The way metrologists conceive of measurement has undergone a major shift in the last two decades. This shift can in great part be traced to a change in the statistical methods used to deal with the expression of measurement results, and, more particularly, with the calculation of measurement uncertainties. Indeed, as we show, the incapacity of the frequentist approach to the calculus of uncertainty to deal with systematic errors has prompted the replacement of the customary frequentist (...) methods by fully Bayesian procedures. The epistemological ramifications of the Bayesian approach merge with a deep empiricist mood tantamount to an “epistemic turn”: measurement results are analysed in terms of degrees of belief, and central concepts such as error and accuracy are called into question. We challenge the perspective entailed by this epistemic turn: we insist on the centrality of the concepts of error and accuracy by underlining the intentional character of measurement that is intimately linked to the process of correction of experimental data. We further circumvent the difficulties posed by the classical analysis of measurement by stressing the social rather than the epistemic dimension of measurement activities. (shrink)

Two types of measures of probabilistic uncertainty are introduced and investigated. Dispersion measures report how diffused the agent’s second-order probability distribution is over the range of first-order probabilities. Robustness measures reflect the extent to which the agent’s assessment of the prior (objective) probability of an event is perturbed by information about whether or not the event actually took place. The properties of both types of measures are investigated. The most obvious type of robustness measure is shown to coincide with (...) one of the major candidates for a dispersion measure, the mean square deviation measure. (shrink)

This article discusses the definitions of ‘‘measurement uncertainty” given in the three editions of the International Vocabulary of Metrology (VIM) and a fourth definition which was suggested for the next edition of this document. It is argued that none of the definitions is satisfying. First, a thorough definition of measurement uncertainty should supply an explanation about the meaning of the concept, which is missing from the VIM2&3. Secondly, when provided, the meanings are not accurate enough: the (...) VIM1 version is flawed and the possible future definition appeals to an overly restrictive notion of ‘‘belief”. Alternative options are then proposed, based on the conclusions that (i) measurement uncertainty is a statement – an inference – made by the experimenter about the measurand; (ii) it is only based on what is accessible to one’s knowledge, and therefore rests on the hypothesis that no unknown systematic error affects the measurement. (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)

Against the tradition, which has considered measurement able to produce pure data on physical systems, the unavoidable role played by the modeling activity in measurement is increasingly acknowledged, particularly with respect to the evaluation of measurement uncertainty. This paper characterizes measurement as a knowledge-based process and proposes a framework to understand the function of models in measurement and to systematically analyze their influence in the production of measurement results and their interpretation. To this (...) aim, a general model of measurement is sketched, which gives the context to highlight the unavoidable, although sometimes implicit, presence of models in measurement and, finally, to propose some remarks on the relations between models and measurement uncertainty, complementarily classified as due to the idealization implied in the models and their realization in the experimental setup. (shrink)

In the last few decades the role played by models and modeling activities has become a central topic in the scientific enterprise. In particular, it has been highlighted both that the development of models constitutes a crucial step for understanding the world and that the developed models operate as mediators between theories and the world. Such perspective is exploited here to cope with the issue as to whether error-based and uncertainty-based modeling of measurement are incompatible, and thus alternative (...) with one another, as sometimes claimed nowadays. The crucial problem is whether assuming this standpoint implies definitely renouncing to maintain a role for truth and the related concepts, particularly accuracy, in measurement. It is argued here that the well known objections against true values in measurement, which would lead to refuse the concept of accuracy as non-operational, or to maintain it as only qualitative, derive from a not clear distinction between three distinct processes: the metrological characterization of measuring systems, their calibration, and finally measurement. Under the hypotheses that (1) the concept of true value is related to the model of a measurement process, (2) the concept of uncertainty is related to the connection between such model and the world, and (3) accuracy is a property of measuring systems (and not of measurement results) and uncertainty is a property of measurement results (and not of measuring systems), not only the compatibility but actually the conjoint need of error-based and uncertainty-based modeling emerges. (shrink)

