A. Drezet
This is a manuscript to be published as a book chapter. The text summarizes some of my critics concerning Everett's theory as seen from the perspective of a Bohmian. This is the second draft and comments are still welcome.
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The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of probability. This is the first of two reviews of the Everett interpretation, and focuses on structure, with particular attention to the role of decoherence theory. Written in terms of the quantum histories formalism, decoherence theory just is the theory of branching structure, in Everett's sense.
The existence of probability in the sense of the frequency interpretation, i.e. probability as "long term relative frequency," is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the Heisenberg picture. This proof is free of the difficulties encountered in applying to the Everett interpretation previous results regarding relative frequency and probability in quantum mechanics. The ontology of the Everett interpretation in the Heisenberg picture is also discussed.
An analysis is made of Deutsch's recent claim to have derived the Born rule from decision-theoretic assumptions. It is argued that Deutsch's proof must be understood in the explicit context of the Everett interpretation, and that in this context, it essentially succeeds. Some comments are made about the criticism of Deutsch's proof by Barnum, Caves, Finkelstein, Fuchs, and Schack; it is argued that the flaw which they point out in the proof does not apply if the Everett interpretation is assumed. A longer version of this paper, entitled "Quantum Probability and Decision Theory, Revisted", is a…
Byrne and Hall (1999) criticized the argument of Chalmers (1996) in favor of the Everett-style interpretation. They claimed to show ``the deep and underappreciated flaw in ANY Everett-style interpretation''. I will argue that it is possible to interpret Chalmers's writing in such a way that most of the criticism by Byrne and Hall does not apply. In any case their general criticism of the many-worlds interpretation is unfounded. The recent recognition that the Everett-style interpretations are good (if not the best) interpretations of quantum mechanics has, therefore, not been negated.
Quantum-mechanical interpretation-related implications of the theory of unitary premeasurement [1] on complete measurement (objectification or collapse included) are investigated in the present article with a view to give an affirmative answer to the question in the title. It is argued that both Bohr's and von Neumann's ideas lead to those of Everett. Hence, the latter can be, in some sense, considered to be a continuation and elaboration of both former approaches. The importance of the idea of relativeness in Everett's theory is emphasized. To free the relative-state theory from its roots bot…
During the last ten years or so, derivations of the Born rule based on decision theory have been proposed and developed, and it is claimed that these are valid in the context of the Everett interpretation. This claim is critically assessed and it is shown that one of its key assumptions, although natural in the context of the Copenhagen interpretation, is not consistent with that of Everett. It is further argued that any interpretation that relates outcome likelihood to the expansion coefficients connecting the wavefunction with the eigenfunctions of the measurement operator must be inconsiste…
Everett's interpretation of quantum mechanics was proposed to avoid problems inherent in the prevailing interpretational frame. It assumes that quantum mechanics can be applied to any system and that the state vector always evolves unitarily. It then claims that whenever an observable is measured, all possible results of the measurement exist. This assertion of multiplicity has been understood in many ways by proponents of Everett's theory. Here we shall illustrate how different views on multiplicity carry onto different views on spacetime.
I discuss the meaning of probability in the Everett-Wheeler interpretation of quantum mechanics, together with the problem of defining histories. To resolve these, I propose an understanding of probability arising from a form of temporal logic: the probability of a future-tense proposition is identified with its truth value in a many-valued and context-dependent logic. In short, probability is degree of truth. These ideas appear to be new (though I expect correction on this), but they are natural and intuitive, and relate to traditional naive ideas of time and chance. Indeed, I argue that Ever…
We analyze quantum superdense coding as would be seen in Everett's many worlds interpretation of measurement, and compare it to Everettian teleportation.
Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is given to a representation in which initial-condition in…
In the many-worlds interpretations (MWIs) of Everett and others, if I am the observer, there are several versions of me but no version is singled out as the one corresponding to my perceptions. However, it can be shown that the probability law implies one version must be singled out. Thus MWIs do not provide a sufficient basis for probability. If we are to have an acceptable description of the physical universe, MWIs must be supplemented by some mechanism, such as hidden variables or collapse, that singles out one version of the observer as the perceiving version.
