Here is the translation of the famous article Bell J.S. about the EPR-paradox, as well as comments to the Bell's conclusions and the original of article's. Article Bella is a convincing mathematical and logical refutation of the arguments of the Einstein about the incompleteness of quantum mechanics and its provisions about so-called «local realism». From the day publishing the article in 1964 to the present day arguments Bella, better known in the form of a «bell's inequalities», are the most common and the main argument in the dispute between the ideas of non-locality of quantum mechanics and a whole class of theories on the basis of «hidden variables» or «additional settings». In the present work provides a translation of the Bell's article and comments to its conclusions. Made assumptions that Bell's conclusions are a compromise between special relativity theory and experimentally observed phenomenon of entanglement with all visible signs of the instant dependence of the two separated systems. This compromise known these days as the non-locality or nonseparability. Non-locality in fact, directly negates the provisions of the traditional theory of the probability of the dependent and independent events and substantiates the new provisions - quantum probability, quantum rules for calculating the probability of events (addition of probability amplitudes). Such a compromise is the soil for the emergence of mystical views on the nature.
Перевод знаменитой статьи Д.С.Белла об ЭПР-парадоксе, а также комментарии к выводам Белла и оригинал статьи. Статья Белла явилась убедительным математико-логическим опровержением доводов Эйнштейна о неполноте квантовой механики и сформулированных им положений так называемого «локального реализма». Со дня опубликования статьи в 1964 году и до наших дней доводы Белла, более известные в форме «неравенств Белла», служат самым распространённым и главным аргументом в споре между представлениями о нелокальности квантовой механики и целым классом теорий на основе «скрытых переменных» или «дополнительных параметров». В предлагаемой работе приводится перевод статьи Белла и комментарии к его выводам. Высказаны предположения, что возражения Белла являются компромиссом между специальной теорией относительности и экспериментально наблюдаемым явлением запутанности, имеющим все видимые признаки мгновенной зависимости двух отделенных друг от друга систем. Этот компромисс известен в наши дни как нелокальность или несепарабельность. Нелокальность фактически отрицает положения традиционной теории вероятности на зависимые и независимые события и обосновывает новые положения – квантовую вероятность, квантовые правила вычисления вероятности событий (сложение амплитуд вероятностей). Подобный компромисс служит почвой для возникновения мистических взглядов на природу.
Here is the translation of the famous article Bell J.S. about the EPR-paradox, as well as comments to the Bell's conclusions and the original of article's. Article Bella is a convincing mathematical and logical refutation of the arguments of the Einstein about the incompleteness of quantum mechanics and its provisions about so-called «local realism». From the day publishing the article in 1964 to the present day arguments Bella, better known in the form of a «bell's inequalities», are the most common and the main argument in the dispute between the ideas of non-locality of quantum mechanics and a whole class of theories on the basis of «hidden variables» or «additional settings». In the present work provides a translation of the Bell's article and comments to its conclusions. Made assumptions that Bell's conclusions are a compromise between special relativity theory and experimentally observed phenomenon of entanglement with all visible signs of the instant dependence of the two separated systems. This compromise known these days as the non-locality or nonseparability. Non-locality in fact, directly negates the provisions of the traditional theory of the probability of the dependent and independent events and substantiates the new provisions - quantum probability, quantum rules for calculating the probability of events (addition of probability amplitudes). Such a compromise is the soil for the emergence of mystical views on the nature.
Перевод знаменитой статьи Д.С.Белла об ЭПР-парадоксе, а также комментарии к выводам Белла и оригинал статьи. Статья Белла явилась убедительным математико-логическим опровержением доводов Эйнштейна о неполноте квантовой механики и сформулированных им положений так называемого «локального реализма». Со дня опубликования статьи в 1964 году и до наших дней доводы Белла, более известные в форме «неравенств Белла», служат самым распространённым и главным аргументом в споре между представлениями о нелокальности квантовой механики и целым классом теорий на основе «скрытых переменных» или «дополнительных параметров». В предлагаемой работе приводится перевод статьи Белла и комментарии к его выводам. Высказаны предположения, что возражения Белла являются компромиссом между специальной теорией относительности и экспериментально наблюдаемым явлением запутанности, имеющим все видимые признаки мгновенной зависимости двух отделенных друг от друга систем. Этот компромисс известен в наши дни как нелокальность или несепарабельность. Нелокальность фактически отрицает положения традиционной теории вероятности на зависимые и независимые события и обосновывает новые положения – квантовую вероятность, квантовые правила вычисления вероятности событий (сложение амплитуд вероятностей). Подобный компромисс служит почвой для возникновения мистических взглядов на природу.
