give a proof of the existence of nonlocal influences acting on correlated spin-1/2 particles in the singlet state which does not require any particular interpretation of quantum mechanics (QM). (Except Stapp holds that the proof fails under a many-worlds interpretation of QM—a claim we analyse in 1.2.) Recently, in responding to Redhead's ([1987], pp. 90-6) criticism that the Stapp 1 proof fails under an indeterministic interpretation of QM, Stapp [1989] (henceforth Stapp 2), has revised the logical structure of his proof (...) including its crucial locality assumption. Our main aim is to show that this revision is a step in the wrong direction because it faces two difficulties which undermine the resulting proof's significance (3.1) and validity (3. 2). We also clarify and extend the Stapp 1 proof (1. 1) with the aid of Lewis' analysis of counterfactuals (1. 2) and causal dependence (2. 2 and 2. 3). In so doing, we are able to identify two new defects in the Stapp 1 proof (1. 3 and 2. 1) in addition to corroborating Redhead's criticism (2. 2). Also, the additional assumptions which save the Stapp 1 proof's validity are detailed (2. 3) and some new difficulties for the determinist are pointed out by exploiting a slightly extended version of the proof (2. 4). In providing this full analysis of the Stapp 1 proof, we also construct the necessary framework within which to provide a critique of Stapp 2's proof (3). *Portions of this paper were presented by R. K. Clifton to the 1988 British Society for the Philosophy of Science Conference at the University of Southampton. R. K. Clifton wishes to thank the Natural Sciences and Engineering Research Council of Canada, the Royal Commission for the Exhibition of 1851, and the Governing Body of Peterhouse at Cambridge University for support during this work. (shrink)

The term ‘locality’ is used in different contexts with different meanings. There have been claims that relational quantum mechanics is local, but it is not clear then how it accounts for the effects that go under the usual name of quantum non-locality. The present article shows that the failure of ‘locality’ in the sense of Bell, once interpreted in the relational framework, reduces to the existence of a common cause in an indeterministic context. In particular, there is (...) no need to appeal to a mysterious space-like influence to understand it. (shrink)

The tension between microscopic reversibility and macroscopic irreversibility remains one of the fundamental puzzles in physics and philosophy of time. While Prigogine's thermodynamics of irreversible processes established time's arrow as intrinsic to non-equilibrium systems, recent quantum experiments demonstrate effective time-reversibility in isolated systems. This paper proposes that quantum non-locality and entanglement serve as architectural principles bridging these seemingly contradictory perspectives across mesoscopic scales. I argue that time's irreversibility is not absolute but contextual—emerging from the relationship between system and environment (...) mediated by non-local correlations. Through examining strange attractors in phase space and various forms of asymptotic stability, I develop a framework where emergent temporal directionality possesses a fundamentally asymptotic character, arising from systems' dynamical approach to equilibrium. This perspective reconciles Prigogine's insights with quantum reversibility by positioning quasi-equilibrium subsystems within a multi-scale dynamical hierarchy where global correlations establish macroscopic order from microscopic dynamics. The resulting ontology suggests that temporal directionality emerges from attractor-mediated causation rather than classical cause-effect chains, offering new pathways for understanding the relationship between quantum mechanics and thermodynamics. (shrink)

