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.

Contemporary scientific perspectivism is primarily viewed as a methodological framework of how we obtain and form scientific knowledge of nature, through a broadly perspectivist process, especially, with reference to quantum mechanics. In the present study, this is implemented by representing categorically the global structure of a quantum algebra of events in terms of structured interconnected families of local Boolean probing frames, realized as suitable perspectives or contexts for measuring physical quantities. The essential philosophical meaning of the proposed (...) approach implies that the quantum world can be consistently approached and comprehended through a multilevel structure of locally variable perspectives, which interlock, in a category-theoretical environment, to form a coherent picture of the whole in a non-trivial way. (shrink)

In this paper we present a new categorical approach which attempts to provide an original understanding of QM. Our logos categorical approach attempts to consider the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about —rather than as problems that need to be bypassed in order to allow a restoration of a classical “common sense” understanding of what there is. In particular, we discuss (...) a solution to Kochen-Specker contextuality through the generalization of the meaning of global valuation. This idea has been already addressed by the so called topos approach to QM —originally proposed by Isham, Butterfiled and D ̈oring— in terms of sieve-valued valuations. The logos approach to QM presents a different solution in terms of the notion of intensive valuation. This new solution stresses an ontological reading of the quantum formalism and the need to restore an objective conceptual representation and understanding of quantum physical reality. (shrink)

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. (shrink)

The paper argues against an intuitive reading of the Stone-von Neumann theorem as a categoricity result, thereby pointing out that this theorem does not entail any model-theoretical difference between the theories that validate it and those that don't.

General metaphysical arguments have been proposed in favour of the thesis that all dispositions have categorical bases (Armstrong; Prior, Pargetter, Jackson). These arguments have been countered by equally general arguments in support of ungrounded dispositions (Molnar, Mumford). I believe that this controversy cannot be settled purely on the level of abstract metaphysical considerations. Instead, I propose to look for ungrounded dispositions in specific physical theories, such as quantum mechanics. I explain why non-classical properties such as spin are (...) best interpreted as irreducible dispositional properties, and I give reasons why even seemingly classical properties, for instance position or momentum, should receive a similar treatment when interpreted in the quantum realm. Contrary to the conventional wisdom, I argue that quantum dispositions should not be limited to probabilistic dispositions (propensities) by showing reasons why even possession of well-defined values of parameters should qualify as a dispositional property. I finally discuss the issue of the actuality of quantum dispositions, arguing that it may be justified to treat them as potentialities whose being has a lesser degree of reality than that of classical categorical properties, due to the incompatibility relations between non-commuting observables. (shrink)

In this paper we consider the notion of quantum entanglement from the perspective of the logos categorical approach [26, 27]. Firstly, we will argue that the widespread distinctions, on the one hand, between pure states and mixed states, and on the other, between separable states and entangled states, are completely superfluous when considering the orthodox mathematical formalism of QM. We will then argue that the introduction of these distinctions within the theory of quanta is due to another two (...) completely unjustified metaphysical presuppositions, namely, the idea that there is a “collapse” of quantum states when being measured and the idea that QM talks about “elementary particles”. At distance from these distinctions and taking the logos approach as a standpoint, we will propose an objective formal account of the notion of entanglement in terms of potential coding which introduces the necessary distinction between intensive relations and effective relations. We will also discuss how this new definition of entanglement provides an anschaulich content to this —supposedly “spooky”— quantum relational feature. (shrink)

This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of language, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of (...) Bohr's principle of correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic. (shrink)

