The paper summarizes, generalizes and reveals the physical content of a recently proposed framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time variables x,t, furnished with an additional indefinite inner product invariant under Poincaré transformations. The indefinite metric is responsible for breaking the symmetry between space and time variables and for selecting a family of Hilbert subspaces that are preserved under Galileo transformations. Within these (...) subspaces the usual quantum mechanics with Shrödinger evolution and t as the evolution parameter is derived. Simultaneously, the Minkowski space-time is embedded into H as a set of point-localized states, Poincaré transformations obtain unique extensions to H and the embedding commutes with Poincaré transformations. Furthermore, the framework accommodates arbitrary pseudo-Riemannian space-times furnished with the action of the diffeomorphism group. (shrink)

Quantum observables can be identified with vector fields on the sphere of normalized states. The resulting {\it vector representation} is used in the paper to undertake a simultaneous treatment of macroscopic and microscopic bodies in quantum mechanics. Components of the velocity and acceleration of state under Schr{\"o}dinger evolution are given a clear physical interpretation. Solutions to Schr{\"o}dinger and Newton equations are shown to be related beyond the Ehrenfest results on the motion of averages. A formula relating the normal probability distribution (...) and the Born rule is found. (shrink)

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrödinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random fluctuations of the (...) perturbed metric, the Born rule for probabilities of collapse is derived. The approach is applied to a two-level quantum system to obtain a simple geometric interpretation of quantum commutators, the uncertainty principle and Planck’s constant. In light of this, a lucid analysis of the double-slit experiment with collapse and an experiment on a pair of entangled particles is presented. (shrink)

The Riemannian manifold structure of the classical (i.e., Einsteinian) space-time is derived from the structure of an abstract infinite-dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H of functions of abstract parameters. The space H is associated with the space of states of a macroscopic test-particle in the universe. The spatial localization of state of the particle through its interaction with the environment is associated with the selection of a submanifold M of realization (...) H. The submanifold M is then identified with the classical space (i.e., a space–like hypersurface in space-time). The mathematical formalism is developed which allows recovering of the usual Riemannian geometry on the classical space and, more generally, on space and time from the Hilbert structure on S. The specific functional realizations of S are capable of generating spacetimes of different geometry and topology. Variation of the length-type action functional on S is shown to produce both the equation of geodesics on M for macroscopic particles and the Schrödinger equation for microscopic particles. (shrink)

Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this setting, also called functional tensor equations, describe families of functional equations on various Hilbert spaces of functions. The principle of functional relativity is introduced which states that quantum theory (QT) is indeed a functional tensor theory, i.e., it can be described by functional tensor (...) equations. The main equations of QT are shown to be compatible with the principle of functional relativity. By accepting the principle as a hypothesis, we then explain the origin of physical dimensions, provide a geometric interpretation of Planck’s constant, and find a simple model of the two-slit experiment and the process of measurement. (shrink)

Coordinate form of tensor algebra on an abstract (infinite-dimensional) Hilbert space is presented. The developed formalism permits one to naturally include the improper states in the apparatus of quantum theory. In the formalism the observables are represented by the self-adjoint extensions of Hermitian operators. The unitary operators become linear isometries. The unitary evolution and the non-unitary collapse processes are interpreted as isometric functional transformations. Several experiments are analyzed in the new context.

Classical mechanics is empirically successful because the probabilistic mean values of quantum mechanical observables follow the classical equations of motion to a good approximation (Messiah 1970, 215). We examine this claim for the one-dimensional motion of a particle in a box, and extend the idea by deriving a special case of the ideal gas law in terms of the mean value of a generalized force used to define "pressure." The examples illustrate the importance of probabilistic averaging as a method of (...) abstracting away from the messy details of microphenomena, not only in physics, but in other sciences as well. (shrink)

Newtonian and Scr{\"o}dinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes beyond the results provided by the Ehrenfest theorem. A formula relating the normal probability distribution and the Born rule was also found. Here the dynamical mechanism responsible for the latter formula is proposed and applied to measurements of macroscopic and microscopic systems. A relationship between the (...) classical Brownian motion and the diffusion of state on the space of states is discovered. The role of measuring devices in quantum theory is investigated in the new framework. It is shown that the so-called collapse of the wave function is not measurement specific and does not require a ``concentration" near the eigenstates of the measured observable. Instead, it is explained by the common diffusion of state over the space of states under interaction with the apparatus and the environment. This in turn provides us with a basic reason for the definite position of macroscopic bodies in space. (shrink)

The paradoxes of the double-slit experiment with an electron are shown to originate in the implicit assumption that the electron is always located in the classical space. It is demonstrated that there exists a natural substitute for this assumption that provides a method of resolving the paradoxes.

