Over the last twenty years, archaeologists have used various process-oriented modes of enquiry to undermine the belief that humans are special. Barad (2007) developed Bohr’s indeterminist interpretation of quantum mechanics into agential realism which offers an ontological basis for distributing agency away from humans and plays a crucial role in underwriting some posthumanist archaeological agendas. But its origins in quantum physics make agential realism difficult to understand and evaluate. Despite the challenge, the first two parts of this paper are devoted (...) to each task in turn, with limited success. Part three turns to the archaeological literature, where the evaluation of agential realism turns out to be even more inadequate and so I advise against its use in support of process-oriented approaches in archaeology. The final section turns to the activity of an art workshop and introduces a playful approach to working with clay. Clayful phenomenology is a way of investigating the relationship between gesture, material and ideation. During sculpting, phenomenological experience is not subjective, stable and external but is generated within a transient creative system where entities, ideas and agency reciprocally, emerge as ephemeral manifestations. Clayful phenomenology and agential realism are ontologically similar and both are controversial but agential realism has a wall of quantum conceptual complexity standing between it and a judgement about credibility whereas playing with clay can be assessed directly, through experience. (shrink)

In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics. We will argue that—leaving aside instrumentalism which restricts the physical meaning of QM to the algorithmic prediction of measurement outcomes—the many interpretations which can be found in the literature can be distinguished through the way they model the measurement process, either in terms of the efficient cause or in terms of the final cause. We (...) will discuss and analyze why both, ‘final cause’ and ‘efficient cause’ models, face severe difficulties to solve the measurement problem. In contradistinction to these schemes we will present a new model based on the immanent cause which, we will argue, provides an intuitive understanding of the measurement process in QM. (shrink)

We go through Bohr's talk about complementary features of quantum theory at the Volta Conference in September 1927, by collating a manuscript that Bohr wrote in Como with the unpublished stenographic report of his talk. We conclude – also with the help of some unpublished letters – that Bohr gave a very concise speech in September. The formulation of his ideas became fully developed only between the fifth Solvay Conference, in Brussels in October, and early 1928. The unpublished stenographic reports (...) of the Solvay Conference suggest that we reconsider the role that discussions with his colleagues possibly had on Bohr's final presentation of the complementary sides of atomic physics in his 1928 papers. (shrink)

A growing number of commentators have, in recent years, noted the important affinities in the views of Immanuel Kant and Niels Bohr. While these commentators are correct, the picture they present of the connections between Bohr and Kant is painted in broad strokes; it is open to the criticism that these affinities are merely superficial. In this essay, I provide a closer, structural, analysis of both Bohr's and Kant's views that makes these connections more explicit. In particular, I demonstrate the (...) similarities between Bohr's argument, on the one hand, that neither the wave nor the particle description of atomic phenomena pick out an object in the ordinary sense of the word, and Kant's requirement, on the other hand, that both ‘mathematical’ (having to do with magnitude) and ‘dynamical’ (having to do with an object's interaction with other objects) principles must be applicable to appearances in order for us to determine them as objects of experience. I argue that Bohr's ‘complementarity interpretation’ of quantum mechanics, which views atomic objects as idealizations, and which licenses the repeal of the principle of causality for the domain of atomic physics, is perfectly compatible with, and indeed follows naturally from a broadly Kantian epistemological framework. (shrink)

Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of lightcnot being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constanthrequires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature evolving continuously “in time”, has to be replaced by an infinite (...) manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics:To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values ofh, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action. (shrink)

: This paper examines the transformation which occurs in Heisenberg's understanding of indeterminacy in quantum mechanics between 1926 and 1928. After his initial but unsuccessful attempt to construct new quantum concepts of space and time, in 1927 Heisenberg presented an operational definition of concepts such as 'position' and 'velocity'. Yet, after discussions with Bohr, he came to the realisation that classical concepts such as position and momentum are indispensable in quantum mechanics in spite of their limited applicability. This transformation in (...) Heisenberg's thought, which centres on his theory of meaning, marks the critical turning point in his interpretation of quantum mechanics. (shrink)