Standard proofs of generalized Bell theorems, aiming to restrict stochastic, local hidden-variable theories for quantum correlation phenomena, employ as a locality condition the requirement of conditional stochastic independence. The connection between this and the no-superluminary-action requirement of the special theory of relativity has been a topic of controversy. In this paper, we introduce an alternative locality condition for stochastic theories, framed in terms of the models of such a theory (§2). It is a natural generalization of a light-cone (...) determination condition that is essentially equivalent to mathematical conditions that have been used to derive Bell inequalities in the deterministic case. Further, it is roughly equivalent to a condition proposed by Bell that, in one investigation, needed to be supplemented with a much stronger assumption in order to yield an inequality violated by some quantum mechanical predictions. It is shown here that this reflects a very general situation: from the proposed locality condition, even adding the strict anticorrelation condition and the auxiliary hypotheses needed to derive experimentally useful (and theoretically telling) inequalities, no Bell-type inequality is derivable. (These independence claims are the burden of §4.) A certain limitation on the scope of the proposed stochastic locality condition is exposed (§5), but it is found to be rather minor. The conclusion is thus supported that conditional stochastic independence, however reasonable on other grounds, is essentially stronger than what is required by the special theory.Our results stand in apparent contradiction with a class of derivations purporting to obtain generalized Bell inequalities from locality alone. It is shown in Appendix (B) that such proofs do not achieve their goal. This fits with our conclusion that generalized Bell theorems are not straightforward generalizations of theorems restricting deterministic hidden-variable theories, and that, in fact, such generalizations do not exist. This leaves open the possibility that a satisfactory, non-deterministic account of the quantum correlation phenomena can be given within the framework of the special theory. (shrink)

Hardy’s $$\psi$$ -ontology theorem proves the reality of the wave function under the assumption of restricted ontic indifference. It has been conjectured that restricted ontic indifference, which is a very strong assumption from the $$\psi$$ -epistemic view, can be derived from two weaker sub-assumptions: an ontic state assumption and a locality assumption. However, Leifer argued that this derivation cannot go through when considering the existence of the vacuum state in the second-quantized description of quantum states. In this paper, I (...) present a new analysis of Hardy’s theorem. First, I argue that the ontic state assumption is valid in the second-quantized description of quantum states. Second, I argue that the locality assumption is a locality assumption for product states and it is weaker than the preparation independence assumption of the PBR theorem. Third, I argue that Leifer’s objection to the derivation of restricted ontic indifference is invalid. Finally, I argue that although the vacuum state is irrelevant, the existence of the tails of the wave function will block the derivation of restricted ontic indifference from the ontic state assumption and the locality assumption. (shrink)

Using as case studies two early diagrams that represent mechanisms of the cell division cycle, we aim to extend prior philosophical analyses of the roles of diagrams in scientific reasoning, and specifically their role in biological reasoning. The diagrams we discuss are, in practice, integral and indispensible elements of reasoning from experimental data about the cell division cycle to mathematical models of the cycle’s molecular mechanisms. In accordance with prior analyses, the diagrams provide functional explanations of the cell cycle and (...) facilitate the construction of mathematical models of the cell cycle. But, extending beyond those analyses, we show how diagrams facilitate the construction of mathematical models, and we argue that the diagrams permit nomological explanations of the cell cycle. We further argue that what makes diagrams integral and indispensible for explanation and model construction is their nature as locality aids: they group together information that is to be used together in a way that sentential representations do not. (shrink)

One motivation for preferring the many worlds interpretation of quantum mechanics over realist rivals, such as collapse and hidden variables theories, is that the interpretation is able to preserve locality (in the sense of no action at a distance) in a way these other theories cannot. The primary goal of this paper is to make this argument for the many worlds interpretation precise, in a way that does not rely on controversial assumptions about the metaphysics of many worlds.

We use the framework of Empirical Models (EM) and Hidden Variables Models (HVM) to analyze the locality and stochasticity properties of relativistic quantum theories, such as Quantum Field Theory (QFT). First, we present the standard definition of properties such as determinism, no signaling, locality, and contextuality for HVM and for EM and their relations. Then, we show that if no other conditions are added, there are only two types of EM: An EM is either classical, by which we (...) mean that it is strongly deterministic, local, and non-contextual; Or else an EM is non-classical, in which case it is weakly deterministic, non-local and contextual. Consequently, we define criteria for an HVM to be Lorentz invariant and prove that Lorentz invariance implies parameter independence. As a result, we show that a Lorentz invariant and contextual model (e.g., relativistic quantum theory) must be genuinely stochastic i.e., it cannot have a deterministic (strong or weak) HVM. This proof is an improved version of a theorem we proved previously, and it has a wider scope. Finally, we discuss Bell’s definition of locality and show that it is equivalent to non-contextuality. We argue that Bell’s justification for this definition tacitly assumes non-contextuality (which is equivalent to strong determinism). We propose an alternative definition of locality for contextual and relativistic theories that accounts for correlations that result from common history and renders QFT a local theory. (shrink)

