John Bell Across Space and Time

The Depth and Breadth of John Bell's Physics

John Bell's investigations in foundations of quantum mechanics, particle physics, and quantum field theory are recalled.

John Bell and the great enterprise

I outline Bell's vision of the "great enterprise" of science, and his view that conventional teachings about quantum mechanics constituted a betrayal of this enterprise. I describe a proposal of his to put the theory on a more satisfactory footing, and review the subsequent uses that have been made of one element of this proposal, namely Bell's transition probabilities regarded as fundamental physical processes.

John Bell's varying interpretations of quantum mechanics

Various interpretations of quantum mechanics, favored (or neglected) by John Bell in the context of his non-locality theorem, are compared and discussed.

Some Personal Reflections on Quantum Non-locality and the Contributions of John Bell

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.

Hidden Variables and the Two Theorems of John Bell

Although skeptical of the prohibitive power of no-hidden-variables theorems, John Bell was himself responsible for the two most important ones. I describe some recent versions of the lesser known of the two (familar to experts as the "Kochen-Specker theorem") which have transparently simple proofs. One of the new versions can be converted without additional analysis into a powerful form of the very much better known "Bell's Theorem", thereby clarifying the conceptual link between these two results of Bell.

Why QBism is not the Copenhagen interpretation and what John Bell might have thought of it

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."

Magic Moments: A Collaboration with John Bell

I want to give an impression of the time I spent together with John S. Bell, of the atmosphere of our collaboration and friendship. I briefly review our work, the methods of nonrelativistic approximations to quantum field theory for calculating the properties of heavy quark-antiquark bound states.

A deterministic Bell model

Following ideas given by John Bell in a paper entitled \textit{Beables for quantum field theory}, we show that it is possible to obtain a realistic and deterministic interpretation of any quantum field-theoretic model involving Fermi fields.

Causarum Investigatio and the Two Bell's Theorems of John Bell

"Bell's theorem" can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination. His 1976 theorem is their incompatibility with the single property of Local Causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with the assumption of Local Causality, even if not by that name. Although the two Bell's theorems are logically equivalent, their assumptions are not. Hence, the earlier and later theorems sugges…

A Chorus of Bells

An account of some of the life and work of John Bell

On the Paradoxical Book of Bell

This is an essay-review on a recently re-issued book of John Bell "Speakable and Unspeakable in Quantum Mechanics". The discussion concentrates around the Bell Theorem, its assumptions, consequences and frequent overinterpretations.

我与 John Stewart Bell 关于量子基础的讨论

My discussions of quantum foundations with John Stewart Bell

本文回顾了作者与John Bell关于量子基础的讨论，指出BI-CHSH不等式的违反未证明量子力学完备性或非局域性，强调应谨慎对待其哲学结论。

The Two Bell's Theorems of John Bell

Many of the heated arguments about the meaning of "Bell's theorem" arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the dual assumptions of locality and determinism. His 1976 theorem is the incompatibility of quantum phenomena with the unitary property of local causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with that single, and indivisible, assumption of local causality (even if not by that name). While there a…

Disproof of Bell's Theorem: Reply to Critics

This is a collection of my responses to the criticisms of my argument against the impossibility proof of John Bell, which aims to undermine any conceivable local realistic completion of quantum mechanics. I plan to periodically update this preprint instead of creating a new one for each response.

Minimal assumption derivation of a Bell-type inequality

John Bell showed that a big class of local hidden-variable models stands in conflict with quantum mechanics and experiment. Recently, there were suggestions that empirical adequate hidden-variable models might exist, which presuppose a weaker notion of local causality. We will show that a Bell-type inequality can be derived also from these weaker assumptions.

Contextuality or nonlocality; what would John Bell choose today?

