We have begun a theory of measurement in which an experimenter and his or her experimental procedure are modeled by algorithms that interact with physical equipment through a simple abstract interface. The theory is based upon using models of physical equipment as oracles to Turing machines. This allows us to investigate the computability and computational complexity of measurement processes. We examine eight different experiments that make measurements and, by introducing the idea of an observable indicator, we (...) identify three distinct forms of measurement process and three types of measurement algorithm. We give axiomatic specifications of three forms of interfaces that enable the three types of experiment to be used as oracles to Turing machines, and lemmas that help certify an experiment satisfies the axiomatic specifications. For experiments that satisfy our axiomatic specifications, we give lower bounds on the computational power of Turing machines in polynomial time using nonuniform complexity classes. These lower bounds break the barrier defined by the Church-Turing Thesis. (shrink)

The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced. This translates into an algebraic and topological definition of measurement space that caters for the distinction between quantum and classical measurements and allows a notion of observer to be derived.

In this paper, we examine the history of the idea among physicists that there is a fundamental limit to physical measuring processes and that this limit is set by noise. In contrast to previous studies, that have focused on the realization of the existence of such a limit, we focus on the noise aspect of this history. In his monograph entitled Noise from 1954, the Dutch-American physicist and pioneer of noise Alder van der Ziel described how noise came to (...) be seen as of practical importance for measurements:The study of spontaneous fluctuations was primarily theoretical as recently as 1925. At that time it. (shrink)

Quantum theory is one the most important and successful theories of modern physical science. It has been estimated that its principles form the basis for about 30 per cent of the world's manufacturing economy. This is all the more remarkable because quantum theory is a theory that nobody understands. The meaning of Quantum Theory introduces science students to the theory's fundamental conceptual and philosophical problems, and the basis of its non-understandability. It does this with the barest minimum of jargon (...) and very little mathematics in the main text. Readers wishing to delve more deeply into the theory's mathematical subtleties can do so in an extended series of appendices. The book brings the reader up to date with the results of new experimental tests of quantum weirdness and reviews the latest thinking on alternative interpretations, the frontiers of quantum cosmology, quantum gravity and potential application of this weirdness in computing, cryptography and teleportation. (shrink)

This paper addresses the doubts voiced by Wigner about the physical relevance of the concept of geometrical points by exploiting some facts known to all but honored by none: Almost all real numbers are transcendental; the explicit representation of any one will require an infinite amount of physical resources. An instrument devised to measure a continuous real variable will need a continuum of internal states to achieve perfect resolution. Consequently, a laboratory instrument for measuring a continuous variable in (...) a finite time can report only a finite number of values, each of which is constrained to be a rational number. It does not matter whether the variable is classical or quantum-mechanical. Now, in von Neumann’s measurement theory (von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, [1955]), an operator A with a continuous spectrum—which has no eigenvectors—cannot be measured, but it can be approximated by operators with discrete spectra which are measurable. The measurable approximant F(A) is not canonically determined; it has to be chosen by the experimentalist. It is argued that this operator can always be chosen in such a way that Sewell’s results (Sewell in Rep. Math. Phys. 56: 271, [2005]; Sewell, Lecture given at the J.T. Lewis Memorial Conference, Dublin, [2005]) on the measurement of a hermitian operator on a finite-dimensional vector space (described in Sect. 3.2) constitute an adequate resolution of the measurement problem in this theory. From this follows our major conclusion, which is that the notion of a geometrical point is as meaningful in nonrelativistic quantum mechanics as it is in classical physics. It is necessary to be sensitive to the fact that there is a gap between theoretical and experimental physics, which reveals itself tellingly as an error inherent in the measurement of a continuous variable. (shrink)

