We define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance ellipsoid of a quantum state on the configuration and momentum spaces form what we call a dual quantum pair. We thereafter show that quantum polarity allows solving the Pauli reconstruction problem for Gaussian wavefunctions. The notion of quantum polarity exhibits a strong (...) interplay between the uncertainty principle and symplectic and convex geometry and our approach could therefore pave the way for a geometric and topological version of quantum indeterminacy. We relate our results to the Blaschke–Santaló inequality and to the Mahler conjecture. We also discuss the Hardy uncertainty principle and the less-known Donoho–Stark principle from the point of view of quantum polarity. (shrink)

This book presents a comprehensive mathematical study of the operators behind the Born-Jordan quantization scheme. The Schrödinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born-Jordan scheme is used. Thus, Born-Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born-Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated (...) approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero. (shrink)

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show that the Schrödinger equation for a nonrelativistic spinless particle is a classical equation which is equivalent to Hamilton’s equations. Our discussion is quite general, and incorporates time-dependent systems. This gives us the opportunity of discussing the group of Hamiltonian canonical transformations which is a non-linear variant of the usual symplectic group.

Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level sets defined by (...) Fermi for the purpose of representing geometrically quantum states. (shrink)

The aim of the famous Born and Jordan 1925 paper was to put Heisenberg’s matrix mechanics on a firm mathematical basis. Born and Jordan showed that if one wants to ensure energy conservation in Heisenberg’s theory it is necessary and sufficient to quantize observables following a certain ordering rule. One apparently unnoticed consequence of this fact is that Schrödinger’s wave mechanics cannot be equivalent to Heisenberg’s more physically motivated matrix mechanics unless its observables are quantized using this rule, and not (...) the more symmetric prescription proposed by Weyl in 1926, which has become the standard procedure in quantum mechanics. This observation confirms the superiority of Born–Jordan quantization, as already suggested by Kauffmann. We also show how to explicitly determine the Born–Jordan quantization of arbitrary classical variables, and discuss the conceptual advantages in using this quantization scheme. We finally suggest that it might be possible to determine the correct quantization scheme by using the results of weak measurement experiments. (shrink)

The rigorous equivalence of the Schrödinger and Heisenberg pictures requires that one uses Born–Jordan quantization in place of Weyl quantization. We confirm this by showing that the much discussed “ angular momentum dilemma” disappears if one uses Born–Jordan quantization. We argue that the latter is the only physically correct quantization procedure. We also briefly discuss a possible redefinition of phase space quantum mechanics, where the usual Wigner distribution has to be replaced with a new quasi-distribution associated with Born–Jordan quantization, and (...) which has proven to be successful in time-frequency analysis. (shrink)

We show that the strong form of Heisenberg’s inequalities due to Robertson and Schrödinger can be formally derived using only classical considerations. This is achieved using a statistical tool known as the “minimum volume ellipsoid” together with the notion of symplectic capacity, which we view as a topological measure of uncertainty invariant under Hamiltonian dynamics. This invariant provides a right measurement tool to define what “quantum scale” is. We take the opportunity to discuss the principle of the symplectic camel, which (...) is at the origin of the definition of symplectic capacities, and which provides an interesting link between classical and quantum physics. (shrink)

The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C 0,2 . This algebra is essentially the geometric algebra describing the rotational properties of space. Hidden within this algebra are symplectic structures with Heisenberg algebras at their core. This algebra also enables us to define a Poisson algebra of all homogeneous quadratic polynomials on a two-dimensional sub-space, $\mathbb{F}^{a}$ of the Euclidean three-space. This enables (...) us to construct a Poisson Clifford algebra, ℍ F , of a finite dimensional phase space which will carry the dynamics. The quantum dynamics appears as a realisation of ℍ F in terms of a Clifford algebra consisting of Hermitian operators. (shrink)

We use the notion of polar duality from convex geometry and the theory of Lagrangian planes from symplectic geometry to construct a fiber bundle over ellipsoids that can be viewed as a quantum-mechanical substitute for the classical symplectic phase space. The total space of this fiber bundle consists of geometric quantum states, products of convex bodies carried by Lagrangian planes by their polar duals with respect to a second transversal Lagrangian plane. Using the theory of the John ellipsoid we relate (...) these geometric quantum states to the notion of “quantum blobs” introduced in previous work; quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle. We show that the set of equivalence classes of unitarily related geometric quantum states is in a one-to-one correspondence with the set of all Gaussian wavepackets. We emphasize that the uncertainty principle appears in this paper as geometric property of the states we define, and is not expressed in terms of variances and covariances, the use of which was criticized by Hilgevoord and Uffink. (shrink)

