Sorkin’s recent proposal for a realist interpretation of quantum theory, the anhomomorphic logic or coevent approach, is based on the idea of a “quantum measure” on the space of histories. This is a generalisation of the classical measure to one which admits pair-wise interference and satisfies a modified version of the Kolmogorov probability sum rule. In standard measure theory the measure on the base set Ω is normalised to one, which encodes the statement that “Ω happens”. (...) Moreover, the Kolmogorov sum rule implies that the measure of any subset A is strictly positive if and only if A cannot be covered by a countable collection of subsets of zero measure. In quantum measure theory on the other hand, simple examples suffice to demonstrate that this is no longer true. We propose an appropriate generalisation, the quantum cover, which in addition to being a cover of A, satisfies the property that if the quantum measure of A is non-zero then this is also the case for at least one of the elements in the cover. Our work implies a non-triviality result for the coevent interpretation for Ω of finite cardinality, and allows us to cast the Peres-Kochen-Specker theorem in terms of quantum covers. (shrink)

We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and continuous-in-time observations. The “collapsed state-vector” after the “objectification” is simply treated as a random vector of the a posterioristate given by the quantum filtering, i.e., the conditioning of the a prioriinduced state on the corresponding reduced algebra. The nonlinear phenomenological equation of “continuous spontaneous (...) localization” has been derived from the Schrödinger equation as a case of the quantum filtering equation for the diffusive nondemolition measurement. The quantum theory of measurement and filtering suggests also another type of the stochastic equation for the dynamical theory of continuous reduction, corresponding to the counting nondemolition measurement, which is more relevant for the quantum experiments. (shrink)

This paper outlines a ‘paradox’ in quantum measurement theory, illustrated with two different types of systems. If this paradox cannot be resolved in ordinary quantum mechanics (as I currently think), it is alarming. If it can be resolved, it can be added to a long list of examples that show the internal consistency of quantum mechanics, and in this case I hope the correct analysis will be an interesting example for students. The immediate paradox involves (...) a failure of Lorentz invariance for measurements on certain types of single particle systems. It seems to show that an absolute frame of reference is required to describe wave function collapse. But if the argument is correct, quantum measurement theory is not merely dependant on the frame of collapse - it is inconsistent, and experimental tests would have to be done to verify whether the apparent non-local effects predicted are real. (shrink)

In the iconic measurements of atomic spin-1/2 or photon polarization, one employs two separate noninteracting detectors. Each detector is binary, registering the presence or absence of the atom or the photon. For measurements on a d-state particle, we recast the standard von Neumann measurement formalism by replacing the familiar pointer variable with an array of such detectors, one for each of the d possible outcomes. We show that the unitary dynamics of the pre-measurement process restricts the detector outputs (...) to the subspace of single outcomes, so that the pointer emerges from the apparatus. We propose a physical extension of this apparatus which replaces each detector with an ancilla qubit coupled to a readout device. This explicitly separates the pointer into distinct quantum and (effectively) classical parts, and delays the quantum to classical transition. As a result, one not only recovers the collapse scenario of an ordinary apparatus, but one can also observe a superposition of the quantum pointer states. (shrink)

The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable to be measured is multiplied by some observable of a probe system. This simple Ansatz has proved extremely fruitful in the development of the foundations of quantum mechanics. While the ensuing type of models has often been argued to be rather artificial, recent advances in quantum optics have demonstrated their principal and practical feasibility. A brief historical (...) review of the standard model together with an outline of its virtues and limitations are presented as an illustration of the mutual inspiration that has always taken place between foundational and experimental research in quantum physics. (shrink)

State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under which it is performed. Each context provides a viewpoint of the quantum system being measured. This gives only a partial picture of the system which may be distorted and in order to obtain a total accurate picture, various contexts need (...) to be employed. We first discuss some basic definitions and results concerning quantum channels. We briefly describe the relationship between this work and ontological models that form the basis for contextuality studies. We then consider properties of channels and contexts. For example, we show that the set of sharp channels can be given a natural partial order in which contexts are the smallest elements. We also study properties of channel maps. The last section considers mutually unbiased contexts. These are related to mutually unbiased bases which have a large current literature. Finally, we connect them to completely random channel maps. (shrink)

