]: 9–11  MWI treats the other histories or worlds as real, since it regards the universal wave function as the "basic physical entity"[5]: 455  or "the fundamental entity, obeying at all times a deterministic wave equation".[4]: 115  The decoherent histories interpretation, on the other hand, needs only one of the histories (or worlds) to be real.[16]: 10 

Several authors, including Everett, John Archibald Wheeler and David Deutsch, call many-worlds a theory or metatheory, rather than just an interpretation.[14][18]: 328  Everett argued that it was the "only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world."[19] Deutsch dismissed the idea that many-worlds is an "interpretation", saying that to call it an interpretation "is like talking about dinosaurs as an 'interpretation' of fossil records."[20]: 382 

Formulation

In his 1957 doctoral dissertation, Everett proposed that, rather than relying on external observation for analysis of isolated quantum systems, one could mathematically model an object, as well as its observers, as purely physical systems within the mathematical framework developed by Paul DiracJohn von Neumann, and others, discarding altogether the ad hoc mechanism of wave function collapse.[4][1]

Relative state

Everett's original work introduced the concept of a relative state. Two (or more) subsystems, after a general interaction, become correlated, or as is now said, entangled. Everett noted that such entangled systems can be expressed as the sum of products of states, where the two or more subsystems are each in a state relative to each other. After a measurement or observation one of the pair (or triple...) is the measured, object or observed system, and one other member is the measuring apparatus (which may include an observer) having recorded the state of the measured system. Each product of subsystem states in the overall superposition evolves over time independently of other products. Once the subsystems interact, their states have become correlated or entangled and can no longer be considered independent. 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.

In the example of Schrödinger's cat, after the box is opened, the entangled system is the cat, the poison vial and the observer. One relative triple of states would be the alive cat, the unbroken vial and the observer seeing an alive cat. Another relative triple of states would be the dead cat, the broken vial and the observer seeing a dead cat.

In the example of a measurement of a continuous variable (e.g., position q) the object-observer system decomposes into a continuum of pairs of relative states: the object system's relative state becomes a Dirac delta function each centered on a particular value of q and the corresponding observer relative state representing an observer having recorded the value of q.[4]: 57–64  The states of the pairs of relative states are, post measurement, correlated with each other.

In Everett's scheme, there is no collapse; instead, the Schrödinger equation, or its quantum field theory, relativistic analog, holds all the time, everywhere. An observation or measurement is modeled by applying the wave equation to the entire system, comprising the object being observed and the observer. One consequence is that every observation causes the combined observer–object's wavefunction to change into a quantum superposition of two or more non-interacting branches.

Thus the process of measurement or observation, or any correlation-inducing interaction, splits the system into sets of relative states, where each set of relative states, forming a branch of the universal wave function, is consistent within itself, and all future measurements (including by multiple observers) will confirm this consistency.

Renamed many-worlds

Everett had referred to the combined observer–object system as split by an observation, each split corresponding to the different or multiple possible outcomes of an observation. These splits generate a branching tree, where each branch is a set of all the states relative to each other. Bryce DeWitt popularized Everett's work with a series of publications calling it the Many Worlds Interpretation. Focusing on the splitting process, DeWitt introduced the term "world" to describe a single branch of that tree, which is a consistent history. All observations or measurements within any branch are consistent within themselves.[4][1]

Since many observation-like events have happened and are constantly happening, Everett's model implies that there are an enormous and growing number of simultaneously existing states or "worlds".[b]

Properties

MWI removes the observer-dependent role in the quantum measurement process by replacing wave function collapse with the established mechanism of quantum decoherence.[22] As the observer's role lies at the heart of all "quantum paradoxes" such as the EPR paradox and von Neumann's "boundary problem", this provides a clearer and easier approach to their resolution.[5]

Since the Copenhagen interpretation requires the existence of a classical domain beyond the one described by quantum mechanics, it has been criticized as inadequate for the study of cosmology.[23] While there is no evidence that Everett was inspired by issues of cosmology,[14]: 7  he developed his theory with the explicit goal of allowing quantum mechanics to be applied to the universe as a whole, hoping to stimulate the discovery of new phenomena.[5] This hope has been realized in the later development of quantum cosmology.[24]

MWI is a realistdeterministic and local theory. It achieves this by removing wave function collapse, which is indeterministic and nonlocal, from the deterministic and local equations of quantum theory.[3]

MWI (like other, broader multiverse theories) provides a context for the anthropic principle, which may provide an explanation for the fine-tuned universe.[25][26]

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

Alternative to 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. When particles of light (or anything else) pass through the double slit, a calculation assuming wavelike behavior of light can be used to identify where the particles are likely to be observed. Yet when the particles are observed in this experiment, they appear as particles (i.e., at definite places) and not as non-localized waves.

Some versions of the Copenhagen interpretation of quantum mechanics proposed a process of "collapse" in which an indeterminate quantum system would probabilistically collapse onto, or select, just one determinate outcome to "explain" this phenomenon of observation. Wave function collapse was widely regarded as artificial and ad hoc,[30] so an alternative interpretation in which the behavior of measurement could be understood from more fundamental physical principles was considered desirable.

