Jonte R. Hance, Sabine Hossenfelder
A recent Nature Physics editorial (Nat. Phys. (2022) 18, 961) falsely claims ``any theory that uses hidden variables still requires non-local physics.'' We correct this claim and explain why it is important to get this right.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Various interpretations of quantum mechanics, favored (or neglected) by John Bell in the context of his non-locality theorem, are compared and discussed.
Alain Aspect's three experiments on Bell's theorem, published in the early 1980s, were a turning point in the history of the research on the foundations of quantum mechanics not only because they corroborated entanglement as the distinctive quantum signature but also because these experiments brought wider recognition to this field of research and Aspect himself. These experiments may be considered the most direct precursors of the research on quantum information, which would blossom a decade later.
The De Broglie-Bohm (DeBB)\cite{DeBB} Causal Quantum Mechanics played a crucial role in Bell's discovery \cite{Bell1964} that quantum mechanics violates EPR local reality \cite{EPR1935}, and also in Bell's search for an exact quantum mechanics. The experiments of Aspect et al \cite{Aspect1981} confirm quantum correlations between plane polarizations of two photons and violation of Bell's inequalities by a factor $\sqrt 2 $. I prove that similar experiments with elliptic polarizers can also show quantum violations of Bell's inequality by the same factor. I summarize our construction of a maxima…
We review the theorems of Einstein-Podolsky-Rosen (EPR), Bell, Greenberger-Horne-Zeilinger (GHZ), and Hardy, and present arguments supporting the idea that quantum mechanics is a complete, causal, non local, and non separable theory.
We give a simple proof of Bell's inequality in quantum mechanics which, in conjunction with experiments, demonstrates that the local hidden variables assumption is false. The proof sheds light on relationships between the notion of causal interaction and interference between particles.
This article discusses von Neumann's "proof" that hidden variable theories are impossible.
A generalized form of EPR state is defined, embracing both classical and nonclassical states. It is shown that for such states, Bell's inequality is equivalent to a constraint on stochastic field theories. Thus, violation of Bell's inequality can be observed also for weak violation of stochastic field theories. The Schrodinger cat state is shown to be an example of this.
We show that a classical fluid mechanical system can violate Bell's inequality because the fluid motion is correlated over large distances.
We derive monogamy relations (tradeoffs) between strengths of violations of Bell's inequalities from the non-signaling condition. Our result applies to general Bell inequalities with an arbitrary large number of partners, outcomes and measurement settings. The method is simple, efficient and does not require linear programming. The results are used to derive optimal fidelity for asymmetric cloning in nonsignaling theories.
Bell's inequalities in the form given by Wigner are derived from the so-called fundamental assumption of statistical mechanics. I then demonstrate the possible relationship between these inequalities and the second law, particularly if assuming the Pauli exclusion principle dictates the expected outcomes.
Bell's theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell's theorem and its many extensions have led to the claim that quantum mechanics and by inference nature herself are nonlocal in the sense that a measurement on a system by an observer at one location has an immediate effect on a distant "entangled" system (one with which the original system has previously interacted). Einstein was repulsed by such "spooky action at a distance" and was led to question whether quantum mechanics coul…
Non-locality, or quantum-non-locality, are buzzwords in the community of quantum foundation and information scientists, which purportedly describe the implications of Bell's theorem. When such phrases are treated seriously, that is it is claimed that Bell's theorem reveals non-locality as an inherent trait of the quantum description of the micro-world, this leads to logical contradictions, which will be discussed here. In fact, Bell's theorem, understood as violation of Bell inequalities by quantum predictions, is consistent with Bohr's notion of complementarity. Thus, if it points to anything…
We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell's inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experiments to show the violation of Bell's inequality and then further deny the local hidden-variables theory. Considering the difference of their expectation values, a generalized Bell's inequality is presented…
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an extremely simple proof of Bell's inequality: a single figure suffices. This simplicity may be useful in the unending debate of what exactly the Bell inequality means, since the hypothesis at the basis of the proof become extremely transparent. It is also a useful didactic tool, as the Bell inequality can be explained in a single intuitive lecture.
