A source of much difficulty and confusion in the interpretation of quantum mechanics is a naive realism about operators. By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about measuring operators that occurs when the subject is quantum mechanics. Without a specification of what should be meant by measuring a quantum observable, such an expression can have no clear meaning. A definite specification is provided by (...) Bohmian mechanics, a theory that emerges from Schrödinger's equation for a system of particles when we merely insist that particles means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm — for example, that we must abandon classical logic or classical probability. The moral is rather simple: Beware naive realism, especially about operators! (shrink)

Quantum philosophy, a peculiar twentieth-century malady, is responsible for most of the conceptual muddle plaguing the foundations of quantum physics. When this philosophy is eschewed, one naturally arrives at Bohmian mechanics, which is what emerges from Schrodinger's equation for a nonrelativistic system of particles when we merely insist that 'particles' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. The quantum formalism emerges when measurement situations are (...) analyzed according to this theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with quantum theory simply evaporate.Bohr's ... approach to atomic problems ... is really remarkable. He is completely convinced that any understanding in the usual sense of the word is impossible. Therefore the conversation is almost immediately driven into philosophical questions, and soon you no longer know whether you really take the position he is attacking, or whether you really must attack the position he is defending. (shrink)

Bohmian mechanics is a theory about point particles moving along trajectories. It has the property that in a world governed by Bohmian mechanics, observers see the same statistics for experimental results as predicted by quantum mechanics. Bohmian mechanics thus provides an explanation of quantum mechanics. Moreover, the Bohmian trajectories are defined in a non-conspiratorial way by a few simple laws.

It is well known that density matrices can be used in quantum mechanics to represent the information available to an observer about either a system with a random wave function (“statistical mixture”) or a system that is entangled with another system (“reduced density matrix”). We point out another role, previously unnoticed in the literature, that a density matrix can play: it can be the “conditional density matrix,” conditional on the configuration of the environment. A precise definition can be given in (...) the context of Bohmian mechanics, whereas orthodox quantum mechanics is too vague to allow a sharp definition, except perhaps in special cases. In contrast to statistical and reduced density matrices, forming the conditional density matrix involves no averaging. In Bohmian mechanics with spin, the conditional density matrix replaces the notion of conditional wave function, as the object with the same dynamical significance as the wave function of a Bohmian system. (shrink)

We analyze the origin of quantum randomness within the framework of a completely deterministic theory of particle motion—Bohmian mechanics. We show that a universe governed by this mechanics evolves in such a way as to give rise to the appearance of randomness, with empirical distributions in agreement with the predictions of the quantum formalism. Crucial ingredients in our analysis are the concept of the effective wave function of a subsystem and that of a random system. The latter is a notion (...) of interest in its own right and is relevant to any discussion of the role of probability in a deterministic universe. (shrink)

Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics (...) and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schrödinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (shrink)

Das vorliegende Buch richtet sich an Studierende der Physik, für die nach der Quantenmechanik-Vorlesung die wesentliche Frage offen geblieben ist: „Was sagt denn nun der mathematische Formalismus, den ich jetzt ausgiebig und ach so mühsam studiert habe, über die Natur aus?“. Bei der Suche nach der Antwort besprechen die Autoren unter anderem die modernen Quantentheorien, die von John Stuart Bell „Theorien ohne Beobachter“ genannt wurden: die Bohmsche Mechanik, die Kollaps-Theorie und die Viele-Welten-Theorie. -/- Neben zielgerichteten mathematischen Aussagen, die in Kursvorlesungen (...) selten vorkommen, erklärt das Buch anhand der neuen Theorien die Rolle der Wellenfunktion und des Zufalls in der Quantenmechanik. Insbesondere beschäftigen sich die Autoren auch mit der Gedankenwelt des Physikers John Stuart Bell, der mit den berühmten, aber leider oft missverstandenen Bellschen Ungleichungen unser physikalisches Weltbild nachhaltig verändert hat. Das Buch eignet sich damit begleitend oder ergänzend zu einer Kursvorlesung über Quantenmechanik oder aber auch zum Selbststudium. (shrink)

Detlef Dürr (1951–2021) was a theoretical and mathematical physicist who worked particularly on the foundations of quantum mechanics, electromagnetism, and statistical mechanics. This piece is a rather personal look back at him and his science.