Everett's PhD work provided such an interpretation. He argued that for a composite system—such as a subject (the "observer" or measuring apparatus) observing an object (the "observed" system, such as a particle)—the claim that either the observer or the observed has a well-defined state is meaningless; in modern parlance, the observer and the observed have become entangled: we can only specify the state of one relative to the other, i.e., the state of the observer and the observed are correlated after the observation is made. This led Everett to derive from the unitary, deterministic dynamics alone (i.e., without assuming wave function collapse) the notion of a relativity of states.

Everett noticed that the unitary, deterministic dynamics alone entailed that after an observation is made each element of the quantum superposition of the combined subject–object wave function 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 wave function collapse has occurred,[1]: 67, 78  which has the consequence that later observations are always consistent with the earlier observations. Thus the appearance of the object's wave function's collapse has emerged from the unitary, deterministic theory itself. (This answered Einstein's early criticism of quantum theory: that the theory should define what is observed, not for the observables to define the theory.)[c] Since the wave function appears to have collapsed then, Everett reasoned, there was no need to actually assume that it had collapsed. And so, invoking Occam's razor, he removed the postulate of wave function collapse from the theory.[1]: 8 

Testability

In 1985, David Deutsch proposed a variant of the Wigner's friend thought experiment as a test of many-worlds versus the Copenhagen interpretation.[32] It consists of an experimenter (Wigner's friend) making a measurement on a quantum system in an isolated laboratory, and another experimenter (Wigner) who would make a measurement on the first one. According to the many-worlds theory, the first experimenter would end up in a macroscopic superposition of seeing one result of the measurement in one branch, and another result in another branch. The second experimenter could then interfere these two branches in order to test whether it is in fact in a macroscopic superposition or has collapsed into a single branch, as predicted by the Copenhagen interpretation. Since then Lockwood, Vaidman, and others have made similar proposals,[33] which require placing macroscopic objects in a coherent superposition and interfering them, a task currently beyond experimental capability.

Probability and the Born rule

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

Everett tried to answer these questions in the paper that introduced many-worlds. To address the incoherence problem, he argued that an observer who makes a sequence of measurements on a quantum system will in general have an apparently random sequence of results in their memory, which justifies the use of probabilities to describe the measurement process.[4]: 69–70  To address the quantitative problem, Everett proposed a derivation of the Born rule based on the properties that a measure on the branches of the wave function should have.[4]: 70–72  His derivation has been criticized as relying on unmotivated assumptions.[35] Since then several other derivations of the Born rule in the many-worlds framework have been proposed. There is no consensus on whether this has been successful.[36][37][38]

Frequentism

DeWitt and Graham[1] and Farhi et al.,[39] among others, have proposed derivations of the Born rule based on a frequentist interpretation of probability. They try to show that in the limit of uncountably many measurements, no worlds would have relative frequencies that didn't match the probabilities given by the Born rule, but these derivations have been shown to be mathematically incorrect.[40][41]

Decision theory

decision-theoretic derivation of the Born rule was produced by David Deutsch (1999)[42] and refined by Wallace[34][43][44][45] and Saunders.[46][47] They consider an agent who takes part in a quantum gamble: the agent makes a measurement on a quantum system, branches as a consequence, and each of the agent's future selves receives a reward that depends on the measurement result. The agent uses decision theory to evaluate the price they would pay to take part in such a gamble, and concludes that the price is given by the utility of the rewards weighted according to the Born rule. Some reviews have been positive, although these arguments remain highly controversial; some theoretical physicists have taken them as supporting the case for parallel universes.[48] For example, a New Scientist story on a 2007 conference about Everettian interpretations[49] quoted physicist Andy Albrecht as saying, "This work will go down as one of the most important developments in the history of science."[48] In contrast, the philosopher Huw Price, also attending the conference, found the Deutsch–Wallace–Saunders approach fundamentally flawed.[50]

Symmetries and invariance

In 2005, Zurek[51] produced a derivation of the Born rule based on the symmetries of entangled states; Schlosshauer and Fine argue that Zurek's derivation is not rigorous, as it does not define what probability is and has several unstated assumptions about how it should behave.[52]

In 2016, Charles Sebens and Sean M. Carroll, building on work by Lev Vaidman,[53] proposed a similar approach based on self-locating uncertainty.[54] In this approach, decoherence creates multiple identical copies of observers, who can assign credences to being on different branches using the Born rule. The Sebens–Carroll approach has been criticized by Adrian Kent,[55] and Vaidman does not find it satisfactory.[56]

Branch counting

In 2021, Simon Saunders produced a branch counting derivation of the Born rule. The crucial feature of this approach is to define the branches so that they all have the same magnitude or 2-norm. The ratios of the numbers of branches thus defined give the probabilities of the various outcomes of a measurement, in accordance with the Born rule.[57]

The preferred basis problem

As originally formulated by Everett and DeWitt, the many-worlds interpretation had a privileged role for measurements: they determined which basis of a quantum system would give rise to the eponymous worlds. Without this the theory was ambiguous, as a quantum state can equally well be described (e.g.) as having a well-defined position or as being a superposition of two delocalized states. The assumption is that the preferred basis to use is the one which assigns a unique measurement outcome to each world. This special role for measurements is problematic for the theory, as it contradicts Everett and DeWitt's goal of having a reductionist theory and undermines their criticism of the ill-defined measurement postulate of the Copenhagen interpretation.[18][35] This is known today as the preferred basis problem.