In this paper, I argue that Heisenberg's mature philosophy of quantum mechanics must be understood in the context of his epistemological project to reinterpret and redefine Kant's notion of the a priori. After discussions with Weizsäcker and Hermann in Leipzig in the 1930s, Heisenberg attempted to ground his interpretation of quantum mechanics on what might be termed a 'practical' transformation of Kantian philosophy. Taking as his starting point, Bohr's doctrine of the indispensability of classical concepts, Heisenberg argued that concepts such (...) as space, time and causality can be regarded as 'practically a priori', in so far as they remain the conditions for the possibility of experience and even of 'objective reality', though they are not universal and necessary in a strictly Kantian sense. We cannot avoid using classical concepts in the description of experiments in quantum theory, despite the fact that there are limits to their applicability. Such concepts are, for Heisenberg, historically contingent, yet indispensable in our time, because we have no other language through which we can describe and conceive of the interaction between 'object' and 'measuring device'. (shrink)

According to the standard view, the so-called ‘Copenhagen interpretation’ of quantum mechanics originated in discussions between Bohr and Heisenberg in 1927, and was defended by Bohr in his classic debate with Einstein. Yet recent scholarship has shown Bohr’s views were never widely accepted, let alone properly understood, by his contemporaries, many of whom held divergent views of the ‘Copenhagen orthodoxy’. This paper examines how the ‘myth of the Copenhagen interpretation’ was constructed by situating it in the context of Soviet Marxist (...) critique of quantum mechanics in the 1950s and the response by physicists such as Heisenberg and Rosenfeld. (shrink)

The determination of the past and the future of a physical system are complementary aims of measurements. An optimal determination of the past of a system can be achieved by an informationally complete set of physical quantities. Such a set is always strongly noncommutative. An optimal determination of the future of a physical system can be obtained by a Boolean complete set of quantities. The two aims can be reconciled to a reasonable degree with using unsharp measurements.

Scientific theories are analyzed in terms of the role that they play in science rather than in terms of their logical structure. It is maintained that theories: provide descriptions of the fundamental features of their domains; on the basis of 1, explain non-fundamental features of their domains; provide a guide for further research in their domains. Any set of propositions that carries out these functions with respect to some domain counts as a theory. This view of theories is developed and (...) defended, and provides the basis for reconsidering a number of issues in the philisophy of science. It is argued that theories need not be unrestrictedly universal with respect to space and time; that the distinction between observable and theoretical entities fails because observables do function as theoretical entities in scientific theories, that there is no genuine philosophical problem of reduction; that the notion of "levels" can be replaced by the notion of "domains"; and that theories are the basic unit of scientific knowledge. (shrink)

The traditional analysis of the basic version of the double-slit experiment leads to the conclusion that wave-particle duality is a fundamental fact of nature. However, such a conclusion means to imply that we are not only required to have two contradictory pictures of reality but also compelled to abandon the objectiveness of the truth values, “true” and “false”. Yet, even if we could accept wave-like behavior of quantum particles as the best explanation for the build-up of an interference pattern in (...) the double-slit experiment, without the objectivity of the truth values we would never have certainty regarding any statement about the world. The present paper discusses ways to reconcile the correct description of the double-slit experiment with the objectiveness of “true” and “false”. (shrink)

We clarify Bohr’s interpretation of quantum mechanics by demonstrating the central role played by his thesis that quantum theory is a rational generalization of classical mechanics. This thesis is essential for an adequate understanding of his insistence on the indispensability of classical concepts, his account of how the quantum formalism gets its meaning, and his belief that hidden variable interpretations are impossible.

Despite remarkable efforts, it remains notoriously difficult to equip quantum theory with a coherent ontology. Hence, Healey (2017, 12) has recently suggested that ‘‘quantum theory has no physical ontology and states no facts about physical objects or events’’, and Fuchs et al. (2014, 752) similarly hold that ‘‘quantum mechanics itself does not deal directly with the objective world’’. While intriguing, these positions either raise the question of how talk of ‘physical reality’ can even remain meaningful, or they must ultimately embrace (...) a hidden variables-view, in tension with their original project. I here offer a neo-Kantian alternative. In particular, I will show how constitutive elements in the sense of Reichenbach (1920) and Friedman (1999, 2001) can be identified within quantum theory, through considerations of symmetries that allow the constitution of a ‘quantum reality’, without invoking any notion of a radically mind-independent reality. The resulting conception will inherit elements from pragmatist and ‘QBist’ approaches, but also differ from them in crucial respects. Furthermore, going beyond the Friedmanian program, I will show how non-fundamental and approximate symmetries can be relevant for identifying constitutive principles. (shrink)