It is shown that the physics and semantics of quantum measurement provide a natural interpretation of the weak neighborhoods of the states on observable algebras without invoking any idea of “a reading error” or “a measured range.” Then the state preparation process in quantum measurement theory is shown to give the normal (or locally normal) states on the observable algebra. Some remarks are made concerning the physical implications of normal states for systems with an infinite (...) number of degrees of freedom, including questions on open and closed algebraic theories. (shrink)

This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann's classic treatise with this title. Fundamental non-classical features of quantum mechanics-indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality-are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides (...) a systematic exposition of the Hilbert space and operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4. Foundations discusses a selection of foundational topics (quantum-classical contrast, Bell nonlocality, measurement limitations, measurement problem, operational axioms) from a measurement theoretic perspective. The book is addressed to physicists, mathematicians and philosophers of physics with an interest in the mathematical and conceptual foundations of quantum physics, specifically from the perspective of measurement theory. (shrink)

We propose a Quantum Field Theory description of beams on a Mach–Zehnder interferometer and apply the method to describe Interaction Free Measurements, concluding that there is a change of momentum of the fields in IFMs. Analysing the factors involved in the probability of emission of low-energy photons, we argue that they do not yield meaningful contributions to the probabilities of the IFMs.

In this paper we explore the possibility of giving a justification of the “semantic information” content and measure, in the framework of the recent coalgebraic approach to quantum systems and quantum computation, extended to QFT systems. In QFT, indeed, any quantum system has to be considered as an “open” system, because it is always interacting with the background fluctuations of the quantum vacuum. Namely, the Hamiltonian in QFT always includes the quantum system and its inseparable (...) thermal bath, formally “entangled” like an algebra with its coalgebra, according to the principle of the “doubling” of the degrees of freedom between them. This is the core of the representation theory of cognitive neuroscience based on QFT. Moreover, in QFT, the probabilities of the quantum states follow a Wigner distribution, based on the notion and measure of quasiprobability, where regions integrated under given expectation values do not represent mutually exclusive states. This means that a computing agent, either natural or artificial, in QFT, against the quantum Turing machine paradigm, is able to change dynamically the representation space of its computations. This depends on the possibility of interpreting QFT system computations within the framework of category theory logic and its principle of duality between opposed categories, such as the algebra and coalgebra categories of QFT. This allows us to justify and not only to suppose, like in the “theory of strong semantic information” of L. Floridi, the definition of modal “local truth” and the notion of semantic information as a measure of it, despite both measures being defined on quasiprobability distributions. (shrink)

Quantum Information Theory and the Foundations of Quantum Mechanics is a conceptual analysis of one of the most prominent and exciting new areas of physics, providing the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. -/- Beginning from a careful, revisionary, analysis of the concepts of information in the everyday and classical information-theory settings, Christopher G. Timpson argues for an ontologically deflationary (...) account of the nature of quantum information. Against what many have supposed, quantum information can be clearly defined (it is not a primitive or vague notion) but it is not part of the material contents of the world. Timpson's account sheds light on the nature of nonlocality and information flow in the presence of entanglement and, in particular, dissolves puzzles surrounding the remarkable process of quantum teleportation. In addition it permits a clear view of what the ontological and methodological lessons provided by quantum information theory are; lessons which bear on the gripping question of what role a concept like information has to play in fundamental physics. Topics discussed include the slogan 'Information is Physical', the prospects for an informational immaterialism (the view that information rather than matter might fundamentally constitute the world), and the status of the Church-Turing hypothesis in light of quantum computation. -/- With a clear grasp of the concept of information in hand, Timpson turns his attention to the pressing question of whether advances in quantum information theory pave the way for the resolution of the traditional conceptual problems of quantum mechanics: the deep problems which loom over measurement, nonlocality and the general nature of quantum ontology. He marks out a number of common pitfalls to be avoided before analysing in detail some concrete proposals, including the radical quantum Bayesian programme of Caves, Fuchs, and Schack. One central moral which is drawn is that, for all the interest that the quantum information-inspired approaches hold, no cheap resolutions to the traditional problems of quantum mechanics are to be had. (shrink)