The preferred basis problem has been solved, according to Saunders and Wallace, among others,[16] by incorporating decoherence into the many-worlds theory.[23][58][59][60] In this approach, the preferred basis does not have to be postulated, but rather is identified as the basis stable under environmental decoherence. In this way measurements no longer play a special role; rather, any interaction that causes decoherence causes the world to split. Since decoherence is never complete, there will always remain some infinitesimal overlap between two worlds, making it arbitrary whether a pair of worlds has split or not.[61] Wallace argues that this is not problematic: it only shows that worlds are not a part of the fundamental ontology, but rather of the emergent ontology, where these approximate, effective descriptions are routine in the physical sciences.[62][15] Since in this approach the worlds are derived, it follows that they must be present in any other interpretation of quantum mechanics that does not have a collapse mechanism, such as Bohmian mechanics.[63]

This approach to deriving the preferred basis has been criticized as creating circularity with derivations of probability in the many-worlds interpretation, as decoherence theory depends on probability and probability depends on the ontology derived from decoherence.[37][51][64] Wallace contends that decoherence theory depends not on probability but only on the notion that one is allowed to do approximations in physics.[13]: 253–254 

History

MWI originated in Everett's Princeton University PhD thesis "The Theory of the Universal Wave Function",[1] developed under his thesis advisor John Archibald Wheeler, a shorter summary of which was published in 1957 under the title "Relative State Formulation of Quantum Mechanics" (Wheeler contributed the title "relative state";[65] Everett originally called his approach the "Correlation Interpretation", where "correlation" refers to quantum entanglement). The phrase "many-worlds" is due to Bryce DeWitt,[1] who was responsible for the wider popularization of Everett's theory, which had been largely ignored for a decade after publication in 1957.[14]

Everett's proposal was not without precedent. In 1952, Erwin Schrödinger gave a lecture in Dublin in which at one point he jocularly warned his audience that what he was about to say might "seem lunatic". He went on to assert that while the Schrödinger equation seemed to be describing several different histories, they were "not alternatives but all really happen simultaneously". According to David Deutsch, this is the earliest known reference to many-worlds; Jeffrey A. Barrett describes it as indicating the similarity of "general views" between Everett and Schrödinger.[66][67][68] Schrödinger's writings from the period also contain elements resembling the modal interpretation originated by Bas van Fraassen. Because Schrödinger subscribed to a kind of post-Machian neutral monism, in which "matter" and "mind" are only different aspects or arrangements of the same common elements, treating the wave function as physical and treating it as information became interchangeable.[69]

Leon Cooper and Deborah Van Vechten developed a very similar approach before reading Everett's work.[70] Zeh also came to the same conclusions as Everett before reading his work, then built a new theory of quantum decoherence based on these ideas.[71]

According to people who knew him, Everett believed in the literal reality of the other quantum worlds.[20] His son and wife reported that he "never wavered in his belief over his many-worlds theory".[72] In their detailed review of Everett's work, Osnaghi, Freitas, and Freire Jr. note that Everett consistently used quotes around "real" to indicate a meaning within scientific practice.[14]: 107 

Reception

MWI's initial reception was overwhelmingly negative, in the sense that it was ignored, with the notable exception of DeWitt. Wheeler made considerable efforts to formulate the theory in a way that would be palatable to Bohr, visited Copenhagen in 1956 to discuss it with him, and convinced Everett to visit as well, which happened in 1959. Nevertheless, Bohr and his collaborators completely rejected the theory.[d] Everett had already left academia in 1957, never to return, and in 1980, Wheeler disavowed the theory.[73]

Support

One of MWI's strongest longtime advocates is David Deutsch.[74] According to him, the single photon interference pattern observed in the double slit experiment can be explained by interference of photons in multiple universes. Viewed 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,[75] Deutsch suggested that parallelism that results from 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". He also proposed that MWI will be testable (at least against "naive" Copenhagenism) when reversible computers become conscious via the reversible observation of spin.[76]

Equivocal

Philosophers of science James Ladyman and Don Ross say that MWI could be true, but do not embrace it. They note that no quantum theory is yet empirically adequate for describing all of reality, given its lack of unification with general relativity, and so do not see a reason to regard any interpretation of quantum mechanics as the final word in metaphysics. They also suggest that the multiple branches may be an artifact of incomplete descriptions and of using quantum mechanics to represent the states of macroscopic objects. They argue that macroscopic objects are significantly different from microscopic objects in not being isolated from the environment, and that using quantum formalism to describe them lacks explanatory and descriptive power and accuracy.[77]

