A common reducible representation space of the Lie algebras su and su is equipped with two different types of scalar products. The representation bases are labeled by the azimuthal and magnetic quantum numbers. The generators of su are the x-, y- and z-components of the orbital angular momentum operator. The representation of each of these Lie algebras is unitary with respect to only one of the scalar products. To each positive magnetic quantum number a family of the su-Barut–Girardello coherent states (...) is associated. The normalization and resolution of the identity condition for the coherent states are realized in two different approaches, i.e. the unitary and the non-unitary approaches. For the coherent states of the non-unitary case we calculate the uncertainty relation for the Hermitian x- and y-components of the angular momentum operator. While the unitary case leads to the known uncertainty relation for the Hermitian x- and y-components of su Lie algebra. (shrink)

Bohr and Heisenberg suggested that the thermodynamical quantities of temperature and energy are complementary in the same way as position and momentum in quantum mechanics. Roughly speaking their idea was that a definite temperature can be attributed to a system only if it is submerged in a heat bath, in which case energy fluctuations are unavoidable. On the other hand, a definite energy can be assigned only to systems in thermal isolation, thus excluding the simultaneous determination of its temperature. Rosenfeld (...) extended this analogy with quantum mechanics and obtained a quantitative uncertainty relation in the form ΔU Δ(1/T) ≥ k, where k is Boltzmann's constant. The two “extreme” cases of this relation would then characterize this complementarity between isolation (U definite) and contact with a heat bath (T definite). Other formulations of the thermodynamical uncertainty relations were proposed by Mandelbrot (1956, 1989), Lindhard (1986), and Lavenda (1987, 1991). This work, however, has not led to a consensus in the literature. It is shown here that the uncertainty relation for temperature and energy in the version of Mandelbrot is indeed exactly analogous to modern formulations of the quantum mechanical uncertainty relations. However, his relation holds only for the canonical distribution, describing a system in contact with a heat bath. There is, therefore, no complementarily between this situation and a thermally isolated system. (shrink)

We investigate the Peres–Horodecki positive partial transpose criterion in the context of conserved quantities and derive a condition of inseparability for a composite bipartite system depending only on the dimensions of its subsystems, which leads to a bi-linear entanglement witness for the two qubit system. A separability inequality using generalized Schrodinger–Robertson uncertainty relation taking suitable operators, has been derived, which proves to be stronger than the bi-linear entanglement witness operator. In the case of mixed density matrices, it identically (...) distinguishes the separable and non separable Werner states. (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)

For a simple set of observables we can express, in terms of transition probabilities alone, the Heisenberg uncertainty relations, so that they are proven to be not only necessary, but sufficient too, in order for the given observables to admit a quantum model. Furthermore distinguished characterizations of strictly complex and real quantum models, with some ancillary results, are presented and discussed.

Stringy corrections to the ordinary Heisenberg uncertainty relations have been known for some time. However, a proper understanding of the underlying new physical principle modifying the ordinary Heisenberg uncertainty relations has not yet emerged. The author has recently proposed a new scale relativity theory as a physical foundation of string and M theories. In this work the stringy uncertainty relations, and corrections thereof, are rigorously derived from this new relativity principle without any ad-hoc assumptions. The precise connection (...) between the Regge trajectory behavior of the string spectrum and the area quantization is also established. (shrink)

The problem of the validity and interpretation of the energy-time uncertainty relation is briefly reviewed and reformulated in a systematic way. The Bohr-Einsteinphoton-box gedanken experiment is seen to illustrate the complementarity of energy andevent time. A more recent experiment with amplitude-modulated Mößbauer quanta yields evidence for the genuine quantum indeterminacy of event time. In this way, event time arises as a quantum observable.

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)

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum features of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson–antimeson systems. In particular, we discuss the entropic Heisenberg uncertainty relation for observables measured at different (...) times at accelerator facilities including the effect of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{CP}$\end{document} violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems. (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)

It is generally believed that the uncertainty relation Δq Δp≥1/2ħ, where Δq and Δp are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of (...) the determination of the path of a particle in an interference experiment (such as the double-slit experiment). (shrink)

It is demonstrated that in quantized general relativity one is led to Jordan-Fock type uncertainty relations implying the occurrence of cut-off lengths. We argue that these lengths (i) represent limitations on the measurability of quantum effects of general relativity and (ii) provide a cut-off length of quantum divergences.

