Relational Interpretations

Building on self-professed perspectival approaches to both scientific knowledge and causation, I explore the potentially radical suggestion that perspectivalism can be extended to account for a type of objectivity in science. Motivated by recent claims from quantum foundations that quantum mechanics must admit the possibility of observer-dependent facts, I develop the notion of 'perspectival objectivity', and suggest that an easier pill to swallow, philosophically speaking, than observer-dependency is perspective-dependency, allowing for a notion of observer-independence indexed to an agent perspective. Working (...) through the case studies of colour perception and causal perspectivalism, I identify two places within which I claim perspectival objectivity is already employed, and make the connection to quantum mechanics through Bohr's philosophy of quantum theory. I contend that perspectival objectivity can ensure, despite the possibility of perspective-dependent scientific facts, the objectivity of scientific inquiry. (shrink)

The relational interpretation of quantum mechanics proposes to solve the measurement problem and reconcile completeness and locality of quantum mechanics by postulating relativity to the observer for events and facts, instead of an absolute “view from nowhere”. The aim of this paper is to clarify this interpretation, and in particular, one of its central claims concerning the possibility for an observer to have knowledge about other observer’s events. I consider three possible readings of this claim, and develop the most promising (...) one, relativism, to show how it fares when confronted with the traditional interpretative problems of quantum mechanics. Although it provides answers to some problems, I claim that there is currently no adapted locality criterion to evaluate whether the resulting interpretation is local or not. (shrink)

We propose a sheaf-theoretic framework for the representation of a quantum observable structure in terms of Boolean information sieves. The algebraic representation of a quantum observable structure in the relational local terms of sheaf theory effectuates a semantic transition from the axiomatic set-theoretic context of orthocomplemented partially ordered sets, la Birkhoff and Von Neumann, to the categorical topos-theoretic context of Boolean information sieves, la Grothendieck. The representation schema is based on the existence of a categorical adjunction, which is used as (...) a theoretical platform for the development of a functorial formulation of information transfer, between quantum observables and Boolean localisation devices in typical quantum measurement situations. We also establish precise criteria of integrability and invariance of quantum information transfer by cohomological means. (shrink)

We construct a sheaf-theoretic representation of quantum observables algebras over a base category equipped with a Grothendieck topology, consisting of epimorphic families of commutative observables algebras, playing the role of local arithmetics in measurement situations. This construction makes possible the adaptation of the methodology of Abstract Differential Geometry (ADG), à la Mallios, in a topos-theoretic environment, and hence, the extension of the “mechanism of differentials” in the quantum regime. The process of gluing information, within diagrams of commutative algebraic localizations, generates (...) dynamics, involving the transition from the classical to the quantum regime, formulated cohomologically in terms of a functorial quantum connection, and subsequently, detected via the associated curvature of that connection. (shrink)

Homologous operational localization processes are effectuated in terms of generalized topological covering systems on structures of physical events. We study localization systems of quantum events' structures by means of Gtothendieck topologies on the base category of Boolean events' algebras. We show that a quantum events algebra is represented by means of a Grothendieck sheaf-theoretic fibred structure, with respect to the global partial order of quantum events' fibres over the base category of local Boolean frames.

In this paper we adopt a category-theoretic viewpoint in order to analyze the semantics of complementarity for quantum systems. Based on the existence of a pair of adjoint functors between the topos of presheaves of the Boolean kind of structure and the category of the quantum kind of structure, we establish a twofold complementarity scheme which constitutes an instance of the concept of adjunction. It is further argued that the established scheme is inextricably connected with a realistic philosophical attitude, although (...) substantially different from the classical one. (shrink)

We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and (...) quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime. (shrink)