Rejection

Some scientists consider some aspects of MWI to be unfalsifiable and hence unscientific because the multiple parallel universes are non-communicating, in the sense that no information can be passed between them.[78][79]

Victor J. Stenger remarked that Murray Gell-Mann's published work explicitly rejects the existence of simultaneous parallel universes.[80] Collaborating with James Hartle, Gell-Mann worked toward the development of a more "palatable" post-Everett quantum mechanics. Stenger thought it fair to say that most physicists find MWI too extreme, though it "has merit in finding a place for the observer inside the system being analyzed and doing away with the troublesome notion of wave function collapse".[e]

Roger Penrose argues that the idea is flawed because it is based on an oversimplified version of quantum mechanics that does not account for gravity. In his view, applying conventional quantum mechanics to the universe implies the MWI, but the lack of a successful theory of quantum gravity negates the claimed universality of conventional quantum mechanics.[27] According to Penrose, "the rules must change when gravity is involved". He further asserts that gravity helps anchor reality and "blurry" events have only one allowable outcome: "electrons, atoms, molecules, etc., are so minute that they require almost no amount of energy to maintain their gravity, and therefore their overlapping states. They can stay in that state forever, as described in standard quantum theory". On the other hand, "in the case of large objects, the duplicate states disappear in an instant due to the fact that these objects create a large gravitational field".[81][82]

Philosopher of science Robert P. Crease says that MWI is "one of the most implausible and unrealistic ideas in the history of science" because it means that everything conceivable happens.[81] Science writer Philip Ball calls MWI's implications fantasies, since "beneath their apparel of scientific equations or symbolic logic, they are acts of imagination, of 'just supposing'".[81]

Theoretical physicist Gerard 't Hooft also dismisses the idea: "I do not believe that we have to live with the many-worlds interpretation. Indeed, it would be a stupendous number of parallel worlds, which are only there because physicists couldn't decide which of them is real."[83]

Asher Peres was an outspoken critic of MWI. A section of his 1993 textbook had the title Everett's interpretation and other bizarre theories. Peres argued that the various many-worlds interpretations merely shift the arbitrariness or vagueness of the collapse postulate to the question of when "worlds" can be regarded as separate, and that no objective criterion for that separation can actually be formulated.[84]

Polls

A poll of 72 "leading quantum cosmologists and other quantum field theorists" conducted before 1991 by L. David Raub showed 58% agreement with "Yes, I think MWI is true".[85]

Max Tegmark reports the result of a "highly unscientific" poll taken at a 1997 quantum mechanics workshop. According to Tegmark, "The many worlds interpretation (MWI) scored second, comfortably ahead of the consistent histories and Bohm interpretations."[86]

In response to Sean M. Carroll's statement "As crazy as it sounds, most working physicists buy into the many-worlds theory",[87] Michael Nielsen counters: "at a quantum computing conference at Cambridge in 1998, a many-worlder surveyed the audience of approximately 200 people... Many-worlds did just fine, garnering support on a level comparable to, but somewhat below, Copenhagen and decoherence." But Nielsen notes that it seemed most attendees found it to be a waste of time: Peres "got a huge and sustained round of applause…when he got up at the end of the polling and asked 'And who here believes the laws of physics are decided by a democratic vote?'"[88]

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.[89]

A 2011 poll of 33 participants at an Austrian conference on quantum foundations found 6 endorsed MWI, 8 "Information-based/information-theoretical", and 14 Copenhagen;[90] the authors remark that MWI received a similar percentage of votes as in Tegmark's 1997 poll.[90]

Speculative implications

DeWitt has said that Everett, Wheeler, and Graham "do not in the end exclude any element of the superposition. All the worlds are there, even those in which everything goes wrong and all the statistical laws break down."[6] Tegmark affirmed that absurd or highly unlikely events are rare but inevitable under MWI: "Things inconsistent with the laws of physics will never happen—everything else will... it's important to keep track of the statistics, since even if everything conceivable happens somewhere, really freak events happen only exponentially rarely."[91] David Deutsch speculates in his book The Beginning of Infinity that some fiction, such as alternate history, could occur somewhere in the multiverse, as long as it is consistent with the laws of physics.[92][93]

According to Ladyman and Ross, many seemingly physically plausible but unrealized possibilities, such as those discussed in other scientific fields, generally have no counterparts in other branches, because they are in fact incompatible with the universal wave function.[77] According to Carroll, human decision-making, contrary to common misconceptions, is best thought of as a classical process, not a quantum one, because it works on the level of neurochemistry rather than fundamental particles. Human decisions do not cause the world to branch into equally realized outcomes; even for subjectively difficult decisions, the "weight" of realized outcomes is almost entirely concentrated in a single branch.[94]: 214–216 