I present philosophical reflections arising from a study of laboratory measurement methods in quantum physics. More specifically, I investigate three major methods of measuring kinetic energy, from the period during which quantum physics was developed and came to be widely accepted: magnetic deflection, electrostatic retardation, and material retardation. The historical material serves as a provocative focus at which many broader philosophical topics come together: the empirical testing of theories, the universal validity of physical laws, the interaction between theoretical (...) and experimental traditions, incommensurability, meaning and definition, realism and instrumentalism, the process of scientific change, and the unity of science. ;I begin the discussion by noting that the measurement methods in question were based on classical theory. Chapter 1 asks how the classical reasoning in measurements can be interpreted in quantum-mechanical terms, and concludes that only a "surface interpretation" is possible, since the classical methods involve many assumptions that conflict with quantum mechanics. Chapter 2 attempts to give a quantitative assessment of the inaccuracies that might result from using the "incorrect" classical theory in the design of measurement methods. Chapter 3 asks how we can know whether a measurement method is reliable, and investigates how different methods of measuring the same quantity can ground each other; this mutual grounding is also seen as a process of concept-formation. Chapter 4 argues that the customary quantum theories of measurement do not describe actual measurements well, and originate from an overly literal interpretation of the operator formalism of quantum mechanics. Chapter 5 examines how the classically reasoned measurement methods were incorporated into quantum physics; that history suggests a model of scientific development which can introduce fundamental changes while preserving much continuity with the old tradition. Chapter 6 develops a philosophical framework which allows a synthetic view of the concrete results presented in the earlier chapters: my work is an attempt to establish "conceptual coherence," creating and clarifying noncontradictory connections among the various conceptual activities that make up quantum physics. (shrink)

The institutionalization of History and Philosophy of Science as a distinct field of scholarly endeavour began comparatively earl- though not always under that name - in the Australasian region. An initial lecturing appointment was made at the University of Melbourne immediately after the Second World War, in 1946, and other appoint ments followed as the subject underwent an expansion during the 1950s and 1960s similar to that which took place in other parts of the world. Today there are major Departments (...) at the University of Melbourne, the University of New South Wales and the University of Wollongong, and smaller groups active in many other parts of Australia and in New Zealand. "Australasian Studies in History and Philosophy of Science" aims to provide a distinctive publication outlet for Australian and New Zealand scholars working in the general area of history, philosophy and social studies of science. Each volume comprises a group of essays on a connected theme, edited by an Australian or a New Zealander with special expertise in that particular area. Papers address general issues, however, rather than local ones; parochial topics are avoided. Further more, though in each volume a majority of the contributors is from Australia or New Zealand, contributions from elsewhere are by no means ruled out. Quite the reverse, in fact - they are actively encour aged wherever appropriate to the balance of the volume in question. (shrink)

Measurement is said to be the basis of exact sciences as the process of assigning numbers to matter (things or their attributes), thus making it possible to apply the mathematically formulated laws of nature to the empirical world. Mathematics and empiria are best accorded to each other in laboratory experiments which function as what Nancy Cartwright calls nomological machine: an arrangement generating (mathematical) regularities. On the basis of accounts of measurement errors and uncertainties, I will argue for two (...) claims: 1) Both fundamental laws of physics, corresponding to ideal nomological machine, and phenomenological laws, corresponding to material nomological machine, lie, being highly idealised relative to the empirical reality; and also laboratory measurement data do not describe properties inherent to the world independently of human understanding of it. 2) Therefore the naive, representational view of measurement and experimentation should be replaced with a more pragmatic or practice-based view. (shrink)

Derived measurements involve problems of coordination. Conducting them often requires detailed theoretical assumptions about their target, while such assumptions can lack sources of evidence that are independent from these very measurements. In this paper, I defend two claims about problems of coordination. I motivate both by a novel case study on a central measurement problem in the history of physical geodesy: the determination of the earth's ellipticity. First, I argue that the severity of problems of coordination varies according (...) to scientists' predictive and experimental control over perturbations of the measurement process. Second, I identify a methodology by which scientists can solve hard problems of coordination and gradually increase their predictive control over perturbations. I dub this methodology ‘operational pluralism’ since it is driven by the introduction of alternative measurement operations that involve different physical indicators. (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)

