Despite their important applications in metrology and in spite of numerous experimental demonstrations, weak measurements are still confusing for part of the community. This sometimes leads to unjustified criticism. Recent papers have experimentally clarified the meaning and practical significance of weak measurements, yet in Kastner, Kastner seems to take us many years backwards in the the debate, casting doubt on the very term “weak value” and the meaning of weak measurements. Kastner appears to ignore both the basics and frontiers of (...) weak measurements and misinterprets the weak measurement process and its outcomes. In addition, she accuses the authors of Aharonov et al. in statements completely opposite to the ones they have actually made. There are many points of disagreement between Kastner and us, but in this short reply I will leave aside the ontology and focus mainly on the injustice in her criticism. I shall add some general comments regarding the broader theory of weak measurements and the two-state-vector formalism, as well as supporting experimental results. Finally, I will point out some recent promising results, which can be proven by projective measurements, without the need of employing weak measurements. (shrink)

We revisit the analogy suggested by Madelung between a non-relativistic time-dependent quantum particle, to a fluid system which is pseudo-barotropic, irrotational and inviscid. We first discuss the hydrodynamical properties of the Madelung description in general, and extract a pressure like term from the Bohm potential. We show that the existence of a pressure gradient force in the fluid description, does not violate Ehrenfest’s theorem since its expectation value is zero. We also point out that incompressibility of the fluid implies conservation (...) of density along a fluid parcel trajectory and in 1D this immediately results in the non-spreading property of wave packets, as the sum of Bohm potential and an exterior potential must be either constant or linear in space. Next we relate to the hydrodynamic description a thermodynamic counterpart, taking the classical behavior of an adiabatic barotopric flow as a reference. We show that while the Bohm potential is not a positive definite quantity, as is expected from internal energy, its expectation value is proportional to the Fisher information whose integrand is positive definite. Moreover, this integrand is exactly equal to half of the square of the imaginary part of the momentum, as the integrand of the kinetic energy is equal to half of the square of the real part of the momentum. This suggests a relation between the Fisher information and the thermodynamic like internal energy of the Madelung fluid. Furthermore, it provides a physical linkage between the inverse of the Fisher information and the measure of disorder in quantum systems—in spontaneous adiabatic gas expansion the amount of disorder increases while the internal energy decreases. (shrink)

The electric activities of cortical pyramidal neurons are supported by structurally stable, morphologically complex axo-dendritic trees. Anatomical differences between axons and dendrites in regard to their length or caliber reflect the underlying functional specializations, for input or output of neural information, respectively. For a proper assessment of the computational capacity of pyramidal neurons, we have analyzed an extensive dataset of three-dimensional digital reconstructions from the NeuroMorphoOrg database, and quantified basic dendritic or axonal morphometric measures in different regions and layers of (...) the mouse, rat or human cerebral cortex. Physical estimates of the total number and type of ions involved in neuronal electric spiking based on the obtained morphometric data, combined with energetics of neurotransmitter release and signaling fueled by glucose consumed by the active brain, support highly efficient cerebral computation performed at the thermodynamically allowed Landauer limit for implementation of irreversible logical operations. Individual proton tunneling events in voltage-sensing S4 protein alpha-helices of Na+, K+ or Ca2+ ion channels are ideally suited to serve as single Landauer elementary logical operations that are then amplified by selective ionic currents traversing the open channel pores. This miniaturization of computational gating allows the execution of over 1.2 zetta logical operations per second in the human cerebral cortex without combusting the brain by the released heat. (shrink)

The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow due to an expansion of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon entropy due to expansion (...) is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the “force” accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum. (shrink)

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete set of orthogonal (...) quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories. (shrink)

A Gedanken experiment is presented where an excited and a ground-state atom are positioned such that, within the former’s half-life time, they exchange a photon with 50% probability. A measurement of their energy state will therefore indicate in 50% of the cases that no photon was exchanged. Yet other measurements would reveal that, by the mere possibility of exchange, the two atoms have become entangled. Consequently, the “no exchange” result, apparently precluding entanglement, is non-locally established between the atoms by this (...) very entanglement. This quantum-mechanical version of the ancient Liar Paradox can be realized with already existing transmission schemes, with the addition of Bell’s theorem applied to the no-exchange cases. Under appropriate probabilities, the initially-excited atom, still excited, can be entangled with additional atoms time and again, or alternatively, exert multipartite nonlocal correlations in an interaction free manner. When densely repeated several times, this result also gives rise to the Quantum Zeno effect, again exerted between distant atoms without photon exchange. We discuss these experiments as variants of interaction-free-measurement, now generalized for both spatial and temporal uncertainties. We next employ weak measurements for elucidating the paradox. Interpretational issues are discussed in the conclusion, and a resolution is offered within the Two-State Vector Formalism and its new Heisenberg framework. (shrink)