We observe a Quantum Brownian Motion (QBM) Model Universe in conjunction with recently established Entanglement Relativity and Parallel Occurrence of Decoherence. The Parallel Occurrence of Decoherence establishes the simultaneous occurrence of decoherence for two mutually irreducible structures (decomposition into subsystems) of the total QBM model universe. First we find that Everett world branching for one structure excludes branching for the alternate structure and in order to reconcile this situation branching cannot be allowed for either of the structures considered. Second, we observe t…
This is a discussion of how we can understand the world-view given to us by the Everett interpretation of quantum mechanics, and in particular the role played by the concept of `world'. The view presented is that we are entitled to use `many-worlds' terminology even if the theory does not specify the worlds in the formalism; this is defended by means of an extensive analogy with the concept of an `instant' or moment of time in relativity, with the lack of a preferred foliation of spacetime being compared with the lack of a preferred basis in quantum theory. Implications for identity of worlds …
It is often objected that the Everett interpretation of QM cannot make sense of quantum probabilities, in one or both of two ways: either it can't make sense of probability at all, or it can't explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections. He argues not only that rational decision under uncertainty makes sense in the Everett interpretation, but also that under reasonable assumptions, the credences of a rational agent in an Everett world should be constrained by the Born rule. David Wallace has developed and defended Deutsch's …
We analyze the objective meaning of probabilities in the context of the many-worlds interpretation of Everett. For this purpose we study in details the weak law of large numbers and the role of typicality and universally negligible probabilities (through the works of Cournot and Borel). We demonstrate that Everett's theory doesn't provide any clue for fixing a probability rule and therefore contradicts irrevocably empirical facts and Born's law.
Everett's interpretation of quantum mechanics was proposed to avoid problems inherent in the prevailing interpretational frame. It assumes that quantum mechanics can be applied to any system and that the state vector always evolves unitarily. It then claims that whenever an observable is measured, all possible results of the measurement exist. This notion of multiplicity has been understood in different ways by proponents of Everett's theory. In fact the spectrum of opinions on various ontological questions raised by Everett's approach is rather large, as we attempt to document in this critica…
I show how the quantum paradoxes occurring when we adopt a standard realist framework (or a framework in which the collapse implies a physical change of the state of the system) vanish if we abandon the idea that a measurement is related (directly or indirectly) to a physical change of state. In Convivial Solipsism, similarly to Everett interpretation, there is no collapse of the wave function. But contrary to Everett interpretation, there is only one world. This allows also to get rid of any non-locality and to provide a solution to the Wigner friend problem and its more recent versions.
Our objective is to demonstrate an inconsistency with both the original and modern Everettian Many Worlds Interpretations. We do this by examining two important corollaries of the universally valid quantum mechanics in the context of the Quantum Brownian Motion (QBM) model: "Entanglement Relativity" and the "parallel occurrence of decoherence." We conclude that the highlighted inconsistency demands that either there is a privileged spatial structure of the QBM model universe or that the Everettian Worlds are not physically real.
The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of probability. This is the second of two reviews of the Everett interpretation, and focuses on probability. Branching processes are identified as chance processes, and the squares of branch amplitudes are chances. Since branching is emergent, physical probability is emergent as well.
Everett's Relative State Interpretation (aka Many Worlds Interpretation) has gained increasing interest due to the progress understanding the role of decoherence. In order to fulfill its promise as an intellectually economic realistic description of the physical world, two postulates are formulated. In short they are 1) for a system with continuous coordinates $\mathbf x$, discrete variable $j$, and state $ψ_j(\mathbf x)$, the density $ρ_j(x)=|ψ_j(x)|^2$ gives the distribution of the location of the system with the respect to the variables $x$ and $j$; 2) an equation of motion for the state $i…
Bell's theorem depends crucially on counterfactual reasoning, and is mistakenly interpreted as ruling out a local explanation for the correlations which can be observed between the results of measurements performed on spatially-separated quantum systems. But in fact the Everett interpretation of quantum mechanics, in the Heisenberg picture, provides an alternative local explanation for such correlations. Measurement-type interactions lead, not to many worlds but, rather, to many local copies of experimental systems and the observers who measure their properties. Transformations of the Heisenbe…
In this brief note, we argue that contrarily to what is still often stated, the Everett many-worlds interpretation of quantum mechanics is not in principle impossible to test. It is actually not more difficult (but not easier either) to test than most other kinds of multiverse theories. We also remind why multiverse scenarios can be falsified.
The role attributed to the observer in various interpretations of quantum mechanics as well as in classical statistical mechanics is discussed, with particular attention being paid to the Everett interpretation. In this context, the important difference between "quasi-classical" (robust against decoherence) and "macroscopically given" (rather than being part of a thermodynamic ensemble) is pointed out.