The entropy-reduction hypothesis claims that the cognitive processing difficulty on a word in sentence context is determined by the word's effect on the uncertainty about the sentence. Here, this hypothesis is tested more thoroughly than has been done before, using a recurrent neural network for estimating entropy and self-paced reading for obtaining measures of cognitive processing load. Results show a positive relation between reading time on a word and the reduction in entropy due to processing that word, supporting the (...) entropy-reduction hypothesis. Although this effect is independent from the effect of word surprisal, we find no evidence that these two measures correspond to cognitively distinct processes. (shrink)

Uncertainty measures must not depend on the choice of origin of the measurement scale; it is therefore argued that quantum-mechanical uncertainty relations, too, should remain invariant under changes of origin. These points have often been neglected in dealing with angle observables. Known measures of location and uncertainty for angles are surveyed. The angle variance angv {ø} is defined and discussed. It is particularly suited to the needs of quantum theory, because of its affinity to the Hilbert (...) space metric, and its use of the basic sine and cosine operators. Corresponding uncertainty relations involving azimuthal or phase angles are indicated, and their relevance to study and definition of coherent states is briefly reviewed. (shrink)

We argue that in the decision making process required for selecting assertible vague descriptions of an object, it is practical that communicating agents adopt an epistemic stance. This corresponds to the assumption that there exists a set of conventions governing the appropriate use of labels, and about which an agent has only partial knowledge and hence significant uncertainty. It is then proposed that this uncertainty is quantified by a measure corresponding to an agent’s subjective belief that a vague (...) concept label can be appropriately used to describe a particular object. We then apply Bayesian networks to investigate, in the case when knowledge of labelling conventions is represented by an ordering or ranking of the labels according to their appropriateness, how measure values allocated to basic labels can be used to directly infer the appropriateness measure of compound expressions. (shrink)

We argue that in the decision making process required for selecting assertible vague descriptions of an object, it is practical that communicating agents adopt an epistemic stance. This corresponds to the assumption that there exists a set of conventions governing the appropriate use of labels, and about which an agent has only partial knowledge and hence significant uncertainty. It is then proposed that this uncertainty is quantified by a measure corresponding to an agent’s subjective belief that a vague (...) concept label can be appropriately used to describe a particular object. We then apply Bayesian networks to investigate, in the case when knowledge of labelling conventions is represented by an ordering or ranking of the labels according to their appropriateness, how measure values allocated to basic labels can be used to directly infer the appropriateness measure of compound expressions. (shrink)

Many studies claim to measure decision-making under risk by employing the Domain-Specific Risk-Taking (DOSPERT) scale, a self-report measure, or the Balloon Analogue Risk Task (BART), a behavioural task. However, these tasks do not measure decision-making under risk but decision-making under uncertainty, a related but distinct concept. The present commentary discusses both the theoretical and empirical basis of the distinction between uncertainty and risk from the viewpoint of several scientific disciplines and reports how many studies wrongfully employ the DOSPERT (...) scale and BART as risk-taking measures. Importantly, we call for proper distinguishing between (tasks measuring) decision-making under uncertainty and decision-making under risk in psychology and related fields. We believe this is vital as research has shown that people’s attitudes, behaviour, and brain activity differ between both concepts, indicating that confusing the concepts may lead researchers to erroneous conclusions. (shrink)

Non-collapse theories of quantum mechanics have the peculiar characteristic that, although their measurements produce definite results, their state vectors remain in a superposition of possible outcomes. David Albert has used this fact to show that the standard uncertainty relations can be violated if self-measurements are made. Bradley Monton, however, has held that Albert has not been careful enough in his treatment of self-measurement and that being more careful (considering mental state supervenience) implies no violation of the relations. In (...) this paper, I will outline both Albert's proposal and Monton's objections. Then, I will show how the uncertainty relations can be violated after all (even after being as careful as Monton). Finally, I will discuss how finding a way around the objections allows us to learn more about what is and what is not possible in non-collapse theories of quantum mechanics. (shrink)

