The book contains a collection of essays on mathematical structures that serve us to model the Universe. The authors discuss such topics as: the interplay between mathematics and physics, geometrical structures in physical models, observational and conceptual aspects of cosmology. The reader can also contemplate the scientific method on the verge of its limits.
Author(s): Michał Heller, Michał Eckstein, Sebastian Szybka
Edition: 1
Publisher: Copernicus Center PRESS
Year: 2014
Language: English
Pages: 457
City: Krakow
Table of Contents
Michał Eckstein, Michael Heller, Sebastian J. Szybka
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Part I
General Relativity and Cosmology
Manuel Hohmann
Observer dependent geometries . . . . . . . . . . . . . . . . . . . . . 13
Krzysztof Drachal &Wiesław Sasin
Classi_cation of classical singularities: a di_erential spaces approach . . 57
Jacek Gruszczak
The smooth beginning of the Universe . . . . . . . . . . . . . . . . . . 69
Mariusz P. Dabrowski
Are singularities the limits of cosmology? . . . . . . . . . . . . . . . . . 101
Boudewijn F. Roukema
Simplicity in cosmology: add virialisation, remove _, keep classical GR . 119
AndrzejWoszczyna & Zdzisław A. Golda
Computer algebra tests physical theories:
the case of relativistic astrophysics . . . . . . . . . . . . . . . . . . . . 127
Sebastian J. Szybka
On gravitational interactions between two bodies . . . . . . . . . . . . 137
Quantum Geometries
Marek Kus
Geometry of quantum correlations . . . . . . . . . . . . . . . . . . . . 155
Jordan François, Serge Lazzarini & Thierry Masson
Gauge _eld theories: various mathematical approaches . . . . . . . . . 177
Harald Grosse & RaimarWulkenhaar
Towards a construction of a quantum _eld theory in four dimensions . 227
Mairi Sakellariadou
Unweaving the fabric of the Universe:
the interplay between mathematics and physics . . . . . . . . . . . . . 259
Jerzy Lukierski
Quantum gravity models – a brief conceptual summary . . . . . . . . . 277
Andrzej Sitarz
Pointless geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Nicolas Franco &Michał Eckstein
Noncommutative geometry, Lorentzian structures and causality . . . . 315
Michael Heller & Dominique Lambert
Ontology and noncommutative geometry . . . . . . . . . . . . . . . . 341
Part III
Overviews
Shahn Majid
The self-representing Universe . . . . . . . . . . . . . . . . . . . . . . . 357
Malcolm A.H. MacCallum
Re_ections on the geometrization of physics . . . . . . . . . . . . . . . 389
Bernard Carr
Metacosmology and the limits of science . . . . . . . . . . . . . . . . . 407
Jerzy Kowalski-Glikman
The price for mathematics . . . . . . . . . . . . . . . . . . . . . . . . . 433
Michael Heller
The _eld of rationality and category theory . . . . . . . . . . . . . . . . 441