We propose that the ontic understanding of quantum mechanics can be extended to a fully realistic theory that describes the evolution of the wavefunction at all times, including during a measurement. In such an approach the wave equation should reduce to the standard wave equation when there is no measurement, and describe state reduction when the system is measured. The general wave equation must be nonlinear and nonlocal, and we require it to be time-symmetric; consequently, this (...) approach is not a new interpretation but a new theory. The wave equation is an integrodifferential equation (IDE). The time symmetry requirement leads to a retrocausal approach, in which the wave equation is solved subject to initial and final conditions to determine history at intermediate times. We propose that different outcomes from (apparently) identically prepared experiments may result from uncontrolled parameters; both the nonlocality and the retrocausality of the theory imply that Bell’s Theorem cannot rule out such “hidden variables.” Beginning with Hamilton’s principle, we demonstrate the construction of such a theory by replacing the action with a functional designed to give rise to a nonlinear, nonlocal IDE as the wave equation. This IDE reduces to the standard wave equation (a differential equation) in the absence of a measurement, but exhibits state reduction to a single eigenvalue when the system interacts with another system with the properties of a measurement apparatus. We demonstrate several desirable features of this theory; for other properties we indicate their plausibility and possible avenues to a proof. (shrink)

A resolution of the quantum measurement problem would require one to explain how it is that we end up with determinate records at the end of our measurements. Metaphysical commitments typically do real work in such an explanation. Indeed, one should not be satisfied with one's metaphysical commitments unless one can provide some account of determinate measurement records. I will explain some of the problems in getting determinate records in relativistic quantum field theory and pay (...) particular attention to the relationship between the measurement problem and a generalized version of Malament's theorem. (shrink)

Christopher G. Timpson provides the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. He argues for an ontologically deflationary account of the nature of quantum information, which is grounded in a revisionary analysis of the concepts of information.

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)

The outcomes of educational assessments undoubtedly have real implications for students, teachers, schools and education in the widest sense. Assessment results are, for example, used to award qualifications that determine future educational or vocational pathways of students. The results obtained by students in assessments are also used to gauge individual teacher quality, to hold schools to account for the standards achieved by their students, and to compare international education systems. Given the current high-stakes nature of educational assessment, it is imperative (...) that the measurement practices involved have stable philosophical foundations. However, this article casts doubt on the theoretical underpinnings of contemporary educational measurement models. Aspects of Wittgenstein’s later philosophy and Bohr’s philosophy of quantum theory are used to argue that a quantum theoretical rather than a Newtonian model is appropriate for educational measurement, and the associated implications for the concept of validity are elucidated. Whilst it is acknowledged that the transition to a quantum theoretical framework would not lead to the demise of educational assessment, it is argued that, where practical, current high-stakes assessments should be reformed to become as ‘low-stakes’ as possible. This article also undermines some of the pro high-stakes testing rhetoric that has a tendency to afflict education. (shrink)

It is assumed that experiments yield results that are not isomorphic with reality, but represent a distorted image of reality. Reality is related to observation via a communication channel of finite capacity. Quantum uncertainties are due to the bound on the amount of information available. Use is made of recent results from information and communication theories.

`Quantum theory' is not a single physical theory but a framework in which many different concrete theories fit. As such, a solution to the quantum measurement problem ought to provide a recipe to interpret each such concrete theory, in a mutually consistent way. But with the exception of the Everett interpretation, the mainextant solutions either try to make sense of the abstract framework as if it were concrete, or else interpret one particular quantum (...) theory under the fiction that it is fundamental and exact. In either case, these approaches are unable to help themselves to the very theory-laden, level-relative ways in which quantum theory makes contact with experiment in mainstream physics, and so are committed to major revisionary projects which have not been carried out even in outline. As such, only the Everett interpretation is currently suited to make sense of quantum physics as we find it. (shrink)

This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics.In it, I aim to review, in a way accessible to foundationally interested physicists as well as physics-informed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don't advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence (...) theory to modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the "traditional" formulation of the problem. (shrink)

A partial ordering in the class of observables (∼ positive operator-valued measures, introduced by Davies and by Ludwig) is explored. The ordering is interpreted as a form of nonideality, and it allows one to compare ideal and nonideal versions of the same observable. Optimality is defined as maximality in the sense of the ordering. The framework gives a generalization of the usual (implicit) definition of self-adjoint operators as optimal observables (von Neumann), but it can, in contrast to this latter definition, (...) be justified operationally. The nonideality notion is compared to other quantum estimation theoretic methods. Measures for the amount of nonideality are derived from information theory. (shrink)

