Vassilios Karakostas

Realism vs. Constructivism in Contemporary Physics: The Impact of the Debate on the Understanding of Quantum Theory and its Instructional Process

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.

A Categorial Semantic Representation of Quantum Event Structures

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.

Realism and objectivism in quantum mechanics

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.

Decoherence in unorthodox formulations of quantum mechanics

The conceptual structure of orthodox quantum mechanics has not provided a fully satisfactory and coherent description of natural phenomena. With particular attention to the measurement problem, we review and investigate two unorthodox formulations. First, there is the model advanced by GRWP, a stochastic modification of the standard Schrödinger dynamics admitting statevector reduction as a real physical process. Second, there is the ontological interpretation of Bohm, a causal reformulation of the usual theory admitting no collapse of the statevector. Within these two seemingly quite different approaches, we discuss in a comparative manner, several points: The meaning of the state vector, the status of quantum probability, the legitimacy of attributing macro objective properties to physical systems, and the possibility of retrieving the classical limit. Finally, we consider aspects of non-locality and relevant difficulties with formulating a relativistic generalization of the two approaches.

The conventionality of simultaneity in the light of the spinor representation of the lorentz group

Abstract The assessment of the conventionality of simultaneity has commonly taken place so far within the traditional formulation of the special theory of relativity. The e-synchrony transformation is presented within this context in a sufficiently general manner that explores the connection of spatiotemporal measures to the choice of an e-simultaneity relation. Subsequently to the recent work of Zangari, the feasibility of the latter is then investigated in terms of the two-component spinor formulation of special relativity. This is motivated by the fact that the spinor formulation provides the most fundamental expression of a spacetime theory that is consistent with the principle of special relativity. It is shown within this context that the transformation elements of the spinor group (unlike its Lorentz counterparts) prevent the groups representations being extended to a representation of the e-class of non-standard synchrony transformations in four-dimensional space. The underlying reasons are traced down and discussed at length, whereas the compatibility of this finding with a general version of the principle of general relativity that is applicable to both tensor and spinor quantities is also demonstrated. It is finally established that the standard simultaneity relations far from constituting just a sensible choice in a range of conventional possibilities, is uniquely and objectively singled out by the properties of a spinor structure in Minkowski spacetime. The desirability of such a structure is anticipated by its fundamental status.

Correspondence Truth and Quantum Mechanics

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.

Limitations on stochastic localization models of state vector reduction

Recently, Ghirardi, Rimini, Weber, and Pearle have proposed a stochastic modification of the Schrödinger equation which dynamically suppresses coherent superpositions of macroscopically distinguishable states and so avoids the infamous cat paradox. We show that the modified dynamics reduces the state vector completely only in the limit of infinite time, and therefore, for any finite timet, no objective local property can be meaningfully assigned to measurement outcomes. Since a physical mechanism giving rise to stochastic spontaneous localizations of the state vector is lacking, we argue that the model (however heuristically interesting) turns out to bead hoc. Finally, we discuss consequences of this latter feature in association with the elusiveness of the two new ‘constants of nature’ appearing in the model.

Contextual semantics in quantum mechanics from a categorical point of view

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.