SummaryThe present paper attemps to demonstrate an analogy between the metascientific, i. e. epistemological, concepts of Niels Bohr and Jean Piaget. To make such a comparison possible a general model of an open circular process of acquiring knowledge is proposed including the following stages: generalization of a successful theory, origin of implicit assumptions, counter‐examples, disclosure of implicit and tacit assumptions ; attempts to eliminate counter‐examples, cul‐de‐sac, emergence of competing theories, explication of fundamental notions, distinction between narrower and broader theories. Parallelly, (...) historical exemplifications on each stage are given. Finally, the argument is advanced that scientific epistemology is only possible at the expense of re‐defining ≫science≪ in such a way that it would cease to be science in its strict classical sense on which the claim to this name has been based so far. (shrink)

A prominent way through which wave-particle duality has been ascribed to photons is by illustrating their “wave-like” behaviour in the Mach-Zehnder interferometer and “particle-like” behaviour in the anti-correlation experiment. This duality has been formulated in two ways. Some have based the claim on the complementarity principle. This formulation, however, has already been shown to be problematic. Others have made a much simpler duality claim by considering that single-photons are analogous to waves and particles in the above experiments. I criticise this (...) formulation by arguing that the analogies cannot be distinctly established. Thus, this duality claim is found to be unsubstantiated. (shrink)

While most new materialists, including Thomas Nail, tend to distance themselves from Deleuze, this essay reads the encounter of Nail's ‘process materialism’ and Deleuzian philosophy as productive rather than contentious. After tracing the affinities of their notions of continuity and discontinuity by way of Deleuze's The Fold: Leibniz and the Baroque and Nail's Lucretius I: An Ontology of Motion and Being and Motion, the essay considers Nail's unfolding of Lucretius’ luminous philosophy in relation to Deleuze's reading of Lucretius from within (...) Deleuze's own ‘philosophical luminism’. Within the multiple overlaps between Nail and Deleuze, particularly vis-à-vis quantum physics and quantum field theory, their divergent readings of the particle–wave duality bring about a productive conceptual tension. Nail's argument about the ontological precedence of waves over particles is illuminated by Deleuze's concept of their ontological complementarity, and vice versa. (shrink)

The aim of this paper is to combine the intellectual and the psychosocial aspects. blurring the distinction between the conceptual and the anecdotal history of quantum mechanics. The full realization of the importance of such “anecdotal” factors leads to the revision of our understanding of the conceptual development itself. The paper concludes with the suggestion that a major part of numerous inconsistencies in the Copenhagen interpretation of quantum physics are of a psychosocial origin.

The main interpretations of the quantum-mechanical wave function are presented emphasizing how they can be divided into two ensembles: The ones that deny and the other ones that attribute a form of reality to quantum waves. It is also shown why these waves cannot be classical and must be submitted to the restriction of the complementarity principle. Applying the concept of smooth complementarity, it is shown that there can be no reason to attribute reality only to the events and not (...) to the wave or to the initial state of a given system. Thereafter, an experiment proposed by the authors is presented, where it is shown that the wave-like behaviour allows predictions that are not allowed on the grounds of a particle-like behaviour. In conclusion, we upheld that quantum waves must be real even if they do not belong to the same ontological level of events, which connected with particle detections. (shrink)

According to a particular interpretation of quantum mechanics, the causal role of human consciousness in the measuring process is called upon to solve a foundational problem called the “measurement problem.” Traditionally, this interpretation is tied up with the metaphysics of substance dualism. As such, this interpretation of quantum mechanics inherits the dualist’s mind-body problem. Our working hypothesis is that a process-based approach to the consciousness causes collapse interpretation (CCCI) ---leaning on Whitehead’s solution to the mind-body problem--- offers a better metaphysical (...) understanding of consciousness and its role in interpreting quantum mechanics. This article is the kickoff for such a research program in the metaphysics of science. (shrink)

In order to demonstrate the great importance of Philosophy in the elaboration of current scientific theories, a parallel was drawn between concepts of pre-Socratic Philosophy and current modern theories. Thus, throughout this essay, the convergences between some elaborations developed by philosophers and their reinterpretation from a scientific point of view, supported by the scientific method and the present technological apparatuses, were exposed. In this sense, having as its core the reflection about the atomic theory of Leucippus and Democritus, we investigate (...) the way in which atomism dialogues with the modern Atomic Theory to the Quantum Theory, through concepts of Kosmos and Cosmology. In a second moment, origin of life theories were revisited from the pre-Socratic concepts of Psykhe. Finally, Philosophy and Science are brought together as possible and complementary tools for the restoration of the amplification of thought and investigative processes. (shrink)