Quantum entanglement is a key resource, which grants quantum systems the ability to accomplish tasks that are classically impossible. Here, we apply Feynman's sum-over-histories formalism to interacting bipartite quantum systems and introduce entanglement measures for bipartite quantum histories. Based on the Schmidt decomposition of the matrix comprised of the Feynman propagator complex coefficients, we prove that bipartite quantum histories are entangled if and only if the Schmidt rank of this matrix is larger than 1. The proposed approach highlights the utility (...) of using a separable basis for constructing the bipartite quantum histories and allows for quantification of their entanglement from the complete set of experimentally measured sequential weak values. We then illustrate the nonclassical nature of entangled histories with the use of Hardy's overlapping interferometers and explain why local hidden variable theories are unable to correctly reproduce all observable quantum outcomes. Our theoretical results elucidate how the composite tensor product structure of multipartite quantum systems is naturally extended across time and clarify the difference between quantum histories viewed as projection operators in the history Hilbert space and those viewed as chain operators and propagators in the standard Hilbert space. (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)

The problem of Cartesian dualism is viewed as falling under a more general problem: the problem of human unity. This problem is both ancient and modern: whether a human being is a substantial unity of soul and body or merely a contingent one. I compare Aristotle's and Descartes's response to this problem. My thesis is that an important factor in generating Cartesian dualism is the rejection implicit in Descartes's metaphysical codification of the new mathematical science of nature, namely, the rejection (...) of Aristotle's radical teleological concept of nature. It is argued that the modern intractable problem of the relation of mind to body turns historically and metaphysically on the Cartesian substitution of the mathematically refined concept of body--three-dimensional extension--for the once-influential Aristotelian teleological concept of corporeal substance. (shrink)

European Journal of Political Theory, Volume 21, Issue 3, Page 585-586, July 2022. Ayelet Shachar's lead essay in The Shifting Border draws out dramatic transformations of bordering practices currently taking place worldwide. These have yielded spatial relocations for bordering, a privatization of enforcement, and legal innovations that tie the border to individual people as they move, among many other changes. Shachar argues in favor of a form of reciprocity, in which states that shape shift their borders are also compelled to (...) recognize rights for people who require humanitarian assistance. In response, Shachar's interlocutors offer an array of reflections and friendly amendments. (shrink)

Theorists of democratic politics have long noted the importance of citizenship to the realization of liberal norms. Citizenship provides an artificial identity to members so that they may meet as equals in the public domain. The constraints of equality dictate that this identity will have a unitary face: citizenship must be a single status if it is to serve its stated purpose. However upon examination, citizenship appears to take multiple forms that reflect a range of political statuses that exist within (...) the confines of democratic politics. The civil, political and social rights of citizenship as well as the status of nationality come unbound from one another in ways that create multiple forms of partial, or semi-citizenship. Semi-citizenships provide states with opportunities to organize and govern otherwise "illegible" or "irrational" sub-sections of the population. They also often offer individuals the chance to adopt identities that diverge from those referenced by classic notions of the citizen. ;This dissertation combines a theoretical inquiry into the realities of modern citizenship with focused case studies examining instances of semi-citizenship. Each case study demonstrates the degree to which semi-citizenship is inevitable in democratic politics both by looking at various national contexts and by recalling the presence of such statuses throughout the history of the modern state. The statuses held by non-nationals, GLBTs, children and convicted felons demonstrate a unique set of state responses to forms of membership that do not correspond to the categories of citizen or non-citizen. Each of these statuses has existed in a wide range of temporal and geographic circumstances. Deprived of nationality, civil rights and political rights, these groups exist in democracies without being governed democratically, yet in some cases they are able to turn such statuses to their advantage. States compensate in a variety of ways ranging from special or additional rights, to benign neglect, to paternalism. While vulnerable to critique, these compensatory measures indicate an acceptance of the fact that citizenship is composed of several distinct forms of membership and may also provide opportunities for tailoring citizenship to meet individual needs. (shrink)

The title of this article has been chosen deliberately, for we find interesting parallels in the careers and outlooks of Alexis de Tocqueville and the great Prussian theorist of war, Carl von Clausewitz whose master work, On War, remains sui generis. They overlapped in time, but, more importantly, their major theoretical works dealt in large measure with the same problem – the democratic revolution and its impact on politics. As Clausewitz argued, the warfare of the new era was caused by (...) the new political conditions which die French Revolution created both in France and in Europe as a whole, conditions that set in motion new means and new forces, and have thus made possible a degree of energy in war diat odierwise would have been inconceivable. It follows that the transformation of the art of war resulted from the transformation of politics. (shrink)

This study develops a pedagogy for the teaching of ethical principles in information systems (IS) classes, and reports on an empirical study that supports the efficacy of the approach. The proposed pedagogy involves having management information systems professors lead questioning and discussion on a list of ethical issues as part of their existing IS courses. The rationale for this pedagogy involves (1) the maturational aspects of ethics, and (2) the importance of repetition, challenge, and practice in developing a personal set (...) of ethics. A study of IS ethics using a pre-post test design found that classes receiving such treatment significantly improved their performance on an IS ethics questionnaire. (shrink)