A philosophical interpretation of quantum mechanics presupposes a clear understanding of what is asserted by this theory. The aim of this paper is to help clarify one specific theorem of quantum mechanics, namely the so-called uncertainty relations. The surprisingly wide spread belief that these relations generally imply a reciprocal or inversely proportional relationship between the respective uncertainties is shown to be mistaken. Several reasons why this mistaken belief has been embraced are suggested. The conditions under which one could say (...) that the uncertainty relations imply an inversely proportional relationship between uncertainties are specified. (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)

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)

The Cramér–Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show that the identification of the mean quantum potential, an important notion in Bohmian mechanics, with the Fisher information, leads, through the Cramér–Rao bound, to an uncertainty principle which is stronger, in general, than both Heisenberg and Robertson–Schrödinger uncertainty relations, allowing to experimentally (...) test the validity of such an identification. (shrink)

Bohr's 1930 derivation of the uncertainty relation c 2 δm δt≥h bears a close relationship to Einstein's 1913 derivation of the “gravitational redshift” via the “equivalence principle.” A rewording of Bohr's argument is presented here, not taking the last step of acceleration as “equivalent” to a uniform gravity field, thus yielding a derivation of the formula c 2 δm δt≥h, avoiding Treder's 1971 objection.

Calling the quantity; 2ΔAΔB/|<[A, B]>|, with non-zero denominator, the uncertainty product ratio or UPR for the pair of observables, (A, B), it is shown that any non-zero correlation coefficient between two observables raises, above unity, the lower bound of the UPR for each member of an infinite collection of pairs of incompatible observables. Conversely, any UPR is subject to lower bounds above unity determined by each of an infinite collection of correlation coefficients. This result generalizes the well known Schroedinger (...) strengthening of the Robertson uncertainty relations (with the former expressed in terms of the correlation coefficient rather than the anticommutator) where the UPR and the correlation coefficient both involve the same pair of observables. Two, independent, derivations of the result are presented to clarify its’ origins and some examples of its’ use are examined. (shrink)

The purpose of this paper is to solve a serious problem for the projection postulate involving the time-energy uncertainty relation. The problem was recently raised by Teller, who believes that the problem is insoluble and, consequently, that the projection postulate should no longer be regarded as a serious focus for interpretive investigation.

E=mc 2 is found to be a special case ofE=σ ±1cn, where σ is any one of four susceptibilities, namely electric, magnetic, gravitational, and elastic. Letl be length,t time,Δt time dilation, andΔl a measure of Fitzgerald-Lorentz contraction. A particle is stated to be the manifestation of a collection of susceptibilities which arise when(Δl)/1=(Δt)/t. Then(ΔE)/E=5 (Δt)/2t=±(Δσ)/σ. Corresponding to susceptibility, special energy particles are postulated which exhibitSU(3) symmetry, Related to the susceptibilities are five new Heisenberg uncertainty relations. Three new conservation laws (...) for particles are proposed. (shrink)

The uncertainty relation in quantum mechanics has been explicated sometimes as a statistical relation and at other times as a relation concerning precision of simultaneous measurements. In the present paper, taking the indefiniteness of individual experiments as represented by diameters of Borel sets in projection-valued measure, we mathematically distinguish four expressions, two statistical and two concerning simultaneous measurements, of the uncertainty relation, study their interrelations, and prove that they are nonequivalent to each other and (...) to the eigenvector condition (EV) in infinite-dimensional Hilbert space. (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.

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.

The discussion of a particular kind of interpretation of the energy-time uncertainty relation, the “pragmatic time” version of the ETUR outlined in Part I of this work [measurement duration (pragmatic time) versus uncertainty of energy disturbance or measurement inaccuracy] is reviewed. Then the Aharonov-Bohm counter-example is reformulated within the modern quantum theory of unsharp measurements and thereby confirmed in a rigorous way.

We consider particles prepared by a single slit diffraction experiment. For those particles the standard deviation σ p of the momentum is discussed. We find out that σ p =∞ is not an exception but a rather typical case. A necessary and sufficient condition for σ p <∞ is given. Finally, the inequality σ p Δx≥π ℏ is derived and it is shown that this bound cannot be improved.

An analysis of some of the applications of Clifford space relativity to the physics behind the modified black hole entropy-area relations, rainbow metrics, generalized dispersion and minimal length stringy uncertainty relations is presented.