Arguments by Sorkin (Impossible measurements on quantum fields. In: Directions in general relativity: proceedings of the 1993 International Symposium, Maryland, vol 2, pp 293–305, 1993) and Borsten et al. (Phys Rev D 104(2), 2021. https://doi.org/10.1103/PhysRevD.104.025012 ) establish that a natural extension of quantum measurement theory from non-relativistic quantum mechanics to relativistic quantum theory leads to the unacceptable consequence that expectation values in one region depend on which unitary operation is performed in a spacelike (...) separated region. Sorkin [ 1 ] labels such scenarios ‘impossible measurements’. We explicitly present these arguments as a no-go result with the logical form of a reductio argument and investigate the consequences for measurement in quantum field theory (QFT). Sorkin-type impossible measurement scenarios clearly illustrate the moral that Microcausality is not by itself sufficient to rule out superluminal signalling in relativistic quantum theories that use Lüders’ rule. We review three different approaches to formulating an account of measurement for QFT and analyze their responses to the ‘impossible measurements’ problem. Two of the approaches are: a measurement theory based on detector models proposed in Polo-Gómez et al. (Phys Rev D, 2022. https://doi.org/10.1103/physrevd.105.065003 ) and a measurement framework for algebraic QFT proposed in Fewster and Verch (Commun Math Phys 378(2):851–889, 2020). Of particular interest for foundations of QFT is that they share common features that may hold general morals about how to represent measurement in QFT. These morals are about the role that dynamics plays in eliminating ‘impossible measurements’, the abandonment of the operational interpretation of local algebras \({\mathcal {A}}(O)\) as representing possible operations carried out in region _O_, and the interpretation of state update rules. Finally, we examine the form that the ‘impossible measurements’ problem takes in histories-based approaches and we discuss the remaining challenges. (shrink)

A theory of the joint measurement of quantum mechanical observables is generalized in order to make it applicable to the measurement of the local observables of field theory. Subsequently, the property of local commutativity, which is usually introduced as a postulate, is derived by means of the theory of measurement from a requirement of mutual nondisturbance, which, for local observables performed at a spacelike distance from each other, is interpreted as a requirement of (...) macrocausality. Alternative attempts at establishing a deductive relationship between relativistic causality and local commutativity are reviewed, but found wanting, either because of the assumption of an unwarranted objectivity of the object system (algebraic approach) or because of the use of a projection postulate (operational approach). Finally, the quantum mechanical nonobjectivity is related to certain features of nonlocality which are present in the formalism of quantum mechanics. (shrink)

The role of completely positive mappings in quantum dynamics and measurement theory is reanalyzed in light of the possibility of a generalized dynamics.

In this paper I put forward a new micro realistic, fundamentally probabilistic, propensiton version of quantum theory. According to this theory, the entities of the quantum domain - electrons, photons, atoms - are neither particles nor fields, but a new kind of fundamentally probabilistic entity, the propensiton - entities which interact with one another probabilistically. This version of quantum theory leaves the Schroedinger equation unchanged, but reinterprets it to specify how propensitons evolve when no (...) probabilistic transitions occur. Probabilisitic transitions occur when new "particles" are created as a result of inelastic interactions. All measurements are just special cases of this. This propensiton version of quantum theory, I argue, solves the wave/particle dilemma, is free of conceptual problems that plague orthodox quantum theory, recovers all the empirical success of orthodox quantum theory, and at the same time yields as yet untested predictions that differ from those of orthodox quantum theory. (shrink)

It is quite extraordinary, philosophically speaking, that according to the orthodox interpretation: (a) quantum mechanics is a complete and comprehensive theory of microphysics, and yet (b) the role of measurement, in quantum mechanics, cannot be analyzed in terms of the collective effects of the microphysical particles making up the apparatus. It follows that, if the orthodox interpretation is correct, the measurement apparatus and its quantum physical effects cannot be accounted for microreductively. This is significant (...) because it is widely believed that the relation between physical wholes and parts is microreductive. Indeed, many philosophers are persuaded of the inevitability of universal microreduction to the basic elements of microphysics. This is the viewpoint embodied in the program for the unity of science, espoused in recent years, most notably by Robert Causey (1977). (shrink)

In this article I present some material of a forthcoming book with the titleQuantum Measures and Spaces. The main theme are generalizations of Gleason's theorem and spaces in which quantum measures exist. Characterizations of such spaces and classifications of their measures are given. The book will contain some supplementary results from the “orthomodular” theory under the heading “Miscellaneous.” It is a sequel to the bookMeasures and Hilbert Lattices of the same author.

