Contextuality and the fundamental theorems of quantum mechanics

Contextuality is a key feature of quantum mechanics, as was first brought to light by Bohr and later realised more technically by Kochen and Specker. Isham and Butterfield put contextuality at the heart of their topos-based formalism and gave a reformulation of the Kochen-Specker theorem in the language of presheaves. Here, we broaden this perspective considerably (partly drawing on existing, but scattered results) and show that apart from the Kochen-Specker theorem, also Wigner's theorem, Gleason's theorem, and Bell's theorem relate fundamentally to contextuality. We provide reformulations of the theorems using the language of presheaves over contexts and give general versions valid for von Neumann algebras. This shows that a very substantial part of the structure of quantum theory is encoded by contextuality.Comment: v2: minor revisions, added definition of Bell presheaf, adjustment of Bell's theorem in contextual for

Simultaneous Block Diagonalization of Matrices of Finite Order

It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we give an efficient algorithm to explicitly compute a transfer matrix which realizes the simultaneous block diagonalization of unitary matrices whose decomposition in irreducible blocks (common invariant subspaces) is known from elsewhere. Our main motivation lies in particle physics, where the resulting transfer matrix must be known explicitly in order to unequivocally determine the action of outer automorphisms such as parity, charge conjugation, or time reversal on the particle spectrum.Comment: 6 pages, accepted by J.Phys.

Stone spectra of von Neumann algebras and foundation of quantum theory

Die in Englisch verfasste Dissertation, die unter der Betreuung von Herrn Prof. Dr. H. F. de Groote, Fachbereich Mathematik, entstand, ist der Mathematischen Physik zuzuordnen. Sie behandelt Stonesche Spektren von Neumannscher Algebren, observable Funktionen sowie einige Anwendungen in der Physik. Das abschließende Kapitel liefert eine Verallgemeinerung des Kochen-Specker-Theorems. Stonesche Spektren und observable Funktionen wurden von de Groote eingeführt. Das Stonesche Spektrum einer von Neumann-Algebra ist eine Verallgemeinerung des Gelfand-Spektrums, die observablen Funktionen verallgemeinern die Gelfand-Transformierten. Da de Grootes Ergebnisse zum großen Teil unveröffentlicht sind, folgt nach dem Einleitungskapitel im zweiten Kapitel eine Übersichtsdarstellung dieser Ergebnisse. Das dritte Kapitel behandelt die Stoneschen Spektren endlicher von Neumann-Algebren. Für Algebren vom Typ In wird eine vollständige Charakterisierung des Stoneschen Spektrums entwickelt. Zu Typ-II1-Algebren werden einige Resultate vorgestellt. Das vierte Kapitel liefert. einige einfache Anwendungen des Formalismus auf die Physik. Das fünfte Kapitel gibt erstmals einen funktionalanalytischen Beweis des Kochen-Specker-Theorems und liefert die Verallgemeinerung dieses Satzes, wobei die Situation für alle von Neumann-Algebren geklärt wird

Kinematik diffeomorphismeninvarianter quantisierter Eichtheorien

Die vorliegende Arbeit ist der mathematischen Physik zuzuordnen und beschäftigt sich mit der Kinematik von diffeomorphismeninvarianten Eichtheorien. Es wird ein Ansatz zur Quantisierung dargestellt, der in der sogenannten Loop-Quantengravitation entwickelt wurde

Some Remarks on the Logic of Quantum Gravity

Abstract We discuss some conceptual issues that any approach to quantum gravity has to confront. In particular, it is argued that one has to find a theory that can be interpreted in a realist manner, because theories with an instrumentalist interpretation are problematic for several wellknown reasons. Since the Hilbert space formalism almost inevitably forces an instrumentalist interpretation on us, we suggest that a theory of quantum gravity should not be based on the Hilbert space formalism. We briefly sketch the topos approach, which makes use of the internal logic of a topos associated with a quantum system and comes with a natural (neo-)realist interpretation. Finally, we make some remarks on the relation between system logic and metalogic

Meta-Containerplattform: Ein wirtschaftlicher Ansatz zur Verbesserung von Sicherheit und Wirtschaftlichkeit in der Containerlogistik?