Quantum suicide is a thought experiment in quantum mechanics and the philosophy of physics that can purportedly distinguish between the Copenhagen interpretation of quantum mechanics and the many-worlds interpretation by a variation of the Schrödinger's cat thought experiment, from the cat's point of view. Quantum immortality refers to the subjective experience of surviving quantum suicide.[95] Most experts believe the experiment would not work in the real world, because the world with the surviving experimenter has a lower "measure" than the world before the experiment, making it less likely that the experimenter will experience their survival.[13]: 371 [33][94][96]

See also

Notes

  1. ^ "Relative states of Everett come to mind. One could speculate about reality of branches with other outcomes. We abstain from this; our discussion is interpretation-free, and this is a virtue."[17]
  2. ^ "every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth into myriads of copies of itself."[6] DeWitt later softened this extreme view, viewing splitting as decoherence driven and local, in line with other modern commentators.[21]
  3. ^ "Whether you can observe a thing or not depends on the theory which you use. It is the theory which decides what can be observed."—Albert Einstein to Werner Heisenberg, objecting to placing observables at the heart of the new quantum mechanics, during Heisenberg's 1926 lecture at Berlin; related by Heisenberg in 1968.[31]
  4. ^ Everett recounted his meeting with Bohr as "that was a hell... doomed from the beginning". Léon Rosenfeld, a close collaborator of Bohr, said "With regard to Everett neither I nor even Niels Bohr could have any patience with him, when he visited us in Copenhagen more than 12 years ago in order to sell the hopelessly wrong ideas he had been encouraged, most unwisely, by Wheeler to develop. He was undescribably[sic] stupid and could not understand the simplest things in quantum mechanics."[14]: 113 
  5. ^ "Gell-Mann and Hartle, along with a score of others, have been working to develop a more palatable interpretation of quantum mechanics that is free of the problems that plague all the interpretations we have considered so far. This new interpretation is called, in its various incarnations, post-Everett quantum mechanics, alternate histories, consistent histories, or decoherent histories. I will not be overly concerned with the detailed differences between these characterizations and will use the terms more or less interchangeably."[80]: 176 

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  82. ^ "If an Electron Can Be in Two Places at Once, Why Can't You?"Discover Magazine.
  83. ^ Melinda, Baldwin (2017-07-11). "Q&A: Gerard 't Hooft on the future of quantum mechanics"Physics Today. No. 7. doi:10.1063/PT.6.4.20170711a.
  84. ^ Peres, Asher (1995). Quantum Theory: Concepts and Methods. Kluwer Academic Publishers. p. 374. ISBN 0-7923-2549-4.
  85. ^ Tipler, Frank (1994). The Physics of Immortality:Modern Cosmology, God and the Resurrection of the Dead. pp. 170–171. In the "yes" column were Stephen Hawking, Richard Feynman, and Murray Gell-Mann
  86. ^ "Max Tegmark on many-worlds (contains MWI poll)".
  87. ^ Caroll, Sean (1 April 2004). "Preposterous Universe". Archived from the original on 8 September 2004.
  88. ^ Nielsen, Michael (3 April 2004). "Michael Nielsen: The Interpretation of Quantum Mechanics". Archived from the original on 20 May 2004.
  89. ^ Survey Results Archived 2010-11-04 at the Wayback Machine
  90. Jump up to:a b Schlosshauer, Maximilian; Kofler, Johannes; Zeilinger, Anton (2013). "A Snapshot of Foundational Attitudes Toward Quantum Mechanics". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics44 (3): 222–230. arXiv:1301.1069Bibcode:2013SHPMP..44..222Sdoi:10.1016/j.shpsb.2013.04.004S2CID 55537196.
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  93. ^ John GribbinSix Impossible Things, Icon Books Limited (2021), ISBN 978-1-7857-8734-8.
  94. Jump up to:a b Carroll, Sean (2019-09-10). Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime. Penguin. ISBN 978-1-5247-4302-4.
  95. ^ Tegmark, Max (November 1998). "Quantum immortality". Retrieved 25 October 2010.
  96. ^ Deutsch, David (2011). "The Beginning". The Beginning of Infinity. Penguin Group.

Further reading



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Wave function collapse

In quantum mechanicswave function collapse, also called reduction of the state vector,[1] occurs when a wave function—initially in a superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is called an observation and is the essence of a measurement in quantum mechanics, which connects the wave function with classical observables such as position and momentum. Collapse is one of the two processes by which quantum systems evolve in time; the other is the continuous evolution governed by the Schrödinger equation.[2]

While standard quantum mechanics postulates wave function collapse to connect quantum to classical models, some extension theories propose physical processes that cause collapse. The in depth study of quantum decoherence has proposed that collapse is related to the interaction of a quantum system with its environment.

Historically, Werner Heisenberg was the first to use the idea of wave function reduction to explain quantum measurement.[3][citation needed]

Mathematical description

In quantum mechanics each measurable physical quantity of a quantum system is called an observable which, for example, could be the position  and the momentum  but also energy  components of spin (), and so on. The observable acts as a linear function on the states of the system; its eigenvectors correspond to the quantum state (i.e. eigenstate) and the eigenvalues to the possible values of the observable. The collection of eigenstates/eigenvalue pairs represent all possible values of the observable. Writing  for an eigenstate and  for the corresponding observed value, any arbitrary state of the quantum system can be expressed as a vector using bra–ket notation:
The kets  specify the different available quantum "alternatives", i.e., particular quantum states.