The paradoxes of the EPR experiment with two particles are shown to originate in the implicit assumption that the particles are always located in the classical space. There exists a substitute for this assumption that yields a new definition of reality and offers a resolution of the paradoxes.

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov} is reviewed. The results of \cite{Kryukov} are applied to the simpliest case of a Hilbert manifold: the abstract Hilbert space. In particular, functional transformations preserving properties of various linear operators on Hilbert spaces are found. Any generalized solution of an arbitrary linear differential equation with constant coefficients is shown to be related to a regular solution by a (functional) coordinate transformation. The results also suggest a way of using generalized functions (...) to solve nonlinear problems on Hilbert spaces. (shrink)

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov}, \cite{Kryukov1} is further analyzed. The main subject here is a comparison of the ordinary and the string bases of eigenvectors of a linear operator as introduced in \cite{Kryukov}. It is shown that the string basis of eigenvectors is a natural generalization of its classical counterpart. It is also shown that the developed formalism forces us to consider any Hermitian operator with continuous spectrum as a restriction to a space of square (...) integrable functions of a self-adjoint operator defined on a space of generalized functions. In the formalism functional coordinate transformations preserving the norm of strings are now linear isometries rather than the unitary transformations. (shrink)

A mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics is proposed. For this a Hilbert space H of functions of four variables x,t furnished with an additional indefinite inner product invariant under Poincare transformations is introduced. For a class of functions in H that are well localized in the time variable the usual formalism of non-relativistic quantum mechanics is derived. In particular, the interference in time for these functions is suppressed; a motion in H becomes (...) the usual Shrodinger evolution with t as a parameter. The relativistic invariance of the construction is proved. The usual theory of relativity on Minkowski space-time is shown to be ``isometrically and equivariantly embedded'' into H. That is, classical space-time is isometrically embedded into H, Poincare transformations have unique extensions to isomorphisms of H and the embedding commutes with Poincare transformations. (shrink)

Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and infinite-dimensional manifolds deeply similar. In this context the infinite-dimensional counterparts of simple notions such as basis, dual basis, orthogonal basis, etc. are shown to be closely related to the choice of a model. It is also shown that in this formalism a single tensor equation on an infinite-dimensional (...) manifold produces a family of functional equations on different spaces of functions. (shrink)

Conformal group of Minkowski space-time M is considered as a group of bundle automorphisms of a vector bundle U over M. 4-component spin-vectors (4-spinors) are sections of a subbundle of the tangent bundle over U. Isotropic 4-vectors are images of 4-spinors under projection. This leads to a particularly clear interpretation of the spin properties of Nature.

Catalog of the collection of the Madamkhand Museum of Art, named after the wife of Batzhargalyn Batbai︠a︡r, businessman and member of the Mongolian Khural.

In the twenty-first century, the debate about life on other worlds is quickly changing from the realm of speculation to the domain of hard science. Within a few years, as a consequence of the rapid discovery by astronomers of planets around other stars, astronomers very likely will have discovered clear evidence of life beyond the Earth. Such a discovery of extraterrestrial life will change everything. Knowing the answer as to whether humanity has company in the universe will trigger one of (...) the greatest intellectual revolutions in history, not the least of which will be a challenge for at least some terrestrial religions. Which religions will handle the discovery of extraterrestrial life with ease and which will struggle to assimilate this new knowledge about our place in the universe? Some religions as currently practiced appear to only be viable on Earth. Other religions could be practiced on distant worlds but nevertheless identify both Earth as a place and humankind as a species of singular spiritual religious importance, while some religions could be practiced equally well anywhere in the universe by any sentient beings. Weintraub guides readers on an invigorating tour of the world's most widely practiced religions. It reveals what, if anything, each religion has to say about the possibility that extraterrestrial life exists and how, or if, a particular religion would work on other planets in distant parts of the universe. (shrink)

Modern scholars have been concerned with the hostility shown to Alexander by the Hellenistic schools of philosophy. Two literary portraits have been distinguished, the Peripatetic and the Stoic, the former deriving from Theophrastus' book on Callisthenes, or starting with this work the Peripatetics worked out a theory of and applied it to Alexander, in order to belittle his achievements. It was a case of giving sophisticated expression to the kind of crude resentment expressed by Demades.