We report on the simultaneous determination of complementary wave and particle aspects of light in a double-slit type “welcher-weg” experiment beyond the limitations set by Bohr’s Principle of Complementarity. Applying classical logic, we verify the presence of sharp interference in the single photon regime, while reliably maintaining the information about the particular pinhole through which each individual photon had passed. This experiment poses interesting questions on the validity of Complementarity in cases where measurements techniques that avoid Heisenberg’s uncertainty principle and (...) quantum entanglement are employed. We further argue that the application of classical concepts of waves and particles as embodied in Complementarity leads to a logical inconsistency in the interpretation of this experiment. (shrink)

We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum particles interact with ordinary matter, nuclei, atoms, molecules, macroscopic material entities, measuring apparatuses, in a similar way to how human concepts interact with memory structures, human minds or artificial memories. We analyze the most characteristic aspects of quantum theory, i.e. entanglement and non-locality, interference and superposition, identity and (...) individuality in the light of this new interpretation, and we put forward a specific explanation and understanding of these aspects. The basic hypothesis of our framework gives rise in a natural way to a Heisenberg uncertainty principle which introduces an understanding of the general situation of ‘the one and the many’ in quantum physics. A specific view on macro and micro different from the common one follows from the basic hypothesis and leads to an analysis of Schrödinger’s Cat paradox and the measurement problem different from the existing ones. We reflect about the influence of this new quantum interpretation and explanatory framework on the global nature and evolutionary aspects of the world and human worldviews, and point out potential explanations for specific situations, such as the generation problem in particle physics, the confinement of quarks and the existence of dark matter. (shrink)

The received view on the contributions of the physics community to the birth of molecular biology tends to present the physics community as sharing a basic level consensus on how physics should be brought to bear on biology. I argue, however, that a close examination of the views of three leading physicists involved in the birth of molecular biology, Bohr, Delbrück, and Schrödinger, suggests that there existed fundamental disagreements on how physics should be employed to solve problems in biology even (...) within the physics community. In particular, I focus on how these three figures differed sharply in their assessment of the relevance of complementarity, the potential of chemical methods, and the relative importance of classical physics. In addition, I assess and develop Roll-Hansen’s attempt to conceptualize this history in terms of models of scientific change advanced by Kuhn and Lakatos. Though neither model is fully successful in explaining the divergence of views among these three physicists, I argue that the extent and quality of difference in their views help elucidate and extend some themes that are left opaque in Kuhn’s model. (shrink)

This book presents a collection of novel contributions and reviews by renowned researchers in the foundations of quantum physics, quantum optics, and neutron physics. It is published in honor of Michael Horne, whose exceptionally clear and groundbreaking work in the foundations of quantum mechanics and interferometry, both of photons and of neutrons, has provided penetrating insight into the implications of modern physics for our understanding of the physical world. He is perhaps best known for the Clauser-Horne-Shimony-Holt (CHSH) inequality. This collection (...) includes an oral history of Michael Horne's contributions to the foundations of physics and his connections to other eminent figures in the history of the subject, among them Clifford Shull and Abner Shimony. Among the editors and contributors are John Clauser and Anton Zeilinger, recipients of the Nobel Prize in Physics 2022. (shrink)

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)

_Braid_’s (Jonathan Blow, 2008) time-bending gameplay allows players to engage with a virtual world in which a player’s perceived ‘past’ can be endlessly rewritten, duration extended, and the ludic arrow of time can be reversed. One could assume that as mistakes can simply be undone, in-game actions cease to have consequences. However, the climax of the game’s narrative arc disrupts our assumption of control over these mechanics and encourages players to reflect on the possible moral implications of actions, both in (...) context of the game world and—through careful invocation of real-world scientific experiments—on everyday life. In this paper, I propose that _Braid_ uses gameplay to explore the difficulty of making moral judgements in a world without an objective past. This is, for the most part, achieved through _Braid_’s utilization of a specific interpretation of quantum theory—in accordance with the game’s lead designer, Jonathan Blow—that “starts to threaten our very existence” by questioning the possibility of a singular, objective, real ‘past’ and the possibility of a definitive account of past actions. I first argue that the game’s mechanics immerse players in a game world inspired by Blow’s understanding of quantum mechanics. Placing an emphasis on certain technical aspects, I outline how the functioning of the game’s central rewind mechanic—although initially seeming to reinforce visions of our reality consistent with C.D. Broad’s ‘growing block’ theory—questions the notion of an objective past and so resonates strongly with both the work of J.A. Wheeler and an agential realist theory of time. With this understanding in place, I go on to analyze the climax of the game, reading it as an exploration of—and challenge to—the role of a presumed objective ‘past’ in understanding the morality of a given situation. Finally, through a reading of the game’s closing moments, I suggest _Braid_ promotes a turn to individual responsibility for agency; _Braid_, I argue, recommends one accept the continuing existence and changeability of the past within the present while embracing one’s own role in the shared process of constantly remaking reality and history. As a result, well-intentioned actions in the present are framed as more important than a focus on precedent to predict outcomes, making a cautious suggestion on how one might live without reference to an objective existence. Although I highlight some of the wider ramifications of this at the end of this paper, _Braid_ is far from a fully developed ethical system; it stands, however, as an engaging attempt to formulate a comment on time, temporality and morality through interactive media. (shrink)

