Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is viewed as a consequence of the Hilbert-space quantum mechanical formalism, avoiding thus any direct recourse to the ramifications of Kochen-Specker's argument or Bell's inequality. Depending on the mode of assignment of states to physical systems (unit state vectors versus non-idempotent density operators) we distinguish between strong/relational and weak/deconstructional forms of quantum nonseparability. The origin of the latter is traced down and discussed at length, whereas its relation to the all important concept of potentiality in forming a coherent picture of the puzzling entangled interconnections among spatially separated systems is also considered. Finally, certain philosophical consequences of quantum nonseparability concerning the nature of quantum objects, the question of realism in quantum mechanics, and possible limitations in revealing the actual character of physical reality in its entirety are explored.

SUMMARY. Standard quantum mechanics undeniably violates the notion of separability that classical physics accustomed us to consider as valid. By relating the phenomenon of quantum nonseparability to the all-important concept of potentiality, we effectively provide a coherent picture of the puzzling entangled correlations among spatially separated systems. We further argue that the generalized phenomenon of quantum nonseparability implies contextuality for the production of well-defined events in the quantum domain, whereas contextuality entails in turn a structural-relational conception of quantal objects, viewed as carriers of dispositional properties. It is finally suggested that contextuality, if considered as a conditionalization preparation procedure of the object to be measured, naturally leads to a separable concept of reality whose elements are experienced as distinct, well-localized objects having determinate properties.In this connection, we find it necessary to distinguish the meaning of the term reality from the criterion of reality for us. The implications of the latter considerations for the notion of objectivity in quantum mechanics are also discussed.Key words: nonseparability, potentiality, holism, contextuality, quantum object, objectivity THE MEANING OF THE SEPARABILITY PRINCIPLE IN CLASSICAL PHYSICSClassical physics is essentially atomistic in character. It portrays a view of the world in terms of analyzable, separately existing but interacting self-contained parts. Classical physics is also reductionistic. It aims at explaining the whole of forms of physical existence, of structures and relations of the natural world in terms of a salient set of elementary material objects linked by forces. Classical physics (and practically any experimental science) is further based on the Cartesian dualism of 'res cogitans' ('thinking substance') and 'res extensa' ('extended substance'), proclaiming a radical separation of an objective external world from the knowing subject that allows no possible intermediary. * Department of Philosophy and History of Science, University of Athens, Athens 157 71, Greece (E-mail: karakost@phs.uoa.gr) 2 In fact, the whole edifice of classical physics  be it point-like analytic, statistical, or field theoretic  is compatible with the following separability principle that can be expressed schematically as follows:Separability Principle: The states of any spatio-temporally separated subsystems S 1 , S 2 , ..., S N of a compound system S are individually well-defined and the states of the compound system are wholly and completely determined by them and their physical interactions including their spatio-temporal relations (cf. Howard 1989;Healey 1991).In the case, for instance, of point-like analytic mechanics, the state of a compound system consisting of N point particles is specified by considering all pairs {q 3N (t), p 3N (t)} of the generalized position and momentum coordinates of the individual particles. Hence, at any temporal moment t, the individual pure state of...

The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved syntactic language to tackle these problems from the set-theoretic to the category-theoretic mode, together with a study of the consequent semantic transition in the logical interpretation of quantum event structures. In the present work, this is realized by representing categorically the global structure of a quantum algebra of events (or propositions) in terms of sheaves of local Boolean frames forming Boolean localization functors. The category of sheaves is a topos providing the possibility of applying the powerful logical classification methodology of topos theory with reference to the quantum world. In particular, we show that the topos-theoretic representation scheme of quantum event algebras by means of Boolean localization functors incorporates an object of truth values, which constitutes the appropriate tool for the definition of quantum truth-value assignments to propositions describing the behavior of quantum systems. Effectively, this scheme induces a revised realist account of truth in the quantum domain of discourse. We also include an appendix, where we compare our topos-theoretic representation scheme of quantum event algebras with other categorial and topos-theoretic approaches.Comment: 35 pages, 6 figure

In the present study we attempt to incorporate the philosophical dialogue about physical reality into the instructional process of quantum mechanics. Taking into account that both scientific realism and constructivism represent, on the basis of a rather broad spectrum, prevalent philosophical currents in the domain of science education, the compatibility of their essential commitments is examined against the conceptual structure of quantum theory. It is argued in this respect that the objects of science do not simply constitute 'personal constructions' of the human mind for interpreting nature, as individualist constructivist consider, neither do they form products of a 'social construction', as sociological constructivist assume; on the contrary, they reflect objective structural aspects of the physical world. A realist interpretation of quantum mechanics, we suggest, is not only possible but also necessary for revealing the inner meaning of the theory's scientific content. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional metaphysical presuppositions. To this end, we put forward an alternative to traditional realism interpretative scheme, that is in harmony with the findings of present-day quantum theory, and which, if adequately introduced into the instructional process of contemporary physics, is expected to promote the conceptual reconstruction of learners towards an appropriate view of nature.

Abstract. The present study attempts to provide a consistent and coherent account of what the world could be like, given the conceptual framework and results of contemporary quantum theory. It is suggested that standard quantum mechanics can, and indeed should, be understood as a realist theory within its domain of application. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional philosophical presuppositions. It is argued, in this direction, that the conceptualization of the nature of reality, as arising out of our most basic physical theory, calls for a kind of contextual realism. Within the domain of quantum mechanics, knowledge of 'reality in itself', 'the real such as it truly is' independent of the way it is contextualized, is impossible in principle. In this connection, the meaning of objectivity in quantum mechanics is analyzed, whilst the important question concerning the nature of quantum objects is explored.

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen-Specker's theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event algebras. We show explicitly that the latter category is equipped with an object of truth values, or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is inherent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature.

The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either 'true' or 'false', describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of 'no go' theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton 'uniqueness theorem' is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The conceptual implications of the resulting account are traced down and analyzed at length. In this light, the traditional conception of correspondence truth may be viewed as a species or as a limit case of the more generic proposed scheme of contextual correspondence when the non-explicit specification of a context of discourse poses no further consequences.Comment: 19 page

It is shown that Lewis' ontological doctrine of Humean supervenience incorporates at its foundation the so-called separability principle of classical physics. In view of the systematic violation of the latter within quantum mechanics, the claim that contemporary physical science may posit nonsupervenient relations beyond the spatiotemporal ones is reinforced on a foundational basis concerning constraints on the state-representation of physical systems. Depending on the mode of assignment of states to physical systems -unit state vectors versus statistical density operators -we distinguish between strongly and weakly non-Humean, non-supervenient relations. It is demonstrated that in either case the relations of quantum entanglement constitute prototypical examples of irreducible physical relations that do not supervene upon a spatiotemporal arrangement of Humean qualities, weakening, thereby, the thesis of Humean supervenience. It is examined, in this respect, the status of Lewis' recombination principle, whereas his conception of lawhood is critically investigated. It is concluded that the assumption of ontological reductionism, as expressed in Lewis' Humean doctrine, cannot be regarded as a reliable code of the nature of the physical world and its contents. It is proposed instead that  due to the undeniable existence of non-supervenient relations  a metaphysic of relations of a moderate kind ought to be acknowledged as an indispensable part of our understanding of the natural world at a fundamental level.