The chapter discusses ethical rules in the context of universality and locality. It begins with a brief overview of the exchange between Kantian ethical universalist Onora O’Neill and Wittgensteinian ethical particularist Cora Diamond. Building on O’Neill’s critique of the Wittgensteinians, it then explores two types of locality in moral thought: emotion-based and practice-based locality. Section 3 examines the universality of rules, particularly with regard to their abstract nature. I argue that O’Neill’s belief that abstraction makes rules universally (...) followable is based on a questionable view of concepts and their relation to our lives. Section 4 briefly discusses some reasons for placing rules at the core of our moral life, and highlights the differences between Kant and O’Neill on this issue. The first part of Section 5 revisits emotion-based and practice-based locality, addressing some confusions from earlier presentations. The second part of Section 5 sums up the prospects for rule-based locality. (shrink)

In this article I investigate several possibilities to define the concept of “temporal non-locality” within the standard framework of quantum theory. In particular, I analyze the notions of “temporally non-local states”, “temporally non-local events” and “temporally non-local observables”. The idea of temporally non-local events is already inherent in the standard formalism of quantum mechanics, and Basil Hiley recently defined an operator in order to measure the degree of such a temporal non-locality. The concept of temporally non-local states enters (...) as soon as “clock-representing states” are introduced in the context of special and general relativity. It is discussed in which way temporally non-local measurements may find an interesting application for experiments which test temporal versions of Bell inequalities. (shrink)

This Chapter provides a brief overview of the interconnections between the various causality and locality concepts in algebraic quantum field theory such as causal dynamics, primitive causality, local primitive causality, no-signaling, selective and nonselective measurements, local determinism, stochastic Einstein locality.

본고에서는 18세기 호서학파의 성리학을 통해 충청의 ‘로컬리티(locality)’를 밝히고자 하였다. 먼저 호서학파가 ‘호론(湖論)’과 ‘낙론(洛論)’으로 분기된 이유를 당시 조선의 사회, 정치적 배경과 함께 살펴보고, 학맥별 학문적 활동과 정치 활동, ‘인물성동이론(人物性同異論)’을 중심으로 살펴보았다. 호서학파의 주류를 이루는 호론은 공통적으로 ‘인기질(因氣質)’로 볼 때, 인의예지의 본성이 인간에게만 존재하므로 ‘인물성이론(人物性異論)’임을 주장하였다. 이것은 ‘도덕적인 인간(노론, 중화中華, 리理)이 동물(소인배, 청/일본, 기氣)들이 판치는 잘못된 세상을 앞장서서 바로잡아야한다’는 논리로 작용하였다. 그러나 호론은 변화된 대내외정세에 능동적으로 대처하지 못하면서 중앙 정계에서 멀어지고 충청의 향촌사회에서만 꾸준히 지속되었다. 이렇게 볼 때, 18세기 호서학학파의 로컬리티는 첫째, (...) 의리와 원칙을 중시하고 둘째, 정통 주자주의의 실천가로서의 성향이 강하며, 셋째, 도덕적 규범을 중시하는 선비정신의 계승의지가 강하다. 또한 자유로우면서도 지적이고 정밀한 토론을 즐기는 문화를 갖고 있으며, 유연성과 개방성을 내포한 보수성을 갖고 있다고 할 수 있다. 이러한 18세기 호서학파의 로컬리티는 현대 충청에도 면면히 전해오고 있다. 겉으로만 화려하고 당장의 이해득실 추구에만 급급한 현대인들에게 18세기 호서학파의 로컬리티는 때로는 어리석고 답답해 보이지만, 올바른 도덕적 가치의 수호와 의리를 지키며 사는 삶의 소중함을 일깨워 준다는 데 의의가 있다. (shrink)

The book contributes to the researches in social philosophy, metaphysics, ontology and epistemology by introducing the notion of locality of reason in order to challenge the dualism between, on the one hand, the apologists of the absolute value of reason and, on the other hand, relativism and historicism.