Multiple sciences have converged, in the past two decades, on a hitherto mostly unremarked question: what is observation? Here, I examine this evolution, focusing on three sciences: physics, especially quantum information theory, developmental biology, especially its molecular and “evo-devo” branches, and cognitive science, especially perceptual psychology and robotics. I trace the history of this question to the late 19th century, and through the conceptual revolutions of the 20th century. I show how the increasing interdisciplinary focus on the process of extracting (...) information from an environment provides an opportunity for conceptual unification, and sketch an outline of what such a unification might look like. (shrink)

Complementarity tells us we cannot know precisely the values of all the properties of a quantum object at the same time: the precise determination of one property implies that the value of some other (complementary) property is undefined. E.g. the precise knowledge of the position of a particle implies that its momentum is undefined. Here we show that a Schrödinger cat has a well defined value of a property that is complementary to its “being dead or alive” property. Then, thanks (...) to complementarity, it has an undefined value of the property “being dead or alive”. In other words, the cat paradox is explained through quantum complementarity: of its many complementary properties, any quantum system, such as a cat, can have a well defined value only of one at a time. Schrödinger’s cat has a definite value of a property which is complementary to “being dead or alive”, so it is neither dead nor alive. Figuratively one can say it is both dead and alive. While this interpretation only uses textbook concepts (the Copenhagen interpretation), apparently it has never explicitly appeared in the literature. We detail how to build an Arduino based simulation of Schrödinger’s experiment based on these concepts for science outreach events. (shrink)

The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of probability. This is the first of two reviews of the Everett interpretation, and focuses on structure, with particular attention to the role of decoherence theory. Written in terms of the quantum histories formalism, decoherence theory just is the theory of branching structure, in Everett's sense.

The book is devoted to the contemporary stage of quantum mechanics – quantum information, and especially to its philosophical interpretation and comprehension: the first one of a series monographs about the philosophy of quantum information. The second will consider Be l l ’ s inequalities, their modified variants and similar to them relations. The beginning of quantum information was in the thirties of the last century. Its speed development has started over the last two decades. The main phenomenon is entanglement. (...) The subareas are quantum computer, quantum communication (and teleportation), and quantum cryptography. The book offers the following main conceptions, theses and hypotheses: – dualistic Phythagoreanism as a new kind among the interpretations of quantum mechanics and information: arithmetical, logical, and metamathematical one; – Gödel ’ s first incompleteness theorem is an undecidable proposition, and consequently the second one,too. – a partial rehabilitation of Hilbert ’ s program for the self-foundation of mathematics; – the dual-foundation of mathematics; – Skolemian relativity between: Cantor ’s kinds of infinity, finiteness and infinity, discreteness and continuity, completeness and incompleteness, etc.; – information is a physical quantity representing the non-reducibility of a system to its parts, particularly nonaddtivity; – there exist pure relations «by itself», which cannot be reduced to predications; – energy conservation can and should be generalized; – Einstein’ s «general covariance» or «principle of relativity» can and should be generalized to cover discrete morphisms where the notion of velocity does not make sense. (shrink)

It is well known that Niels Bohr insisted on the necessity of classical concepts in the account of quantum phenomena. But there is little consensus concerning his reasons, and what he exactly meant by this. In this paper, I re-examine Bohr’s interpretation of quantum mechanics, and argue that the necessity of the classical can be seen as part of his response to the measurement problem. More generally, I attempt to clarify Bohr’s view on the classical/quantum divide, arguing that the relation (...) between the two theories is that of mutual dependence. An important element in this clarification consists in distinguishing Bohr’s idea of the wave function as symbolic from both a purely epistemic and an ontological interpretation. Together with new evidence concerning Bohr’s conception of the wave function collapse, this sets his interpretation apart from both standard versions of the Copenhagen interpretation, and from some of the reconstructions of his view found in the literature. I conclude with a few remarks on how Bohr’s ideas make much sense also when modern developments in quantum gravity and early universe cosmology are taken into account. (shrink)