Amid the wide variety of interpretations of quantum mechanics, the notion of a fully coherent ontological interpretation has seen a promising evolution over the last few decades. Despite this progress, however, the old dualistic categorical constraints of subjectivity and objectivity, correlate with the metrically restricted definition of local and global, have remained largely in place – a reflection of the broader, persistent inheritance of these comfortable strictures throughout the evolution of modern science. If one traces this inheritance (...) back to its ancient roots in Plato and Aristotle, it is clear that the coherence, scientific utility, and historical durability of the various natural philosophies that followed have been directly proportional to their commitment, tacit or explicit, to object-oriented realism. As Simondon might put it, it is a commitment to the primacy of individuated substance over the process of individuation. For Whitehead, it is the misplaced assimilation of becoming to being, of potentiality to actuality. Quantum mechanics has challenged this commitment with a combined breadth and depth of force that far exceeds any other theory in the history of science. The theory’s objectively demonstrable empirical application is manifest only by way of a fundamentally subjective, context-dependent mechanism of measurement. More compelling still, actual system states are always actualizations of locally contextualized yet globally conditioned potential system states, such that “globally objective” reality is no longer merely the object of local measurement, but also its product. Thus, any coherent, ontological interpretation of quantum theory must include a conceptual framework by which objectivity and subjectivity, actuality and potentiality, global and local, being and becoming, individuated fact and process of individuation, are no longer understood as merely epistemic, mutually exclusive category pairs descriptive of an already extant, closed reality – but rather as mutually implicative ontological categories explicative of an ontogenetic, open reality-in-process. (shrink)

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valua- tion 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 al- gebras. 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 in- herent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical im- plications 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. In this light, the transcendence condition of the usual concep- tion of correspondence truth is superseded by a reflective-like transcendental reasoning of the proposed account of truth that is suitable to the quantum domain of discourse. (shrink)

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 by representing categorically the global structure of a quantum algebra of events 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 contextualist account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to state the totality of facts of nature. (shrink)

It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are (...) usually categorically rejected, because of Bell’s powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions. (shrink)

As a metaphysical theory, radical ontic structural realism is characterised mainly in terms of the ontological primacy it places on relations and structures, as opposed to the individual relata and objects that inhabit these relations/structures. The most popular criticism of ROSR is that its central thesis is incoherent. Bain attempts to address this criticism by arguing that the mathematical language of category theory allows for a coherent articulation of ROSR’s key thesis. Subsequently, Wüthrich and Lam and Lal and Teh have (...) criticised Bain’s arguments and claimed that category theory fares no better than set theory in coherently articulating the main ideas of ROSR. In this paper, we defend Bain’s main arguments against these critiques, and attempt to elaborate on the sense in which category theory can be seen as providing a coherent articulation of ROSR. We also consider the relationship between ROSR and Categorical Quantum Mechanics. (shrink)

This paper provides an algebraic reconstruction of Einstein’s argument for the incompleteness of quantum mechanics, in order to clarify the assumptions that underlie an understanding of Einstein completeness as categoricity.

In this paper I examine the role of dispositional properties in the most frequently discussed interpretations of non-relativistic quantum mechanics. After offering some motivation for this project, I briefly characterize the distinction between non-dispositional and dispositional properties in the context of quantum mechanics by suggesting a necessary condition for dispositionality – namely contextuality – and, consequently, a sufficient condition for non-dispositionality, namely non-contextuality. Having made sure that the distinction is conceptually sound, I then analyze the plausibility (...) of the widespread, monistic ontological thesis about the reducibility of dispositional properties to categorical properties in the context of the philosophy of quantum mechanics. I conclude that with the exception of Bohmian mechanics, the other “minimally realist” views of quantum mechanics require essential dispositions, i.e., dispositions of a non-reducible kind. Interestingly, seen behind the lenses of dispositionalism, Bohr’s and Bohm’s interpretations of quantum mechanics are much closer than it is usually recognized, a fact that could teach us something about the way the quantum world is. (shrink)

This volume develops a fundamentally different categorical framework for conceptualizing time and reality. The actual taking place of reality is conceived as a “constellatory self-unfolding” characterized by strong self-referentiality and occurring in the primordial form of time, the not yet sequentially structured “time-space of the present.” Concomitantly, both the sequentially ordered aspect of time and the factual aspect of reality appear as emergent phenomena that come into being only after reality has actually taken place. In this new framework, time (...) functions as an ontophainetic [H1] platform, i.e., as the stage on which reality can first occur. Events are merely the “tracks” that the actual taking place of reality leaves behind on the co-emergent “canvas’’ of local spacetime. -/- The view of time proposed here is particularly relevant to the recent debate over the “ER=EPR” conjecture targeting the relation between quantum physics and general relativity theory. The novelty of this radically different framework is that it allows quantum reduction and singularities to be addressed as inverse transitions into and out of the factual layer of reality: In quantum physical state reduction, reality “gains” the chrono-ontological format of facticity, and the sequential aspect of time becomes applicable. In singularities, by contrast, the opposite happens: Reality loses its local spacetime formation and reverts back to its primordial, pre-local shape – making the use of causality relations, Boolean logic and the dichotomization of subject and object obsolete in the process. -/- For our understanding of the relation between quantum and relativistic physics, this new view opens up fundamentally new perspectives: Both are legitimate views of time and reality; they simply address very different chrono-ontological portraits, and thus should not lead us to erroneously prefer one view over the other. -/- The task of the book is to provide a formal framework in which this radically different view of time and reality can be suitably addressed. The mathematical approach is based on the logical and topological features of the Borromean Rings, and draws upon concepts and methods from algebraic and geometric topology – especially the theory of sheaves and links, group theory, logic and information theory in relation to the standard constructions employed in quantum mechanics and general relativity, shedding new light on the problems of their compatibility. The intended audience includes physicists, mathematicians and philosophers with an interest in the conceptual and mathematical foundations of modern physics. (shrink)