All the typical global quantum mechanical observables are complex relative phases obtained by interference phenomena. They are described by means of some global geometric phase factor, which is thought of as the “memory” of a quantum system undergoing a “cyclic evolution” after coming back to its original physical state. The origin of a geometric phase factor can be traced to the local phase invariance of the transition probability assignment in quantum mechanics. Beyond this invariance, transition probabilities also remain invariant under (...) the operation of complex conjugation. Most important, geometric phase factors distinguish between unitary and antiunitary transformations in terms of complex conjugation. These two types of invariance functions as an anchor point to investigate the role of loops and based loops in the state space of a quantum system as well as their links and interrelations. We show that arbitrary transition probabilities can be calculated using projective invariants of loops in the space of rays. The case of the double slit experiment serves as a model for this purpose. We also represent the action of one-parameter unitary groups in terms of oppositely oriented-based loops at a fixed ray. In this context, we explain the relation among observables, local Boolean frames of projectors, and one-parameter unitary groups. Next, we exploit the non-commutative group structure of oriented-based loops in 3-d space and demonstrate that it carries the topological semantics of a Borromean link. Finally, we prove that there exists a representation of this group structure in terms of one-parameter unitary groups that realizes the topological linking properties of the Borromean link. (shrink)

This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to "physical geometry". In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory (...) of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums. (shrink)

We show that the Bub-Clifton uniqueness theorem (1996) for 'no collapse' interpretations of quantum mechanics can be proved without the 'weak separability' assumption.

We prove a uniqueness theorem showing that, subject to certain natural constraints, all 'no collapse' interpretations of quantum mechanics can be uniquely characterized and reduced to the choice of a particular preferred observable as determine (definite, sharp). We show how certain versions of the modal interpretation, Bohm's 'causal' interpretation, Bohr's complementarity interpretation, and the orthodox (Dirac-von Neumann) interpretation without the projection postulate can be recovered from the theorem. Bohr's complementarity and Einstein's realism appear as two quite different proposals for selecting (...) the preferred determinate observable--either settled pragmatically by what we choose to observe, or fixed once and for all, as the Einsteinian realist would require, in which case the preferred observable is a 'beable' in Bell's sense, as in Bohm's interpretation (where the preferred observable is position in configuration space). (shrink)

The framework of quantum frames can help unravel some of the interpretive difficulties i the foundation of quantum mechanics. In this paper, I begin by tracing the origins of this concept in Bohr's discussion of quantum theory and his theory of complementarity. Engaging with various interpreters and followers of Bohr, I argue that the correct account of quantum frames must be extended beyond literal space–time reference frames to frames defined by relations between a quantum system and the exosystem or external (...) physical frame, of which measurement contexts are a particularly important example. This approach provides superior solutions to key EPR-type measurement and locality paradoxes. (shrink)

In 2005, an essay was published in Nature asserting that the universe is mental and that we must abandon our tendency to conceptualize observations as things. Since then, experiments have confirmed that — as predicted by quantum mechanics — reality is contextual, which contradicts at least intuitive formulations of realism and corroborates the hypothesis of a mental universe. Yet, to give this hypothesis a coherent rendering, one must explain how a mental universe can — at least in principle — accommodate (...) (a) our experience of ourselves as distinct individual minds sharing a world beyond the control of our volition; and (b) the empirical fact that this world is contextual despite being seemingly shared. By combining a modern formulation of the ontology of idealism with the relational interpretation of quantum mechanics, the present paper attempts to provide a viable explanatory framework for both points. In the process of doing so, the paper also addresses key philosophical qualms of the relational interpretation. (shrink)