This paper presents a new modified quantum mechanics, Critical Complexity Quantum Mechanics, which includes a new account of wavefunction collapse. This modified quantum mechanics is shown to arise naturally from a fully discrete physics, where all physical quantities are discrete rather than continuous. I compare this theory with the spontaneous collapse theories of Ghirardi, Rimini, Weber and Pearle and discuss some implications of these theories and CCQM for a realist view of the quantum realm.

After an outline of the macrorealistic solutions to the difficulties of the measurement theory, a new paradox is proposed and then discussed in the light of three different interpretations of quantum mechanics.

The path-integral approach to quantum theory of continuous measurements has been developed in preceding works of the author. According to this approach the measurement amplitude determining probabilities of different outputs of the measurement can be evaluated in the form of a restricted path integral (a path integral “in finite limits”). With the help of the measurement amplitude, maximum deviation of measurement outputs from the classical one can be easily determined. The aim of the present (...) paper is to express this variance in a simpler and transparent form of a specific uncertainty principle (called the action uncertainty principle, AUP). The most simple (but weak) form of AUP is δS≳ℏ, whereS is the action functional. It can be applied for simple derivation of the Bohr-Rosenfeld inequality for measurability of gravitational field. A stronger (and having wider application) form of AUP (for ideal measurements performed in the quantum regime) is |∫ ′ t″ (δS[q]/δq(t))Δq(t)dt|≃ℏ, where the paths [q] and [Δq] stand correspondingly for the measurement output and for the measurement error. It can also be presented in symbolic form as Δ(Equation) Δ(Path) ≃ ℏ. This means that deviation of the observed (measured) motion from that obeying the classical equation of motion is reciprocally proportional to the uncertainty in a path (the latter uncertainty resulting from the measurement error). The consequence of AUP is that improving the measurement precision beyond the threshold of the quantum regime leads to decreasing information resulting from the measurement. (shrink)

Researchers have suggested since the early days of quantum theory that there are strong analogies between quantum phenomena and mental phenomena and these have developed into a vibrant new field of quantum cognition during recent decades. After revisiting some early analogies by Niels Bohr and David Bohm, this paper focuses upon Bohm and Hiley’s ontological interpretation of quantum theory which suggests further analogies between quantum phenomena and biological and psychological phenomena, including the proposal (...) that the human brain operates in some ways like a quantum measuring apparatus. After discussing these analogies I will also consider, from a quantum perspective, Hintikka’s suggestion that Kant’s notion of things in themselves can be better understood by making an analogy between our knowledge-seeking activities and an elaborate measuring apparatus. (shrink)

Together with relativity theory, quantum mechanics stands as the conceptual foundation of modern physics. It forms the basis by which we understand the minute workings of the subatomic world. But at its core lies a paradox--it is unmeasurable. This book presents a powerful and energetic new approach to the measurement dilemma.

In a series of lectures written around 1952, Schrödinger refers to von Neumann’s account of measurement in quantum mechanics as follows:I said quantum physicists bother very little about accounting, according to the accepted law, for the supposed change of the wave-function by measurement. I know of only one attempt in this direction, to which Dr. Balazs recently directed my attention. You find it in John von Neumann’s well-known book. With great acuity he constructs one analytical example. (...) It does not refer to any actual experiment, it is purely analytical. He indicates in a simple case a supplementary operator which, when added to the internal wave operator, would with any desired approximation turn the wave function as time goes on into an eigenfunction of the observable that is measured. He found it necessary to show that such a mechanism is analytically possible. The idea has not been taken up and worked out since — in about twenty years or more. Indeed I do not think it would pay. I do not believe any real measuring device is of this kind. (shrink)

A highly abstracted theory of measurement is synthesized from classical measurement theory, fuzzy set theory, generalized information theory, and predicate calculus. The theory does not require specific truth value concepts, nor does it specify what subsets of the reals can be observed, thus avoiding the usual fundamental difficulties. Problems such as the definition of systems, the significance of observations, numerical scales and observables, etc. are examined. The general logico-algebraic approach to quantum/classical physics (...) is justified as a special case of measurement theory. (shrink)