Excited state decay is examined within the framework of strictly Everett-like (SEL) formulations of quantum mechanics. Even though these formulations were developed for systems of particles as part of a larger system that includes a measurement apparatus, the analysis is carried out in terms of isolated particles because excited state decay measurements are performed under conditions that approximate isolation. It is shown that the time evolution of the wave function describing each particle in a sample of well-isolated identical particles in their lowest excited state must satisfy the same br…
The Everett-interpretation description of isolated measurements, i.e., measurements involving interaction between a measuring apparatus and a measured system but not interaction with the environment, is shown to be unambiguous, claims in the literature to the contrary notwithstanding. The appearance of ambiguity in such measurements is engendered by the fact that, in the Schroedinger picture, information on splitting into Everett copies must be inferred from the history of the combined system. In the Heisenberg picture this information is contained in mathematical quantities associated with a …
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well as those of standard quantum mechanics. It has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Most importantly, the Born rule can be derived by straightforward application of the Laplacian rule, without reliance on a "quantum equilibrium hypothesis" that is crucial for Bohmia…
Geometric phases, Everett's many-worlds interpretation of quantum mechanics, and wormholes
本文利用绝热几何相位构造几何实现，具象化埃弗雷特多世界诠释，并借虫洞概念与量子引力（矩阵模型）建立一致性。
An Elementary Proof That Everett's Quantum Multiverse Is Nonlocal: Bell-Locality and Branch-Symmetry in the Many-Worlds Interpretation
本文针对埃弗雷特多世界理论常被认为具有Bell定域性的观点，通过分析GHZ非定域性定理证明其不满足Bell定域性，指出分支强对称性导致其无法定义概率与还原统计，仅靠添加类Bohm隐变量修正后的理论才明确具有Bell非定域性。
About ten years ago, Itamar Pitowsky and I wrote a paper, 'Two dogmas about quantum mechanics,' in which we outlined an information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. Here I revisit the paper and, following Frauchiger and Renner, I show that the Everett interpretation leads to modal contradictions in 'Wigner's-Friend'-type scenarios that involve 'encapsulated' measurements, where a super-observer (which could be a quantum automaton), with unrestricted ability to measure any arbitrary observable of a complex quantum system, measures th…
Proponents of the Everett interpretation of Quantum Theory have made efforts to show that to an observer in a branch, everything happens as if the projection postulate were true without postulating it. In this paper, we will indicate that it is only possible to deduce this rule if one introduces another postulate that is logically equivalent to introducing the projection postulate as an extra assumption. We do this by examining the consequences of changing the projection postulate into an alternative one, while keeping the unitary part of quantum theory, and indicate that this is a consistent …
We discuss the role that intuitive theories of physics play in the interpretation of quantum mechanics. We compare and contrast naïve physics with quantum mechanics and argue that quantum mechanics is not just hard to understand but that it is difficult to believe, often appearing magical in nature. Quantum mechanics is often discussed in the context of "quantum weirdness" and quantum entanglement is known as "spooky action at a distance." This spookiness is more than just because quantum mechanics doesn't match everyday experience; it ruffles the feathers of our naïve physics cognitive module…
Everett's relative states interpretation of quantum mechanics has met with problems related to probability, the preferred basis, and multiplicity. The third theme, I argue, is the most important one. It has led to developments of the original approach into many-worlds, many-minds, and decoherence-based approaches. The latter especially have been advocated in recent years, in an effort to understand multiplicity without resorting to what is often perceived as extravagant constructions. Drawing from and adding to arguments of others, I show that proponents of decoherence-based approaches have no…
Quantum gravity may have as much to tell us about the foundations and interpretation of quantum mechanics as it does about gravity. The Copenhagen interpretation of quantum mechanics and Everett's Relative State Formulation are complementary descriptions which in a sense are dual to one another. My purpose here is to discuss this duality in the light of the of ER=EPR conjecture.
Physical probability in the Everett interpretation and Bell inequalities
本文提出基于Everett解释的物理概率理论，推导Born规则并推翻贝尔不等式，同时揭示局部因果性原则下的两个漏洞。
Physical Probability in the Everett Interpretation and Bell Inequalities
本文提出一种适用于 Everett 诠释的物理概率理论，该理论与 Born 规则一致，违反贝尔不等式，并展示了其与局部因果性原理的一致性。
The notion of objective probability or chance, as a physical trait of the world, has proved elusive; the identification of chances with actual frequencies does not succeed. An adequate theory of chance should explain not only the connection of chance with statistics, but with degrees of belief, and more broadly the entire phenomenology of (seemingly) chance events and their measurement. Branching structure in the decoherence-based many worlds theory provides an account of what chance is that satisfies all these desiderata, including the requirement that chance involves uncertainty.