Multisource information systems and multigranulation intuitionistic fuzzy rough sets are important extended types of Pawlak’s classical rough set model. Multigranulation intuitionistic fuzzy rough sets have been investigated in depth in recent years. However, few studies have considered this combination of multisource information systems and intuitionistic fuzzy rough sets. In this paper, we give the uncertainty measure for multisource intuitionistic fuzzy information system. Against the background of multisource intuitionistic fuzzy information system, each information source is regarded as a granularity level. (...) Considering the different importance of information sources, we assign different weights to them. Firstly, the paper proposes an optimal source selection method. Secondly, we study the weighted generalized, weighted optimistic, and weighted pessimistic multigranularity intuitionistic fuzzy rough set models and uncertainty measurement methods in the multisource intuitionistic fuzzy information system, and we further study the relationship between the three models and related properties. Finally, an example is given to verify the validity of the models and methods. (shrink)

A data provenance framework is subject to security threats and risks, which increase the uncertainty, or lack of trust, in provenance information. Information assurance is challenged by incomplete information; one cannot exhaustively characterize all threats or all vulnerabilities. One technique that specifically incorporates a probabilistic notion of uncertainty is subjective logic. Subjective logic allows belief and uncertainty, due to incomplete information, to be specified and operated upon in a coherent manner. A mapping from the standard definition of (...) information assurance to a more quantitative subjective logic framework is suggested with a focus on the specific application of data provenance. Finally, specific consideration is given to the notion of uncertainty within subjective logic and its relation to information entropy. Information entropy is an alternative measure of uncertainty and a fundamental relationship is hypothesized between uncertainty in subjective logic and entropy. (shrink)

Quantum measurement is a physical process. A system and an apparatus interact for a certain time period, and during this interaction, information about an observable is transferred from the system to the apparatus. In this study, we quantify the energy fluctuation of the quantum apparatus required for this physical process to occur autonomously. We first examine the so-called standard model of measurement, which is free from any non-trivial energy–time uncertainty relation, to find that it needs an external (...) system that switches on the interaction between the system and the apparatus. In such a sense this model is not closed. Therefore to treat a measurement process in a fully quantum manner we need to consider a “larger” quantum apparatus which works also as a timing device switching on the interaction. In this setting we prove that a trade-off relation, \, holds between the energy fluctuation \ of the quantum apparatus and the measurement time \. We use this trade-off relation to discuss the spacetime uncertainty relation concerning the operational meaning of the microscopic structure of spacetime. In addition, we derive another trade-off inequality between the measurement time and the strength of interaction between the system and the apparatus. (shrink)

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)

In the Copenhagen interpretation the Heisenberg inequality ΔQΔP≥ℏ/2 is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint measurement of incompatible observables. This interpretation was criticized a long time ago and has recently been challenged in an experimental way. These criticisms can be substantiated by using the generalized formalism of positive operator-valued measures, from which an inequality, different from the Heisenberg inequality, can be derived, precisely illustrating (...) the Copenhagen concept of complementarity. The different roles of preparation and measurement in creating uncertainty in quantum mechanics are discussed. (shrink)

The paper addresses the question, how policy decisions under uncertainty depend on the underlying welfare concept. We study three different welfare measures: The first is directly based on the ex ante (expected) utility of a representative consumer whereas the second relies on an ex ante and the third on an ex post valuation of policy changes compared to the status quo. We show that decisions based on these measures coincide if and only if risk-neutral expected utility maximization is applied. (...) Differences between the decisions are analyzed for both, risk-averse expected utility maximization and the MaxiMin criterion. For risk-averse decision makers, differences between the first and the second concept arise if the absolute risk-aversion of the decision maker is not constant in income. For risk-aversion and the MaxiMin criterion, the effort levels to provide a public good based on an optimization of ex post utility changes exceed those based on the first or second concept. Implications for environmental policy decisions based on the concepts of abatement costs and benefits from abatement are discussed. (shrink)

Using a recently introduced entropy-like measure of uncertainty of quantum mechanical states, the problem of hidden variables is redefined in operator algebraic framework of quantum mechanics in the following way: if A, , E(A), E() are von Neumann algebras and their state spaces respectively, (, E()) is said to be an entropic hidden theory of (A, E(A)) via a positive map L from onto A if for all states E(A) the composite state ° L E() can be obtained as (...) an average over states in E() that have smaller entropic uncertainty than the entropic uncertainty of . It is shown that if L is a Jordan homomorphism then (, E()) is not an entropic hidden theory of (A, E(A)) via L. (shrink)

