Relational interpretation of the wave function and a possible way around Bell's theorem

The famous ``spooky action at a distance'' in the EPR-szenario is shown to be a local interaction, once entanglement is interpreted as a kind of ``nearest neighbor'' relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the ``nearest neighbor'' relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, ``position'' becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the ``weird'' aspects, like the particle-wave duality, the non-locality of entanglement, or the ``mystery'' of the double-slit experiment, disappear. Furthermore, this picture cirumvents the restrictions set by Bell's inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics.Comment: Accepted for publication in "International Journal of Theoretical Physics

The Combinatorics of Alternating Tangles: from theory to computerized enumeration

We study the enumeration of alternating links and tangles, considered up to topological (flype) equivalences. A weight $n$ is given to each connected component, and in particular the limit $n\to 0$ yields information about (alternating) knots. Using a finite renormalization scheme for an associated matrix model, we first reduce the task to that of enumerating planar tetravalent diagrams with two types of vertices (self-intersections and tangencies), where now the subtle issue of topological equivalences has been eliminated. The number of such diagrams with $p$ vertices scales as $12^p$ for $p\to\infty$. We next show how to efficiently enumerate these diagrams (in time $\sim 2.7^p$) by using a transfer matrix method. We give results for various generating functions up to 22 crossings. We then comment on their large-order asymptotic behavior.Comment: proceedings European Summer School St-Petersburg 200

Spinoza

"Spinoza", second edition. Encyclopedia entry for the Springer Encyclopedia of EM Phil and the Sciences, ed. D. Jalobeanu and C. T. Wolfe

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

A Dodecalogue of Basic Didactics from Applications of Abstract Differential Geometry to Quantum Gravity

We summarize the twelve most important in our view novel concepts that have arisen, based on results that have been obtained, from various applications of Abstract Differential Geometry (ADG) to Quantum Gravity (QG). The present document may be used as a concise, yet informal, discursive and peripatetic conceptual guide-cum-terminological glossary to the voluminous technical research literature on the subject. In a bonus section at the end, we dwell on the significance of introducing new conceptual terminology in future QG research by means of `poetic language'Comment: 16 pages, preliminary versio

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

The Self Model and the Conception of Biological Identity in Immunology

The self/non-self model, first proposed by F.M. Burnet, has dominated immunology for sixty years now. According to this model, any foreign element will trigger an immune reaction in an organism, whereas endogenous elements will not, in normal circumstances, induce an immune reaction. In this paper we show that the self/non-self model is no longer an appropriate explanation of experimental data in immunology, and that this inadequacy may be rooted in an excessively strong metaphysical conception of biological identity. We suggest that another hypothesis, one based on the notion of continuity, gives a better account of immune phenomena. Finally, we underscore the mapping between this metaphysical deflation from self to continuity in immunology and the philosophical debate between substantialism and empiricism about identity

Gravitomagnetism and the Clock Effect

The main theoretical aspects of gravitomagnetism are reviewed. It is shown that the gravitomagnetic precession of a gyroscope is intimately connected with the special temporal structure around a rotating mass that is revealed by the gravitomagnetic clock effect. This remarkable effect, which involves the difference in the proper periods of a standard clock in prograde and retrograde circular geodesic orbits around a rotating mass, is discussed in detail. The implications of this effect for the notion of ``inertial dragging'' in the general theory of relativity are presented. The theory of the clock effect is developed within the PPN framework and the possibility of measuring it via spaceborne clocks is examined.Comment: 27 pages, LaTeX, submitted to Proc. Bad Honnef Meeting on: GYROS, CLOCKS, AND INTERFEROMETERS: TESTING GENERAL RELATIVITY IN SPACE (22 - 27 August 1999; Bad Honnef, Germany