Personal Identity and Uncertainty in the Everett Interpretation of Quantum Mechanics
本文论证测量前不确定性方法无法在不违背物理主义基本原则的前提下解决EQM的不连贯问题，并以分叉观点为例加以说明。
The Open Systems View and the Everett Interpretation
本文提出，埃弗雷特（多世界）诠释的支持者应采纳开放系统通用量子理论（GT）作为研究框架，该理论未修改量子形式体系，仅以开放系统视角将系统动力学表征为非幺正的开放形式，且具备与标准量子理论同等的经验支持，契合埃弗雷特诠释精神。
A defence is offered of a version of the branch-counting rule for probability in the Everett interpretation (otherwise known as many-worlds interpretation) of quantum mechanics that both depends on the state and is continuous in the norm topology on Hilbert space. The well-known branch-counting rule, for realistic models of measurements, in which branches are defined by decoherence theory, fails this test. The new rule hinges on the use of decoherence theory in defining branching structure, and specifically decoherent histories theory. On this basis ratios of branch numbers are defined, free o…
We modify the Relative State Interpretation (RSI) of Quantum Mechanics so that it does not imply many worlds and parallel realities. We drop the assumption that probability amplitudes correspond one-to-one with reality: Not all information is contained in amplitudes, and not all amplitudes need be realized. Amplitudes do not "collapse" after a measurement, but evolve continuously, including unrealized ones. After each "event" only one possible outcome is realized. Therefore, if a value is measured, that value is real, all others are not; there is only one reality and one world. Reality content…
Since the scalar product is the only internal structure of a Hilbert space, all vectors of norm 1 are equivalent, in the sense that they form a perfect sphere in the Hilbert space, on which every vector looks the same. The state vector of the universe contains no information that distinguishes it from other state vectors of the same Hilbert space. If the state vector is considered as the only fundamental entity, the world is completely structureless. The illusion of interacting subsystems is due to a "bad" choice of factorization (i.e. decomposition into subsystems) of the Hilbert space. There…
Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer's consciousness into quantum theory of measurements. Most naturally this is achieved in the framework of Everett's "many-worlds interpretation" of quantum mechanics. According to this interpretation, various classical alternatives are perceived by consciousness separately from each other. In the Extended Everett Concept (EEC) proposed by the present author, the separation of the alternatives is identified with the phenomenon of consciousness. This…
Two works related to the concept of probability in the framework of the many-worlds interpretation are presented. The first deals with recent controversy in classical probability theory. Elga and D. Lewis argues that Sleeping Beauty should have different credences for the result of a fair coin toss in a particular situation. It is argued that when the coin is replaced by a quantum coin, the credence is unambiguous and since one should not expect a difference between classical and quantum coins, this provides a particular resolution of the controversy. Second work is an analysis of a recent cri…
The Many Worlds of Uncertainty
本文在新埃弗里特多重世界诠释下考察不确定性关系的含义，并分析不相容可观测量的联合与重复测量问题，揭示该理论对统计陈述的根本不同诠释。
Algorithmic probability has shown some promise in dealing with the probability problem in the Everett interpretation, since it provides an objective, single-case probability measure. Many find the Everettian cosmology to be overly extravagant, however, and algorithmic probability has also provided improved models of subjective probability and Bayesian reasoning. I attempt here to generalize algorithmic Everettianism to more Bayesian and subjectivist interpretations. I present a general framework for applying generative probability, of which algorithmic probability can be considered a special c…
We propose a set of simple quantum optics experiments that test for an entirely new domain of physical laws that govern how an individual's conscious experience traverses the multiverse within Everett's many worlds interpretation of quantum mechanics. These experiments imply an exception to the Born rule in a proposed ''observer-specific'' reference frame. These experiments must be done by you, the reader. If it is performed by anyone else, other than you, the reader, you will observe that the person performing the experiment will observe an outcome that is not special, interesting, or differe…
The paper entitled ``Against Many-Worlds Interpretations'' by A. Kent, which has recently been submitted to the e-Print archive (gr-qc/9703089) contained some misconceptions. The claims on Everett's many-worlds interpretation are quoted and answered.
It is shown that Non-unitary Newtonian Gravity (NNG) model admits a simple interpretation in terms of Feynman path integral, in which the sum over all possible histories is replaced by a summation over pairs of paths. Correlations between different paths are allowed by a fundamental decoherence mechanism of gravitational origin and can be interpreted as a kind of communication between different branches of the wave function. The ensuing formulation could be used in turn as a motivation to introduce Non-unitary Gravity itself.