Climate change harmfully affects social and natural systems. These outcomes adversely affect the human and natural systems, resulting in adopting related-response measures whose implementation yields similar outcomes, especially when poorly designed. Climate-related projects, actions, and policies cause harmful environmental impacts, even though the United Nations Convention on Climate Change and its subsequent instruments urge parties, when dealing with climate change, to employ methods that preserve the quality of the environment. Few studies have established the effects of these environmentally, economically, culturally, (...) and socially unsound mechanisms on public participation, although research usually proves that ecological and environmental citizenship can enhance climate action. The study also highlights gaps in the common understanding of public participation in climate action. This reflection analyses the relationships between public participation and climate response measures and concludes that uncertainty related to response measures could affect the perception of climate action by the public. The reflection, therefore, shows that many international environmental law legal instruments, policies, and scholarships attempt to address the issue. (shrink)

Objective:Fear of Cancer Recurrence (FCR), Health Anxiety (HA), worry, and uncertainty in illness are psychological concerns commonly faced by cancer patients. In survivorship research, these similar, yet different constructs are frequently used interchangeably and multiple instruments are used in to measure them. The lack of clear and consistent conceptualization and measurement can lead to diverse or contradictory interpretations. The purpose of this scoping review was to review, compare, and analyze the current conceptualization and measurements used for FCR, HA, (...) worry, and uncertainty in the breast cancer survivorship literature to improve research and practice.Inclusion Criteria:We considered quantitative, qualitative, and mixed methods studies of breast cancer survivors that examined FCR, HA, worry, or uncertainty in illness as a main topic and included a definition or assessment of the constructs.Methods and Analysis:The six-staged framework was used to guide the scoping review process. Searches of PubMed, CINAHL, and PsycINFO databases were conducted. The principle-based qualitative analysis and simultaneous content analysis procedures were employed to synthesize and map the findings.Findings:After duplicate removal, the search revealed 3,299 articles, of which 82 studies met the inclusion criteria. Several critical attributes overlapped the four constructs, for example, all were triggered by internal somatic and external cues. However, several unique attributes were found (e.g., a sense of loss of security in the body is observed only among survivors experiencing FCR). Overall, findings showed that FCR and uncertainty in illness are more likely to be triggered by cancer-specific factors, while worry and HA have more trait-like in terms of characteristics, theoretical features, and correlates. We found that the measures used to assess each construct were on par with their intended constructs. Eighteen approaches were used to measure FCR, 15 for HA, 8 for worry, and 4 for uncertainty.Conclusion:While consensus on the conceptualization and measurement of the four constructs has not yet been reached, this scoping review identifies key similarities and differences to aid in their selection and measurement. Considering the observed overlap between the four studied constructs, further research delineating the unique attributes for each construct is warranted. (shrink)

We study uncertainty relations for a general class of canonically conjugate observables. It is known that such variables can be approached within a limiting procedure of the Pegg–Barnett type. We show that uncertainty relations for conjugate observables in terms of generalized entropies can be obtained on the base of genuine finite-dimensional consideration. Due to the Riesz theorem, there exists an inequality between norm-like functionals of two probability distributions in finite dimensions. Using a limiting procedure of the Pegg–Barnett type, (...) we take the infinite-dimensional limit right for this inequality. Hence, uncertainty relations are derived in terms of generalized entropies. In particular, the case of measurements with a finite precision is addressed. It takes into account that in any experiment an accuracy of performed measurements is always limited. (shrink)

We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as an objective and a subjective source respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of (...) the Pareto principle. After characterizing the ex ante and ex post criteria, we present a first solution to their conflict that extends the former as much possible in the direction of the latter. Then, we present a second solution, which goes in the opposite direction, and is also maximally assertive. Both solutions translate the assumed Pareto conditions into weighted additive utility representations, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of two conceptual arguments, i.e., the by now classic spurious unanimity argument and a novel informational argument labelled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms, but for the sake of completeness, also considers a construal of objective uncertainty based on the assumption of an exogeneously given probability measure. JEL classification: D70; D81. (shrink)