In 1887 Helmholtz discussed the foundations of measurement in science as a last contribution to his philosophy of knowledge. This essay borrowed from earlier debates on the foundations of mathematics, on the possibility of quantitative psychology, and on the meaning of temperature measurement. Late nineteenth-century scrutinisers of the foundations of mathematics made little of Helmholtz’s essay. Yet it inspired two mathematicians with an eye on physics, and a few philosopher-physicists. The aim of the present paper is to situate (...) Helmholtz’s contribution in this complex array of nineteenth-century philosophies of number, quantity, and measurement.Author Keywords: Helmholtz; Measurement; Arithmetic; P. Du Bois-Reymond; H. and R. Grassmann; J. von Kries. (shrink)

Physical activity, and likely the motivation for it, varies throughout the day. The aim of this investigation was to create a short assessment (CRAVE: Cravings for Rest and Volitional Energy Expenditure) to measure motivation states (wants, desires, urges) for physical activity and sedentary behaviors. Five studies were conducted to develop and evaluate the construct validity and reliability of the scale, with 1,035 participants completing the scale a total of 1,697 times. In Study 1, 402 university students completed a (...) questionnaire inquiring about the want or desire to perform behaviors “at the present moment (right now).” Items related to physical activity (e.g., “move my body”) and sedentary behaviors (e.g., “do nothing active”). An exploratory structural equation model (ESEM) revealed that 10 items should be retained, loading onto two factors (5 each for Move and Rest). In Study 2, an independent sample (n= 444) confirmed these results and found that Move and Rest desires were associated with stage-of-change for exercise behavior. In Study 3, 127 community-residing participants completed the CRAVE at 6-month intervals over two years- two times each session. Across-session interclass correlations (ICC) for Move (ICC = 0.72–0.95) and Rest (ICC = 0.69–0.88) were higher than when they were measured across 24-months (Move: ICC = 0.53; Rest: ICC = 0.49), indicating wants/desires have state-like qualities. In Study 4, a maximal treadmill test was completed by 21 university students. The CRAVE was completed immediately pre and post. Move desires decreased 26% and Rest increased 74%. Changes in Move and Rest desires were moderately associated with changes in perceived physical fatigue and energy. In Study 5, 41 university students sat quietly during a 50-min lecture. They completed the CRAVE at 3 time points. Move increased 19.6% and Rest decreased 16.7%. Small correlations were detected between move and both perceived energy and tiredness, but not calmness or tension. In conclusion, the CRAVE scale has good psychometric properties. These data also support tenets of the WANT model of motivation states for movement and rest (Stults-Kolehmainen et al., 2020a). Future studies need to explore how desires to move/rest relate to dynamic changes in physical activity and sedentarism. (shrink)

The use of real clocks and measuring rods in quantum mechanics implies a natural loss of unitarity in the description of the theory. We briefly review this point and then discuss the implications it has for the measurement problem in quantum mechanics. The intrinsic loss of coherence allows to circumvent some of the usual objections to the measurement process as due to environmental decoherence.

In a recent paper, Prugovečki offered a theory of simultaneous measurements based upon an axiomatic description of the measurement act which excludes certain illustrations of simultaneous measurement previously discussed by the present writers. In this article, the fundamental conceptions of state preparation, state determination, and measurement which underlie our research are compared to Prugovečki's interpretations of the analogous constructs in his theory of measurement.

Summary This paper explores the legacy of the great French experimental physicist Victor Regnault through the example of Gabriel Lippmann, whose engagement with electrical standardization during the early 1880s was guided by Regnault's methodological precept to measure ‘directly’. Lippmann's education reveals that the theoretical practice of ‘direct’ measurement entailed eliminating extraneous physical effects through the experimental design, rather than, like physicists in Britain and Germany, making numerical ‘corrections’ to measured values. It also provides, paradoxically, exemplars of the qualitative (...) theoretical practices that sustained Regnault's misguided ambition to avoid theory. By considering the largely negative reactions to Lippmann's proposals for selecting suitable electrical units and methods of measuring the ohm, this paper associates these theoretical practices with the ineffectual rhetorical strategies employed by Lippmann to promote his work, and thereby indicates that the practice of direct measurement was limited to French experimental physics. Whilst this result aligns readily with the existence of divergent nineteenth century British and German cultures of precision, it emerges from a very different disciplinary context in which the practice of precision electrical measurement developed independently of submarine telegraphy. This is because, as this paper illustrates, telegraphic engineering and experimental physics remained separate professions in France. (shrink)