A physical basis for the minimal time-energy uncertainty relation is formulated from basic high-energy hadronic properties such as the resonance mass spectrum, the form factor behavior, and the peculiarities of Feynman's parton picture. It is shown that the covariant oscillator formalism combines covariantly this time-energy uncertainty relation with Heisenberg's space-momentum uncertainty relation. A pictorial method is developed to describe the spacetime distribution of the localized probability density.

It is demonstrated that one can in principle register an arbitrarily small force acting on a free particle by employing only measurements of its coordinates.

The article discusses the uncertainty of legal definitions of aviation safety and and aviation security, the implementation of which often result in certain restrictions of human rights. In the article, a hypothesis is made that, despite usually treated as well-known concepts, safety and security are not so clear and well-defined, often leaving the reader to guess at their precise meaning. The aim of this article is to identify the core features that characterise aviation safety and aviation security and could (...) disclose their legal content when assessing their comparative weight in relation to the protection of human rights. Supported by holistic approach from different perspectives (socio-cultural, historical, etc.), the phenomenological and hermeneutic analysis allowed providing an in-depth understanding of various meanings of safety and security concepts. An overview of the existing linguistic peculiarities of the use of the terms ‘safety’ and ‘security’ with an emphasis on the importance of determining the context in which they are used as primary evidence of their meaning is followed by the analysis of the common features and differences between the concepts of safety and security that supplements the discourse on the dilemma of combining subjective and objective, relative and absolute perceptions of safety and security. The research from the view point of normative jurisprudence reveals the polysemy inherent in aviation safety and aviation security, especially in terms of the values they represent, suggesting the conclusion that legal definitions of ‘aviation safety’ and ‘aviation security’ should in part be treated as a sort of ad hoc definitions, which have to be developed (clarified) in each particular case. (shrink)

It is shown that the time operatorQ 0 appearing in the realization of the RCCR's [Qμ,Pv]=−jhgμv, on Minkowski quantum spacetime is a self adjoint operator on Hilbert space of square integrable functions over Σ m =σ×v m , where σ is a timelike hyperplane. This result leads to time-energy uncertainty relations that match their space-momentum counterparts. The operators Qμ appearing in Born's metric operator in quantum spacetime emerge as internal spacetime operators for exciton states, and the condition that the (...) metric operator should possess a ground exciton state assumes the significance of achieving minimal spacetime4-momentum uncertainty in fundamental standards for spacetime measurements. (shrink)

Non-compensatory aggregation rules are applied in a variety of problems such as voting theory, multi-criteria analysis, composite indicators, web ranking algorithms and so on. A major open problem is the fact that non-compensability implies the analytical cost of loosing all available information about intensity of preference, i.e. if some variables are measured on interval or ratio scales, they have to be treated as measured on an ordinal scale. Here this problem has been tackled in its most general formulation, that is (...) when mixed measurement scales (interval, ratio and ordinal) are used and both stochastic and fuzzy uncertainties are present. Objectives of this article are first to present a comprehensive review of useful solutions already proposed in the literature and second to advance the state of the art mainly in the theoretical guarantee that weights have the meaning of importance coefficients and they can be summarized in a voting matrix. This is a key result for using non-compensatory Condorcet consistent rules. A proof on the probability of existence of ties in the voting matrix is also developed. (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)

Both economists and psychologists are interested in understanding decision making under uncertainty. Yet, they rely on different concepts to analyse human behaviour: economists use economic preference parameters rooted in utility theory, while psychologists use personality traits to describe responses to uncertain situations. Using a large sample of university students, this study examines and contrasts five economic preference parameters and six psychological personality traits that are commonly used to study individuals’ attitudes towards uncertainty. A novelty of this paper is (...) including both the economic concept of ambiguity aversion as well as the personality trait of ambiguity intolerance. We find that standard economic preference measures based on incentivized choice tasks seem to capture rather different characteristics than psychological personality traits. In contrast, economic preference measures obtained from self-assessment questions appear more related to personality traits, especially ambiguity intolerance. (shrink)