Créée par Éric Rochant, Le Bureau des légendes (Canal +, 2015-2020) explore le monde du renseignement en décrivant le travail du service des agents clandestins de la DGSE. Face aux incertitudes et aux complexités géopolitiques du monde contemporain, elle fait le choix d’une immersion au cœur du « renseignement humain ». Cet article envisage l’hypothèse selon laquelle une telle fiction permet de restaurer la confiance des spectateurs vis-à-vis de la capacité d’une démocratie à lutter contre ce qui la menace. En (...) plongeant son spectateur dans les coulisses du renseignement, en le familiarisant avec des personnages complexes, la série questionne la légitimité de la confiance qu’il est possible d’accorder à un service de renseignement. La faillibilité des agents, mise en scène de façon détaillée, réfléchie par la série elle-même, rassure parce qu’elle permet de comprendre et de partager une forme de vie spécifique qui est celle de l’action secrète. L’espionnage, le contre-espionnage et le contre-terrorisme apparaissent alors comme des pratiques reposant en dernier ressort, non pas sur une maîtrise absolue, mais sur la décision de faire confiance ou au contraire de se méfier. Mobilisant les recherches de la sociologie contemporaine à propos de la confiance (Giddens, 1994 et Luhmann 2006), il s’agit de décrire Le Bureau des légendes comme une fiction projetant sur nos écrans, la possibilité d’une restauration de la confiance ou pour le dire à la manière de Stanley Cavell, une issue possible au scepticisme. (shrink)

Nearly fifteen years after the Council of Europe first called for a pan‐European convention on issues in bioethics to harmonize disparate national regulations, in November 1996 the council's Committee of Ministers approved the Convention on Human Rights and Biomedicine for formal adoption. The draft convention, released in July 1994, provoked strong public, professional, and governmental debate among European nations, particularly regarding provisions for biomedical research with subjects unable to give informed consent. If ratified, the “bioethics convention” will become the first (...) such document to have binding force internationally. (shrink)

It is generally accepted that bioethics is an interdisciplinary science. Why this is so and what it means is not always clear or agreed upon and, in this author's view, its implications are insufficiently researched. On the basis of involvement in projects which were labelled interdisciplinary, the author reflects upon the method of interdisciplinarity, especially its starting point. It is suggested that interdisciplinarity cannot thrive unless it curbs, from the very start, the inevitable reductions of all monodisciplinary approaches. This effort (...) is called methodical epochè, ideally the temporary suspension of all known methods. Its purpose is to achieve an interdisciplinary way of stating the question. Until then no breakdown of the global question by particular methods of single disciplines ought to be attempted. Realistic variations of this ideal are also discussed. CiteULike Connotea Del.icio.us What's this? (shrink)

La Pensée d’Ibn al-Muqaffaʿ: Un «agent double» dans le monde persan et arabe. By István T. Kristó-Nagy. Studia Arabica, vol. 19. Paris: Éditions de Paris, 2013. Pp. 605. €34.

For 150 years after Galileo’s condemnation in 1633, there were many references to the trial, but no sustained, heated or polarized discussions. Then came the thesis that Galileo was condemned not for being a good astronomer but for being a bad theologian ; it began in 1784–1785 with an apology of the Inquisition by Mallet du Pan in the Mercure de France and the printing in Tiraboschi’s Storia della letteratura italiana of an apocryphal letter attributed to Galileo but forged by (...) Onorato Gaetani. This thesis is not only untenable and false but inverts and subverts the truth; it proved to be long-lasting and widely accepted; so it may be labeled a myth. It was held by such writers as Bergier; Bergier; B; Feller; Cooper; Purcell; Marini; Reumont; Madden and Duhem. Afterwards, it was generally abandoned, its death knell being pope John Paul II’s speeches in 1979–1992. The myth seems to have acted as a catalyst insofar as its creation encouraged the proliferation of pro-clerical accounts and the articulation of pro-Galilean ones, thus making the discussion of Galileo’s trial the cause célèbre it is today.Author Keywords: Galileo; Galileo affair; Science versus religion; Theology; Biblical exegesis; Myth. (shrink)