Die vorliegende Veröffentlichung stellt eine Würdigung der Naturphilosophie und Erkenntnistheorie der Philosophin Grete Henry-Hermann dar. Die Schülerin der Mathematikerin Emmy Noether und des Philosophen Leonard Nelson gehört zu den frühen Interpret(inn)en der Quantenmechanik. Werner Heisenberg setzte ihr in seinem Buch „Der Teil und das Ganze“ ein Denkmal. Erstmals sind in einem Band ihre naturphilosophischen und erkenntnistheoretischen Schriften zusammengefasst. Eine umfangreiche Einleitung verschiedener Autoren führt in das Werk von Grete Henry-Hermann ein. Ergänzt wird diese Ausgabe durch Auszüge aus der Korrespondenz über (...) naturphilosophische und erkenntnistheoretische Themen, darunter auch ein Briefwechsel mit Carl Friedrich von Weizsäcker, Werner Heisenberg und Gustav Heckmann. -/- Der Inhalt ● Grete Henry-Hermanns Beitrag zur Interpretation Quantenmechanik ● Grete Henry-Hermanns Arbeiten zum Verhältnis von moderner Physik und Transzendentalphilosophie ● Die Dissertation von Grete Hermann: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale (1925) ● Erörterungen zur Frage der Willensfreiheit und zur Bedeutung der Verhaltensforschung für die Kritik der Vernunft ● Auszüge aus dem Briefwechsel aus den Jahren 1925 bis 1982 -/- Der Herausgeber Privatdozent Dr. phil. Dipl.-Phys. Kay Herrmann lehrt Wissenschaftstheorie an der Technischen Universität Chemnitz -/- . (shrink)

In this paper I present and critically discuss the main strategies that Bohr used and could have used to fend off the charge that his interpretation does not provide a clear-cut distinction between the classical and the quantum domain. In particular, in the first part of the paper I reassess the main arguments used by Bohr to advocate the indispensability of a classical framework to refer to quantum phenomena. In this respect, by using a distinction coming from an apparently unrelated (...) philosophical corner, we could say that Bohr is not a revisionist philosopher of physics but rather a descriptivist one in the sense of Strawson. I will then go on discussing the nature of the holistic link between classical measurement apparatuses and observed system that he also advocated. The oft-repeated conclusion that Bohr’s interpretation of the quantum formalism is untenable can only be established by giving his arguments as much force as possible, which is what I will try to do in the following by remaining as faithful as possible to his published work. (shrink)

Rovelli’s RQM is first characterized by contrast with both Everett’s and Bohr’s interpretations of quantum mechanics. Then, it is shown that a basic difficulty arises from the choice of formulating RQM in a naturalistic framework. Even though, according to Rovelli’s interpretation, statements about the world only make sense relative to certain naturalized observers described by means of quantum mechanics, this very meta-statement seems to make sense relative to a sort of super-observer which does not partake of the naturalized status of (...) ordinary observers. The difficulty is solved by substituting functional reference frames for physical (or naturalized) observers throughout. Instead of being relative to physical observers, statements about the state vector of physical systems are here relative to well-defined projects of probabilistic prediction which may be embodied by several physical observers. (shrink)

In the first part of the paper I argue that an ontology of events is precise, flexible and general enough so as to cover the three main alternative formulations of quantum mechanics as well as theories advocating an antirealistic view of the wave function. Since these formulations advocate a primitive ontology of entities living in four-dimensional spacetime, they are good candidates to connect that quantum image with the manifest image of the world. However, to the extent that some form of (...) realism about the wave function is also necessary, one needs to endorse also the idea that the wave function refers to some kind of power. In the second part, I discuss some difficulties raised by the recent proposal that in Bohmian mechanics this power is holistically possessed by all the particles in the universe. (shrink)

The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the (...) so-called “quantum liar paradox,” an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW’s implications for quantum gravity. (shrink)

We introduce a new interpretation of non-relativistic quantum mechanics (QM) called Relational Blockworld (RBW). We motivate the interpretation by outlining two results due to Kaiser, Bohr, Ulfeck, Mottelson, and Anandan, independently. First, the canonical commutation relations for position and momentum can be obtained from boost and translation operators,respectively, in a spacetime where the relativity of simultaneity holds. Second, the QM density operator can be obtained from the spacetime symmetry group of the experimental configuration exclusively. We show how QM, obtained from (...) relativistic quantum field theory per RBW, explains the twin-slit experiment and conclude by resolving the standard conceptual problems of QM, i.e., the measurement problem, entanglement and non-locality. (shrink)

