Related papers: Kurt Goedel and His Universe
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
The present Editorial introduces the Special Issue dedicated by the journal Universe to the General Theory of Relativity, the beautiful theory of gravitation of Einstein, a century after its birth. It reviews some of its key features in a…
With his General Theory of Relativity, Albert Einstein produced a revolution in our conception of reality and of the knowledge we can obtain from it. This revolution can be viewed from philosophy as leading to one of the great paradigms in…
Detlef D\"urr (1951-2021) was a theoretical and mathematical physicist who worked particularly on the foundations of quantum mechanics, electromagnetism, and statistical mechanics. This piece is a rather personal look back at him and his…
In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.
The literature dealing with G\"{o}del's legacy is largely preoccupied with challenging his philosophical views, regarding them as outdated. We believe that such an approach prevents us from seeing G\"{o}del's views in the right light and…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
The standard model of modern cosmology, which is based on the Friedmann-Lema\^itre-Robertson-Walker metric, allows the definition of an absolute time. However, there exist (cosmological) models consistent with the theory of general…
The life and accomplishments of Grete Hermann are described. During the early twentieth century, she worked in physics, mathematics, philosophy and education. Her most notable accomplishments in physics were in the interpretation of quantum…
I discuss a memorandum entitled " A True state of the Case and Controversy between Sir Isaak Newton and Dr. Robert Hooke as the Priority of that Noble Hypothesis of motion of ye Planets about ye Sun as their Centers", where Hooke summarizes…
Despite being known for his pioneering work on chaotic unpredictability, the key discovery at the core of meteorologist Ed Lorenz's work is the link between space-time calculus and state-space fractal geometry. Indeed, properties of…
The analytic hyperbolic geometric viewpoint of Einstein's special theory of relativity is presented.
The set-theoretical model of Goedel's system T is not fully abstract. We also briefly discuss fully abstract models of system T.
In this work, the classical Godel solution from general relativity is extended into the framework of modified gravity theories based on non-metricity $Q$ and the trace of the energy-momentum tensor $T$ in the context of $f(Q,T)$ gravity.…
We compare and contrast the different points of view of rotation in general relativity, put forward by Mach, Thirring and Lense, and Goedel. Our analysis relies on two tools: (i) the Sagnac effect which allows us to measure rotations of a…
An odd look at "standard" physics (Galileo, Newton, Einstein, Dirac) leading to a radical change of our concept of inertial motion and to new heuristic approaches of gravitation and the cosmological constant.
a 10-page biography of Raoul Bott followed by a 25-page discussion of his major papers
A conservative extension of general relativity by integrable Weyl geometry is formulated, and a new class of cosmological models ({\em Weyl universes}) is introduced and studied. A short discussion of how these new models behave in the…
This is an introductory set of lecture notes on quantum cosmology, given in 1995 to an audience with interests ranging from astronomy to particle physics. Topics covered: 1. Introduction: 1.1 Quantum cosmology and quantum gravity; 1.2 A…
From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental role of geometric imagination in…