I propose and motivate a new account of fundamental physical laws, the Measurability Account of Laws (MAL). This account has a distinctive logical form, in that it takes the primary nomological concept to be that of a law relative to a given theory, and defines a law simpliciter as a law relative to some true theory. What makes a proposition a law relative to a theory is that it plays an indispensable role in demonstrating that some quantity posited by (...) that theory is measurable. In Section 1, I motivate the project of seeking a philosophical account of fundamental physical laws, as opposed to laws of nature in general. In Section 2, I motivate seeking an account with the distinctive logical form of the MAL. In Section 3, I present the MAL and illustrate the way it works by applying it to a simple example. (shrink)

At a certain stage of advance in any science it may be well to re-examine and perhaps to rearrange its fundamentals. One seeks an ideal, logical order of development, which may or may not be the best pedagogical order. Many a high school beginner in physics has become acquainted with “force” as something that gets in between two bodies of matter and pulls them together or pushes them apart, like himself between two carts or like “magnetism” between two magnets. Whether (...) or not this might ever be a proper view, the mature student of today will consider that for him, a knowledge of accelerations and strains, inter alia, is prerequisite to a knowledge of force. (shrink)

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.

In the present paper the relation between objective and subjective time is studied from a neutral non-dualist perspective Adoption of the relational concept of time leads to fundamental problems of time measurement of the uniformity of time measures, and of a native measure of duration in subjective experience. Experimental data on discrimination and reproduction of time intervals are reviewed and relevant models of internal time representations are discussed. Special attention is given to the 'dual klepsydra model' (DKM)and to the (...) outstanding properties of the reproduction func- tion yielded by the DKM Time scales generated by a DKM-based reproduction mechanisms are studied It is shown that such 'klepsydraic clocks' generate time measures which are non-uniform with respect to objective time yet internally consistent within an ensemble of such clocks and in this sense 'quasi-uniform' . Competing concepts of subjective time and modeling principles of internal time representation are briefly discussed Some interesting parallels be- tween our psychophysical approach and E.A. Milne's treatment of the problem of uniform time are drawn in the Appendix. (shrink)

Starting with the Born interpretation of quantum mechanics, we show that the quantum theory of measurement, supplemented by the strong law of large numbers, leads to a measurement statistics interpretation of quantum mechanics. A probabilistic characterization of the spectrum of a physical quantity is given, and an analysis of the notions of possible values and possible measurement results is carried out.

This article develops a historico-critical analysis of uncertainty and accuracy in measurement through a case-study of the adjustment of the fundamental physical constants, in order to investigate the sceptical “problem of unknowability” undermining realist accounts of measurement. Every scientific result must include a “measurement uncertainty”, but uncertainty cannot be be eval- uated against the unknown, and therefore cannot be taken as an assessment of “accuracy”, defined in the metrological vocabulary as the closeness to the truth. The (...) way scientists use and interpret uncertainty in the adjustment activity illustrates how they try to overcome this predicament. I iden- tify two operative roles of measurement uncertainty, in the comparison and in the combination of measurement results. This duality implies a tension between selection and combination when aggregating results, leading to a crucial question: should the evaluation of uncertainties favour safety over precision? I present contrasting answers and identify a specific account of physicists who implicitly try to conciliate realism with the problem of unknowability. I argue that this invites us to reconsider accuracy from a dynamical standpoint, as the gradual achievement of scientific progress through error correction. Finally, I present two interpretations of measurement uncertainty, objective and epistemic, which I criticize and suggest improvements to. (shrink)

The formal methods of the representational theory of measurement (RTM) are applied to the extensive scales of physical science, with some modifications of interpretation and of formalism. The interpretative modification is in the direction of theoretical realism rather than the narrow empiricism which is characteristic of RTM. The formal issues concern the formal representational conditions which extensive scales should be assumed to satisfy; I argue in the physical case for conditions related to weak rather than strong extensive (...) measurement, in the sense of Holman 1969 and Colonius 1978. The problem of justifying representational conditions is addressed in more detail than is customary in the RTM literature; this continues the study of the foundations of RTM begun in an earlier paper. The most important formal consequence of the present interpretation of physical extensive scales is that the basic existence and uniqueness properties of scales (representation theorem) may be derived without appeal to an Archimedean axiom; this parallels a conclusion drawn by Narens for representations of qualitative probability. It is concluded that there is no physical basis for postulation of an Archimedean axiom. (shrink)