We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras. The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet axiomatization (...) at the level of events, to the sheaf-theoretic gluing conditions at the level of Boolean localization systems. (shrink)

The many-Hilbert-spaces theory of quantum measurements, which was originally proposed by S. Machida and the present author, is reviewed and developed. Dividing a typical quantum measurement in two successive steps, the first being responsible for spectral decomposition and the second for detection, we point out that the wave packet reduction by measurement takes place at the latter step, through interaction of an object system with one of the local systems of detectors. First we discuss the (...) physics of the detection process, using numerical simulations for a simple detector model, and then formulate a general theory of quantum measurements to give the wave packet reduction in an explicit form as a sort of phase transition. The derivation is based on the macroscopic nature of the local system, to be represented in a continuous direct sum of many Hilbert spaces, and on the finite-size effect of the local system, to give phase shifts proportional to size parameters. We give a definite criterion for examining any instrument as to whether it works well as a detector or not. Finally, we compare the present theory with famous measurement theories and propose a possible experimental test to discriminate it from others. A few solvable detector models are also discussed. (shrink)

A situated observer is an observer as modeled within the world characterized by one’s physical theory. A physical theory arguably only makes empirical predictions if it makes predictions for the records of a situated observer. In this spirit, one has a satisfactory solution to the measurement problem only if one has a formulation of quantum mechanics that makes the right empirical predictions for the records of a situated observer. Bohmian mechanics addresses the measurement problem by (...) explaining what measurement records are, how a situated observer might produce them, and why a situated observer should expect the standard quantum predictions. The notion of an effective wave function is crucial in understanding how the theory makes empirical predictions. (shrink)

This conference proceedings would be of interest to theoretical and experimental physicists in the areas of foundations of physics, nature of time, foundations of quantum mechanics, quantum measurement, quantum computation. Philosophers of science and physics. Retrocausation, the process whereby the future affects its past, is central to the modern movement to understand the fundamental physical nature of time. This conference volume presents the most recent theoretical and experimental results at the forefront of the nascent field of (...) physical chronology. (shrink)

Quantum mechanical measurements on a physical system are represented by observables - Hermitian operators on the state space of the observed system. It is an important question whether all observables may be realized, in principle, as measurements on a physical system. Dirac’s influential text ( [1], page 37) makes the following assertion on the question: The question now presents itself – Can every observable be measured? The answer theoretically is yes. In practice it may be very awkward, or perhaps (...) even beyond the ingenuity of the experimenter, to devise an apparatus which could measure some particular observable, but the theory always allows one to imagine that the measurement can be made. This Letter re-examines the question of whether it is possible, even in principle, to measure every quantum mechanical observable. Unexpectedly, ideas from com-. (shrink)

This is an entry to the Compendium of Quantum Physics, edited by F Weinert, K Hentschel and D Greenberger, to be published by Springer-Verlag.

Quantum field theory provides the framework for many fundamental theories in modern physics, and over the last few years there has been growing interest in its historical and philosophical foundations. This anthology on the foundations of QFT brings together 15 essays by well-known researchers in physics, the philosophy of physics, and analytic philosophy.Many of these essays were first presented as papers at the conference?Ontological Aspects of Quantum Field Theory?, held at the Zentrum fr interdisziplin„re Forschung, Bielefeld, (...) Germany. The essays contain cutting-edge work on ontological aspects of QFT, including: the role of measurement and experimental evidence, corpuscular versus field-theoretic interpretations of QFT, the interpretation of gauge symmetry, and localization.This book is ideally suited to anyone with an interest in the foundations of quantum physics, including physicists, philosophers and historians of physics, as well as general readers interested in philosophy or science. (shrink)

Consecutive measurements performed on the same quantum system can reveal fundamental insights into quantum theory’s causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen interpretation, measurements affect the quantum system in such a way that the quantum superposition collapses after each measurement, erasing any memory of the prior state. We show here that counter to this view, un-amplified measurements have coherent ancilla density matrices that encode the (...) memory of the entire set of quantum measurements that came before, and that the chain of this entire set is therefore non-Markovian. In contrast, sequences of amplified measurements are equivalent to a quantum Markov chain. We argue that the non-Markovian nature of quantum measurement has empirical consequences that are incompatible with the assumption of wave function collapse, thus elevating the collapse assumption into a testable hypothesis. Finally, we find that all of the information necessary to reconstruct an arbitrary non-Markovian quantum chain of measurements is encoded on the boundary of that chain, reminiscent of the holographic principle. (shrink)