Three classes of local hidden-variable models that violate both Bell and Leggett inequalities are presented. The models, however, do not reproduce the quantum mechanical predictions, hence they are experimentally testable. It is concluded that on one hand neither Bell or Leggett inequality fully captures the essential counterintuitiveness of quantum mechanics, while on the other hand the hypothesis of outcome independence and that of locality are uncorrelated.
We point out that, if one accepts the validity of quantum mechanics, the Bell parameter for the polarization state of two photons can be measured in a simpler way than by the standard procedure [Clauser, Horne, Shimony, and Holt, Phys. Rev. Lett. 23, 880 (1969)]. The proposed method requires only two measurements with parallel linear-polarizer settings for Alice and Bob at 0 and 45 degrees, and yields a significantly smaller statistical error for a large Bell parameter.
The Evolution of the Bell Notion of Beable: from Bohr to Primitive Ontology
本文梳理贝尔“可存在量”概念从早期受玻尔影响但用于批判哥本哈根诠释的表述，到后来启发原始本体论进路的成熟表述的演变，并论证只有后者才真正为量子力学的无歧义表述奠定基础。
No-signaling theories, which can contain nonlocal correlations stronger than classical correlations but limited by the no-signaling condition, have deepened our understanding of the quantum theory. In principle, the nonlocality of these theories can be verified via Bell tests. In practice, however, inefficient detectors may make Bell tests unreliable, which is called the detection efficiency loophole. In this work, we show almost tight lower and upper bounds of the detector efficiency requirement for demonstrating the nonlocality of no-signaling theories, by designing a general class of Bell t…
Both the quantum mechanical and classical Bells experiment are within the focus of this paper. The fact that one measures different probabilities in both experiments is traced back to the superposition of two orthogonal but nonentangled substates in the quantum mechanical case. This superposition results in an interference term that can be splitted into two additional states representing a sink and a source of probabilities in the classical event space related to Bells experiment. As a consequence, a statistical operator can be related to the quantum mechanical Bells experiment that contains a…
In a recent article, Kiukas and Werner claim to have shown that Bohmian Mechanics does not make the same empirical predictions as ordinary Quantum Mechanics. More precisely, they have shown that ordinary Quantum Mechanics predicts maximal violations of the CHSH-Bell inequality for a certain experiment in which only position measurements are performed on two noninteracting entangled free non-relativistic particles. Kiukas and Werner claim that Bohmian Mechanics doesn't predict a violation of the CHSH-Bell inequality for that experiment. We explain that such claim is wrong and that the argument …
The meaning of superselection rules in Bohm-Bell theories (i.e., quantum theories with particle trajectories) is different from that in orthodox quantum theory. More precisely, there are two concepts of superselection rule, a weak and a strong one. Weak superselection rules exist both in orthodox quantum theory and in Bohm-Bell theories and represent the conventional understanding of superselection rules. We introduce the concept of strong superselection rule, which does not exist in orthodox quantum theory. It relies on the clear ontology of Bohm-Bell theories and is a sharper and, in the Boh…
In Bohmian mechanics particles follow continuous trajectories, hence 2-time position correlations are well defined. Nevertheless, Bohmian mechanics predicts the violation of Bell inequalities. Motivated by this fact we investigate position measurements in Bohmian mechanics by coupling the particles to macroscopic pointers. This explains the violation of Bell inequalities despite 2-time position correlations. We relate this fact to so-called surrealistic trajectories that, in our model, correspond to slowly moving pointers. Next, we emphasize that the nice feature of Bohmian mechanics, which do…
According to a widespread view, the Bell theorem establishes the untenability of so-called 'local realism'. On the basis of this view, recent proposals by Leggett, Zeilinger and others have been developed according to which it can be proved that even some non-local realistic theories have to be ruled out. As a consequence, within this view the Bell theorem allows one to establish that no reasonable form of realism, be it local or non-local, can be made compatible with the (experimentally tested) predictions of quantum mechanics. In the present paper it is argued that the Bell theorem has demon…
Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates `local causality') became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about the mathe…
On the representations of Bell's operators in Quantum Mechanics
该研究发现维数大于2的希尔伯特空间中Bell-CHSH不等式的Bell算符存在幺正不等价表示，不同表示违反程度不同，最大违反由Tsirelson界给出，源于空间模式配对机制。
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however,…
This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical balance and entanglement, (b) the thinking that led to the derivation of the original Bell inequality, and (c) the range of claimed implications, including realism, locality and others which attract less attention. The main conclusion is that violation of Bell inequalities appears to have some implications for the nature of physical reality, but that none of the…
We propose a definition of determinism for a physical system that includes, besides the measurement device, the surrounding environment. This enlarged system is assumed to follow a predefined trajectory starting from some (unknown) initial conditions that play the role of hidden variables for the experiment. These assumptions, which are different from realism, allow us to derive a type of time Bell inequalities, which are violated by Quantum Mechanics. In order to illustrate this violation, we discuss the particular case of measurements on a spin 1/2 particle.