From the date of publication in 1964 article «On the Einstein Podolsky Rosen paradox» and to our day’s arguments Bella, better known in the form of a «bell's inequalities», are the most common and the main argument in the dispute between the ideas of non-locality of quantum mechanics and a whole class of theories on the basis of «hidden variables» or «additional parameters», formulated in the most General form. Bell showed that there are some conditions (called the «bell's inequalities»), which are correct for local theories, but their violate by quantum mechanics. In the proposed article argues that the predictions of quantum mechanics and local theories are relevant to fundamentally different types of pairs of particles: classic EPR-pairs and probabilistic, independent (pseudo - entangled) pairs of particles. Has examined the predictions of the two theories for both classes of pairs and shown that they coincide. In the case of pseudo-entangled pairs, who examined by the theory of additional parameters, bell's inequality is not violated also to predictions of quantum mechanics. In turn, for the classic EPR pairs theory of additional parameters gives such predictions that, what and quantum mechanics, and together with it requires «non-locality», what is actually a disguised refusal from the relativism («illusionary long-range action»).
Путенихин Петр Васильевич. Со дня опубликования в 1964 году статьи «On the Einstein Podolsky Rosen paradox» и до наших дней доводы Белла, более известные в форме «неравенств Белла», служат самым распространённым и главным аргументом в споре между представлениями о нелокальности квантовой механики и целым классом теорий на основе «скрытых переменных» или «дополнительных параметров», сформулированных в самом обще виде. Белл показал, что существуют некоторые условия (названные впоследствии «неравенствами Белла»), которые соблюдаются для локальных теорий, но нарушаются квантовой механикой. В предлагаемой статье утверждается, что предсказания квантовой механики и локальных теорий относятся к принципиально разным видам пар частиц: классическим ЭПР-парам и вероятностным, независимым (псевдо-запутанным) парам частиц. Рассмотрены предсказания двух теорий для обоих классов пар и показано, что они полностью совпадают. В случае псевдо-запутанных пар, которые рассматривают теории дополнительных параметров, неравенства Белла не нарушаются и для предсказаний квантовой механики. В свою очередь для классических ЭПР-пар теория дополнительных параметров дает такие же предсказания, что и квантовая механика, и вместе с нею также требует «нелокальности», которая фактически является завуалированным отказом от релятивизма («призрачное дальнодействие»).
Bell's inequality is used as the main argument in the dispute between the local realism Einstein and quantum non-locality. If we carefully analyze an argument, you can recognize: Einstein rights - quantum mechanics is incomplete, and «modern physics has turned, in fact, a continuation of mathematics, completely lost all hope of understanding the nature of the studied phenomena».
Путенихин Петр Васильевич. Неравенства Белла используются в качестве основного аргумента в споре между локальным реализмом Эйнштейна и квантовой нелокальностью. Если тщательно проанализировать доводы, то можно признать: Эйнштейн прав – квантовая механика неполна, а «современная физика, превратилась, по сути дела, в продолжение математики, совершенно утратив все надежды на понимание природы изучаемых явлений».
In 1935 Einstein, Podolsky, and Rosen (EPR) published an important paper in which they claimed that the whole formalism of quantum mechanics together with what they called "Reality Criterion" imply that quantum mechanics cannot be complete. That is, there must exist some elements of reality that are not described by quantum mechanics. There must be, they concluded, a more complete description of physical reality behind quantum mechanics. There must be a state, a hidden variable, characterizing the state of affairs in the world in more details than the quantum mechanical state, something that also reflects the missing elements of reality. Under some further but quite plausible assumptions, this conclusion implies that in some spin-correlation experiments the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities). The paradox consists in the fact that quantum probabilities do not satisfy these inequalities. And this paradoxical fact has been confirmed by several laboratory experiments in the last three decades. The problem is still open and hotly debated among both physicists and philosophers. It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will.
Most physicists agree that the Einstein–Podolsky–Rosen–Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell’s inequality are locality and counterfactual definiteness but not scientific realism, determinism, or hidden variables as are often suggested. We further examine the resulting constraints on physical theory with an illustration from the many-worlds interpretation of quantum mechanics—an interpretation that we argue is deterministic, local, and realist but that nonetheless violates the Bell inequality.
