The Depth and Breadth of John Bell's Physics

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.

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

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…

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…

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…

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.

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…

Bringing Bell's theorem back to the domain of Particle Physics & Cosmology

John St. Bell was a physicist working most of his time at CERN and contributing intensively and sustainably to the development of Particle Physics and Collider Physics. As a hobby he worked on so-called "foundations of quantum theory", that was that time very unpopular, even considered to be scientifically taboo. His 1964-theorem, showing that predictions of local realistic theories are different to those of quantum theory, initiated a new field in quantum physics: quantum information theory. The violation of Bell's theorem, for instance, is a necessary and sufficient criterion for generating …

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.

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。

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…

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…

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。

The GRW flash theory: a relativistic quantum ontology of matter in space-time?

John Bell proposed an ontology for the GRW modification of quantum mechanics in terms of flashes occurring at space-time points. The paper spells out the motivation for this ontology, enquires into the status of the wave-function in it, critically examines the claim of its being Lorentz-invariant and considers whether it is a parsimonious, but nevertheless physically adequate ontology.

From Einstein's Theorem to Bell's Theorem: A History of Quantum Nonlocality

In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to popular opinion, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality-locality-completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness o…

Bell 对 Bell：关于量子不完备性的一场激烈争论

Bell vs Bell: a ding-dong battle over quantum incompleteness

本文通过反例和严谨推导，澄清贝尔关于定域性与决定论关系的争论，指出EPR论证的漏洞并证明贝尔主张的合理性。

Quantum entanglement

Expository paper providing a historical survey of the gradual transformation of the "philosophical discussions" between Bohr, Einstein and Schrödinger on foundational issues in quantum mechanics into a quantitative prediction of a new quantum effect, its experimental verification and its proposed (and loudly advertised) applications. The basic idea of the 1935 paper of Einstein-Podolsky-Rosen (EPR) was reformulated by David Bohm for a finite dimensional spin system. This allowed John Bell to derive his inequalities that separate the prediction of quantum entanglement from its possible classica…

穿越地球的回飞镖：当自由下落不能最大化固有时间时

Boomeranging through the Earth: when free fall doesn't maximize proper time

该研究结合贝尔与惠勒的教学思路，通过思想实验指出广义相对论标准启发式的错误，验证古老时间膨胀启发式的可靠性，强调勿以新口号取代合理旧直觉。

定域性加完美关联是否意味着决定论？

Does locality plus perfect correlation imply determinism?

本文针对贝尔是否从定域性与完美关联推导决定论的争议展开研究，证明弱定域性不足、结果独立性可推导决定论且意味着量子力学不完备，指出贝尔援引的EPR论证存在漏洞并给出修正方法，还探讨了相关量子诠释等问题。

On the Unconditional Validity of J. von Neumann's Proof of the Impossibility of Hidden Variables in Quantum Mechanics

The impossibility of theories with hidden variables as an alternative and replacement for quantum mechanics was discussed by J. von Neumann in 1932. His proof was criticized as being logically circular, by Grete Hermann soon after, and as fundamentally flawed, by John Bell in 1964. Bell's severe criticism of Neumann's proof and the explicit (counter) example of a hidden variable model for the measurement of a quantum spin are considered by most researchers, though not all, as the definitive demonstration that Neumann's proof is inadequate. Despite being an argument of mathematical physics, an …

There Is No Action at a Distance in Quantum Mechanics, Spooky or Otherwise

I feel compelled to respond to the frequent references to spooky action at a distance that often accompany reports of experiments investigating entangled quantum mechanical states. Most, but not all, of these articles have appeared in the popular press. As an experimentalist I have great admiration for such experiments and the concomitant advances in quantum information and quantum computing, but accompanying claims of action at a distance are quite simply nonsense. Some physicists and philosophers of science have bought into the story by promoting the nonlocal nature of quantum mechanics. In …

EPR Paradox, Quantum Nonlocality and Physical Reality

Eighty years ago Einstein demonstrated that a particular interpretation of the reduction of wave function led to a paradox and that this paradox disappeared if statistical interpretation of quantum mechanics was adopted. According to the statistical interpretation a wave function describes only an ensemble of identically prepared physical systems. Searching for an intuitive explanation of long range correlations between outcomes of distant measurements, performed on pairs of physical systems prepared in a spin singlet state, John Bell analysed local realistic hidden variable models and proved …

Understanding quantum physics through simple experiments: from wave-particle duality to Bell's theorem

Quantum physics, which describes the strange behavior of light and matter at the smallest scales, is one of the most successful descriptions of reality, yet it is notoriously inaccessible. Here we provide an approachable explanation of quantum physics using simple thought experiments. We derive all relevant quantum predictions using minimal mathematics, without introducing the advanced calculations that are typically used to describe quantum physics. We focus on the two key surprises of quantum physics, namely wave-particle duality, a term that was introduced to capture the fact that single qu…

物理学的大裂谷

The Great Rift in Physics

本文指出量子理论与广义相对论在预言上存在根本不相容，而非仅是张力，强调贝尔定理和爱因斯坦的要求揭示这一冲突，并认为相对论的时空描述必须让位于量子理论。

Quantum Dynamical Relativity and the Nature of Spacetime

Einstein's special theory of relativity starts with assumptions about how observations conducted in relatively moving inertial frames must compare. From these assumptions, conclusions can be drawn regarding the laws of physics in any one frame. Can we do the reverse, that is, build the correct physics entirely from considerations within a single frame and infer therefrom the results of measurements in moving frames? Can we, in this project, supply the "elementary foundations" that Einstein found lacking in his own theory, thereby converting special relativity from (in Einstein's terminology) a…

模拟 Nelson 量子场论

Simulating Nelsonian Quantum Field Theory

本文将 Nelson 随机力学推广到格点正则化量子场论，通过随机过程数值模拟生成各量子态的典型场构型，解释真空 beable 与激发态的类粒子特征。

量子形式主义再探

The Quantum Formalism Revisited

本文通过对比量子力学与经典力学的结构要素，探讨了量子非交换性及其在原子光谱分析中的发现过程，并通过不等式和相关理论展示其核心贡献。