This paper charts P.A.M. Dirac’s development of his theory of the electron, and its radical picture of empty space as an almost-full plenum. Dirac’s Quantum Electrodynamics famously accomplished more than the unification of special relativity and quantum mechanics. It also accounted for the ‘duplexity phenomena’ of spectral line splitting that we now attribute to electron spin. But the extra mathematical terms that allowed for spin were not alone, and this paper charts Dirac’s struggle to ignore or account for them as (...) a sea of strange, negative-energy, particles with positive ‘holes’. This work was not done in solitude, but rather in exchanges with Dirac’s correspondence network. This social context for Dirac’s work contests his image as a lone genius, and documents a community wrestling with the ontological consequences of their work. Unification, consistency, causality, and community are common factors in explanations in the history of physics. This paper argues on the basis of materials in Dirac’s archive that — in addition — mathematical beauty was an epistemological factor in the development of the electron and hole theory. In fact, if we believe that Dirac’s beautiful mathematics captures something of the world, then there is both an epistemology and an ontology of mathematical beauty. (shrink)

We explore the different meanings of “quantum uncertainty” contained in Heisenberg’s seminal paper from 1927, and also some of the precise definitions that were developed later. We recount the controversy about “Anschaulichkeit”, visualizability of the theory, which Heisenberg claims to resolve. Moreover, we consider Heisenberg’s programme of operational analysis of concepts, in which he sees himself as following Einstein. Heisenberg’s work is marked by the tensions between semiclassical arguments and the emerging modern quantum theory, between intuition and rigour, and between (...) shaky arguments and overarching claims. Nevertheless, the main message can be taken into the new quantum theory, and can be brought into the form of general theorems. They come in two kinds, not distinguished by Heisenberg. These are, on one hand, constraints on preparations, like the usual textbook uncertainty relation, and, on the other, constraints on joint measurability, including trade-offs between accuracy and disturbance. (shrink)

Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a brief introduction to quantum probability (...) theory and a concrete example is provided to illustrate how a quantum cognitive model can be developed to explain paradoxical empirical findings in psychological literature. (shrink)

Quantum mechanics studies physical phenomena on a microscopic scale. These phenomena are far beyond the reach of our observation, and the connection between QM's mathematical formalism and the experimental results is very indirect. Furthermore, quantum indeterminism defies common sense. Microphysical experiments have shown that, according to the empirical context, electrons and quanta of light behave as waves and other times as particles, even though it is impossible to design an experiment that manifests both behaviors at the same time. Unlike Newtonian (...) physics, the properties of quantum systems are not all well-defined simultaneously. Moreover, quantum systems are not characterized by their properties, but by a wave function. Although one of the principles of the theory is the uncertainty principle, the trajectory of the wave function is controlled by the deterministic Schrödinger equations. But what is the wave function? Like other theories of the physical sciences, quantum theory assigns states to systems. The wave function is a particular mathematical representation of the quantum state of a physical system, which contains information about the possible states of the system and the respective probabilities of each state. (shrink)

It is generally believed that the uncertainty relation Δq Δp≥1/2ħ, where Δq and Δp are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path (...) of a particle in an interference experiment (such as the double-slit experiment).The failure of the uncertainty relation to produce these results is not a question of the interpretation of the formalism; it is a mathematical fact which follows from general considerations about the widths of wave functions.To express the uncertainty principle, one must distinguish two aspects of the spread of a wave function: its extent and its fine structure. We define the overall widthW Ψ and the mean peak width wψ of a general wave function ψ and show that the productW Ψ w φ is bounded from below if φ is the Fourier transform of ψ. It is shown that this relation expresses the uncertainty principle as it is used in the single- and double-slit experiments. (shrink)

The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from common objections: that it is solipsist; that it is too instrumentalist; that it cannot deal with Wigner's friend scenarios. Three more substantive problems are raised: Can a reasonable ontology be found for the approach? Can it account for explanation in quantum theory? Are subjective (...) probabilities on their own adequate in the quantum domain? The first question is answered in the affirmative, drawing on elements from Nancy Cartwright's philosophy of science. The second two are not: it is argued that these present outstanding difficulties for the project. A quantum Bayesian version of Moore's paradox is developed to illustrate difficulties with the subjectivist account of pure state assignments. (shrink)