(*) Este es el capítulo 16 de su obra monumental titulada Retrying Galileo, 1633-1992, publicado en el 2005 por la University of California Press, Berkeley. Este libro es un examen del affair Galileo desde el momento de la condena del científico toscano por la Inquisición en 1633, hasta su supuesta rehabilitación por el Papa Juan Pablo II en 1992. Su enfoque es en temas tales como: si acaso la condena fue justa, y si probaría la incompatibilidad entre ciencia y religión; (...) pone énfasis en los textos que constituyen las fuentes primarias, y de los cuales emergen los hechos históricos y los distintos temas controversiales. El capítulo 17 del mismo estudio del profesor Finocchiaro, contiene una evaluación precisa, realista y balanceada, de los esfuerzos del Papa Juan Pablo II para poner a la Iglesia al día frente al caso Galileo, conjuntamente con una estimación negativa tanto de la comisión papal encargada de su reexamen, como de su presidente, el Cardenal Paul Pourpard. La traducción es de Hermes H. Benítez, y ha sido expresamente autorizadapor la editorial. (shrink)

The editors welcome letters from readers, although we cannot guarantee that all will be published. To ensure timeliness, correspondents must respond to an article within seven weeks and not exceed two double‐spaced pages. Letters become the property of the editors and may be edited and shortened at our discretion.

In lieu of an abstract, here is a brief excerpt of the content:13o JOURNAL OF THE HISTORY OF PHILOSOPHY 28:1 JANUARY 1990 ceived scope of philosophy in the Renaissance, in comparison with the Middle Ages and early modern periods. Most impressive of all, aside from the extremely high quality of all its parts, is this volume's fidelity to its subject and the placement of that subject in an accurate historical context. For that we have to thank each contributor, and, most (...) of all, the vision of Charles Schmitt. In addition to setdng a new standard for a reference work of this type, The CambridgeHistory of ReniassancePhilosophymay well prove to be his most enduring legacy. MARCIA L. COLISn Oberlin College Pietro Redondi. GalileoHeretic. Translated by Raymond Rosenthal. Princeton: Princeton University Press, 1987. Pp. x + 356. $29.95. The trial of Galileo by the Inquisition in 1633 is a classic episode that invites continual reinterpretation and reevaluation for all sorts of reasons. Karl yon Gebler's Galileoand the Roman Curia (1879) was partly a response to the availability of new documents; Giorgio de Santillana's Crime of Galileo (1955) was partly meant to shed light on the phenomenon of McCarthyism; Arthur Koestler's Sleepwalkers (1959) was partly intended to come to terms with the crisis of secularism; Jerome Langford's Galileo, Science, and the Church (1966) was partly an updating of the apologetic interpretation; Stillman Drake's Galileo(198o) was partly a personal synthesis of his and others' recent contributions to scholarship. Such reappraisals perform a valuable function, and so one welcomes this translation of a 1983 Italian book, for it advances a radically new interpretation. Redondi was motivated by his accidental discovery of a document in the Roman Archiv.es of the Congregation for the Doctrine of the Faith--the current name of the Inquisition. The document is an anonymous complaint about Galileo's Assayer(1623). The complaint is that this book advances an atomic theory of matter, that this theory conflicts with the Catholic doctrine of the Eucharist, and that therefore the book is heretical. The specific element of atomism that worries the writer is the distinction between primary and secondary qualities, including the thesis that secondary qualities do not really exist in the object but only in the subject. The doctrine of the Eucharist asserts that the consecration of bread and wine (which occurs during mass) involves the miracle of transubstantiation: the bread and wine retain all their accidental qualities, but their substance changes into the body and blood of Jesus Christ. The conflict is that atomism would make transubstantiation impossible, for all accidental qualities of bread and wine are sensory manifestations of their atoms. Thus, if the qualities do not change, neither do the atoms. But if the atoms do not change, neither does the substance. This complaint is anonymous only in the sense that the document lacks a signature, and there is no other way for us to know the identity of the author. But the complaint is written in the form of a letter to an authoritative churchman, and the author asks the addressee to let him know whether his accusation is correct and what action should be taken about the matter. Thus, it is obvious that the plaintiff was known to the addressee. BOOK REVIEWS 131 Normally such a discovery would lead one to search the archives in question to learn from other documents as much relevant information as possible: not only the identity of the letter's author and addressee, but its date, its repercussions, and so on. But the Roman Archives of the Inquisition are, understandably, not generally open to scholars. Redondi himself had been granted a rare privilege by being allowed to consult some specific manuscripts in connection with his project which, though related, did not involve Galileo's trial as such. Therefore, in the excitement of his discovery, Redondi did the next best thing he could do. He was led to the following. According to Redondi, the complaint's author was Orazio Grassi, a Jesuit with whom Galileo had a bitter dispute about comets, which occasioned The Assayer, among other works. The complaint was written in 1624 or a6~5, at which time no action was taken by the Inquisition, partly... (shrink)