In this paper we intend to discuss the importance of providing a physical representation of quantum superpositions which goes beyond the mere reference to mathematical structures and measurement outcomes. This proposal goes in the opposite direction to the project present in orthodox contemporary philosophy of physics which attempts to “bridge the gap” between the quantum formalism and common sense “classical reality”—precluding, right from the start, the possibility of interpreting quantum superpositions through non-classical notions. We will argue that in (...) order to restate the problem of interpretation of quantum mechanics in truly ontological terms we require a radical revision of the problems and definitions addressed within the orthodox literature. On the one hand, we will discuss the need of providing a formal redefinition of superpositions which captures explicitly their contextual character. On the other hand, we will attempt to replace the focus on the measurement problem, which concentrates on the justification of measurement outcomes from “weird” superposed states, and introduce the superposition problem which focuses instead on the conceptual representation of superpositions themselves. In this respect, after presenting three necessary conditions for objective physical representation, we will provide arguments which show why the classical representation of physics faces severe difficulties to solve the superposition problem. Finally, we will also argue that, if we are willing to abandon the presupposition according to which ‘Actuality = Reality’, then there is plenty of room to construct a conceptual representation for quantum superpositions. (shrink)

A wide range of countries decided to go into lockdown to contain the coronavirus disease (COVID-19) pandemic of 2020, a setting separating people and restricting their movements. We investigated how musicians dealt with this sudden restriction in mobility. Responses of 234 people were collected. The majority of respondents (95%) resided in Belgium or the Netherlands. Results indicated a decrease of 79% of live music making in social settings during lockdown compared with before lockdown. In contrast, an increase of 264% was (...) demonstrated for online joint music making. However, results showed that most respondents were largely or even completely unaccustomed with specialized platforms for online joint music making (e.g., JamKazam, Jamulus). Respondents reported to mostly use well-known video-conferencing platforms such as Zoom and Skype when playing together virtually. However, when such video-conferencing platforms were used, they were often not employed for synchronized playing and were generally reported to insufficiently deal with latency issues. Furthermore, respondents depending on music making as their main source of income explored online real-time methods significantly more than those relying on other income sources. Results also demonstrated an increase of 93% in the use of alternative remote joint music-making methods (e.g., recording parts separately and subsequently circulating these digital recordings). All in all, results of this study provide a more in-depth view on joint music making during the first weeks of lockdown induced by the COVID-19 pandemic of 2020, and demonstrate users’ perceptions of performance and usability of online real-time platforms as well as alternative methods for musical interaction. (shrink)

SummaryFaraday's concept of force is described by six assumptions. These specify a concept that is quite distinct from ‘mechanical’ conceptions of his contemporaries and interpreters. Analysis of the role of these assumptions clarifies Faraday's weighting of experimental evidence and shows how closely-linked Faraday's chemistry and physics were to his theology. It is argued that Faraday was unable to secularize his concept of force by breaking the ties between his physics and his theology of nature. Examination of his basic assumptions also (...) explains Faraday's failure to quantify his principle of conservation of force, his rejection of mechanical concepts of force and energy, and his early attempt to develop a wave-model for the conversion and transmission of electricity, magnetism, light and heat. (shrink)

Quantum physics is believed to be the fundamental theory underlying our understanding of the physical universe. However, it is based on concepts and principles that have always been difficult to understand and controversial in their interpretation. This book aims to explain these issues using a minimum of technical language and mathematics. After a brief introduction to the ideas of quantum physics, the problems of interpretation are identified and explained. The rest of the book surveys, describes and criticises a range (...) of suggestions that have been made with the aim of resolving these problems; these include the traditional, or 'Copenhagen' interpretation, the possible role of the conscious mind in measurement, and the postulate of parallel universes. This new edition has been revised throughout to take into account developments in this field over the past fifteen years, including the idea of 'consistent histories' to which a completely new chapter is devoted. (shrink)