Several studies have suggested a matrilateral bias in allomaternal (non-maternal) infant and child caregiving. The bias has been associated with the allomother’s certainty of genetic relatedness, where allomothers with high certainty of genetic relatedness will invest more in children because of potential fitness benefits. Using quantitative behavioral observations collected on Ngandu 8- to 12-month-old infants from the Central African Republic, I examine who is caring for infants and test whether certainty of genetic relatedness may influence investment by allomothers. Results indicate (...) a matrilateral bias in caregiving by extended kin members, but this does not affect the total level of care infants receive when fathers and siblings are included in the analysis. These results replicate a previous study done among an adjacent foraging population and emphasize the importance of examining children’s complete social environments when addressing caregiving and child development. (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)

In this work I propose an analogy between Pythagoras's theorem and the logical-formal structure of Werner Heisenberg's "relations of uncertainty." The reasons that they have pushed to me to place this analogy have been determined from the following ascertainment: Often, when in exact sciences a problem of measurement precision arises, it has been resolved with the resource of the elevation to the square. To me it seems also that the aporie deriving from the uncertainty principle can find one (...) solution with the resource to this stratagem. In fact, if the first classic example of the argument is the solution of the incommensurability between catheti and the hypotenuse of the triangle rectangle, one of the last cases is that which is represented from Heisenberg's principle of uncertainty. (shrink)

The Uncertainty of Analysis pursues key issues raised in the author's earlier Discourse of Modernism, a ground-breaking work which focused attention on the nature of discourse and the ways in which one culturally dominant "discursive class" may be replaced by another. In this timely and provocative collection of his essays, Timothy J. Reiss shows how efforts to reconfirm the force and power of modernist, analytico-referential discourse in the late nineteenth and the twentieth centuries have actually brought to the fore (...) internal contradictions, have made clear the problematic nature of the dominant discourse, and have precipitated the emergence of competing discourses. Reiss considers the explorations in foundational logic by Frege and Peirce; examinations of language and its relations to mind by Saussure, Greimas, and Chomsky; work in linguistic and scientific epistemology by Wittgenstein and Heisenberg; and the attempts to analyze the nature of society by Sartre and other Western Marxists. Reiss turns to some practitioners of literary criticism and theory who have sought to escape past constraints, and he points to what appear to be erroneous routes away from the dilemmas raised by these philosophers and critics. (shrink)

Again and again utopian hopes are connected with the life sciences (no hunger, health for everyone; life without diseases, longevity), but simultaneously serious research shows uncertain, incoherent, and ambivalent results. It is unrealistic to expect that these uncertainties will disappear. We start by providing a not exhaustive list of five different types of uncertainties end-users of nutrigenomics have to cope with without being able to perceive them as risks and to subject them to risk-analysis. First, genes connected with the human (...) body or nutrients can have different functions in interaction with their environment (for instance, one nutrient can be healthy for the heart, but can also be a high risk in relation to cancer). Secondly, uncertainties are formed by risk analyses. Will it be possible to calculate a certain risk of getting a certain condition with a certain lifestyle? Will it be difficult to separate the genetic component and the lifestyle component? How high will these risks be? How will these risks be handled by the actors? In the case of personal genotyping, it is unclear how frequent an adverse polymorphism will occur. Will every individual have a certain vulnerability to a certain disease or will it only be applicable to a small group of the population or particular populations? Thirdly, dietary advices are subject to uncertainties and still to be developed professional standards: some will have adverse outcomes, some will not delay the disease, and some will assume uncertain associations between nutrients, lifestyle, and genetic vulnerabilities. Fourth, with regard to the usefulness of tests it is uncertain to what extent risks indications about obesity and diabetes and other vulnerabilities really influence people to live healthier and therefore will help to prevent these conditions. Fifth, it is uncertain how and what nutrigenomics products will be developed and used. Will it be possible to develop more effectively health improving products? Or is this too difficult and will nutrigenomics continue to be used in not always justified health claims as a commercial and marketing tool? Present-day ethics and theories of responsibilities presuppose that uncertainties will disappear and concentrate on what seems to be fixed and stable in science. We develop provisional thoughts that assume that the dynamic of science to produce uncertainties and dilemmas is endemic, and we stress the need for consumers to institutionalize value searching, exploring, and deliberating devices in the health and food sector to find out the most important uncertainties and correspondingly socially desirable research priorities. (shrink)