A strand of contemporary philosophy has turned from the traditional focus on universality toward conceptions of “one’s own,” “place,” and “particularity.” In the recovery of “place” and “Iocation,” no attempt has been made to distinguish betwen these terms nor to investigate their different implications even though there is an incipient distinction between them in Heidegger’s late work. This meditation on the relationship between place (Ort) and locality (Ortschaft) begins from Heidegger’s texts in which the distinction was made. The second (...) part follows the thought of location further. Third, the implication of this distinctionfor the task of thinking and its distinction from poetry is explored. In conclusion, some implicationsfor the interpretation and application of Heidegger’s work and for the place that a definition and defence of particularity and locality might have in contemporary philosophy are explored. Une certaine voie de la philosophie contemporaine a déplacé son attention traditionnelle portée à I’universeI pour se tourner vers des conceptions du “propre,” du “lieu,” du “particulier.” Dans la récupération des concepts de “lieu” et d’ “emplacement,” on n’a pas, jusqu’ ici, tenté de distinguer ces terms ou d'etudier leurs implications respectives, bien qu 'une distinction emerge dans I’oeuvre tardive de Heidegger. La présente méditation sur la relation entre lieu (Ort) et localité (Ortschaft) part du texte heideggérien dans lequel la distinction a été faite. Le seconde partie poursuit la pensée de la localité. La troisième sonde la portée de cette distinction pour la tâche de la pensée et la façon dont elle se démarque de la poésie. En conclusion, j’explore I’incidence qu ’une definition et une défense de la particularité et de la localité pourrait avoir sur I’interpretation et I’application de I’oeuvre de Heidegger en philosophie contemporaine. (shrink)

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 signal locality plus 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 is possible to reproduce quantum mechanics with deterministic models that violate locality as well as indeterministic models that satisfy locality. On the other hand, the operational assumption of signal locality is an empirically testable (and well-tested) consequence of relativity. Thus Bell inequality violations imply that we can trust that some events are fundamentally unpredictable, even if we cannot trust that they are indeterministic. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the assumption of no superluminal signalling, regardless of any postulates of quantum mechanics. It also sheds a new light on an early stage of the historical debate between Einstein and Bohr. (shrink)

In an accompanying paper Gomes, we have put forward an interpretation of quantum mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed Universe M, existing on timeless configuration space \ of some field over M. However, not much was said there about the role of locality, which was not assumed. This paper is an attempt to fill that gap. Locality in full can only emerge dynamically, and is not postulated. This new understanding of locality is (...) based solely on the properties of extremal paths in configuration space. I do not demand locality from the start, as it is usually done, but showed conditions under which certain systems exhibit it spontaneously. In this way we recover semi-classical local behavior when regions dynamically decouple from each other, a notion more appropriate for extension into quantum mechanics. The dynamics of a sub-region O within the closed manifold M is independent of its complement, \, if the projection of extremal curves on \ onto the space of extremal curves intrinsic to O is a surjective map. This roughly corresponds to \, where \ is a linear projection. This criterion for locality can be made approximate—an impossible feat had it been already postulated—and it can be applied for theories which do not have hyperbolic equations of motion, and/or no fixed causal structure. When two regions are mutually independent according to the criterion proposed here, the semi-classical path integral kernel factorizes, showing cluster decomposition which is the ultimate aim of a definition of locality. (shrink)