This volume commemorates the scientific contributions of Detlef Dürr (1951–2021) to foundational questions of physics. It presents new contributions from his former students, collaborators, and colleagues about their current research on topics inspired or influenced by Dürr. These topics are drawn from physics, mathematics, and philosophy of nature, and concern interpretations of quantum theory, new developments of Bohmian mechanics, the role of typicality, quantum physics in relativistic space-time, classical and quantum electrodynamics, and statistical mechanics. The volume thus also gives (...) a snapshot of present research in the foundations of physics. (shrink)

Detlef Dürr was a remarkable figure in many different ways. I recall some adventures we had with him in Abu Dhabi.

Kaum ein anderer lebender Naturwissenschaftler besitzt die Fähigkeit, mit solcher Geistesklarheit die tiefsten Einsichten von moderner Quantenphysik mit dem uralten spirituellen Menschheitswissen zu verknüpfen wie - Hans-Peter Dürr! Es gelingt Dürr scheinbar mühelos, eine Synthese zwischen den meditativen Einsichten der Weisen des Ostens und den aktuellen Erkenntnissen der modernen Naturwissenschaften herzustellen. Dabei verliert er sich niemals in langatmigen akademischen Erläuterungen, sondern hat stets den Menschen und die gesellschaftliche Wirklichkeit des 21. Jahrhunderts im Blick. Ein Brückenschlag zwischen zwei Welten, der vielleicht (...) niemals notwendiger war als zurzeit. Eine kleines Meisterwerk, das in einleuchtender Weise aufzeigt - alles Leben ist EINS! (shrink)

Segundo as descobertas da Física Moderna (Física Quántica), Realidade (Wirklichkeit em Alemão) não é mais o real que nos é familiar e tangível (cousal), mas algo bem diferente, tanto espacial como temporalmente, algo claramente mais aberto. Trata-se de algo holístico, uma Gestalt de carácter a-material, uma relação depura inter-conexão ("a-dvaita"), uma potencialidade inseparável, similar ao amor espiritual e omnicompreensivo. Ou seja, segundo o autor, a realidade está possuída por uma tonalidade processual, uma inspiração holística e intimamente conectada, uma transformação, um (...) processo contínuo de criação e aniquilamento, com o potencial de se manifestar a si mesma de um modo em que predomina uma essencial complementaridade dual energético-material. Assim, para o autor do artigo, o mundo em que vivemos, Wirklichkeit, não pode ser propriamente compreendido em termos puramente ontológicos. Segundo o autor, a questão : O que é, o que é que existe? torna-se uma questão desprovida de sentido. Em sua opinião, admissíveis seriam apenas questões acerca do que propriamente actua (wirkt), do que acontece, do que conecta, ou, por outras palavras, a questão do "entre". Consequentemente, a evolução no tempo e no espaço não procede mais de leis causais estritamente determinadas, pois o que existe são apenas tendências gerais intrínsecas (expectações), caracterizadas por probabilidades relativas a uma infinidade de realizações possíveis, as quais em média, pelo processo de sobreposições descoerentes, nos fazem voltar à nossa concepção comum do mundo como sendo uma realidade tangível dominada por leis naturais rigorosa e universalmente válidas. /// According to the findings of modern physics (quantum physics) Reality (in German more appropriate: Wirklichkeitj is basically no more the familiar, tangible (thing-like) reality but quite different and, spatially and temporally, more open. It is a holistic a-material "Gestalt", a pure connectedness ("a-dvaita"), an inseparable potentiality, similar to the spiritual and to all-embracing love. It relates to a processlike holistic and intimately connected inspiration and transformation, a continuous creation and annihilation, with the potential manifesting itself with some vagueness in complementary dual and essentially energetic/material diversified fashion. Hence, for the author, the world in which we are living, Wirklichkeit, cannot be understood strictly in an ontological way. The question: What is, what exists? becomes meaningless. Questions still admissible are: What acts (wirkt), happens, binds?, the question for the "in-between". The evolution in time does not follow anymore from strictly determined causal laws but there are only general intrinsic tendencies ("expectations"), characterised by probabilities for infinitely many possible realizations, which on average (decoherent superpositions) lead back to our familiar conception of the world as an objective tangible reality with its rigorously valid natural laws. (shrink)