The wave function is a specific representation of a quantum state. Wave functions can therefore always be expressed as eigenstates of an observable though the converse is not necessarily true.

Collapse

[edit]

To account for the experimental result that repeated measurements of a quantum system give the same results, the theory postulates a "collapse" or "reduction of the state vector" upon observation,[4]: 566 abruptly converting an arbitrary state into a single component eigenstate of the observable:

where the arrow represents a measurement of the observable corresponding to the  basis.[5] For any single event, only one eigenvalue is measured, chosen randomly from among the possible values.

Meaning of the expansion coefficients

The complex coefficients  in the expansion of a quantum state in terms of eigenstates ,
can be written as an (complex) overlap of the corresponding eigenstate and the quantum state:
They are called the probability amplitudes. The square modulus  is the probability that a measurement of the observable yields the eigenstate . The sum of the probability over all possible outcomes must be one:[6]

As examples, individual counts in a double slit experiment with electrons appear at random locations on the detector; after many counts are summed the distribution shows a wave interference pattern.[7] In a Stern-Gerlach experiment with silver atoms, each particle appears in one of two areas unpredictably, but the final conclusion has equal numbers of events in each area.

This statistical aspect of quantum measurements differs fundamentally from classical mechanics. In quantum mechanics the only information we have about a system is its wave function and measurements of its wave function can only give statistical information.[4]: 17 

Terminology

The two terms "reduction of the state vector" (or "state reduction" for short) and "wave function collapse" are used to describe the same concept. A quantum state is a mathematical description of a quantum system; a quantum state vector uses Hilbert space vectors for the description.[8]: 159  Reduction of the state vector replaces the full state vector with a single eigenstate of the observable.

The term "wave function" is typically used for a different mathematical representation of the quantum state, one that uses spatial coordinates also called the "position representation".[8]: 324  When the wave function representation is used, the "reduction" is called "wave function collapse".

The measurement problem

The Schrödinger equation describes quantum systems but does not describe their measurement. Solution to the equations include all possible observable values for measurements, but measurements only result in one definite outcome. This difference is called the measurement problem of quantum mechanics. To predict measurement outcomes from quantum solutions, the orthodox interpretation of quantum theory postulates wave function collapse and uses the Born rule to compute the probable outcomes.[9] Despite the widespread quantitative success of these postulates scientists remain dissatisfied and have sought more detailed physical models. Rather than suspending the Schrödinger equation during the process of measurement, the measurement apparatus should be included and governed by the laws of quantum mechanics.[10]: 127 

Physical approaches to collapse

Quantum theory offers no dynamical description of the "collapse" of the wave function. Viewed as a statistical theory, no description is expected. As Fuchs and Peres put it, "collapse is something that happens in our description of the system, not to the system itself".[11]

Various interpretations of quantum mechanics attempt to provide a physical model for collapse.[12]: 816  Three treatments of collapse can be found among the common interpretations. The first group includes hidden-variable theories like de Broglie–Bohm theory; here random outcomes only result from unknown values of hidden variables. Results from tests of Bell's theorem shows that these variables would need to be non-local. The second group models measurement as quantum entanglement between the quantum state and the measurement apparatus. This results in a simulation of classical statistics called quantum decoherence. This group includes the many-worlds interpretation and consistent histories models. The third group postulates additional, but as yet undetected, physical basis for the randomness; this group includes for example the objective-collapse interpretations. While models in all groups have contributed to better understanding of quantum theory, no alternative explanation for individual events has emerged as more useful than collapse followed by statistical prediction with the Born rule.[12]: 819 

The significance ascribed to the wave function varies from interpretation to interpretation and even within an interpretation (such as the Copenhagen interpretation). If the wave function merely encodes an observer's knowledge of the universe, then the wave function collapse corresponds to the receipt of new information. This is somewhat analogous to the situation in classical physics, except that the classical "wave function" does not necessarily obey a wave equation. If the wave function is physically real, in some sense and to some extent, then the collapse of the wave function is also seen as a real process, to the same extent.[citation needed]

Quantum decoherence

Quantum decoherence explains why a system interacting with an environment transitions from being a pure state, exhibiting superpositions, to a mixed state, an incoherent combination of classical alternatives.[13] This transition is fundamentally reversible, as the combined state of system and environment is still pure, but for all practical purposes irreversible in the same sense as in the second law of thermodynamics: the environment is a very large and complex quantum system, and it is not feasible to reverse their interaction. Decoherence is thus very important for explaining the classical limit of quantum mechanics, but cannot explain wave function collapse, as all classical alternatives are still present in the mixed state, and wave function collapse selects only one of them.[14][15][13]