In the paper, the proof of the non-locality of quantum mechanics, given by Bedford and Stapp (1995), and appealing to the GHZ example, is analyzed. The proof does not contain any explicit assumption of realism, but instead it uses formal methods and techniques of the Lewis calculus of counterfactuals. To ascertain the validity of the proof, a formal semantic model for counterfactuals is constructed. With the help of this model it can be shown that the proof is faulty, because (...) it appeals to the unwarranted principle of “elimination of eliminated conditions” (EEC). As an additional way of showing unreasonableness of the assumption (EEC), it is argued that yet another alleged and highly controversial proof of non-locality of QM, using the Hardy example, can be made almost trivial with the help of (EEC). Finally, a general argument is produced to the effect that the locality condition in the form accepted by Stapp and Bedford is consistent with the quantum-mechanical predictions for the GHZ case under the assumption of indeterminism. This result undermines any future attempts of proving the incompatibility between the predictions of quantum theory and the idea of no faster-than-light influence in the GHZ case, quite independently of the negative assessment of the particular derivation proposed by Stapp and Bedford. (shrink)

Modern physics was born from two great revolutions: relativity and quantum theory. Relativity imposed a locality constraint on physical theories: since nothing can go faster than light, very distant events cannot influence one another. Only in the last few decades has it become clear that quantum theory violates this constraint. The work of J. S. Bell has demonstrated that no local theory can return the predictions of quantum theory. Thus it would seem that the central pillars of modern physics (...) are contradictory. Quantum Non-Locality and Relativity examines the nature and possible resolution of this conflict. Beginning with accurate but non-technical presentations of Bell's work and of Special Relativity, there follows a close examination of different interpretations of relativity and of the sort of locality each demands. The story continues with a brief discussion of the General Theory of Relativity. This second edition also includes a new author's preface and an additional appendix. The book introduces philosophers to the relevant physics and demonstrates how philosophical analysis can help to resolve some of the problems. All of the physics is presented from first principles, and as much as possible is presented pictorially. Book jacket. (shrink)

Two principles of locality used in discussions about quantum mechanics are distinguished. The intuitive no-action-at-a distance requirement is called physical locality. There is also a mathematical requirement of a kind of factorizability which is referred to as "locality". It is argued in this paper that factorizability is not necessary for physical locality. Ways of producing models that are physically local although not factorizable which are concerned with correlations between the behavior of pairs of particles are suggested. (...) These models can account for all the quantum mechanical single and joint probabilities. (shrink)

This book examines in detail two of the fundamental questions raised by quantum mechanics. First, is the world indeterministic? Second, are there connections between spatially separated objects? In the first part, the author examines several interpretations, focusing on how each proposes to solve the measurement problem and on how each treats probability. In the second part, the relationship between probability (specifically determinism and indeterminism) and non-locality is examined, and it is argued that there is a non-trivial relationship between probability (...) and non-locality. The author then re-examines some of the interpretations of part one of the book in the light of this argument, and considers how they fare with regard to locality and Lorentz invariance. The book will appeal to anyone with an interest in the interpretation of quantum mechanics, including researchers in the philosophy of physics and theoretical physics, as well as graduate students in those fields. (shrink)

Heritability is routinely interpreted causally. Yet, what such an interpretation amounts to is often unclear. Here, I provide a causal interpretation of this concept in terms of range of causal influence, one of several causal dimensions proposed within the interventionist account of causation. An information-theoretic measure of range of causal influence has recently been put forward in the literature. Starting from this formalization and relying upon Woodward’s analysis, I show that an important problem associated with interpreting heritability causally, namely the (...) locality problem, amounts, at least partly, to a low invariance and low stability between the genotype/environment and the phenotype of individuals. In light of this, I plead for a causal interpretation of heritability that takes the notions of Woodward’s invariance and stability into consideration. In doing so, I defuse naive causal interpretations of heritability. (shrink)