A critical reconsideration of the EPR (Einstein-Podolsky-Rosen) paper shows that the EPR argument can be developed without using the concept of `element of physical reality', thus eliminating any philosophical element in the logical chains of the paper. Deprived of its philosophical ornament, the EPR argument plainly reduces to require what quantum mechanics can not do: to assign definite values to two incompatible physical quantities. Hidden variables theories built up according to Bell - type theorems are formulated on the basis of the assumption that the locality condition implies the statistical independence between two measurements space - like separated. This assumption is valid only with the additional one that statistical dependence between two measurements requires a causal connection between them. This additional assumption rules out the possibility that statistical dependence may due to an intrinsic property of the physical system under study. Therefore, hidden variables theories are built up with a restriction which leads them to be disproved by experiment. Quantum mechanical non - locality, invoked for describing EPR - type experiments, is strictly connected to the hypothesis (NDV hypothesis) according to which the twin photons of entangled pairs do not have a definite polarization before measurements. Both hypotheses are used only for describing EPR experiments and not for making predictions. Therefore, they can be dropped without reducing the predictive power of quantum mechanics concerning entangled photons pairs. Furthermore, both hypotheses can be experimentally tested by a modification of a standard experimental apparatus designed for studying entangled photons pairs.
This work offers a foundational, ontological re-examination of the Einstein-Podolsky-Rosen (EPR) paradox and the violation of Bell inequalities. It argues that the apparent "nonlocality" in quantum mechanics stems not from a physical mechanism of interaction, but from an inadequate ontological premise shared by classical reasoning and many interpretations of quantum theory. Core Thesis: The paradox arises from the implicit assumption that measurement outcomes in entangled systems represent independent, local facts that pre-exist or can be defined separately. The work rejects this premise. Instead, it proposes that entangled states describe indivisible ontological structures, where correlated outcomes are not separate entities to be coordinated, but inseparable aspects of a single whole. Key Conceptual Innovations: The JED Postulate (Ontological Simultaneity): The cornerstone of the framework. It posits a global constraint on the co-realization of facts: for an entangled state, individual outcomes cannot exist as autonomous facts. They can only be realized as elements of an admissible pair (e.g., {Alice+, Bob-} or {Alice-, Bob+}). This is not a temporal or causal constraint, but a structural condition for existence. Formalism of Frames and Admissibility Relations: The ontology is formalized using "frames" (sets of co-existing facts) and an "admissibility relation" R, which encodes the structure of an entangled state (e.g., for a singlet: R = {(+, -), (-, +)}). The JED postulate ensures that a frame containing one element of a related pair must contain its counterpart. The "Broken Mirror" Metaphor: A central heuristic. Entanglement is likened to a mirror broken into two complementary halves. The halves do not "communicate" to match; their perfect fit is a consequence of their common origin in a single act of breaking. Asking "which half appeared first?" or "how does one half know about the other?" is ontologically meaningless—there is no process that produces only one isolated half. Resolution of the EPR Paradox: The paradox dissolves because its first step—treating Alice's local outcome as an independent fact—is invalid within the JED ontology. There is no independent fact for locality to protect, hence no contradiction between correlations and relativistic locality. Interpretation of Bell's Theorem: The work reframes Bell's theorem. Its violation is not proof of nonlocality, but empirical evidence against the ontology of independent local facts. Bell's mathematics is correct, but its physical significance depends on ontological axioms that may not hold. The JED ontology provides a local, realistic (but not fact-local) framework consistent with the correlations. Distinction from Hidden Variables: The approach is explicitly not a hidden-variable theory. It introduces no hidden parameters λ governing individual outcomes. The relation R is a structural definition of the entangled whole, not a hidden cause of correlations. Probabilities are treated as a descriptive layer over the admissible ontological structures. Methodology: The work is developed in the spirit of the "pencil-case" methodology, constructing minimal ontological models to analyze the logical roots of physical puzzles without adding new dynamical mechanisms. Scope and Intent: The present work should be read as a contribution to the philosophy of physics: it does not aim at proposing a new physical theory, but at clarifying the ontological assumptions underlying existing formalisms. It seeks to shift the discussion from "how do the parts communicate?" to "what kind of whole do the parts constitute?" The formalism is shown to be logically consistent with the standard quantum correlation function (e.g., E(θ,φ) = -cos(θ-φ)), without deriving it, thereby separating the ontological question of admissibility from the empirical-statistical question of probability distribution. Keywords: EPR Paradox, Bell's Theorem