Quantum field theory (QFT) combines quantum mechanics with Einstein's special theory of relativity and underlies elementary particle physics. This book presents a philosophical analysis of QFT. It is the first treatise in which the philosophies of space-time, quantum phenomena, and particle interactions are encompassed in a unified framework. Describing the physics in nontechnical terms, and schematically illustrating complex ideas, the book also serves as an introduction to fundamental physical theories. The philosophical interpretation both upholds the reality (...) of the quantum world and acknowledges the irreducible cognitive elements in its representation. The interpretation is based on an analysis of our ways of thinking as the are embedded in the logical structure of QFT. The author argues that philosophical categories are significant only if they play active and essential roles in our knowledge and hence constitute part of the theories in actual use. Thus she regards physical theories as primary, extracts their categorical structure, and uses it to rethink key philosophical questions. Among the questions this book tries to answer are: What are the quantum properties independent of measurements? How do we refer to individual things in a continuous field? How do theories relate to objects? What are the general conditions of the world and of our ways of thinking that make possible our knowledge of the microscopic realm, which is so intangible and counterintuitive? As a penetrating analysis of vital themes in contemporary science, the book will engage the interest of students and professionals in physics and philosophy alike. (shrink)

This paper studies the notion of virtuality in the Bohr-Kramers-Slater theory of 1924. We situate the virtual entities of BKS within the tradition of the correspondence principle and the radiation theory of the Bohr model. We show how, in this context, virtual oscillators emerged as classical substitute radiators and were used to describe the otherwise elusive quantum transitions. They played an effective role in the quantum theory of radiation while remaining categorically distinct and ontologically separated from the (...) class='Hi'>quantum world of the Bohr model. The notion of virtuality thus differs markedly from its counterpart in quantum mechanics or QFT. (shrink)

An Aristotelian philosophy of nature offers an alternative to reduction for the conception of the inter-theoretical relationships between molecular chemistry and quantum mechanics. A basic ingredient for such an approach is an ontology of fundamental causal powers, and this work aims to develop such an ontology by drawing on quantum-chemical entities, particularly, the electron density. This notion is central to the Quantum Theory of Atoms in Molecules, a theory of molecular structure developed by Richard F. W. (...) Bader, which describes molecules and atoms in terms precisely of the electron density. Then, by identifying a philosophical tension in Bader’s discourse about the nature of electron density, the work will analyze this central notion in terms of the categorical/dispositional distinction regarding properties. The central idea is that electron density can be conceived as categorical and dispositional at once, and this very characterization can avoid Bader’s philosophical tension. (shrink)

After some suggestions about how to clarify the confused metaphysical distinctions between dispositional and non-dispositional or categorical properties, I review some of the main interpretations of QM in order to show that – with the relevant exception of Bohm’s minimalist interpretation – quantum ontology is irreducibly dispositional. Such an irreducible character of dispositions must be explained differently in different interpretations, but the reducibility of the contextual properties in the case of Bohmian mechanics is guaranteed by the fact (...) that the positions of particles play the role of the categorical basis, a role that in other interpretations cannot be filled by anything else. In Bohr’s and Everett-type interpretations, dispositionalism is instrumentalism in disguise. (shrink)