As corporate social responsibility involves a voluntary business endeavour to address social and environmental issues beyond legal compliance, governments cannot fall back on hierarchical command-and-control policies to support it. As such, it is complementary with the increasing popularity of public policies known as New Governance policies, where the government is engaged in a horizontal inter-organizational network of societal actors and where public policy is both formed and executed by the interacting and voluntary efforts from a multitude of stakeholders. However, such (...) policies are known to generate substantive uncertainty about the content of CSR and its related issues, strategic uncertainty regarding the behavior of the actors involved and institutional uncertainty related to the interaction process involved in the institutional change. We explore New Governance policy instruments to address these uncertainties in the context CSR and discuss the experiences with these methods in the European Union. (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)

Uncertainty and emotion are an inevitable part of everyday life and play a vital role in mental health. Yet, our understanding of how uncertainty and emotion interact is limited. Here, an online survey was conducted to examine whether uncertainty evokes and modulates a range of negative and positive emotions. The data show that uncertainty is predominantly associated with negative emotional states such as fear/anxiety. However, uncertainty was also found to modulate a variety of other negative (...) and positive emotional states, depending on the valence of an anticipated outcome and the sub parameter of uncertainty. Uncertainty increased the intensity of negative emotional states and decreased the intensity of positive emotional states. These findings support prior research suggesting that uncertainty is aversive and associated with negative emotional states such as fear and anxiety. However, the findings also revealed that uncertainty is involved in eliciting and modulating a wide array of emotional phenomena beyond fear and anxiety. This study highlights an opportunity for further study of how uncertainty and emotion interactions are conceptualised generally and in relation to mental health. (shrink)

The main purpose of the paper is to develop a concept of _model uncertainty_ as opposed to the existing and well-established concept of model risk. Up to date the broad literature on probability not only developed complete probability systems, but also correctly noticed limitations of probability calculus. Despite the acknowledgement of such probability restrictions, drawbacks of modeling are often related to model risk. We present an argument here to distinguish a feature limiting models even further: model uncertainty. The tenets (...) of it already exist in the literature on probability, but were not properly emphasized while the idea of model risk was developed. Our plan it to start with a broad overview of the existing knowledge about probability in order to start with fundamental principles. From them we are deriving a new concept of model uncertainty. (shrink)

This book outlines the characteristics and implications of a potential geography of uncertainty. In doing so, it analyses this concept in reference to both the origins of uncertainty in Early Modern Age as well as the current geopolitical situation. The book adopts an interdisciplinary approach to uncertainty, drawing on global perspectives and literature to define its meanings and characteristics. In order to develop a thorough and precise understanding of the geography of uncertainty a broad perspective is (...) adopted, that includes other forms of knowledge in which the concept of uncertainty is firmly established. As such the book creates temporal links, that may occasionally be far off from one another, to present a geographical perspective of uncertainty. It provides an interpretation of the phenomenon of globalization in a new way, relating it to the first European openness to global spaces, the Early Modern Age, and identifying the transition from the medieval world to the Modern Age as the first manifestation of uncertainty in geography. Uncertainty is more prevalent than ever in today's geopolitical, economic, financial, and social reality, as well as the ongoing emergencies and crises. The book adopts an interdisciplinary approach rooted in the geography of Early Modernity by referring to geopolitical scenarios, literature, and philosophy, to target the historical roots and the prevailing configuration of the geography of uncertainty. It will appeal to scholars and students of human and political geography, politics, philosophy, international relations, economics, and history. (shrink)

There is a profound paradox in modern medical knowledge production: The more we know, the more we know that we (still) do not know. Nowhere is this more visible than in diagnostics and early detection of disease. As we identify ever more markers, predictors, precursors, and risk factors of disease ever earlier, we realize that we need knowledge about whether they develop into something experienced by the person and threatening to the person’s health. This study investigates how advancements in science (...) and technology alter one type of uncertainty, i.e., temporal uncertainty of disease diagnosis. As diagnosis is related to anamnesis and prognosis it identifies how uncertainties in all these fields are interconnected. In particular, the study finds that uncertainty in disease diagnosis has become more subject to prognostic uncertainty because diagnosis is more connected to technologically detected indicators and less closely connected to manifest and experienced disease. These temporal uncertainties pose basic epistemological and ethical challenges as they can result in overdiagnosis, overtreatment, unnecessary anxiety and fear, useless and even harmful diagnostic odysseys, as well as vast opportunity costs. The point is not to stop our quest for knowledge about disease but to encourage real diagnostic improvements that help more people in ever better manner as early as possible. To do so, we need to pay careful attention to specific types of temporal uncertainty in modern diagnostics. (shrink)