This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? -/- The goal of the workshop, and of this book, (...) is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher-level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spacetime theories.” -/- This work will be of interest to physicists, as well as philosophers and historians of science working with or interested in General Relativity and/or Space, Time and Gravitation more generally. (shrink)

Hermann Weyl was one of the early contributors to the mathematics of general relativity. This article argues that in 1929, for the formulation of a general relativistic framework of the Dirac equation, he both abolished and preserved in modified form the conceptual perspective that he had developed earlier in his “analysis of the problem of space.” The ideas of infinitesimal congruence from the early 1920s were aufgehoben in the general relativistic framework for the Dirac equation. He preserved the central idea (...) of gauge as a “purely infinitesimal” aspect of symmetries in a group extension schema. With respect to methodology, however, Weyl gave up his earlier preferences for relatively a-priori arguments and tried to incorporate as much empiricism as he could. This signified a clearly expressed empirical turn for him. Moreover, in this step he emphasized that the mathematical objects used for the representation of matter structures stood at the center of the construction, rather than interaction fields which, in the early 1920s, he had considered as more or less derivable from geometrico-philosophical considerations. (shrink)

During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in (...) the context of the later development of gauge theories. (shrink)

Dans un discours prononcé à Zurich vers la fin des années 1940, Hermann Weyl a examiné l'épistémologie dialectique de Ferdinand Gonseth et l'a considérée comme trop strictement limitée aux aspects de changement historique. Son expérience de la philosophie diaclectique post-kantienne, en particulier la dérivation du concept de l'espace et de la matière chez Johann Gottlieb Fichte, avait constitué une base dialectique solide pour ses propres études de 1918 en une géométrie purement infinitésimale et la théorie antérieure d'un champ de matière (...) géométriquement unifié (en prolongement du programme Mie-Hilbert). Bien que Weyl se fût alors éloigné des aspects spéculatifs de la philosophie de sa jeunesse et eût montré, en particulier, moins d'enthousiasme qu'auparavant pour Fichte, il nourrissait encore de nombreux doutes sur la base culturelle de la science mathématique moderne et sur son rôle dans la culture matérielle du modernisme de pointe. Pour Weyl, la « réflexion » philosophique était une nécessité culturelle ; il se tourna alors vers lexistentialisme de Karl Jaspers et de Martin Heidegger pour trouver des raisons plus profondes, dans un mouvement comparable à son orientation vers la philosophie de Fichte après la Première Guerre mondiale. Le débat de la fin des années 1940 peut être compris comme une sorte de supplément postérieur à la Seconde Guerre mondiale par rapport à ses commentaires plus connus sur les mathématiques et les sciences naturelles publiés au milieu des années 1920. (shrink)

We study a Weyl geometric scalar tensor theory of gravity with scalar field \ and scale invariant “aquadratic” kinematical Lagrange density. The Weylian scale connection in Einstein gauge induces an additional acceleration. In the weak field, static, low velocity limit it acquires the deep MOND form of Milgrom/Bekenstein’s gravity. The energy momentum of \ leads to another add on to Newton acceleration. Both additional accelerations together imply a MOND-ian phenomenology of the model. It has unusual transition functions \, \nu _w\). (...) They imply higher phantom energy density than in the case of the more common MOND models with transition functions \, \, \mu _2\). A considerable part of it is due to the scalar field’s energy density which, in our model, gives a scale and generally covariant expression for the self-energy of the gravitational field. (shrink)

Nous présentons dans cet article la genèse du projet de l'Édition Hausdorff, ainsi que sa structure organisationnelle ; une discussion suit sur un des aspects centraux de l'œuvre de Hausdorff.

Nous présentons dans cet article la genèse du projet de l'Édition Hausdorff, ainsi que sa structure organisationnelle ; une discussion suit sur un des aspects centraux de l'œuvre de Hausdorff.

info:eu-repo/semantics/publishedVersion.