Die Globalisierung und Liberalisierung der Märkte haben zu komplexen internationalen Wertschöpfungsnetzwerken geführt. Zugleich haben in den vergangenen Jahren Entwicklungen wie die Prinzipien der Lean Production an Bedeutung gewonnen. In der Konsequenz operieren Wertschöpfungsnetzwerke mit einem minimalen Sicherheitspuffer an Beständen und Zeit, was sie zunehmend verwundbar macht. Ein Großteil der erforderlichen Verbringung von Waren innerhalb der Netzwerke wird mit Hilfe von Containern abgewickelt. Diese Transporte sind gegenüber rein nationalen Beförderungen, nicht zuletzt aufgrund der gestiegenen Transportentfernung und -dauer sowie zunehmenden Umschlagsvorgängen und Zwischenlagerungen, deutlich mehr Risiken ausgesetzt. Zugleich bestehen beim Transport von Containern weiterhin Intransparenzen, welche Ineffizienzen verursachen und Risiken treiben. Die vorliegende Dissertation verfolgt das Ziel, durch die Untersuchung der Vernetzung von IT-Systemen in der Logistik und deren Anbindung an eine zentrale Plattform, aus wissenschaftlicher wie anwendungsbezogener Sicht einen Beitrag zur potenziellen Gestaltung von transparenten, effizienten und sicheren Containertransporten und damit ganzheitlichen Supply Chains zu liefern.The globalization and liberalization of markets have led to complex international supply networks. Additionally, developments like the principles of lean production have gained in importance in the last years. As a consequence, supply networks operate with minimal safety buffers with regards to time and inventory, which makes them increasingly vulnerable. The majority of goods in these networks is being transported in containers. These transports face exposed risks when compared to national haulages, which can be explained partially through longer transport distances and duration as well as increased transshipment and interim storage processes. At the same time, container transportation is still characterized by a lack of transparency, which causes inefficiencies and drives risks. From a scientific as well as an application viewpoint, this dissertation aims to contribute to the potential design of transparent, efficient, secure container transports and entire supply networks by integrating logistical IT systems and connecting them to a central platform

Quality of life of patients after retropubic prostatectomy - Pre- and postoperative scores of the EORTC QLQ-C30 and QLQ-PR25

<p>Abstract</p> <p>Background</p> <p>Patients with newly diagnosed early stage prostate cancer (PCa) face a difficult choice of different treatment options with curative intention. They must consider both goals of optimising quantity and quality of life. The quality of life (QoL) is a psychometric outcome which is measured using validated questionnaires. Only few data are published concerning pre - and postoperative QoL.</p> <p>Methods</p> <p>This study investigated pre perative QoL of 185 patients who consecutively underwent open radical retropubic prostatectomy for organ-confined PCa to postoperative QoL of another 185 patients. The EORTC QLQ-C30, EORTC QLQPR25 module and 24 h ICS pad test were used (mean follow-up 28.6 months).</p> <p>Results</p> <p>The examined symptom scores of the EORTC QLQ-PR25 were on lowest level. In the dyspnoea symptom score differences of age emerged: the amount of patients who are short of breath rose significantly in older patients after surgery (p < 0.05 paired, two-tailed student's t-test).. Lastly, the urinary symptom score was found postal-therapeutically low; this fact was age independent. The results of sexual symptom score need to be taken into consideration, since prostatectomy resulted in a significant reduction of sexual activity independent of age. All functioning scales postoperatively reached high values without significant changes (p > 0.05 student's t-test ), which implies a high QoL after surgery. A reliable and satisfying status of continence was found in our patients after retropubic prostatectomy. A high rate of patients (89.2%) would choose retropubic prostatectomy again.</p> <p>Conclusion</p> <p>Retropubic prostatectomy represents a reliable and accepted procedure in the treatment of organ-confined PCa. For the first time it could be shown that patients` QoL remained on a high level after retropubic prostatectomy. Nevertheless, the primary avoidance or postoperative therapy of erectile dysfunction should be in the focus of surgeons.</p