Bogen and Woodward characterized data as embedded in the context in which they are produced (‘local’) and claims about phenomena as retaining their significance beyond that context (‘nonlocal’). This view does not fit sciences such as biology, which successfully disseminate data via packaging processes that include appropriate labels, vehicles, and human interventions. These processes enhance the evidential scope of data and ensure that claims about phenomena are understood in the same way across research communities. I conclude that the degree of (...) locality of both data and claims about phenomena varies depending on the packaging used to make them travel and on the research setting in which they are used. †To contact the author, please write to: ESRC Centre for Genomics in Society, University of Exeter, Byrne House, St. Germans Road, EX4 4PJ Exeter, United Kingdom; e‐mail: [email protected]. (shrink)

Perspectivalism is a natural ingredient of unitary one-world quantum mechanics. After briefly reviewing arguments for this thesis, we argue that a radical version of perspectivalism is able to provide local and relativistically covariant accounts of physical processes, and thus offers a way out of several no-go theorems. According to this radical perspectivalism, different perspectives are independent of each other and remain so even when they make causal contact. This leads to a worldview that is highly counter-intuitive, but does not lead (...) to conflicts with experience. Moreover, locality and compatibility with relativity theory are positive points of radical perspectivalism. (shrink)

I discuss various formulations of stochastic Einstein locality (SEL), which is a version of the idea of relativistic causality, that is, the idea that influences propagate at most as fast as light. SEL is similar to Reichenbach's Principle of the Common Cause (PCC), and Bell's Local Causality. My main aim is to discuss formulations of SEL for a fixed background spacetime. I previously argued that SEL is violated by the outcome dependence shown by Bell correlations, both in quantum mechanics (...) and in quantum field theory. Here I reassess those verdicts in the light of some recent literature which argues that outcome dependence does not violate the PCC. I argue that the verdicts about SEL still stand. Finally, I briefly discuss how to formulate relativistic causality if there is no fixed background spacetime. (shrink)

In the present paper we show that in a certain sense the violation of Bell’s inequality does not entail a real non-locality. We define materiality as the capacity to be modified; and it results that in the case of the singlet state the non-locality previewed by quantum mechanics and experimentally confirmed is not material.

A model for measurement in collapse-free nonrelativistic fermionic quantum field theory is presented. In addition to local propagation and effectively-local interactions, the model incorporates explicit representations of localized observers, thus extending an earlier model of entanglement generation in Everett quantum field theory (Rubin in Found. Phys. 32:1495–1523, 2002). Transformations of the field operators from the Heisenberg picture to the Deutsch-Hayden picture, involving fictitious auxiliary fields, establish the locality of the model. The model is applied to manifestly-local calculations of the (...) results of measurements, using a type of sudden approximation and in the limit of massive systems in narrow-wavepacket states. Detection of the presence of a spin-1/2 system in a given spin state by a freely-moving two-state observer illustrates the features of the model and the nonperturbative computational methodology. With the help of perturbation theory the model is applied to a calculation of the quintessential “nonlocal” quantum phenomenon, spin correlations in the Einstein-Podolsky-Rosen-Bohm experiment. (shrink)

An Objectivity Principle (O) and a Locality Principle (L) are considered with respect to two simple, but fundamental Gedanken experiments, namely a “Welcher-Weg” Gedanken experiment and an Einstein-Podolsky-Rosen (EPR) Gedanken experiment. It is shown that, if both principles (O) and (L) are assumed to be valid, a contradiction, in the EPR case Bell’s inequality, can be derived implying that at least one of the two principles (O) and (L) has to be denied. It is shown that, if (O) is (...) denied, (L) is preserved in the EPR-Gedanken experiment. For a more adequate discussion, in particular of (L), the two experiments are described in Minkowskian space-time of special relativity. (shrink)

