Related papers: Kurt Goedel and His Universe
A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious…
In this paper, conformal invariant gravitation, based on Weyl geometry, is considered. In addition to the gravitational and matter action integrals, the interaction between the Weyl vector (entered in Weyl geometry) and the vector,…
This review presents an introduction to Quantum Cosmology, including the mathematical methods essential to the canonical approach, some of the existing conceptual problems and the connection of the models to possible observables.
Taking a ring-theoretic perspective as our motivation, the main aim of this series is to establish a comprehensive theory of ideals in commutative quantales with an identity element. This particular article focuses on an examination of…
A recent essay [1] reminds us of how richly Boltzmann deserves to be admiringly commemorated for the originality of his ideas on the occasion of his 150th birthday. Without any doubt, the scientific community owes Boltzmann a great debt of…
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and…
A small and unsystematic selection of my favorite appearances of mathematicians and mathematics in German literature. It includes classic and romantic (Lessing, Goethe, Wezel, F. Schlegel, Kleist, Novalis, Grillparzer, Heine), modern…
We survey several generalizations of the Weyl algebra including generalized Weyl algebras, twisted generalized Weyl algebras, quantized Weyl algebras, and Bell-Rogalski algebras. Attention is paid to ring-theoretic properties,…
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.
A number of philosophers and scientists have discussed the possibility of inseparability between the subject (i.e., the observer) and the object (i.e., the observed universe). In particular, it has recently been proposed that this…
I report on recent progress in the exciting field of Numerical Relativity, with special attention to black hole horizons.
For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and…
John Bell's investigations in foundations of quantum mechanics, particle physics, and quantum field theory are recalled.
We discuss the scientific contributions of Edsger Wybe Dijkstra, his opinions and his legacy.
These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…
This paper is a greatly expanded version of a talk I gave in April 2009 at KunenFest. It describes Ken's work in algebra, particularly using automated deduction tools.
Albert Einstein's practice in physics and his philosophical positions gradually reoriented themselves from more empiricist towards rationalist viewpoints. This change accompanied his turn towards unified field theory and different…
Here the 1930's work of Milne on the relationship between the universes of relativistic cosmology and those which follow from Newtonian theory is reviewed. The extension to the case of non-zero pressure is considered also. In each case, any…
An introductory guide to mathematical cosmology is given focusing on the issue of the genericity of various important results which have been obtained during the last thirty or so years. Some of the unsolved problems along with certain new…
The aim of this set of lectures is a systematic presentation of a 1+3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic 1+3 covariant relations…