In ‘Normative Uncertainty as a Voting Problem’, William MacAskill argues that positive credence in ordinal-structured or intertheoretically incomparable normative theories does not prevent an agent from rationally accounting for her normative uncertainties in practical deliberation. Rather, such an agent can aggregate the theories in which she has positive credence by methods borrowed from voting theory—specifically, MacAskill suggests, by a kind of weighted Borda count. The appeal to voting methods opens up a promising new avenue for theories of rational choice (...) under normative uncertainty. The Borda rule, however, is open to at least two serious objections. First, it seems implicitly to ‘cardinalize’ ordinal theories, and so does not fully face up to the problem of merely ordinal theories. Second, the Borda rule faces a problem of option individuation. MacAskill attempts to solve this problem by invoking a measure on the set of practical options. But it is unclear that there is any natural way of defining such a measure that will not make the output of the Borda rule implausibly sensitive to irrelevant empirical features of decision-situations. After developing these objections, I suggest an alternative: the McKelvey uncovered set, a Condorcet method that selects all and only the maximal options under a strong pairwise defeat relation. This decision rule has several advantages over Borda and mostly avoids the force of MacAskill’s objection to Condorcet methods in general. (shrink)

The need for quantitative measurement represents a unifying bond that links all the physical, biological, and social sciences. Measurements of such disparate phenomena as subatomic masses, uncertainty, information, and human values share common features whose explication is central to the achievement of foundational work in any particular mathematical science as well as for the development of a coherent philosophy of science. This book presents a theory of measurement, one that is "abstract" in that it is concerned with (...) highly general axiomatizations of empirical and qualitative settings and how these can be represented quantitatively. It was inspired by, and represents a generalization and extension of, the last major research work in this field, Foundations of Measurement Vol. I, by Krantz, Luce, Suppes, and Tversky published in 1971. (shrink)

A lot of attention has been devoted to the study of discoveries in high energy physics, but less on measurements aiming at improving an existing theory like the standard model of particle physics, getting more precise values for the parameters of the theory or establishing relationships between them. This paper provides a detailed and critical study of how measurements are performed in recent HEP experiments, taking examples from differential cross section measurements with the ATLAS detector at the LHC. This study (...) will be used to provide an elucidation of the concept of event used in HEP, in order to determine what constitutes an observation and what does not. It will highlight the essential place taken by theory-ladenness in order to produce observational facts, and will show how uncertainty and sensitivity estimates constitute an operational approach to robustness, inside the practice of science, avoiding potential circularity problem traditionally implied by theory-ladenness. This is in contrast to robustness analyses typically considered in the literature. A careful analysis of systematic uncertainty estimates and of statistical tests used to set empirical conclusions from the observations will however demonstrate that quantitative statements obtained from these statistical tests cannot be more than simple guiding arguments for the production of knowledge, but do not determine it. This indicates that the frontier between theory and observation is blurry and that the dichotomy theory-experiment should be revised. (shrink)

The current study investigates how native speakers of a morphologically complex language handle uncertainty related to linguistic forms that have gaps in their inflectional paradigms. We analyze their strategies of dealing with paradigmatic defectivity and how these strategies are motivated by subjective contemporaneousness, frequency, acceptability, and other lexical and structural characteristics of words. We administered a verb production task with Finnish native speakers using verbs from a small non-productive inflectional type that has many paradigmatic gaps and asked participants to (...) inflect the verbs in a given context. Inflectional uncertainty was measured by the number of different forms the participants produced for each verb. We classified produced forms that were not expected as either synonymous or novel and measured their optimal string alignment distance to expected forms. Our analyses revealed that a usage-based approach to paradigmatic defectivity fits better with the obtained results than a classical approach typically met in dictionaries and descriptive grammars. Thus, we argue, that paradigmatic defectivity can be better described as a dynamic rather than a static system, where gaps represent a continuum of possible inflectional choices rather than a lack of an inflectional variant. (shrink)