Das Wirken Gabriel Biels, eines der bedeutendsten Theologen des Spatmittelalters, ist nicht nur durch scharfsinniges, vor allem an Ockham, aber auch an Scotus orientiertes theologisches Nachdenken gekennzeichnet. Es ist ebenso gepragt durch die Devotio moderna. Aus dieser Quelle speist sich sein unermuedlicher Einsatz fuer eine Kirchenreform wie auch seine tiefe Frommigkeit. Trotz Kenntnis der Bedeutung dieser Linie fuer Biels Frommigkeitspraxis blieb sein Verhaltnis zur Mystik bisher unerforscht. Das vorliegende Buch fuellt diese Luecke. Es sammelt aus Biels Hauptwerken, dem Collectorium und (...) der Auslegung des Meakanons, die mystischen Elemente (wie z.B. raptus, Einwohnung, unio, transformatio) und analysiert deren Rezeption. Dabei beruecksichtigt es auch das Vorfeld von Mystik in Gebet und Meditation. Einen anderen Schwerpunkt bildet Biels Stellung zum Phanomen religioser und mystischer Erfahrung. Einen qualifizierten Begriff religioser Erfahrung entwickelt Biel nicht. Er wertet sie durchaus positiv, doch gilt ihm als das Hochste im Christenleben die Liebe. Betrachtet man aber die Funktion der Mystik in Biels Werken, so ist seine Theologie im weiteren Sinne mystagogisch. In devoter Tradition stehend, will er zur Frommigkeit hinfuehren. Nicht zu hoch veranschlagt werden darf die Relevanz des Nominalismus fuer Biels Mystik-Rezeption. Mit Register. "Es ist M. gelungen, in seiner grundgelehrten Untersuchung einmal die Forschung der Theologie Biels erheblich weiter voranzutreiben, und er hat zugleich zu uebergeordneten Fragen substantielle Beitrage geleistet." Theologische Rundschau "a ein solider und fuer die Erforschung der spatmittelalterlichen Theologie und Frommigkeit unentbehrlicher Beitraga" Rottenburger Jahrbuch fuer Kirchengeschichte "Durch sorgfaltige Analysen diesen verkannten theologischen Denker in die Gegenwart geholt zu haben - dies ist ein Verdienst dieser Arbeit." Hulda "Die beeindruckenden Starken der Arbeit liegen in der behutsamen, differenzierten Einzelanalyse" Theologische Literaturzeitung. (shrink)

Detlef Breitenband gibt in seinem Buch einen problemorientierten Überblick über die Rechtstheorien von Immanuel Kant und Jürgen Habermas. Im Zentrum steht die Frage nach der Leistungsfähigkeit beider Rechtstheorien, da diese den Konsens aller Rechtsadressaten zur Grundlage haben, aber nicht davon ausgegangen wird, dass jemals über eine Rechtsnorm ein faktischer Konsens erzeugt wird. Der Autor arbeitet die radikal-demokratischen Implikationen des Kantischen Republikanismus heraus und leistet einen wichtigen Beitrag zur Klärung des Begriffs der Legitimation von Rechtsnormen.

Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard quantum mechanics only the wave function or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical (...) limit becomes very simple: when do the Bohmian trajectories look Newtonian? (shrink)

This article deals with the notion of jurisdictional discourse, which, as a specific type of complex discourse, always poses a real challenge to translators. The authors present a contrastive analysis of the texts of legal decisions in French, German and Polish in order to demonstrate the difficulties in translation and the consequences which they entail, and to suggest a strategy for overcoming them. Firstly, the authors briefly compare the texts of judicial decisions indicating their characteristics both in terms of the (...) macrostructure of the text and in terms of syntactic and lexical units. Secondly, they explain the origin of the difficulties in translation resulting from the qualitative differences of the legal systems. Thirdly, the different types of difficulties are described and illustrated by practical examples, in order to make experienced translators and apprentice translators sensitive to them. The corpus used for the analysis consists of the integral and documented texts of the French, German and Polish judgments rendered in matters of civil law [37]. It should also be noted that the analyzed texts are comparable texts, which are a valuable tool for translators and allow them to acquire means of expression that are as natural as possible [40]. Regarding the methodology, the authors adopt for the analysis the contrastive method, borrowed from the theory of cultural transfer [15]. (shrink)

Dr. theol. Dr. phil. Detlef Schwartz, Jahrgang 1954, Pfarrer i. R. und langjähriger nebenamtlicher Universitätsdozent, mit Stationen in Deutschland und den USA sowie Lateinamerika, zieht eine vorläufige Bilanz seiner bisherigen Arbeit im Auslandsdienst der Evangelischen Kirche in Deutschland. Er ordnet diese ein in Erfahrungen in einem Pfarramt der United Church of Christ, USA, und seinen Beobachtungen in der Millionenmetropole Los Angeles. Die Konsequenz eines verstärkten Dialogs der Religionen, besonders mit dem Islam, koppelt er zurück an die Frage nach der (...) Notwendigkeit eines Paradigmenwechsels im Religionsunterricht hin zu einem den Dialog fördernden Kulturunterrichts."-- Back cover. (shrink)