The locus classicus for Plutarch's own views on his methods is in the Alexander He has begun by asking for the indulgence of his readers if they do not find all the exploits of Alexander and Caesar recounted by the biographer or if they discover him not reporting some famous incident in detail (); and he goes on to compare his own search for evidence which will indicate the kind of soul, with the activity of the painter, who, in order (...) to create a likeness, concentrates on the eyes and pays little attention to the other parts. Commentators and critics have been right to take this as a key text for the purpose of understanding Plutarch's attitude towards his biographical work; nevertheless there are other passages in the Lives where we can at least glimpse his attitude to his subject, and we can only see the Alexander-remarks in correct perspective if we take these other passages into account. I propose therefore, starting with the Alexander, to see how far these critical remarks apply to Plutarch's theory and practice elsewhere in the Lives. (shrink)

According to the Ars Amatoria the notorious rape took place on the occasion of a primitive dramatic entertainment staged in a theatre, in which the seats and furnishings were also primitive. There is no time for a description of the arts of the performers—a tibicen and a ludius—before the Romans, impatient for action, receive their signal from Romulus. Nor is there any mention of a god in whose honour the entertainment had been provided.

Trope theory is a leading metaphysical theory in analytic ontology. One of its classic statements is found in the work of Donald C. Williams who argued that tropes qua abstract particulars are the very alphabet of being. The concept of an abstract particular has been repeatedly attacked in the literature. Opponents and proponents of trope theory alike have levelled their criticisms at the abstractness of tropes and the associated act of abstraction. In this paper I defend the concept of a (...) trope qua abstract particular by rejecting arguments that purport to show that tropes should not be understood as abstract and by arguing that the abstractness of tropes plays an indispensable role in one of our more promising trope-theoretic analyses of universals and of concrete objects. (shrink)

Pursuing Justice, Second Edition, examines the issue of justice by considering the origins of the idea, formal systems of justice, current global issues of justice, and ways in which justice might be achieved by individuals, organizations, and the global community. Part 1 demonstrates how the idea of justice has emerged over time, starting with religion and philosophy, then moving to the justice as a concern of the state, and finally to the concept of social justice. Part 2 outlines the very (...) different mechanisms used by various nations for achieving state justice, including systems based on common law, civil law, and Islamic law, with a separate discussion of the US justice system. Part 3 focuses on four contemporary issues of justice: war, genocide, slavery, and the environment. Finally, Part 4 shows how individuals and organizations can go about pursuing justice, and describes the rise of global justice. This updated timely book helps students understand the complexities and nuances of a society's pursuit of justice. It provides students with the foundations of global justice systems, integrating Greek philosophies and major religious perspectives into a justice perspective, and contributes to undergraduate understanding of international justice bodies, NGOs, and institutions. New edition is completely updated and revised to achieve relevance for today's students Covers concepts of justice as well as ideas for pursuing and achieving justice Examines how our modern laws began, and traces their evolution to today's laws Presents concepts and issues in justice studies as well as a comparison of several systems of law Teaching resources include discussion questions and real-world examples. (shrink)

This essay brings psychoanalytic theory on trauma together with film and television criticism on rape narrative in an analysis of Michael Coel’s 2020 series I May Destroy You. Beyond the limited carceral framework of the police procedural, which dislocates the act of violence from the survivor’s history and context, Coel’s polyvalent, looping narrative metabolizes rape television’s forms and genres in order to stage and restage both trauma and genre again and anew. Contesting common conceptions of vulnerability and susceptibility that prefigure (...) a violent breach of autonomy, Coel’s series and her interviews about it invite an ethics of looking that embraces a curiosity in the unknowable and untreatable kernel of subjective experience and defies and resists a policing of the survivor’s thoughts and emotions. By emphasizing and exploring what psychoanalysis calls the “afterwardness” of trauma, Coel foregrounds her main character’s subjectivity prior to her victimization, widens the sphere of consequence beyond the victim and criminal justice system to the survivor’s larger community, and entreats that community to preserve a space for her to look and look again at everything, without judgment. (shrink)

The concept of instantiation is realized differently across a variety of metaphysical theories. A certain realization of the concept in a given theory depends on what roles are specified and associated with the concept and its corresponding term as well as what entities are suited to fill those roles. In this paper, the classic realization of the concept of instantiation in a one-category ontology of abstract particulars or tropes is articulated in a novel way and defended against unaddressed objections.

It is argued that causal understanding originates in experiences of acting on objects. Such experiences have consistent features that can be used as clues to causal identification and judgment. These are singular clues, meaning that they can be detected in single instances. A catalog of 14 singular clues is proposed. The clues function as heuristics for generating causal judgments under uncertainty and are a pervasive source of bias in causal judgment. More sophisticated clues such as mechanism clues and repeated interventions (...) are derived from the 14. Research on the use of empirical information and conditional probabilities to identify causes has used scenarios in which several of the clues are present, and the use of empirical association information for causal judgment depends on the presence of singular clues. It is the singular clues and their origin that are basic to causal understanding, not multiple instance clues such as empirical association, contingency, and conditional probabilities. (shrink)

A revision of George Kennedy's translation of, introdution to, and commentary on Aristotle's On Rhetoric. His translation is most accurate, his general introduction is the most thorough and insightful, and his brief introductions to sections of the work, along with his explanatory footnotes, are the most useful available.