I present the background of the Bohm approach that led John Bell to a study of quantum non-locality from which his famous inequalities emerged. I recall the early experiments done at Birkbeck with an aim to explore the possibility of `spontaneous collapse', a way suggested by Schrödinger to avoid the conclusion that quantum mechanics was grossly non-local. I also review some of the work that John did which directly impinged on my own investigations into the foundations of quantum mechanics and report some new investigations towards a more fundamental theory.
We introduce a new interpretation of quantum mechanics by examining the Einstein, Podolsky and Rosen's (EPR) paradox and Bell's inequality experiments under the assumption that the vacuum has an inhomogeneous texture for energy levels below the Heisenberg time-energy uncertainty relation. In this article, selected results from the most reliable Bell's inequality experiments will be quantitatively analyzed to show that our interpretation of quantum mechanics creates a new loophole in Bell's inequality, and that the past experimental findings do not contradict our new interpretation. Under the v…
It is widely accepted that the violation of Bell inequalities excludes local theories of the quantum realm. This paper presents a new derivation of the inequalities from non-trivial non-local theories and formulates a stronger Bell argument excluding also these non-local theories. Taking into account all possible theories, the conclusion of this stronger argument provably is the strongest possible consequence from the violation of Bell inequalities on a qualitative probabilistic level (given usual background assumptions). Among the forbidden theories is a subset of outcome dependent theories s…
Christopher Fuchs and Rüdiger Schack have developed a way of understanding science, which, among other things, resolves many of the conceptual puzzles of quantum mechanics that have vexed people for the past nine decades. They call it QBism. I speculate on how John Bell might have reacted to QBism, and I explain the many ways in which QBism differs importantly from the orthodox ways of thinking about quantum mechanics associated with the term "Copenhagen interpretation."
One examines putative corrections to the Bell operator due to the noncommutativity in the phase-space. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations…
Using a new approach to quantum mechanics we revisit Hardy's proof for Bell's theorem and point out a loophole in it. We also demonstrate on this example that quantum mechanics is a local realistic theory.
Errors in Eberly's derivation of several Bell inequalities are pointed out: (1) it is based on an equation that is incorrect; (2) it uses neither two-particle states nor locality to derive Bell's inequalities and; (3) it does not use entanglement to obtain violations of Bell's inequalities. Even leading and outstanding physicists -- as certainly is the case of Prof. Eberly -- sometimes make elementary mistakes, and this by no means diminishes the importance of their scientific contribution. In general, this is a consequence of an excessive attachment to an idea (nowadays it has become fashiona…
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and empiricist interpretations of the mathematical formalism of quantum mechanics, iii) the distinction between measurement and preparation. It will be demonstrated that an interpretation of violation of Bell's inequality by quantum mechanics as evidence of non-locality of the quantum world is a consequence of a particular choice between these alternatives. Also a…
Separation theorems and Bell inequalities in algebraic quantum mechanics
本文在代数量子力学框架下梳理系统分离定理，沟通 C*-代数与 W*-代数表述，并将 Raggio 的 Bell 不等式刻画改写为 C*-代数形式。
This is a polemical response to Howard Wiseman's recent paper, "The two Bell's theorems of John Bell". Wiseman argues that, in 1964, Bell established a conflict between the quantum mechanical predictions and the joint assumptions of determinism and (what is now usually known as) "parameter independence". Only later, in 1976, did Bell, according to Wiseman, first establish a conflict between the quantum mechanical predictions and locality alone (in the specific form that Bell would sometimes call "local causality"). Thus, according to Wiseman, the long-standing disagreements about what, exactly…
We formulate the expectation value of the Bell-Zukowski operator acting on qubit states of a two-particle Bell experiment. By using the equivalence between a set of N copies of a two-qubit experiment and a standard two-setting Bell experiment in an entangled 2N-particle state, we obtain an inequality, which we may call the Bell-Zukowski inequality. It determines whether the measured correlation functions of two-particle states can be modeled locally and realistically. In this Bell experiment of two particles, the conflict between local realism and quantum mechanics is discussed in conjunction …