A violation of Bell-CHSH inequalities does not justify speculations about quantum non-locality, conspiracy and retro-causation. Such speculations are rooted in a belief that setting dependence of hidden variables in a probabilistic model, called a violation of measurement independence, would mean a violation of experimenters freedom of choice. This belief is unfounded because it is based on a questionable use of Bayes Theorem and on incorrect causal interpretation of conditional probabilities. In Bell-local realistic model, hidden variables describe only photonic beams created by a source, thu…

The continuum limit of the Bell model

In a paper entitled Beables for Quantum Field Theory, John Bell has shown that it was possible to build a realistic interpretation of any hamiltonian lattice quantum field theory involving Fermi fields. His model is stochastic but Bell thought that it would become deterministic in the continuum limit. We show that it is indeed the case, under an assumption about the state of the universe, namely that the universe is in a state obtained from the positronic sea (all positron states occupied) by creating a finite number of negative charges. Moreover, the continuum model can be established directl…

John Stuart Bell: recollections of a great scientist and a great man

This contribution to the book in honour of J.S. Bell will probably differ from the remaining ones, in particular since only a part of it will be devoted to specific technical arguments. In fact I have considered appropriate to share with the community of physicists interested in the foundational problems of our best theory the repeated interactions I had with him in the last four years of his life, the deep discussions in which we have been involved in particular in connection with the elaboration of collapse theories and their interpretation, the contributions he gave to the development of th…

Measurement and Macroscopicity: Overcoming Conceptual Imprecision in Quantum Measurement Theory

John S. Bell is well known for the result now referred to simply as "Bell's theorem," which removed from serious consideration by physics of local hidden-variable theories. Under these circumstances, if quantum theory is to serve as a truly {\em fundamental} theory, conceptual precision in its interpretation is not only even more desirable but paramount. John Bell was accordingly concerned about what he viewed as conceptual imprecision, from the physical point of view, in the standard approaches to the theory. He saw this as most acute in the case of their treatment of {\em measurement at the …

CHSH-贝尔不等式在滤波随机态下的保真度鲁棒性

On the Fidelity Robustness of CHSH--Bell Inequality via Filtered Random States

本文研究随机混合态下两量子比特系统的非局域性，并通过CHSH-贝尔不等式分析接近高非经典态的态在固定实验装置下违反局域实在论的鲁棒性。

Classifying 50 years of Bell inequalities

Since John S. Bell demonstrated the interest of studying linear combinations of probabilities in relation with the EPR paradox in 1964, Bell inequalities have lead to numerous developments. Unfortunately, the description of Bell inequalities is subject to several degeneracies, which make any exchange of information about them unnecessarily hard. Here, we analyze these degeneracies and propose a decomposition for Bell-like inequalities based on a set of reference expressions which is not affected by them. These reference expressions set a common ground for comparing Bell inequalities. We provid…

Homer nodded: von Neumann's surprising oversight

We review the famous no-hidden-variables theorem in John von Neumann's 1932 book on the mathematical foundations of quantum mechanics. We describe the notorious gap in von Neumann's argument, pointed out by Grete Hermann in 1935 and, more famously, by John Bell in 1966. We disagree with recent papers claiming that Hermann and Bell failed to understand what von Neumann was actually doing.

Cosmic Inflation, Quantum Information and the Pioneering Role of John S Bell in Cosmology

According to the theory of cosmic inflation, the large scale structures observed in our Universe (galaxies, clusters of galaxies, Cosmic Background Microwave - CMB - anisotropy ...) are of quantum mechanical origin. They are nothing but vacuum fluctuations, stretched to cosmological scales by the cosmic expansion and amplified by gravitational instability. At the end of inflation, these perturbations are placed in a two-mode squeezed state with the strongest squeezing ever produced in Nature (much larger than anything that can be made in the laboratory on Earth). This article studies whether a…

Bell-Type Quantum Field Theories

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…

Beables for Quantum Electrodynamics

We show that it is possible to obtain a realistic and deterministic model, based on a previous work of John Bell, which reproduces the experimental predictions of the orthodox interpretation of quantum electrodynamics.

Two theorems of Jhon Bell and Communication Complexity

John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidden variable theory. The impossibility of replacing quantum mechanics by non-contextual Hidden Variable Theory can be turned to a impossible coloring pseudo-telepathy game to be played by two distant players. The game can not be won without communication in the classical world. But if the players share entangled state (quantum correlation) the game can be won deterministically using no communication. This again shows that though quantum correlation can not be used for communication, two parties can …

Can violations of Bell's inequalities be considere as the final proof of quantum physics ?