In de Ronde and Massri it was argued against the orthodox definition of quantum entanglement in terms of pure and separable states. In this paper we attempt to discuss how the logos categorical approach to quantum mechanics is able to provide an objective formal account of the notion of entanglement—completely independent of both purity and separability—in terms of the potential coding of intensive relations and effective relations. We will show how our novel redefinition allows us to (...) provide an anschaulich content to the notion of entanglement, erasing in this way the “spookiness” still present within its orthodox understanding in terms of space-time separated collapse particles. (shrink)

While quantum theory cannot be described by a local hidden variable model, it is nevertheless possible to construct such models that exhibit features commonly associated with quantum mechanics. These models are also used to explore the question of \-ontic versus \-epistemic theories for quantum mechanics. Spekkens’ toy theory is one such model. It arises from classical probabilistic mechanics via a limit on the knowledge an observer may have about the state of a system. The (...) toy theory for the simplest possible underlying system closely resembles stabilizer quantum mechanics, a fragment of quantum theory which is efficiently classically simulable but also non-local. Further analysis of the similarities and differences between those two theories can thus yield new insights into what distinguishes quantum theory from classical theories, and \-ontic from \-epistemic theories. In this paper, we develop a graphical language for Spekkens’ toy theory. Graphical languages offer intuitive and rigorous formalisms for the analysis of quantum mechanics and similar theories. To compare quantum mechanics and a toy model, it is useful to have similar formalisms for both. We show that our language fully describes Spekkens’ toy theory and in particular, that it is complete: meaning any equality that can be derived using other formalisms can also be derived entirely graphically. Our language is inspired by a similar graphical language for quantum mechanics called the ZX-calculus. Thus Spekkens’ toy bit theory and stabilizer quantum mechanics can be analysed and compared using analogous graphical formalisms. (shrink)

A short scientific biography emphasising the main phases of Abramsky’s research: duality theory and domains in logical form, game semantics, categorical quantum mechanics, the sheaf-theoretic approach to contextuality, and game comonads and a structural view of resources and descriptive complexity.

In contrast to the theories of relativity, quantum mechanics is not yet based on a generally accepted conceptual foundation. It is proposed here that the missing principle may be identified through the observation that all knowledge in physics has to be expressed in propositions and that therefore the most elementary system represents the truth value of one proposition, i.e., it carries just one bit of information. Therefore an elementary system can only give a definite result in one specific (...) measurement. The irreducible randomness in other measurements is then a necessary consequence. For composite systems entanglement results if all possible information is exhausted in specifying joint properties of the constituents. (shrink)

We generalize the modal interpretation of quantum mechanics so that it may be applied to composite systems represented by arbitrary density operators. We discuss the interpretation these density operators receive and relate this to the discussion about the interpretation of proper and improper mixtures in the standard interpretation.

‘Shallow’ and ‘deep’ versions of scientific realism may be distinguished as follows: the shallow realist is satisfied with belief in the existence of the posits of our best scientific theories; by contrast, deep realists claim that realism can be legitimate only if such entities are described in metaphysical terms. We argue that this methodological discussion can be fruitfully applied in Everettian quantum mechanics, specifically on the debate concerning the existence of worlds and the recent dispute between Everettian actualism (...) and quantum modal realism. After presenting what is involved in such dispute, we point to a dilemma for realists: either we don’t have the available metaphysical tools to answer the deep realist’s demands, and realism is not justified in this case, or such demands of metaphysical dressing are not mandatory for scientific realism, and deep versions of realism are not really required. (shrink)

Karl Popper and Paul Feyerabend were among the most influential philosophers of science of the twentieth century. Extensive studies have been dedicated to the development of their controversial relationship, which saw Feyerabend turning from a student and supporter of Popper to one of his harshest critics. Yet, it is not as well known that the rift between Popper and Feyerabend arose mainly in the context of their studies on the foundations of quantum mechanics, which has been the main (...) subject of their discussions for about two decades. This paper reconstructs in detail their diatribe over the foundations of quantum mechanics, emphasising also the major role that their personal relationship played in their distancing. (shrink)

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In (...) order to make the theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In (...) order to make the theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