This chapter, from the Routledge Companion to the Philosophy of Physics (Eleanor Knox and Alastair Wilson, eds., 2021), is an overview of the constraints that relativity places on interpretations of quantum theory. It focuses on four main avenues of approach: (i) additional beables theories, which include "hidden-variables" theories and modal interpretations, (ii) dynamical collapse theories, (iii) Everettian, or "many-worlds" interpretations, and (iv) non-realist interpretations, which deny that quantum states represent anything in physical reality independent of considerations of agents and …
There have been many attempts over the years to derive the Born Rule from the wave equation since Everett's Many Worlds Interpretation was proposed; however, none of these have been satisfactory as shown when critics pointed out loopholes and unsupported assumptions. In this paper the case is made that the currently fashionable decision-theoretic approach founded by David Deutsch and explicated by David Wallace is likewise unsatisfactory. A more fundamental computationalist approach is advocated.
Nonlinear modifications of quantum mechanics have a troubled history. They were initially studied for many promising reasons: resolving the measurement problem, testing the limits of standard quantum mechanics, and reconciling it with gravity. Two results substantially undermined the credibility of non-linear theories. Some have been experimentally refuted, and more importantly, all deterministic non-linear theories can be used for superluminal communication. However, these results are unconvincing because they overlook the fact that the distribution of measurement results predicted by non-lin…
Based on the Sheaf Logic approach to set theoretic forcing, a hierarchy of Quantum Variable Sets is constructed which generalizes and simplifies the analogous construction developed by Takeuti on boolean valued models of set theory. Over this model two alternative proofs of Takeuti's correspondence, between self adjoint operators and the real numbers of the model, are given. This approach results to be more constructive showing a direct relation with the Gelfand representation theorem, revealing also the importance of these results with respect to the interpretation of Quantum Mechanics in clo…
Everettian Branching in the World and of the World
本文研究波函数分支通过与环境的纠缠形成和传播的机制，构建局部相互作用系统的理想化模型，展示分支与违反Bell不等式关联及相对论的相容性，为量子物理基础研究提供具体实例。
Quantum Computation and Many Worlds
本文阐述Saunders与Zurek的Everett多世界诠释，并以此物理描述量子计算过程，同时讨论相关反对意见。
The linear mathematics of quantum mechanics gives many versions of reality instead of the single version we perceive, with the perceived version chosen at random according to a probability law. Because of these peculiarities, the theory requires an interpretation to be fully understood. Over 50 years ago, Everett proposed in his many-worlds interpretation that these characteristics could be accounted for if the mathematics itself, with no collapse or hidden variables, was carefully analyzed. We show this is incorrect; the linear mathematics cannot account for the probability law. Thus the many…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points, both "time" and "world" are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and of Everett's many-worlds interpretation, it has a clear ontology and a set o…
I argue that Deutsch's model for the behavior of systems traveling around closed timelike curves (CTCs) relies implicitly on a substantive metaphysical assumption. Deutsch is employing a version of quantum theory with a significantly supplemented ontology of parallel existent worlds, which differ in kind from the many worlds of the Everett interpretation. Standard Everett does not support the existence of multiple identical copies of the world, which the D-CTC model requires. This has been obscured because he often refers to the branching structure of Everett as a "multiverse", and describes q…
This is an attempt to apply Nagel's distinction between internal and external statements to the interpretation of quantum mechanics. I propose that this distinction resolves the contradiction between unitary evolution and the projection postulate. I also propose a more empirically realistic version of the projection postulate. The result is a version of Everett's relative-state interpretation, including a proposal for how probabilities are to be understood. Based on a talk given at the 9th UK Foundations of Physics meeting in Birmingham on 12 September 2000.
Hugh Everett III presented pure wave mechanics, sometimes referred to as the many-worlds interpretation, as a solution to the quantum measurement problem. While pure wave mechanics is an objectively deterministic physical theory with no probabilities, Everett sought to show how the theory might be understood as making the standard quantum statistical predictions as appearances to observers who were themselves described by the theory. We will consider his argument and how it depends on a particular notion of branch typicality. We will also consider responses to Everett and the relationship betw…
Everett's Many-Worlds Interpretation of quantum mechanics is discussed in the context of other physics disputes and other proposed kinds of parallel universes. We find that only a small fraction of the usual objections to Everett's theory are specific to quantum mechanics, and that all of the most controversial issues crop up also in settings that have nothing to do with quantum mechanics.
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