A perspective on Everett's relative state formulation is proposed, leading to a simple relational quantum mechanics. There are inevitably a large number of different versions of the world in which a specific observer could exist, and in the universe of the unitary wave function they are all existing and coincident. If these different versions of the world are superposed, the effective physical environment in the functional frame of reference of this observer would be highly indeterminate, since every possible variation of (...) the world is included; only where observed by the observer is this world determinate, as in Rovelli's Relational Quantum Mechanics. Although the identity of the observer as a physical body does not fit this concept, it applies inevitably to the functional identity of an observer as depicted by Everett, the state of the memory defining the record of observations. In this relativised quantum mechanics the collapse dynamics applies only to the functional frame of reference of the observer and raises no incompatibility with the linear dynamics. (shrink)

Everett demonstrates the appearance of collapse, within the context of the unitary linear dynamics. However, he does not state clearly how observers are to have determinate measurement records, hence 50 years of debate. This, however, is inherent. He defines the observer as the record of observations, which, naturally, is the record of correlations established with the physical environment. As in Rovelli's Relational Quantum Mechanics, the correlations record is the sole determinant of the effective physical environment, here the quantum mechanical frame (...) of reference: due to multiple realisation of the functional identity of the observer, the physical environment is a simultaneity of all the physical environments in which it is instantiated, a 'universe superposition', in which only the environment correlated with the observer by observations is determinate. This effects a discrete and idiosyncratic physical environment for each version of an observer, in which determinate measurement records are recorded. Quantum mechanics is on this view fully relational, demonstrated as not only viable but necessary by Rovelli & Laudisa. The quantum mechanical frame of reference is Everett's 'Relative State', and on Tegmark's 'inside view', the time evolution follows the standard von Neumann-Dirac formulation. Thus observers get precisely the measurement records predicted by the standard formulation, but since objectively there is only the appearance of collapse, there is neither a measurement problem nor a disparity with relativity. The linear dynamics and the collapse dynamics are directly experienced, as the passage of time and the making of observations, respectively. (shrink)

The nature and topology of time remains an open question in philosophy, both tensed and tenseless concepts of time appear to have merit. A concept of time including both kinds of time evolution of physical systems in quantum mechanics subsumes the properties of both notions. The linear dynamics defines the universe probabilistically throughout space-time, and can be seen as the definition of a block universe. The collapse dynamics is the time evolution of the linear dynamics, and is thus of different (...) logical type to the linear dynamics. These two different kinds of time evolution are respectively tensed and tenseless. Ascribing tensed semantics to the collapse dynamics is problematic in the light of special relativity, but this difficulty does not apply to a relational quantum mechanics. In this context, while the linear dynamics is the time evolution of the universe objectively, the collapse dynamics is the time evolution of the universe subjectively, applying solely in the functional frame of reference of the observer. (shrink)

A perspective on Everett's relative state formulation is proposed leading to a relational quantum mechanics. There are inevitably a large number of different versions of the universe in which a specific observer could exist, and in the universe of the unitary wave function they are all existing and coincident. If these different versions of the universe are superposed the result is a universe in which the superposition of all of the identical copies sums to a single observer. The effective universe (...) in the functional frame of reference of this observer would be highly indeterminate but determinate where observed by this observer. This would naturally relativise the universe of the conventional view since each observer would inhabit an effective universe in which different aspects were determinate. Although the identity of the observer as a physical body does not readily fit this concept, it appears to apply inevitably to the functional identity of an observer as depicted by Everett. In this relational quantum mechanics a collapse dynamics applies only to the functional frame of reference of the observer and raises no incompatibility with the linear dynamics. (shrink)