Nowadays, it is commonly admitted that the experimental violation of Bell's inequalities that was successfully demonstrated in the last decades by many experimenters, are indeed the ultimate proof of quantum physics and of its ability to describe the whole microscopic world and beyond. But the historical and scientific story may not be envisioned so clearly: it starts with the original paper of Einstein, Podolsky and Rosen (EPR) aiming at demonstrating that the formalism of quantum theory is incomplete. It then goes through the works of D. Bohm, to finally proceed to the famous John Bell's rel…

Bell nonlocality, signal locality and unpredictability (or What Bohr could have told Einstein at Solvay had he known about Bell experiments)

The 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the assumptions of locality and determinism. On the other hand, the assumptions of \emph{signal locality} plus \emph{predictability} are also sufficient to derive Bell inequalities. This simple theorem, previously noted but published only relatively recently by Masanes, Acin and Gisin, has fundamental implications not entirely appreciated. Firstly, nothing can be concluded about the ontological assumptions of locality or determinism independently of each other -- it…

How to teach Quantum Mechanics

In the spirit and style of John S. Bell's well known paper on How to Teach Special Relativity it is argued, that a ``Bohmian pedagogy''provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter.

Irrelevance of Bell's Theorem for experiments involving correlations in space and time: a specific loophole-free computer-example

John Bell is generally credited to have accomplished the remarkable "proof" that any theory of physics, which is both Einstein-local and "realistic" (counterfactually definite), results in a strong upper bound to the correlations that are measured in space and time. He thus predicts that Einstein-Podolsky-Rosen experiments cannot violate Bell- type inequalities. We present a counterexample to this claim, based on discrete-event computer simulations. Our model-results fully agree with the predictions of quantum theory for Einstein-Podolsky-Rosen-Bohm experiments and are free of the detection- o…

Separable quantum states do not have stronger correlations than local realism. A comment on quant-ph/0611126 of Z. Chen

Chen (quant-ph/0611126) has recently claimed ``exponential violation of local realism by separable states", in the sense that multi-partite separable quantum states are supposed to give rise to correlations and fluctuations that violate a Bell-type inequality that Chen takes to be satisfied by local realism. However, this can not be true since all predictions (including all correlations and fluctuations) that separable quantum states give rise to have a local realistic description and thus satisfy all Bell-type inequalities, and this holds for all number of parties. Since Chen claims otherwise…

Bell-like examples for spin-1 hidden variable theories

Though John Bell had claimed that his spin-1/2 example of a hidden-variable theory(HV) is an \emph{explicit} counterexample to von Neumann's proof of the non-existence of hidden variable theories empirically equivalent to quantum mechanics, such examples can be so construed only if they met all of von Neumann's requirements. In particular, that they reproduced all the observed predictions of quantum theory. To shed light on these aspects, we have, on the one hand, simplified and critically examined Bell's original example and on the other hand, constructed explicit such examples for spin-1 sys…

Many-body Bell inequalities for bosonic qubits

Since John Bell formulated his paramount inequality for a pair of spin-$1/2$ particles, quantum mechanics has been confronted with the postulates of local realism with various equivalent configurations. Current technology, with its advanced manipulation and detection methods, allows to extend the Bell tests to more complex structures. The aim of this work is to analyze a set of Bell inequalities suitable for a possibly broad family of many-body systems with the focus on bosonic qubits. We develop a method that allows for a step-by-step study of the many-body Bell correlations, for instance amo…

Several foundational and information theoretic implications of Bell's theorem

In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics. EPR also postulated the existence of more fundamental theory where physical reality of any system would be completely describe by the variables/states of that fundamental theory. This variable is commonly called hidden variable and the theory is called hidden variable theory (HVT). In 1964, John Bell proposed an empirically verifiable criterion to test for the existence of these HVTs. He derived an inequ…

