The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction - the direct quantisation of Einstein's general theory of relativity and string theory - are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that (...) a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantisation of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantisation, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centres around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantisation of black holes, quantum cosmology, the indications of a discrete structure of spacetime, and the origin of irreversibility. This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science. (shrink)

The compact and, with \ M\, very massive object located at the center of the Milky Way is currently the very best candidate for a supermassive black hole in our immediate vicinity. The strongest evidence for this is provided by measurements of stellar orbits, variable X-ray emission, and strongly variable polarized near-infrared emission from the location of the radio source Sagittarius A* in the middle of the central stellar cluster. Simultaneous near-infrared and X-ray observations of SgrA* have revealed insights into (...) the emission mechanisms responsible for the powerful near-infrared and X-ray flares from within a few tens to one hundred Schwarzschild radii of such a putative SMBH. If SgrA* is indeed a SMBH it will, in projection onto the sky, have the largest event horizon and will certainly be the first and most important target for very long baseline interferometry observations currently being prepared by the event horizon telescope. These observations in combination with the infrared interferometry experiment GRAVITY at the very large telescope interferometer and other experiments across the electromagnetic spectrum might yield proof for the presence of a black hole at the center of the Milky Way. The large body of evidence continues to discriminate the identification of SgrA* as a SMBH from alternative possibilities. It is, however, unclear when the ever mounting evidence for SgrA* being associated with a SMBH will suffice as a convincing proof. Additional compelling evidence may come from future gravitational wave observatories. This manuscript reviews the observational facts, theoretical grounds and conceptual aspects for the case of SgrA* being a black hole. We treat theory and observations in the framework of the philosophical discussions about “realism and underdetermination”, as this line of arguments allows us to describe the situation in observational astrophysics with respect to supermassive black holes. Questions concerning the existence of supermassive black holes and in particular SgrA* are discussed using causation as an indispensable element. We show that the results of our investigation are convincingly mapped out by this combination of concepts. (shrink)

Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a “problem of time”. In my essay, I investigate those consequences for the concept of time that may be drawn without a detailed knowledge of quantum gravity. The only assumptions are the experimentally supported universality of the linear structure of quantum theory and the recovery of general relativity in the classical limit. Among the consequences (...) are the fundamental timelessness of quantum gravity, the approximate nature of a semiclassical time, and the correlation of entropy with the size of the Universe. (shrink)

I argue that quantum theory can, and in fact must, be applied to the Universe as a whole. After a general introduction, I discuss two concepts that are essential for my chain of arguments: the universality of quantum theory and the emergence of classical behaviors by decoherence. A further motivation is given by the open problem of quantum gravity. I then present the main ingredients of quantum cosmology and discuss their relevance for the interpretation of quantum theory. I end with (...) some brief epistemological remarks. (shrink)

A unique description of the phenomena that arise from the interaction between quantum systems and their environment. Because of the novel character of the approach discussed, the book addresses scientists from all fields of physics and related disciplines as well as students of physics.

I address the question whether the wave function in quantum theory exists as a real quantity or not. For this purpose, I discuss the essentials of the quantum formalism and emphasize the central role of the superposition principle. I then explain the measurement problem and discuss the process of decoherence. Finally, I address the special features that the quantization of gravity brings into the game. From all of this I conclude that the wave function really exists, that is, it is (...) a real feature of Nature. (shrink)

Die Aufstellung einer vereinheitlichten Theorie der Naturbeschreibung gehört zu den bisher unerfüllten Wünschen der modernen Physik. In meinem Beitrag schildere ich die Gründe, die für die Existenz einer solchen Theorie sprechen und bespreche den gegenwärtigen Stand der Suche. Eine fundamentale Rolle spielt hierbei die Vereinigung von Gravitation und Quantentheorie.

Vom 30. Mai bis 1. Juni 1963 fand an der Cornell-Universität eine kleine Tagung zur Natur der Zeit statt, ausgerichtet von den aus Wien stammenden Astrophysikern Hermann Bondi und Thomas Gold. Kurt Gödel war nicht anwesend. Dabei hatte der berühmte Mathematiker etwa 15 Jahre zuvor Arbeiten veröffentlicht, die ganz wesentlich und weitreichend mit dem Begriff der Zeit zu tun hatten.

From 30 May to 1 June Cornell University hosted a small conference on the nature of time, organised by the originally Viennese astro-physicists Hermann Bondi and Thomas Gold. Kurt Gödel did not attend, although roughly 15 years earlier the famous mathematician had made a significant contribution to this field.