A widespread view in physics holds that the implementation of time reversal in standard quantum mechanics must be given by an anti-unitary operator. In foundations and philosophy of physics, however, there has been some discussion about the conceptual grounds of this orthodoxy, largely relying on either its obviousness or its mathematical-physical virtues. My aim in this paper is to substantively change the traditional structure of the debate by highlighting the philosophical commitments underlying the orthodoxy. I argue that the (...) persuasive force of the orthodoxy can benefit from a relational metaphysics of time and a by-stipulation view on symmetries. Within such philosophical background, I submit, the orthodoxy of time reversal in standard quantum mechanics could find a fertile terrain to lay the groundwork for a more thorough conceptual justification. (shrink)

Samson Abramsky’s wide-ranging contributions to logical and structural aspects of Computer Science have had a major influence on the field. This book is a rich collection of papers, inspired by and extending Abramsky’s work. It contains both survey material and new results, organised around six major themes: domains and duality, game semantics, contextuality and quantum computation, comonads and descriptive complexity, categorical and logical semantics, and probabilistic computation. These relate to different stages and aspects of Abramsky’s work, reflecting its (...) exceptionally broad scope and his ability to illuminate and unify diverse topics. Chapters in the volume include a review of his entire body of work, spanning from philosophical aspects to logic, programming language theory, quantum theory, economics and psychology, and relating it to a theory of unification of sciences using dual adjunctions. The section on game semantics shows how Abramsky’s work has led to a powerful new paradigm for the semantics of computation. The work on contextuality and categorical quantum mechanics has been highly influential, and provides the foundation for increasingly widely used methods in quantum computing. The work on comonads and descriptive complexity is building bridges between currently disjoint research areas in computer science, relating Structure to Power. The volume also includes a scientific autobiography, and an overview of the contributions. The outstanding set of contributors to this volume, including both senior and early career academics, serve as testament to Samson Abramsky’s enduring influence. It will provide an invaluable and unique resource for both students and established researchers. (shrink)

A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept (...) of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a causal category . We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics. (shrink)

Perhaps the hottest topic in the philosophy of chemistry is that of the relationship between chemistry and physics. The problem finds one of its main manifestations in the debate about the nature of molecular structure, given by the spatial arrangement of the nuclei in a molecule. The traditional strategy to address the problem is to consider chemical cases that challenge the definition of molecular structure in quantum–mechanical terms. Instead of taking that top-down strategy, in this paper we face the (...) problem of the reduction of molecular structure to quantum mechanics from a bottom-up perspective: our aim is to show how the theoretical peculiarities of quantum mechanics stand against the possibility of molecular structure, defined in terms of the spatial relations of the nuclei conceived as individual localized objects. We will argue that, according to the theory, quantum “particles” are not individuals that can be identified as different from others and that can be reidentified through time; therefore, they do not have the ontological stability necessary to maintain the relations that can lead to a spatially definite system with an identifiable shape. On the other hand, although quantum chemists use the resources supplied by quantum mechanics with successful results, this does no mean reduction: their “approximations” add certain assumptions that are not justified in the context of quantum mechanics or are even inconsistent with the very formal structure of the theory. (shrink)

Differing views on reduction are briefly reviewed and a suggestion is made for a working definition of 'approximate reduction'. Ab initio studies in quantum chemistry are then considered, including the issues of convergence and error bounds. This includes an examination of the classic studies on CH2 and the recent work on the Si2C molecule. I conclude that chemistry has not even been approximately reduced.

The modal-Hamiltonian interpretation belongs to the modal family of interpretations of quantum mechanics. By endowing the Hamiltonian with the role of selecting the subset of the definite-valued observables of the system, it accounts for ideal and non-ideal measurements, and also supplies a criterion to distinguish between reliable and non-reliable measurements in the non-ideal case. It can be reformulated in an explicitly invariant form, in terms of the Casimir operators of the Galilean group, and the compatibility of the MHI (...) with the theory of decoherence has been proved. Nevertheless, perhaps its main advantage in the eyes of a scientist is given by its several applications to well-known physical situations, leading to results compatible with experimental evidence. The purpose of this paper is to add a new application to the list: the case of optical isomerism, which is a central issue for the philosophy of physics and of chemistry since it points to the core of the problem of the relationship between physics and chemistry. Here it will be shown that the MHI supplies a direct and physically natural solution to the problem, a solution that does not require putting classical assumptions in “by hand.”. (shrink)