Computationalism, a specie of functionalism, posits that a mental state like pain is realized by a ‘core’ computational state within a particular causal network of such states. This entails that what is realized by the core state is contingent on events remote in space and time, which puts computationalism at odds with the locality principle of physics. If computationalism is amended to respect locality, then it posits that a type of phenomenal experience is determined by a single type (...) of computational state. But a computational state, considered by itself, is of no determinate type—it has no particular symbolic content, since it could be embedded in any of an infinite number of algorithms. Hence, if locality is respected, then the type of experience that is realized by a computational state, or whether any experience at all is realized, is under-determined by the computational nature of the state. Accordingly, Block’s absent and inverted qualia arguments against functionalism find support in the locality principle of physics. If computationalism denies locality to avoid this problem, then it cannot be considered a physicalist theory since it would entail a commitment to phenomena, like teleological causation and action-at-a-distance, that have long been rejected by modern science. The remaining theoretical alternative is to accept the locality principle for macro events and deny that formal, computational operations are sufficient to realize a phenomenal mental state. (shrink)

This is an excellent book, by one of the philosophy of quantum theory's brightest stars. It combines a clear presentation of determinism, probability and non-locality in several current interpretations of quantum theory, with a good deal of detailed analysis, both reporting other people's and Dickson's own results, and developing his own ideas|which are often heterodox, but always well-defended and thought-provoking. The treatment is often concise, especially when reporting standard material or others' results. There are also frequent changes of gear; (...) both because the issues are complexly related to each other, and because Dickson sensibly does not aim for a de nitive treatment of issues that are at present so controversial|accordingly, he weaves about, not forcing his material into some single line of argument. So this is a monograph, not a textbook for teaching or a treatise summing up a conquered eld. But the style is clear and vigourous; the book is packed with information (sometimes about ancillary issues); and as we shall see, Dickson does have some provocative main claims, if not an overarching single line of argument. In this short space, I can only praise the book's general virtues and state some of the main claims. (shrink)

We use κ-free but not Whitehead Abelian groups to constructElementary Classes (AEC) which satisfy the amalgamation property but fail various conditions on the locality of Galois-types. We introduce the notion that an AEC admits intersections. We conclude that for AEC which admit intersections, the amalgamation property can have no positive effect on locality: there is a transformation of AEC's which preserves non-locality but takes any AEC which admits intersections to one with amalgamation. More specifically we have: Theorem (...) 5.3. There is an AEC with amalgamation which is not (N₀, N₁)-tame but is 2(N0, ∞)-tame; Theorem 3.3. It is consistent with ZFC that there is an AEC with amalgamation which is not (≤ N₂, ≤ N₂)-compact. (shrink)

The Measurement problem and Non-locality are classical problems in Quantum Mechanics and still unsolved in spite of the many proposed solutions. A new interpretation is proposed here, based on the idea that they are closely related problems. But it requires that we consider space and time not as objective mediums but as features of our representation of reality, as Kant explained more than two centuries ago.

In a preceding paper, I studied the significance of Jarrett's and Shimony's analyses of 'factorisability' into 'parameter independence' and 'outcome independence' for clarifying the nature of non-locality in quantum phenomena. I focused on four types of non-locality; superluminal signalling, action-at-a-distance, non-separability and holism. In this paper, I consider a fifth type of non-locality: superluminal causation according to 'logically weak' concepts of causation, where causal dependence requires neither action nor signalling. I conclude by considering the compatibility of non-factorisable (...) theories with relativity theory. In this connection, I pay special attention to the difficulties that superluminal causation raises in relativistic spacetime. My main findings in this paper are: first, parameter-dependent and outcome-dependent theories both involve superluminal causal connections between outcomes and between settings and outcomes. Second, while relativistic deterministic parameter-dependent theories seem impossible on pain of causal paradoxes, relativistic indeterministic parameter-dependent theories are not subjected to the same challenge. Third, current relativistic non-factorisable theories seem to have some rather unattractive characteristics. (shrink)