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 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)

Galt Xenokrates in der bisherigen Forschung nur als subalterner Dogmatiker, so wirft diese Arbeit ein neues Licht auf den dritten Akademieleiter. Die Gesamtdarstellung seiner Philosophie enthält neben der Kosmologie, Theologie und Ontologie erstmalig auch seine Prinzipienlehre. Diese findet sich im berühmten Sextus-Bericht, Adv. Math., X §§ 248-283, der auf der Folie der Philosophie des Xenokrates neu gelesen wird. Die darin vorgestellte monistische Prinzipienlehre stammt von Xenokrates, der in seine Berichterstattung über Platons Ungeschriebene Lehre seine eigenen Lehrsätze mit einfließen ließ. Diese (...) Prinzipienlehre stellt das Bindeglied zwischen der Seinsmetaphysik des Aristoteles und der Einheitsmetaphysik Platons dar, da das erste Prinzip, die absolute Monas, nushaft und seinstranszendent ist. Xenokrates erweist sich als platontreuer und innovativer Denker, als 'Fels', auf den Platon seine Lehre und seine Schule gründen konnte. (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)

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)

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.

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)

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)

It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrödinger's equation. This book will be of (...) value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science. (shrink)

This article was found among the papers left by Prof. Laugwitz (May 5, 1932–April 17, 2000). The following abstract is extracted from a lecture he gave at the Fourth Austrain Symposion on the History of Mathematics (Neuhofen/ybbs, November 10, 1995).About 100 years ago, the Cantor-Veronese controversy found wide interest and lasted for more than 20 years. It is concerned with “actual infinity” in mathematics. Cantor, supported by Peano and others, believed to have shown the non-existence of infinitely small quantities, and (...) therefore he fought against the infinitely large and small numbers in Veronese’s geometry, but also against the non-archimedean systems of Thomae, du Bois-Reymond, and Stolz. As a positive consequence of the controversy the distinction between Cantor’s transfinite arithmetic and the theory of ordered algebraic structures becomes clear. (shrink)