The purpose of this comment is to show that a reinterpretation of the results from the Letter: "Physics and Metaphysics of Wigner's Friends: Even performed pre-measurements have no results" allows for reaching the conclusion "pre-measurements have no resul" [arXiv:2003.07464] based only on postulates of quantum mechanics without additional assumptions on irreversibility. Additionally, with supplementary reasoning based on Bell's theorem, one can show that unitary decoherence cannot be solely responsible for the quantum-to-classical transition, and an additional irreversibility model is require…
Bell's theorem of 1965 is a proof that all realistic interpretations of quantum mechanics must be non-local. Bell's theorem consists of two parts: first a correlation inequality is derived that must be satisfied by all local realistic theories; second it is demonstrated that quantum mechanical probabilities violate this inequality in certain cases. In the case of ideal experiments, Bell's theorem has been proven. However, in the case of real experiments where polarizers and detectors are non-ideal, the theorem has not yet been proven since the proof always requires some arbitrary and {\em ad h…
The Einstein-Podolsky-Rosen (EPR) paradox that argues for the incompleteness of quantum mechanics as a description of physical reality has been put to rest by John Bell's famous theorem, which inspired numerous experimental tests and brought about further affirmations of quantum reality. Nevertheless, in his writings and public presentations, Richard Feynman never acknowledged the significance of Bell's contribution to the resolution of the EPR paradox. In this paper, we discuss several variants of the Bell inequalities (including one that was specifically espoused by Feynman), and explore the…
Physical theories constrained with local quantum structure and satisfying the no-signalling principle can allow beyond-quantum global states. In a standard Bell experiment, correlations obtained from any such beyond-quantum bipartite state can always be reproduced by quantum states and measurements, suggesting local quantum structure and no-signalling to be the axioms to isolate quantum correlations. In this letter, however, we show that if the Bell experiment is generalized to allow local quantum inputs, then beyond-quantum correlations can be generated by every beyond-quantum state. This giv…
Generation of bipartite mechanical cat state by performing projective Bell state measurement
提出利用投影贝尔态测量实现纠缠交换，生成四种二分体声子贝尔猫态，并基于CHSH不等式进行贝尔不等式测试，为连续变量量子网络处理器提供新方法。
Introduction to Bell's inequality in Quantum Mechanics
本文以教学方式介绍贝尔不等式，通过多个示例展示其应用，并推广至梅尔明不等式和GHZ态。
By implicitly assuming that all measurements occur simultaneously, Bell's Theorem only applied to local theories that violated Heisenberg's Uncertainty Principle. By explicitly introducing time into our derivation of Bell's theorem, an extra term related to the time-ordering of actual measurements is found to augment (i.e. weaken) the upper bound of the inequality. Since the same locality assumptions hold for this rederivation as for the original, we conclude that only {\em classical} measurement-order independent local hidden variable theories are constrained by Bell's inequality; time depend…
In [Phys. Rep. 137, 49 (1986)] John S. Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |Psi|^2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; such processes we call Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of jump rates, how to obtain the proc…
Quantum Mechanical description of Bell's experiment assumes Locality
本文证明贝尔实验的量子力学标准描述预设统计独立性而非非定域性，从而质疑非定域效应存在，并影响量子随机数生成与量子密钥分发安全性。
This paper investigates dynamical relaxation to quantum equilibrium in the stochastic de Broglie-Bohm-Bell formulation of quantum mechanics. The time-dependent probability distributions are computed as in a Markov process with slowly varying transition matrices. Numerical simulations, supported by exact results for the large-time behavior of sequences of (slowly varying) transition matrices, confirm previous findings that indicate that de Broglie-Bohm-Bell dynamics allows an arbitrary initial probability distribution to relax to quantum equilibrium; i.e., there is no need to make the ad-hoc as…
