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)

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)

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.

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)

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)

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

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)

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.

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)

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.

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)

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)

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)

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.

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.

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.

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 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)

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.

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)

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)

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.

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.

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)

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.

In an age where issues like climate change and the unintended consequences of technological innovation are high on the ethical and political agenda, questions about the nature and extent of our responsibilities to future generations have never been more important, yet simultaneously so difficult to answer. This book takes a unique approach to the problem by drawing on diverse traditions of thinking about care (including developmental psychology, phenomenology and feminist ethics) to explore the nature and meaning of our relationship with (...) the future. Demonstrating that many influential perspectives on intergenerational ethics, including positions advanced by John Rawls, Brian Barry, and Ulrich Beck are undermined by problems relating to uncertainty, it shows that an approach based on care ethics can confront the uncertain future successfully and give a viable account of the nature and scope of future-oriented responsibilities. (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)

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)

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)

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)

This paper develops a philosophical account of moral disruption. According to Robert Baker (2013), moral disruption is a process in which technological innovations undermine established moral norms without clearly leading to a new set of norms. Here I analyze this process in terms of moral uncertainty, formulating a philosophical account with two variants. On the Harm Account, such uncertainty is always harmful because it blocks our knowledge of our own and others’ moral obligations. On the Qualified Harm Account, (...) there is no harm in cases where moral uncertainty is related to innovation that is “for the best” in historical perspective, or where uncertainty is the expression of a deliberative virtue. The two accounts are compared by applying them to Baker’s historical case of the introduction of mechanical ventilation and organ transplantation technologies, as well as the present-day case of mass data practices in the health domain. (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)

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)

Ever since the hard problem of consciousness (Chalmers, 1996, 1995) first entered the scene in the debate over consciousness many have taken it to show the limitations of a scientific or naturalist explanation of consciousness. The hard problem is the problem of explaining why there is any experience associated with certain physical processes, that is, why there is anything it is like associated with such physical processes? The character of one’s experience doesn’t seem to be entailed by physical processes and (...) so an explanation which can overcome such a worry must (1) explain how physical processes give rise to experience (explain the entailment), (2) give an explanation which doesn’t rely on such physical processes, or (3) show why the hard problem is misguided in some sense. Recently, a rather ambitious and novel theory of consciousness has entered the scene – Integrated Information Theory (IIT) of Consciousness (Oizumi et al., 2014; Tononi, 2008; Tononi et al., 2016) – and proposes that consciousness is the result of a specific type of information processing, what those developing the theory call integrated information. The central aim of this dissertation is to philosophically investigate IIT and see whether it has the ability to overcome the hard problem and related worries. I then aim to use this philosophical investigation to answer a set of related questions which guide this dissertation, which are the following: Is it possible to give an information-theoretic explanation of consciousness? What would the nature of such an explanation be and would it result in a novel metaphysics of consciousness? In this dissertation, I begin in chapter one by first setting up the hard problem and related arguments against the backdrop of IIT (Mindt, 2017). I show that given a certain understanding of structural and dynamical properties IIT fails to overcome the hard problem of consciousness. I go on in chapter two to argue that a deflationary account of causation is the best view for IIT to overcome the causal exclusion problem (Baxendale and Mindt, 2018). In chapter three, I explain IIT’s account of how the qualitative character of our experience arises (qualia) and what view of intentionality (the directedness of our mental states) IIT advocates. I then move on in chapter four to show why the hard problem mischaracterizes structural and dynamical properties and misses important nuances that may shed light on giving a naturalized explanation of consciousness. In the last and fifth chapter, I outline a sketch of a novel metaphysics of consciousness that takes the conjunction of Neutral Monism and Information-Theoretic Structural Realism to give what I call Information-Theoretic Neutral-Structuralism. (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)

Several theoretical perspectives have generated research on grandparental investment, notably socialization and evolutionary psychological perspectives. Using data collected from more than 200 older adults (mean age 67 years), we test three hypotheses derived from socialization and evolutionary perspectives about grandparents’ relationships with and investment in grandchildren. Results indicate that (1) emotional closeness with both children and children-in-law is positively related to reports of emotional closeness with grandchildren; (2) maternal grandmothers invest more in grandchildren than do other grandparents; and (3) grandparents (...) invest more in daughters’ children than in sons’ children. Discussion addresses limitations of self-report methodology in this context and situates the current findings within the body of research indicating the existence of psychological mechanisms designed to guide differential nepotism. (shrink)

A coherent account of the connections and contrasts between the principles of complementarity and uncertainty is developed starting from a survey of the various formalizations of these principles. The conceptual analysis is illustrated by means of a set of experimental schemes based on Mach-Zehnder interferometry. In particular, path detection via entanglement with a probe system and (quantitative) quantum erasure are exhibited to constitute instances of joint unsharp measurements of complementary pairs of physical quantities, path and interference observables. The analysis (...) uses the representation of observables as positive-operator-valued measures (POVMs). The reconciliation of complementary experimental options in the sense of simultaneous unsharp preparations and measurements is expressed in terms of uncertainty relations of different kinds. The feature of complementarity, manifest in the present examples in the mutual exclusivity of path detection and interference observation, is recovered as a limit case from the appropriate uncertainty relation. It is noted that the complementarity and uncertainty principles are neither completely logically independent nor logical consequences of one another. Since entanglement is an instance of the uncertainty of quantum properties (of compound systems), it is moot to play out uncertainty and entanglement against each other as possible mechanisms enforcing complementarity. (shrink)

Normative judgments involve two gradable features. First, the judgments themselves can come in degrees; second, the strength of reasons represented in the judgments can come in degrees. Michael Smith has argued that non-cognitivism cannot accommodate both of these gradable dimensions. The degrees of a non-cognitive state can stand in for degrees of judgment, or degrees of reason strength represented in judgment, but not both. I argue that (a) there are brands of noncognitivism that can surmount Smith’s challenge, and (b) any (...) brand of non-cognitivism that has even a chance of solving the Frege–Geach Problem and some related problems involving probabilistic consistency can also thereby solve Smith’s problem. Because only versions of non-cognitivism that can solve the Frege–Geach Problem are otherwise plausible, all otherwise plausible versions of noncognitivism can meet Smith’s challenge. (shrink)