The object of the book is to meet and combat false conceptions, to co-ordinate true notions, and so to furnish the reader with some general information on the old and the new scholasticism. The advantage of the book is its two-sided perspective that contains historical investigations about the ancient sources of the scholastic philosophy and the decline from it. But it contains also a systematic perspective by which the doctrines of the scholastic philosophizing are collected systematically. Therefore this book is (...) an scholarly introduction into the scholastic philosophy dedicated for undergraduate’s. (shrink)

Our team at the Centre for Clinical Ethics has long been engaged in internal discussion about the purpose and value of ethics debriefs and their purported role in reducing moral distress (Morley an...

Subtitled "Rejections of Cartesian Dualism" this collection of essays traces through western Philosophy the strong but often overlooked idea that the body and the mind are not two different kinds of entity somehow reconciled in man, but rather a unity that is man. The editor's introduction sets forth Aristotle's ideas, concentrating on the dictum that it is the same man that thinks and runs. Spicker also treats Descartes' view, and the view of the Cartesians, ably separating the two when necessary. (...) The rest of the book is basically arranged chronologically, starting with extracts from Spinoza's Ethics, an essay on these extracts by Hans Jonas, and then moving through Julien de la Mettrie and two short essays by Kant. The second part of the book contains interesting essays on the human body by John Dewey, Douglas Long, and B. A. O. Williams, all defending the essential unity of body and soul. The third and last section of the book is itself divided into two parts, the first of which, entitled "Philosophy of Embodiment" contains four extracts from the works of prominent phenomenologists, Max Scheler, Gabriel Marcel, Jean-Paul Sartre, and Maurice Merleau-Ponty. These essays all center around the necessity of a concept of the "lived body" to the understanding of man's being-in-the-world. In the last section, the quality of the essays drops, although it is delightfully leavened by a witty essay by Richard Griffith on the foot. This section contains essays on particular parts of the human body, such as sight and the upright posture, by Herbert Plügge, Hans Jonas, and Erwin W. Straus. There is a selected bibliography for those who are captured by this basic thread of western thought.--W. A. de V. (shrink)

We argue in this paper that so-called new wave reductionism fails to capture the nature of the interlevel relations between psychology and neuroscience. Bickle (1995, Psychoneural reduction of the genuinely cognitive: some accomplished facts, Philosophical Psychology, 8, 265-285; 1998, Psychoneural reduction: the new wave, Cambridge, MA: MIT Press) has claimed that a (bottom-up) reduction of the psychological concepts of learning and memory to the concepts of neuroscience has in fact already been accomplished. An investigation of current research on the phenomenon (...) of long-term potentiation reveals that this claim overstates the facts. Both the psychological and the neural concepts involved have not yet stabilized and face further correction under the influence of both bottom-up and top-down selection pressures. In addition, psychological concepts often refer to functions, and functions are indispensable and irreducible. Function ascriptions pick out objective patterns involving historical factors and distal goals. This view of functions implies that psychological facts cannot be simply read off from the neurophysiological facts. Although psychological theorizing is constrained by neurophysiology (and vice versa), psychology remains distinct at least to some degree. (shrink)

The doctrine of eliminative materialism holds that belief-desire psychology is massively referentially disconnected. We claim, however, that it is not at all obvious what it means to be referentially (dis)connected. The two major accounts of reference both lead to serious difficulties for eliminativism: it seems that elimination is either impossible or omnipresent. We explore the idea that reference fixation is a much more local, partial, and context-dependent process than was supposed by the classical accounts. This pragmatic view suggests that elimination (...) is not the prime model for understanding the complex relations between the mind and brain sciences, and that we have little ground for concluding that in general psychological kinds do not exist. We suggest that reference changes are better seen as continuous rather than completely eliminative. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Gold & Stoljar are right in rejecting the radical neuron doctrine, but we argue that their distinction between determination and explanation is not principled enough to support their conclusion. We claim that the notions of multiple supervenience and screening-off offer a more precise construal of the dissociation between explanation and determination that lies at the heart of the antireductionist position.