Einstein's philosophy of physics (as clarified by Fine, Howard, and Held) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, Held, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic (...) quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the doctrines of Bohr and Einstein are equivalent. Thus - upon our specific formalization - quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on. (shrink)

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. (shrink)

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. (shrink)

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 non-separability 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. (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...) of projections indexed by a partially ordered set C(A) of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that C(A) consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Hey ting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n x n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski-Mulvey) of the "Bohrification" A̱ of A, which is a commutative Rickart C*-algebra in the topos of functors from C(A) to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns-Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hubert space H and probability valuations on the internal Gelfand spectrum of A̱ for A = B(H). (shrink)

We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a ‘point-free’ definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.

Kellert (In the Wake of Chars, University of Chicago press, Chicago, 1993) has argued that Laplacean determinism in classical physics is actually a layered concept, where various properties or layers composing this form of determinism can be peeled away. Here, I argue that a layered conception of determinism is inappropriate and that we should think in terms of different deterministic models applicable to different kinds of systems. The upshot of this analysis is that the notion of state is more closely (...) tied to the kind of system being investigated than is usually considered in discussions of determinism. So when investigating determinism corresponding changes to the appropriate notion of state – and, perhaps, the state space itself – also need to be considered. (shrink)

Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohr's view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein's ontically oriented position.

Od samih početaka razvoja kvantne mehanike javlja se potreba metafizičkog razgraničenja “makro” svijeta opisanog “svakodnevnim jezikom” i “mikro” svijeta kojim se bavi formalizam teorije . U tekstu se raspravlja o potrebi pomirenja ovako umjetno razgraničenih svjetova, uz pregled najvažnijih pravaca tumačenja formalizma teorije. Posebno se izlaže Bohrovo “kopenhaško” tumačenje i problemi koje pred njega postavlja EPR misaoni eksperiment. Pregledom Bohrovih odgovora na dani eksperiment, pokazuje se da njegovo tumačenje traži više od ograničenja svakodnevne deskriptivne metafizike pri opisu pojava na mikro-nivou. (...) Na taj način gubi se Bohrovo povlašteno mjesto meðu tumačenjima formalizma teorije. Pokazuje se da se niti MacKinnonov detaljniji shematski prikaz spajanja teoretskog i svakodnevnog jezika ne može primijeniti na zaključke EPR eksperimenta i Bohorov odgovor na njih. Sam MacKinnon nudi prijedloge izmjena “svakodnevnog” jezika uvjetovane matematičkim zaključcima kvantne mehanike, ali se i one pokazuju previše radikalnima i grubima da bi zauzele povlašteno mjesto u odnosu na ostala tumačenja teoretskog formalizma koja sa sobom nose velike ontološke i konceptualne zahtjeve.Ever since the beginning of development of Quantum Mechanics there was a metaphysical division between the “macro” world as described in “everyday language” and the “micro” world described by quantum formalism . A discussion is offered of the need to reunite these arbitrarily divided worlds through an overview of the main interpretations of the formalism. Bohr’s Copenhagen interpretation, as well as the problems it faces due to EPR thought experiment, is presented in greater detail. It is claimed that Bohr’s answers to the said experiment demand more than a restriction of everyday descriptive metaphysics, when describing phenomena at the micro-level. Thus, the special place Bohr’s interpretation takes among other interpretations of the formalism is forfeited. It is also shown that MacKinnon’s more detailed schema aiming to connect the theoretical and everyday language cannot be applied to EPR conclusions and Bohr’s reply to those. MacKinnon’s own modifications of the “everyday language” induced by the mathematical conclusions of Quantum Mechanics are considered too radical and too coarse to take the vacated special place among formalism interpretations. (shrink)

Dual-aspect monism and neutral monism offer interesting alternatives to mainstream positions concerning the mind-matter problem. Both assume a domain underlying the mind-matter distinction, but they also differ in definitive ways. In the twentieth century, variants of both positions have been advanced by a number of protagonists. One of these variants, the dual-aspect monism due toWolfgang Pauli and Carl Gustav Jung, will be described and commented on in detail. As a unique feature in the Pauli-Jung conception, the duality of mental and (...) material aspects is specified in terms of a complementarity. This sounds innocent, but entails a number of peculiarities distinguishing their conjecture from other approaches. (shrink)

The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (shrink)

Philosophical discourse traditionally distinguishes between ontology and epistemology and generally enforces this distinction by keeping the two subject areas separated. However, the relationship between the two areas is of central importance to physics and philosophy of physics. For instance, many measurement-related problems force us to consider both our knowledge of the states and observables of a system and its states and observables independent of such knowledge. This applies to quantum systems in particular. This contribution presents an example showing the importance (...) of distinguishing between ontic and epistemic levels of description even for classical systems. Corresponding conceptions of ontic and epistemic states and their evolution are introduced and discussed with respect to aspects of stability and information flow. These aspects show why the ontic/epistemic distinction is particularly important for systems exhibiting deterministic chaos. Moreover, this distinction provides some understanding of the relationships between determinism, causation, predictability, randomness, and stochasticity. (shrink)

This contribution explores Wolfgang Pauli's idea that mind and matter are complementary aspects of the same reality. We adopt the working hypothesis that there is an undivided timeless primordial reality (the primordial "one world''). Breaking its symmetry, we obtain a contextual description of the holistic reality in terms of two categorically different domains, one tensed and the other tenseless. The tensed domain includes, in addition to tensed time, nonmaterial processes and mental events. The tenseless domain refers to matter and physical (...) energy. This concept implies that mind cannot be reduced to matter, and that matter cannot be reduced to mind. The non-Boolean logical framework of modern quantum theory is general enough to implement this idea. Time is not taken to be an a priori concept, but an archetypal acausal order is assumed which can be represented by a one-parameter group of automorphisms, generating a time operator which parametrizes all processes, whether material or nonmaterial. The time-reversal symmetry is broken in the nonmaterial domain, resulting in a universal direction of time for the material domain as well. (shrink)