According to the Bell theorem, local hidden variable theories cannot reproduce all the predictions of quantum mechanics. An important consequence is that under physically reasonable assumptions quantum mechanics predicts correlations that seem impossible to obtain from a realistic system. In this paper, two simple binary apparatuses are discussed that can accurately mimic correlations predicted by quantum mechanics \textit{if} the correlations are determined by a coincidence measurement as is commonly done. It is argued that in order to exclude local hidden variables, coincidence monitors shou…
Bell's theorem is a statement by which averages obtained from specific types of statistical distributions must conform to a family of inequalities. These models, in accordance with the EPR argument, provide for the simultaneous existence of quantum mechanically incompatible quantities. We first recall several contradictions arising between the assumption of a joint distribution for incompatible observables and the probability structure of quantum-mechanics, and conclude that Bell's theorem is not expected to be relevant to quantum phenomena described by non-commuting observables, irrespective …
In this paper, we explore Bell inequality violation for $2\rightarrow2$ scattering in Effective Field Theories (EFTs) of photons, gluons, and gravitons. Using the CGLMP Bell parameter ($I_2$), we show that, starting from an appropriate initial non-product state, the Bell inequality can always be violated in the final state (i.e.,$I_2 >2$) at least for some scattering angle. For an initial product state, we demonstrate that abelian gauge theories behave qualitatively differently than non-abelian gauge theories (or Gravity) from the point of view of Bell violation in the final state: in the non-…
We derive N-particle Bell-type inequalities under the assumption of partial separability, i.e. that the N-particle system is composed of subsystems which may be correlated in any way (e.g. entangled) but which are uncorrelated with respect to each other. These inequalities provide, upon violation, experimentally accessible sufficient conditions for full N-particle entanglement, i.e. for N-particle entanglement that cannot be reduced to mixtures of states in which a smaller number of particles are entangled. The inequalities are shown to be maximally violated by the N-particle Greenberger-Horne…
The view exists that the Bell inequality is a mere inconsistent application of classical concepts to a well-established quantum world. In the article, ``Nonlocality claims are inconsistent with Hilbert-space quantum mechanics'' [Phys. Rev. A, 101, 022117, (2020)], Robert B. Griffiths advocates for quantum theory's locality. Although R. B. Griffiths presents valuable insights in favor of quantum mechanics' local character, he argues the Bell inequality is an inconsistent application of classical physics to quantum mechanics. We explain why a correct assessment of the Bell inequality does not in…
Proposal of an optical Bell's experiment to test the boundary between determinism and indeterminism in Quantum Mechanics
本文提出通过光学贝尔实验，记录结果字符串分布，以检验量子力学中决定论与不定论边界的性质，并讨论实验条件。
It is shown that correlations of dichotomic functions can not conform to results from Quantum Mechanics. Also, it is seen that the assumptions attendant to optical tests of Bell's Inequalities actually are consistent with classical physics so that in conclusion, Bell's Theorems do not preclude hidden variable interpretations of Quantum Mechanics.
In an article published in 2010, Kiukas and Werner claim to have shown that Bohmian Mechanics does not make the same empirical predictions as ordinary Quantum Mechanics. We explain that such claim is wrong.
By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by 't Hooft. We view these ontological states as the ones embedded with realism and compare them to the (usual) quantum states that represent superpositions, viewing the latter as mere information of the system they describe. Such a deterministic model puts forward conditions for the applicability of Bell's inequality: the usual inequality cannot be applied to the usual experiments. We buil…
Quantum theories with local information flow
本文针对贝尔定理引发的局域性争议，提出四类量子理论范畴，指出局域确定性描述被忽视的原因，并给出局域量子信息流实例以评估实验与科学哲学能否区分不同诠释。
Nonlocality, one of the most remarkable aspects of quantum mechanics, is closely related to Bayesian game theory. Quantum mechanics can offer advantages to some Bayesian games, if the payoff functions are related to Bell inequalities in some way. Most of these Bayesian games that have been discussed are common interest games. Recently the first conflicting interest Bayesian game is proposed in Phys. Rev. Lett. 114, 020401 (2015). In the present paper we present three new conflicting interest Bayesian games where quantum mechanics offers advantages. The first game is linked with Cereceda inequa…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。