Effective public policy to mitigate climate change footprints should build on data-driven analysis of firm-level strategies. This article’s conceptual approach augments the resource-based view of the firm and identifies investments in four firm-level resource domains to develop capabilities in climate change impact mitigation. The authors denote the resulting framework as the GISTe model, which frames their analysis and public policy recommendations. This research uses the 2008 Carbon Disclosure Project database, with high-quality information on firm-level climate change strategies for 552 companies (...) from North America and Europe. In contrast to the widely accepted myth that European firms are performing better than North American ones, the authors find a different result. Many firms, whether European or North American, do not just “talk” about climate change impact mitigation, but actually do “walk the talk.” European firms appear to be better than their North American counterparts in “walk I,” denoting attention to governance, information management, and systems. But when it comes down to “walk II,” meaning actual Technology-related investments, North American firms’ performance is equal or superior to that of the European companies. The authors formulate public policy recommendations to accelerate firm-level, sector-level, and cluster-level implementation of climate change strategies. (shrink)

SECTION ONE THE STATE OF OURWORLD It may easily be said that our so called modern twentieth century was one of the most barbaric and wasteful centuries of human history. Here are the statistics: World War I (9.7 million military and 9 ...

En este libro, la autora desarrolla su concepción del juicio reflexionante inspirada en Emmanuel Kant y en Hannah Arendt para concentrarse en cómo cierto tipo de narraciones modelan nuestras nociones de lo que consideramos moral. Lara nos ofrece distintas concepciones sobre el mal en su formulación histórica mediante los ejemplos de las tragedias griegas, las diferentes concepciones sobre el mal en la obra de Shakespeare, el uso literario de la metáfora en la obra de Joseph Conrad y en narraciones fílmicas (...) que describen la crueldad humana. Lara sugiere que el aprendizaje moral es un proceso en el que intervienen las instituciones sociales, la voluntad de los individuos y de las sociedades para comprometerse a un debate abierto y con ello modelar los juicios colectivos sobre el pasado. Lara enfatiza que el juicio reflexionante se da entre un evento, una narración de dicho evento y la recepción pública de dicha narrativa. En este libro se aportan importantes métodos para la comprensión del fenómeno moral del mal, porque introducen nuevas verdades desvelatorias acerca de eventos particulares que no pueden ser simplemente captados por medio de categorías conceptuales. Lara utiliza como fuentes a Jürgen Habermas, Walter Benjamin, Primo Levi, Giorgio Agamben y Ariel Dorfman para probar la conclusión de este tipo de narraciones: la acción (de crueldad) ata de manera definitiva al perpetrador con su víctima. (shrink)

In the good old days, when general philosophy of science ruled the Earth, a simple division was often invoked to talk about philosophical issues specific to particular kinds of science: that between the natural sciences and the social sciences. Over the last 20 years, philosophical studies shaped around this dichotomy have given way to those organized by more fine-grained categories, corresponding to specific disciplines, as the literatures on the philosophy of physics, biology, economics and psychology--to take the most prominent four (...) examples--have blossomed. In general terms, work in each of these areas has become increasingly enmeshed with that in the corresponding science itself, increasingly naturalistic (in at least one sense of that term), and in my view, increasingly interesting. (shrink)

The master narrative of Apartheid South Africa created a specific identity for white boys and men and, together with this identity, a very particular role and place within the South African context. This identity was exemplified in the men who were conscripted into the military from 1967 until 1994, and who participated in operations on the border regions of Namibia and Angola as well as within local townships in the war of liberation against apartheid and minority rule. Many veterans have (...) been left grappling not only with the traumas associated with combat but also with the loss of their identities as war heroes in a country under changed political control. As a result, many of their personal stories and experiences of combat have been silenced by society at large and also, to varying degrees, within their own families, the Church, and among the younger generation who have grown up under a different dispensation. The conflict between vacillating narratives of villains who fought on the wrong side of history and victims of a closed socialisation system has supported the identity struggle faced by many veterans today. Against this backstory, this article explores the effects of storytelling as a trauma release using a narrative approach.Contribution: This article offers a contribution to the use of storytelling in pastoral conversations as a trauma release for untold stories. This insight links to the focus and scope of the journal as a pastoral narrative approach has been used under the umbrella of Practical Theology. (shrink)