Spin-1 photons, spin-1/2 electrons, Bell's inequalities, and Feynman's special perspective on quantum mechanics

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…

Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal

Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann's 'no hidden variables' proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense 'like Bohm's theory.' His seminal result provides a positive answer to the question. I argue that Bell's analysis misconstrues von Neumann's argument. What von Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (de…

关于量子纠缠与非局域性

On Quantum Entanglement and Nonlocality

本文通过贝尔不等式探讨量子纠缠与非局域性，指出光子偏振的本地因果性可解释贝尔测试结果，且光子滤波器相互作用不违反相对论。

Bell's Universe: A Personal Recollection

My collaboration and friendship with John Bell is recollected. I will explain his outstanding contributions in particle physics, in accelerator physics, and his joint work with Mary Bell. Mary's work in accelerator physics is also summarized. I recall our quantum debates, mention some personal reminiscences, and give my personal view on Bell's fundamental work on quantum theory, in particular, on the concept of contextuality and nonlocality of quantum physics. Finally, I describe the huge influence Bell had on my own work, in particular on entanglement and Bell inequalities in particle physics…

In praise of measurement

The role of measurement in quantum computation is examined in the light of John Bell's critique of the how the term ``measurement'' is used in quantum mechanics. I argue that within the field of quantum computer science the concept of measurement is precisely defined, unproblematic, amd forms the foundation of the entire subject.

Hidden Variables and Nonlocality in Quantum Mechanics

In this paper, we show that Erwin Schroedinger's generalization of the Einstein Podolsky Rosen argument can be connected to certain mathematical theorems - Gleason's and also Kochen and Specker's - in a manner analogous to the relation of EPR itself with Bell's theorem. In both cases, the conclusion is quantum nonlocality, as we discuss. The "Schroedinger nonlocality" proofs share some features with the Greenberger, Horne, and Zeilinger quantum-nonlocality work, yet also differ in significant ways. For clarity and completeness, we begin with a detailed discussion of the topic of hidden variabl…

History of Quantum Mechanics or the Comedy of Errors

The goal of this paper is to explain how the views of Albert Einstein, John Bell and others, about nonlocality and the conceptual issues raised by quantum mechanics, have been rather systematically misunderstood by the majority of physicists.

Bell inequalities and hidden variables over all possible paths in a quantum system

Bell's theorem rests on the following fundamental condition for a local system: P(a,b|alpha, beta, lambda)= P(a|alpha, lambda)P(b|beta, lambda). Here a and b are the outcomes respectively for measurements alpha on one side, and beta on the other, of an experiment involving two entangled particles traveling in opposite directions from a source. The parameter lambda (the set of "hidden variables") represents a more complete description of the joint state of the two particles. Because of lambda, the joint probability of detection is now dependent only on lambda and the local measurement setting o…

Global Existence of Bell's Time-Inhomogeneous Jump Process for Lattice Quantum Field Theory

We consider the time-inhomogeneous Markovian jump process introduced by John S. Bell [Phys.Rep. 137, 49] for a lattice quantum field theory, which runs on the associated configuration space. Its jump rates, tailored to give the process the quantum distribution $|Ψ_t|^2$ at all times $t$, typically exhibit singularities. We establish the existence of a unique such process for all times, under suitable assumptions on the Hamiltonian or the initial state vector $Ψ_0$. The proof of non-explosion takes advantage of the special role of the $|Ψ_t|^2$ distribution.

量子非定域性：从被贬斥到诺贝尔奖，经由量子密码学

Quantum non-locality: from denigration to the Nobel prize, via quantum cryptography

本文回顾了1960年代末John Clauser为验证量子理论预测而挑战John Stewart Bell被忽视的量子非定域性结果的历史过程。

Comment on "Dr. Bertlmann's Socks in a Quaternionic World of Ambidextral Reality"

I point out critical errors in the paper "Dr. Bertlmann's Socks in a Quaternionic World of Ambidextral Reality" by Joy~Christian, published in IEEE Access. Christian's model does not generate the singlet correlations but in fact simply reproduces the Bertlmann effect. John Bell's friend and colleague Reinhold Bertlmann of CERN, in his younger days, always wore one pink and one blue sock, at random. The moment you saw his left foot, you knew what colour sock would be on his right foot. Action at a distance? As John Bell liked to explain, quantum entanglement cannot be explained away in such an …

Bohmian Mechanics and the Quantum Revolution

This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena---are contrasted, with each other and with the orthodox approach to these issues.

Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km

For more than 80 years, the counterintuitive predictions of quantum theory have stimulated debate about the nature of reality. In his seminal work, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. Bell showed that in any local realist theory the correlations between distant measurements satisfy an inequality and, moreover, that this inequality can be violated according to quantum theory. This provided a recipe for experimental tests of the fundamental principles underlying the laws of nature. In the past decades, num…

The Einstein-Podolsky-Rosen Paradox and SU(2) relativity

The EPR paradox dates back to 1935 when Einstein et al., through the use of non commuting operators, proposed that quantum mechanics was not complete in that it suggested a `spooky action at a distance.' Later in 1964 John Bell was able to express the dilemma in a simple inequality involving spin-singlet states. If the inequality were satisfied then Einstein was correct and if it were violated then it favored the quantum mechanics point of view. In what follows, we present two approaches to Bell's inequality, and then offer an interpretation from the viewpoint of quantum mechanics based on the…

Bell Nonlocality and the Reality of Quantum Wavefunction

Status of quantum wavefunction is one of the most debated issues in quantum foundations -- whether it corresponds directly to the reality or just represents knowledge or information about some aspect of reality. In this letter we propose a {\it $ψ$-ontology} theorem that excludes a class of ontological explanations where quantum wavefunction is treated as mere information. Our result, unlike the acclaimed Pusey-Barrett-Rudolph's theorem, does not presume the absence of holistic ontological properties for product quantum preparations. At the core of our derivation we utilize the seminal no-go r…

A Relativistic Version of the Ghirardi-Rimini-Weber Model

Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi-Rimini-Weber (GRW) model of spontaneous wavefunction collapse. The GRW model was proposed as a solution of the measurement problem of quantum mechanics and involves a stochastic and nonlinear modification of the Schrödinger equation. It deviates very little from the Schrödinger equation for microscopic systems but efficiently suppresses, for macroscopic systems, superpositions of macroscopically different states. As suggested by Bell, we take the primitive ontology, or local be…

How Does Nature Accomplish Spooky Action at a Distance?

The enigmatic nonlocal quantum correlation that was famously derided by Einstein as "spooky action at a distance" has now been experimentally demonstrated to be authentic. The quantum entanglement and nonlocal correlations emerged as inevitable consequences of John Bell's epochal paper on Bell's inequality. However, in spite of some extraordinary applications as well as attempts to explain the reason for quantum nonlocality, a satisfactory account of how Nature accomplishes this astounding phenomenon is yet to emerge. A cogent mechanism for the occurrence of this incredible event is presented …

Real or Not Real that is the question

My discussions with John Bell about reality in quantum mechanics are recollected. I would like to introduce the reader to Bell's vision of reality which was for him a natural position for a scientist. Bell had a strong aversion against "quantum jumps" and insisted to be clear in phrasing quantum mechanics, his "words to be forbidden" proclaimed with seriousness and wit -- both typical Bell characteristics -- became legendary. I will summarize the Bell-type experiments and what Nature responded, and discuss the implications for the physical quantities considered, the real entities and the nonlo…

Whose Knowledge?

Sir Rudolph Peierls, in a reply to John Bell's last critique of the state of our understanding of quantum mechanics, maintained that it is easy to give an acceptable account of the physical significance of the quantum theory. The key is to recognize that all the density matrix characterizing a physical system ever represents is knowledge about that system. In answer to Bell's implicit rejoinder "Whose knowledge?" Peierls offered two simple consistency conditions that must be satisfied by density matrices that convey the knowledge different people might have about one and the same physical syst…

贝尔的“可存在量”概念的演变：从玻尔到原始本体论

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。