Medicine seeks to overcome one of the most fundamental fragilities of being human, the fragility of good health. No matter how robust our current state of health, we are inevitably susceptible to future illness and disease, while current disease serves to remind us of various frailties inherent in the human condition. This article examines the relationship between fragility and uncertainty with regard to health, and argues that there are reasons to accept rather than deny at least some forms of (...) uncertainty. In situations of current ill health, both patients and doctors seek to manage this fragility through diagnoses that explain suffering and provide some certainty about prognosis as well as treatment. However, both diagnosis and prognosis are inevitably uncertain to some degree, leading to questions about how much uncertainty health professionals should disclose, and how to manage when diagnosis is elusive, leaving patients in uncertainty. We argue that patients can benefit when they are able to acknowledge, and appropriately accept, some uncertainty. Healthy people may seek to protect the fragility of their good health by undertaking preventative measures including various tests and screenings. However, these attempts to secure oneself against the onset of biological fragility can cause harm by creating rather than eliminating uncertainty. Finally, we argue that there are good reasons for accepting the fragility of health, along with the associated uncertainties. (shrink)

Everettian accounts of quantum mechanics entail that people branch; every possible result of a measurement actually occurs, and I have one successor for each result. Is there room for probability in such an account? The prima facie answer is no; there are no ontic chances here, and no ignorance about what will happen. But since any adequate quantum mechanical theory must make probabilistic predictions, much recent philosophical labor has gone into trying to construct an account of probability for branching (...) selves. One popular strategy involves arguing that branching selves introduce a new kind of subjective uncertainty. I argue here that the variants of this strategy in the literature all fail, either because the uncertainty is spurious, or because it is in the wrong place to yield probabilistic predictions. I conclude that uncertainty cannot be the ground for probability in Everettian quantum mechanics. (shrink)

Quantum uncertainty relations have deep-rooted significance in the formalism of quantum mechanics. Heisenberg’s uncertainty relations attracted a renewed interest for its applications in quantum information science. Following the discovery of the Heisenberg uncertainty principle, Robertson derived a general form of Heisenberg’s uncertainty relations for a pair of arbitrary observables represented by Hermitian operators. In the present work, we discover a temporal version of the Heisenberg–Robertson uncertainty relations for the measurement of two observables at two (...) different times, where the dynamical uncertainties crucially depend on the time evolution of the observables. The uncertainties not only depend on the choice of observables but also depend on the times at which the physical observables are measured. The time correlated two-time commutator dictates the trade-off between the dynamical uncertainties. We demonstrate the dynamics of these uncertainty relations for a spin-1/2 quantum system and for a quantum harmonic oscillator. We also present the dynamical uncertainty relation in terms of entropies, where the temporal entropic uncertainties are restricted by a time-dependent complementarity factor. The temporal uncertainty relations explored in this work can be experimentally verified with the present quantum technology. (shrink)

Everettian accounts of quantum mechanics entail that people branch; every possible result of a measurement actually occurs, and I have one successor for each result. Is there room for probability in such an account? The prima facie answer is no; there are no ontic chances here, and no ignorance about what will happen. But since any adequate quantum mechanical theory must make probabilistic predictions, much recent philosophical labor has gone into trying to construct an account of probability for branching (...) selves. One popular strategy involves arguing that branching selves introduce a new kind of subjective uncertainty. I argue here that the variants of this strategy in the literature all fail, either because the uncertainty is spurious, or because it is in the wrong place to yield probabilistic predictions. I conclude that uncertainty cannot be the ground for probability in Everettian quantum mechanics. (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)

A challenge faced by defenders of the precautionary principle is to clarify when the evidence that a harmful event might occur suffices to regard this prospect as a real possibility. Plausible versions of the principle must articulate some epistemic threshold, orde minimisrequirement, which specifies when precautionary measures are justified. Critics have argued that formulating such a threshold is problematic in the context of the precautionary principle. First, this is because the precautionary principle appears to be ambiguous about the distinction between (...) risk and uncertainty: should the principle merely be invoked when evidential probabilities are absent, or also when probabilities have low epistemic credentials? Secondly, defenders of the precautionary principle face an aggregation puzzle: in judging whether or not thede minimisrequirement has been met, how should first-order evidential probabilities and their second-order epistemic standing be aggregated? This article argues that the ambiguity can be resolved, and the epistemological puzzle can be solved. Focusing on decisions in the context of climate uncertainty, I advance a version of the precautionary principle that serves as a plausible decision rule, to be adopted in situations where its main alternative—cost–benefit analysis—does not deliver. (shrink)