Reichenbach's interpretation of quantum mechanics has been narrowly reduced to the advocacy of a three‐valued logic. His interpretation rests, though, on the same rich epistemological framework that shapes his influential analysis of space‐time theories. Different interpretations of the quantum formalism, with their conflicting ontologies and causes, emerge in this view as “equivalent descriptions”. One casualty of the conventionalist approach is the measurement problem. I give reasons for why Reichenbach's view on the nature of interpretations of quantum (...) theory cannot be defended. (shrink)

Reichenbach's interpretation of quantum mechanics has been narrowly reduced to the advocacy of a three‐valued logic. His interpretation rests, though, on the same rich epistemological framework that shapes his influential analysis of space‐time theories. Different interpretations of the quantum formalism, with their conflicting ontologies and causes, emerge in this view as “equivalent descriptions”. One casualty of the conventionalist approach is the measurement problem. I give reasons for why Reichenbach's view on the nature of interpretations of quantum (...) theory cannot be defended. (shrink)

After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles, the automata theory is quantum ab-initio, (...) and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements, solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (shrink)

It is argued that a reformulation of classical measure theory is necessary if the theory is to accurately describe measurements of physical phenomena. The postulates of a generalized measure theory are given and the fundamentals of this theory are developed, and the reader is introduced to some open questions and possible applications. Specifically, generalized measure spaces and integration theory are considered, the partial order structure is studied, and applications to hidden variables and the logic of (...) quantum mechanics are given. (shrink)

Any realist interpretation of quantum theory must grapple with the measurement problem and the status of state-vector collapse. In a no-collapse approach, measurement is typically modeled as a dynamical process involving decoherence. We describe how the minimal modal interpretation closes a gap in this dynamical description, leading to a complete and consistent resolution to the measurement problem and an effective form of state collapse. Our interpretation also provides insight into the indivisible nature of measurement—the (...) fact that you can't stop a measurement part-way through and uncover the underlying 'ontic' dynamics of the system in question. Having discussed the hidden dynamics of a system's ontic state during measurement, we turn to more general forms of open-system dynamics and explore the extent to which the details of the underlying ontic behavior of a system can be described. We construct a space of ontic trajectories and describe obstructions to defining a probability measure on this space. (shrink)

This proposes a new theory of Quantum measurement; a state reduction theory in which reduction is to the elements of the number operator basis of a system, triggered by the occurrence of annihilation or creation (or lowering or raising) operators in the time evolution of a system. It is from these operator types that the acronym ‘LARC’ is derived. Reduction does not occur immediately after the trigger event; it occurs at some later time with probability P (...) t per unit time, where P t is very small. Localisation of macroscopic objects occurs in the natural way: photons from an illumination field are reflected off a body and later absorbed by another body. Each possible absorption of a photon by a molecule in the second body generates annihilation and raising operators, which in turn trigger a probability per unit time P t of a state reduction into the number operator basis for the photon field and the number operator basis of the electron orbitals of the molecule. Since all photons in the illumination field have come from the location of the first body, wherever that is, a single reduction leads to a reduction of the position state of the first body relative to the second, with a total probability of mP t , where m is the number of photon absorption events. Unusually for a reduction theory, the larc theory is naturally relativistic. (shrink)

With the example of a Stern–Gerlach measurement on a spin-1/2 atom, we show that a superposition of both paths may be observed compatibly with properties attributed to state collapse—for example, the singleness (or mutual exclusivity) of outcomes. This is done by inserting a quantum two-state system (an ancilla) in each path, capable of responding to the passage of the atom, and thus acting as a virtual detector. We then consider real measurements on the compound system of atomic spin (...) and two ancillae. Nondestructive measurements of a set of compatible joint observables can be performed, one for a superposition and others for collapse properties. A novel perspective is given as to why, within unitary quantum theory, ordinary measurements are blind to such superpositions. Implications for the theory of measurement are discussed. (shrink)