The form of decoherence known as environment-induced superselection proposes that when a quantum system interacts with the environment, the superpositions apparently reduce to mixtures of classical alternatives. The combined wave function of the system and environment continue to obey the Schrödinger equation throughout this apparent collapse.[16] More importantly, this is not enough to explain actual wave function collapse, as decoherence does not reduce it to a single eigenstate.[14][13]

History

The concept of wavefunction collapse was introduced by Werner Heisenberg in his 1927 paper on the uncertainty principle, "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik", and incorporated into the mathematical formulation of quantum mechanics by John von Neumann, in his 1932 treatise Mathematische Grundlagen der Quantenmechanik.[17] Heisenberg did not try to specify exactly what the collapse of the wavefunction meant. However, he emphasized that it should not be understood as a physical process.[18] Niels Bohr never mentions wave function collapse in his published work, but he repeatedly cautioned that we must give up a "pictorial representation". Despite the differences between Bohr and Heisenberg, their views are often grouped together as the "Copenhagen interpretation", of which wave function collapse is regarded as a key feature.[19]

John von Neumann's influential 1932 work Mathematical Foundations of Quantum Mechanics took a more formal approach, developing an "ideal" measurement scheme[20][21]: 1270 that postulated that there were two processes of wave function change:

  1. The probabilistic, non-unitarynon-local, discontinuous change brought about by observation and measurement (state reduction or collapse).
  2. The deterministic, unitary, continuous time evolution of an isolated system that obeys the Schrödinger equation.

In 1957 Hugh Everett III proposed a model of quantum mechanics that dropped von Neumann's first postulate. Everett observed that the measurement apparatus was also a quantum system and its quantum interaction with the system under observation should determine the results. He proposed that the discontinuous change is instead a splitting of a wave function representing the universe.[21]: 1288  While Everett's approach rekindled interest in foundational quantum mechanics, it left core issues unresolved. Two key issues relate to origin of the observed classical results: what causes quantum systems to appear classical and to resolve with the observed probabilities of the Born rule.[21]: 1290 [20]: 5 

Beginning in 1970 H. Dieter Zeh sought a detailed quantum decoherence model for the discontinuous change without postulating collapse. Further work by Wojciech H. Zurek in 1980 lead eventually to a large number of papers on many aspects of the concept.[22] Decoherence assumes that every quantum system interacts quantum mechanically with its environment and such interaction is not separable from the system, a concept called an "open system".[21]: 1273  Decoherence has been shown to work very quickly and within a minimal environment, but as yet it has not succeeded in a providing a detailed model replacing the collapse postulate of orthodox quantum mechanics.[21]: 1302 

By explicitly dealing with the interaction of object and measuring instrument, von Neumann[2] described a quantum mechanical measurement scheme consistent with wave function collapse. However, he did not prove the necessity of such a collapse. Von Neumann's projection postulate was conceived based on experimental evidence available during the 1930s, in particular Compton scattering. Later work refined the notion of measurements into the more easily discussed first kind, that will give the same value when immediately repeated, and the second kind that give different values when repeated.[23][24][25]