A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers are in a position of self-locating uncertainty during the period between the branches of the wave function splitting via decoherence and the observer registering the outcome of the measurement. In this period it is tempting to regard each branch as equiprobable, (...) but we argue that the temptation should be resisted. Applying lessons from this analysis, we demonstrate (using methods similar to those of Zurek's envariance-based derivation) that the Born rule is the uniquely rational way of apportioning credence in Everettian quantum mechanics. In doing so, we rely on a single key principle: changes purely to the environment do not affect the probabilities one ought to assign to measurement outcomes in a local subsystem. We arrive at a method for assigning probabilities in cases that involve both classical and quantum self-locating uncertainty. This method provides unique answers to quantum Sleeping Beauty problems, as well as a well-defined procedure for calculating probabilities in quantum cosmological multiverses with multiple similar observers. (shrink)

The last 20 years or so has seen an intense search carried out within Dempster–Shafer theory, with the aim of finding a generalization of the Shannon entropy for belief functions. In that time, there has also been much progress made in credal set theory—another generalization of the traditional Bayesian epistemic representation—albeit not in this particular area. In credal set theory, sets of probability functions are utilized to represent the epistemic state of rational agents instead of the single probability function of (...) traditional Bayesian theory. The Shannon entropy has been shown to uniquely capture certain highly intuitive properties of uncertainty, and can thus be considered a measure of that quantity. This article presents two measures developed with the purpose of generalizing the Shannon entropy for (1) unordered convex credal sets and (2) possibly non-convex credal sets ordered by second order probability, thereby providing uncertainty measures for such epistemic representations. There is also a comparison with the results of the measure AU developed within Dempster–Shafer theory in a few instances where unordered convex credal set theory and Dempster–Shafer theory overlap. (shrink)

It is widely accepted that a liberal state has a general duty to protect its people from undue health risks. However, the unprecedented emergent measures against the COVID-19 pandemic taken by governments worldwide give rise to questions regarding the extent to which this duty may be used to justify suspending a vaccine rollout on marginal safety grounds. -/- In this chapter, I use the case of vaccination to argue that while a liberal state has a general duty to protect its (...) people’s health, there is a limit to the measures this duty can be used to justify. First, I argue that since every available option involves different risks and benefits, the incommensurability of the involved risks and benefits forbids the prioritisation of a particular vaccine. Second, I argue that given epistemic limitations and uncertainty, policies that favour certain vaccines are not only epistemically ill-founded but also morally unacceptable. I conclude that in a highly uncertain situation such as the unfolding pandemic, the duty a liberal state ought to uphold is to properly communicate the knowns and unknowns to the general public and help people decide which option to choose for themselves. I call this duty the duty to facilitate risk-taking. (shrink)

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum (...) state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle. (shrink)

The concepts of uncertainty in prediction and inference are introduced and illustrated using the diffraction of light as an example. The close relationship between the concepts of uncertainty in inference and resolving power is noted. A general quantitative measure of uncertainty in inference can be obtained by means of the so-called statistical distance between probability distributions. When applied to quantum mechanics, this distance leads to a measure of the distinguishability of quantum states, which essentially is the absolute (...) value of the matrix element between the states. The importance of this result to the quantum mechanical uncertainty principle is noted. The second part of the paper provides a derivation of the statistical distance on the basis of the so-called method of support. (shrink)

We recast subjective probabilities by rejecting behaviourist accounts of belief by explicitly distinguishing between judgements of uncertainty and expressions of those judgements. We argue that this entails rejecting that orderings of uncertainty be complete. This in turn leads naturally to several generalizations of the probability calculus. We define probability-like functions over incomplete algebras that reflect a subject’s incomplete judgements of uncertainty. These functions can be further generalized to inner and outer measures that reflect approximate elicitations.