To honor Henry Margenau on the occasion of his 90th birthday, we attempt in this essay to integrate certain aspects of the physics, philosophy, and pedagogy of quantum mechanics in a manner very much inspired by Margenau's idealist scientific epistemology. Over half a century ago, Margenau was perhaps the first philosopher of science to recognize and elaborate upon the essential distinction between thepreparation of a quantum state and themeasurement of an observable associated with a system in that state; yet in (...) contemporary quantum texts that distinction rarely receives adequate emphasis even though, as we demonstrate, it may be explicated through a series of simple illustrations. (shrink)

Effective communication during a pandemic, such as the current COVID-19 crisis, can save lives. At the present time, social and physical distancing measures are the lead strategy in combating the spread of COVID-19. In this study, a survey was administered to 705 adults from Switzerland about their support and practice of social distancing measures to examine if their responses depended on (1) whether these measures were supported by a government official or an internationally recognized celebrity as a spokesperson, (2) (...) whether this spokesperson was liked, and (3) the respondent’s age. We also considered several attitudinal and demographic variables that may influence the degree to which people support and comply with social distancing measures. We found that the government official was more effective in eliciting responses supportive of social distancing, particularly as manifested in the stated current compliance with social distancing measures. The effect was substantially stronger among older respondents, although these respondents expressed a lower risk perception. Although there was a general trend for greater endorsement of the social distancing measures among participants who liked the spokesperson, this was non-significant. In addition, respondents’ greater support and compliance was positively associated with (1) higher concern for the current situation, (2) higher concern for the well-being of others, and (3) greater belief that others were practicing social distancing, and negatively with (4) greater self-reported mobility. Current compliance correlated negatively with (5) household size. Since different parts of the population appear to have different perceptions of risk and crisis, our preliminary results suggest that different spokespersons may be needed for different segments of the population, and particularly for younger and older populations. The development of evidence-based knowledge is required to further identify who would be the most effective spokesperson, and in particular to groups with low risk perception and low compliance. (shrink)

The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be seen as informational in a (...) generalized sense. This implies a fundamental connection between the physical and material, on the one hand, and the mathematical and ideal, on the other hand. Quantum measure unifies them by a common and joint informational unit. Quantum mechanics and general relativity can be understood correspondingly as the holistic and temporal aspect of one and the same, the state of a quantum system, e.g. that of the universe as a whole. (shrink)

Do sensory measurements deserve the label of “measurement”? We argue that they do. They fit with an epistemological view of measurement held in current philosophy of science, and they face the same kinds of epistemological challenges as physical measurements do: the problem of coordination and the problem of standardization. These problems are addressed through the process of “epistemic iteration,” for all measurements. We also argue for distinguishing the problem of standardization from the problem of coordination. To exemplify (...) our claims, we draw on olfactory performance tests, especially studies linking olfactory decline to neurodegenerative disorders. (shrink)

I flesh out the sense in which the informational approach to interpreting quantum mechanics, as defended by Pitowsky and Bub and lately by a number of other authors, is (neo-)Bohrian. I argue that on this approach, quantum mechanics represents what Bohr called a “natural generalisation of the ordinary causal description” in the sense that the idea (which philosophers of science like Stein have argued for on the grounds of practical and epistemic necessity) that understanding a theory as a theory of (...) physics requires that one be able to “schematise the observer” within it is elevated in quantum mechanics to the level of a postulate in the sense that interpreting the outcome of a measurement interaction, as providing us with information about the world, requires as a matter of principle, the specification of a schematic representation of an observer in the form of a ‘Boolean frame’—the Boolean algebra representing the yes-or-no questions associated with a given observable representative of a given experimental context. I argue that the approach’s central concern is with the methodological question of how to assign physical properties to what one takes to be a system in a given experimental context, rather than the metaphysical question of what a given state vector represents independently of any context, and I show how the quantum generalisation of the concept of an open system may be used to assuage Einstein’s complaint that the orthodox approach to quantum mechanics runs afoul of the supposedly fundamental methodological requirement to the effect that one must always be able, according to Einstein, to treat spatially separated systems as isolated from one another. (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)