Fifteen philosophers offer new essays exploring the metaphysics of relations from antiquity to the present day. They address topics as diverse as ancient and medieval reasons for scepticism about polyadic properties; recent attempts to reduce causal and spatiotemporal relations; recent work on the directionality of relational properties; powers ontologies and their associated problems; whether the most promising interpretations of quantum mechanics posit a fundamentally relational world; and whether the very idea of such a world is coherent. From those who question (...) whether there are relational properties at all, to those who hold they are a fundamental part of reality, The Metaphysics of Relations covers a broad spectrum of positions on the nature and ontological status of relations, from antiquity to the present day. (shrink)

We study the process of observation (measurement), within the framework of a “perspectival” (“relational,” “relative state”) version of the modal interpretation of quantum mechanics. We show that if we assume certain features of discreteness and determinism in the operation of the measuring device (which could be a part of the observer's nerve system), this gives rise to classical characteristics of the observed properties, in the first place to spatial localization. We investigate to what extent semi-classical behavior of the object system (...) itself (as opposed to the observational system) is needed for the emergence of classicality. Decoherence is an essential element in the mechanism of observation that we assume, but it turns out that in our approach no environment-induced decoherence on the level of the object system is required for the emergence of classical properties. (shrink)

Pekka Lahti is a prominent exponent of the renaissance of foundational studies in quantum mechanics that has taken place during the last few decades. Among other things, he and coworkers have drawn renewed attention to, and have analyzed with fresh mathematical rigor, the threat of inconsistency at the basis of quantum theory: ordinary measurement interactions, described within the mathematical formalism by Schrödinger-type equations of motion, seem to be unable to lead to the occurrence of definite measurement outcomes, whereas the same (...) formalism is interpreted in terms of probabilities of precisely such definite outcomes. Of course, it is essential here to be explicit about how definite measurement results (or definite properties in general) should be represented in the formalism. To this end Lahti et al. have introduced their objectification requirement that says that a system can be taken to possess a definite property if it is certain (in the sense of probability 1) that this property will be found upon measurement. As they have gone on to demonstrate, this requirement entails that in general definite outcomes cannot arise in unitary measuring processes.In this paper we investigate whether it is possible to escape from this deadlock. As we shall argue, there is a way out in which the objectification requirement is fully maintained. The key idea is to adapt the notion of objectivity itself, by introducing relational or perspectival properties. It seems that such a “relational perspective” offers prospects of overcoming some of the long-standing problems in the interpretation of quantum mechanics. (shrink)

The underlying physical reality is a central notion in the interpretations of quantum mechanics. The a priori physical reality notion affects the corresponding interpretation. This paper explore the possibility to establish a relationship between philosophical concept of physical reality in Nagarjuna's epistemology (emptiness) and the picture of underlying physical reality in Einstein, Rovelli and Zeilinger positions. This analysis brings us to conclude that the notion of property of a quantum object is untenable. We can only speak about relational property of (...) the object. On this basis, we are stimulated to build a new ontology of underlying physical reality: a relational ontology. Finally, we argue that Nagarjuna's view is comparable with Rovelli's interpretation of quantum mechanics. These views eliminate the privileged role of the observer. (shrink)

Carlo Rovelli's relational interpretation of quantum mechanics holds that a system's states or the values of its physical quantities as normally conceived only exist relative to a cut between a system and an observer or measuring instrument. Furthermore, on Rovelli's account, the appearance of determinate observations from pure quantum superpositions happens only relative to the interaction of the system and observer. Jeffrey Barrett ([1999]) has pointed out that certain relational interpretations suffer from what we might call the ‘determinacy problem', but (...) Barrett misclassifies Rovelli's interpretation by lumping it in with Mermin's view, as Rovelli's view is quite different and has resources to escape the particular criticisms that Barrett makes of Mermin's view. Rovelli's interpretation still leaves us with a paradox having to do with the determinacy of measurement outcomes, which can be accepted only if we are willing to give up on certain elements of the ‘absolute’ view of the world. (shrink)