See also

References

  1. ^ Penrose, Roger (May 1996). "On Gravity's role in Quantum State Reduction"General Relativity and Gravitation28 (5): 581–600. doi:10.1007/BF02105068ISSN 0001-7701.
  2. Jump up to:a b J. von Neumann (1932). Mathematische Grundlagen der Quantenmechanik (in German). Berlin: Springer.
    J. von Neumann (1955). Mathematical Foundations of Quantum MechanicsPrinceton University Press.
  3. ^ Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. Phys. 43: 172–198. Translation as "The actual content of quantum theoretical kinematics and mechanics".
  4. Jump up to:a b Griffiths, David J.; Schroeter, Darrell F. (2018). Introduction to quantum mechanics (3 ed.). Cambridge; New York, NY: Cambridge University Press. ISBN 978-1-107-18963-8.
  5. ^ Hall, Brian C. (2013). Quantum theory for mathematicians. Graduate texts in mathematics. New York: Springer. p. 68. ISBN 978-1-4614-7115-8.
  6. ^ Griffiths, David J. (2005). Introduction to Quantum Mechanics, 2e. Upper Saddle River, New Jersey: Pearson Prentice Hall. p. 107. ISBN 0131118927.
  7. ^ Bach, Roger; Pope, Damian; Liou, Sy-Hwang; Batelaan, Herman (2013-03-13). "Controlled double-slit electron diffraction"New Journal of Physics15 (3). IOP Publishing: 033018. arXiv:1210.6243Bibcode:2013NJPh...15c3018Bdoi:10.1088/1367-2630/15/3/033018ISSN 1367-2630S2CID 832961.
  8. Jump up to:a b Messiah, Albert (1966). Quantum Mechanics. North Holland, John Wiley & Sons. ISBN 0486409244.
  9. ^ Zurek, Wojciech Hubert (2003-05-22). "Decoherence, einselection, and the quantum origins of the classical"Reviews of Modern Physics75 (3): 715–775. arXiv:quant-ph/0105127doi:10.1103/RevModPhys.75.715ISSN 0034-6861.
  10. ^ Susskind, Leonard; Friedman, Art; Susskind, Leonard (2014). Quantum mechanics: the theoretical minimum; [what you need to know to start doing physics]. The theoretical minimum / Leonard Susskind and George Hrabovsky. New York, NY: Basic Books. ISBN 978-0-465-06290-4.
  11. ^ Fuchs, Christopher A.; Peres, Asher (2000-03-01). "Quantum Theory Needs No 'Interpretation'"Physics Today53 (3): 70–71. doi:10.1063/1.883004ISSN 0031-9228.
  12. Jump up to:a b Stamatescu, Ion-Olimpiu (2009). Greenberger, Daniel; Hentschel, Klaus; Weinert, Friedel (eds.). Wave Function Collapse. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 813–822. doi:10.1007/978-3-540-70626-7_230ISBN 978-3-540-70622-9.
  13. Jump up to:a b c Fine, Arthur (2020). "The Role of Decoherence in Quantum Mechanics"Stanford Encyclopedia of Philosophy. Center for the Study of Language and Information, Stanford University website. Retrieved 11 April 2021.
  14. Jump up to:a b Schlosshauer, Maximilian (2005). "Decoherence, the measurement problem, and interpretations of quantum mechanics". Rev. Mod. Phys76 (4): 1267–1305. arXiv:quant-ph/0312059Bibcode:2004RvMP...76.1267Sdoi:10.1103/RevModPhys.76.1267S2CID 7295619.
  15. ^ Wojciech H. Zurek (2003). "Decoherence, einselection, and the quantum origins of the classical". Reviews of Modern Physics75 (3): 715. arXiv:quant-ph/0105127Bibcode:2003RvMP...75..715Zdoi:10.1103/RevModPhys.75.715S2CID 14759237.
  16. ^ Zurek, Wojciech Hubert (2009). "Quantum Darwinism". Nature Physics5 (3): 181–188. arXiv:0903.5082Bibcode:2009NatPh...5..181Zdoi:10.1038/nphys1202S2CID 119205282.
  17. ^ C. Kiefer (2002). "On the interpretation of quantum theory—from Copenhagen to the present day". arXiv:quant-ph/0210152.
  18. ^ G. Jaeger (2017). ""Wave-Packet Reduction" and the Quantum Character of the Actualization of Potentia"Entropy19 (10): 13. Bibcode:2017Entrp..19..513Jdoi:10.3390/e19100513hdl:2144/41814.
  19. ^ Henrik Zinkernagel (2016). "Niels Bohr on the wave function and the classical/quantum divide". Studies in History and Philosophy of Modern Physics539–19. arXiv:1603.00353Bibcode:2016SHPMP..53....9Zdoi:10.1016/j.shpsb.2015.11.001S2CID 18890207Among Bohr scholars it is common to assert that Bohr never mentions the wave function collapse (see e.g. Howard, 2004 and Faye, 2008). It is true that in Bohr's published writings, he does not discuss the status or existence of this standard component in the popular image of the Copenhagen interpretation.
  20. Jump up to:a b Hartle, James B. "The quantum mechanics of cosmology." Notes from the lectures by the author at the 7th Jerusalem Winter School 1990 on Quantum Cosmology and Baby Universes. arXiv:1805.12246 (2018).
  21. Jump up to:a b c d e Schlosshauer, Maximilian (2005-02-23). "Decoherence, the measurement problem, and interpretations of quantum mechanics"Reviews of Modern Physics761267–1305. arXiv:quant-ph/0312059doi:10.1103/RevModPhys.76.1267ISSN 0034-6861.
  22. ^ Camilleri, Kristian (2009-12-01). "A history of entanglement: Decoherence and the interpretation problem"Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. On The History Of The Quantum. 40 (4): 290–302. doi:10.1016/j.shpsb.2009.09.003ISSN 1355-2198.
  23. ^ W. Pauli (1958). "Die allgemeinen Prinzipien der Wellenmechanik". In S. Flügge (ed.). Handbuch der Physik (in German). Vol. V. Berlin: Springer-Verlag. p. 73.
  24. ^ L. Landau & R. Peierls (1931). "Erweiterung des Unbestimmtheitsprinzips für die relativistische Quantentheorie". Zeitschrift für Physik (in German). 69 (1–2): 56–69. Bibcode:1931ZPhy...69...56Ldoi:10.1007/BF01391513S2CID 123160388.)
  25. ^ Discussions of measurements of the second kind can be found in most treatments on the foundations of quantum mechanics, for instance, J. M. Jauch (1968). Foundations of Quantum Mechanics. Addison-Wesley. p. 165.B. d'Espagnat (1976). Conceptual Foundations of Quantum Mechanics. W. A. Benjamin. pp. 18, 159.; and W. M. de Muynck (2002). Foundations of Quantum Mechanics: An Empiricist Approach. Kluwer Academic Publishers. section 3.2.4.

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