On several levels, there is now a debate whether the concept of God can be made compatible with modern science. In an attempt to elucidate this debate, I give an account of my own experiences from writing a book on the foundation of quantum mechanics. In my opinion, one can give two independent arguments for the existence of God by taking as departure an epistemic (knowledge-based) interpretation of quantum theory. However, I also argue that any religious belief (...) should be the result of an existential choice governed by each person’s own context (history and culture). In particular, I give my account of Christianity as a religion connected to our western culture, how one as a scientist can relate to the relevant dogmas. (shrink)

I show why old and new claims on the role of counterfactual reasoning for the EPR argument and Bell’s theorem are unjustified: once the logical relation between locality and counterfactual reasoning is clarified, the use of the latter does no harm and the nonlocality result can well follow from the EPR premises. To show why, after emphasizing the role of incompleteness arguments that Einstein developed before the EPR paper, I critically review more recent claims that equate the use of counterfactual (...) reasoning with the assumption of a strong form of realism and argue that such claims are untenable. (shrink)

The aim of this paper is to reconstruct and correct one argument in support of the symmetrization postulate in quantum mechanics. I identify the central premise of the argument as a thesis specifying a particular ontic property of quantum superpositions. The precise form of this thesis depends on some underlying assumptions of a metaphysical character. I compare the exchange degeneracy argument with alternative formal arguments for the symmetrization postulate, and I discuss the role and meaning of labels (...) in the symmetric/antisymmetric representations of the states of many particles. (shrink)

Everettian quantum mechanics results in ‘multiple, emergent, branching quasi-classical realities’ . The possible outcomes of measurement as per ‘orthodox’ quantum mechanics are, in EQM, all instantiated. Given this metaphysics, Everettians face the ‘probability problem’—how to make sense of probabilities and recover the Born rule. To solve the probability problem, Wallace, following Deutsch , has derived a quantum representation theorem. I argue that Wallace’s solution to the probability problem is unsuccessful, as follows. First, I examine one (...) of the axioms of rationality used to derive the theorem, ‘branching indifference’ . I argue that Wallace is not successful in showing that BI is rational. While I think it is correct to put the burden of proof on Wallace to motivate BI as an axiom of rationality, it does not follow from his failing to do so that BI is not rational. Thus, second, I show that there is an alternative strategy for setting one’s credences in the face of branching which is rational and which violates BI. This is ‘branch counting’ . Wallace is aware of BC and has proffered various arguments against it. However, third, I argue that Wallace’s arguments against BC are unpersuasive. I conclude that the probability problem in EQM persists. 1 Introduction2 Branching Indifference2.1 The positive argument for branching indifference2.2 The negative argument for branching indifference2.3 Branching indifference section summary3 Branch Counting3.1 Branch counting is rational under the subjective-uncertainty viewpoint3.2 Branch counting is rational under the objective-determinism viewpoint3.3 Branch counting section summary4 Number of Branches4.1 Veracity of the framework4.2 No such thing as the number of branches4.2.1 The number of branches is indeterminate4.2.2 The number of branches is indeterminable4.3 Rationality and weight5 Conclusion. (shrink)

Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schr¨ odinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. Indeed, they succeed in serving that purpose (...) in the context of a theory known as Bohmian mechanics, to which this article is an introduction. (shrink)

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the ¯h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains (...) in its own structure the possibility of describing real objects in an observer-independent way. (shrink)

The possibility that zitterbewegung opens a window to particle substructure in quantum mechanics is explored by constructing a particle model with structural features inherent in the Dirac equation. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. The model admits periodic solutions with quantized energy, and the correct magnetic moment is generated by charge circulation. It attributes to the electron an electric dipole moment rotating with ultrahigh frequency, (...) and the possibility of observing this directly as a resonance in electron channeling is analyzed in detail. Correspondence with the Dirac equation is discussed. A modification of the Dirac equation is suggested to incorporate the rotating dipole moment. (shrink)

All suggested notions of reduction of two scientific theories are critically reviewed and analyzed. In particular those applied to the case of the alleged reduction of Chemistry to Quantum mechanics are examined. Since it is recognized that the weakness of this field of research is the lack of a definition of a scientific theory, it is suggested that a scientific theory is characterized by two choices regarding two dichotomies, that is, the kind of mathematics and the kind of (...) logic. According to this view a reduction is only possible between two theories in which the same choices are shared. As a consequence, only one case of reduction in the history of physics is recognized: physical optics to electromagnetism, a case that is commonly accepted. The other cases of claimed reductions are recognized as impossible, owing to the different choices of the two theories at issue and hence the radical variations in meaning of their shared basic notions. In particular, the claimed reduction of Chemistry to Quantum mechanics is disproved in detail. (shrink)

I argue that the Causal Markov Condition (CMC) is in principle applicable to the Einstein–Podolsky–Rosen (EPR) correlations. This is in line with my defence in the past of the applicability of the Principle of Common Cause to quantum mechanics. I first review a contrary claim by Dan Hausman and Jim Woodward, who endeavour to preserve the CMC against a possible counterexample by asserting that the conditions for the application of the CMC are not met in the EPR experiment. (...) In their view the CMC is inapplicable to the EPR correlations—i.e. it neither obtains nor fails. The view is grounded upon the non-separability of the quantum state, and the consequent unavailability of interventions. I urge that whether interventions are available in EPR—and why—is a complex and contextual question that does not have a unique or uniform answer. Instead, I argue that different combinations of causal hypotheses under test and interpretations of quantum mechanics yield different answers to the question. (shrink)

The previous three articles have discussed scientific ontology, resolving the contradictions between quantum mechanics and relativity using the cosmic origin philosophical framework, and interpreting the principles of natural philosophy through physics. Aristotle established material philosophy and material science, relegating the philosophical concepts of cosmic ontology and the cosmic origin to metaphysics and theology. As a result, philosophy was divided into first philosophy and second philosophy as scientific considerations. When material science developed into the ontology of the universe, able (...) to explain the cosmic origin principle, a major issue arose: after 2500 years of development, humanity has only grasped the meaning of “matter.” Yet, what are “energy” and “information”? We still haven’t figured that out. Modern physics has brought both benefits and contradictions to humanity. To resolve these contradictions, we need to redefine the scientific consideration of “philosophy” and its philosophical concepts. This article continues to explore the contradictions between quantum mechanics and relativity using the principles of cosmic origin, reflecting on the basic concepts of philosophy and human thought. (shrink)

This paper introduces an extension of the de Broglie-Bohm-Bell formulation of quantum mechanics, which includes intrinsic particle degrees of freedom, such as spin, as elements of reality. To evade constraints from the Kochen-Specker theorem the discrete spin values refer to a specific basis – i.e., a single spin vector orientation for each particle; these spin orientations are, however, not predetermined, but dynamic and guided by the wave function of the system, which is conditional on the realized location values (...) of the particles. In this way, the unavoidable contextuality of spin is provided by the wave function and its realized particle configuration, whereas spin is still expressed as a local property of the individual particles. This formulation, which furthermore features a rigorous discrete-time stochastic dynamics, allows for numerical simulations of particle systems with entangled spin, such as Bohm’s version of the EPR experiment. (shrink)

is every bit as intelligible and philosophically respectable as many other doctrines currently in favor, e.g., the doctrine that mental events are identical with brain events; the attempt to give a linguistic construal of this latter doctrine meets many of the same sorts of difficulties encountered above (see Hempel, op. cit.). Secondly, I think that evidence for universal determinism may not, as a matter of fact, be so hard to come by as one might imagine. It is a striking fact (...) about our world that we never observe any genuine cases of parallelism; it always seems possible to design some sort of interaction between any two genuine empirical magnitudes. If this is correct, then a true theory T can be deterministic only if universal determinism reigns. (shrink)

This paper examines the epistemological significance of the present situation of underdetermination in quantum mechanics. After analyzing this underdetermination at three levels---formal, ontological, and methodological---the paper considers implications for a number of variants of the thesis of scientific realism in fundamental physics and reassesses Lakatos‘ characterization of progress in physical theory in light of the present situation. Next, this paper considers the implications of underdetermination for Weinberg’s ‘‘dream of a final theory.’’ Finally, the paper concludes by suggesting how (...) one might still think of realism and progress in fundamental physics despite the possibility of persistent underdetermination in quantum mechanics. (shrink)