Theory of gravitation theories: a no-progress report

Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore, interesting enough to deserve further investigation. From this perspective, an alternative title of the present paper could be ``why are we still unable to write a guide on how to propose viable alternatives to general relativity?''. Attempting to answer this question, it is argued here that earlier efforts to turn qualitative statements, such as the Einstein Equivalence Principle, into quantitative ones, such as the metric postulates, stand on rather shaky grounds -- probably contrary to popular belief -- as they appear to depend strongly on particular representations of the theory. This includes ambiguities in the identification of matter and gravitational fields, dependence of frequently used definitions, such as those of the stress-energy tensor or classical vacuum, on the choice of variables, etc. Various examples are discussed and possible approaches to this problem are pointed out. In the course of this study, several common misconceptions related to the various forms of the Equivalence Principle, the use of conformal frames and equivalence between theories are clarified.Comment: Invited paper in the Gravity Research Foundation 2007 special issue to be published by Int. J. Mod. Phys.

The Riddle of Gravitation

There is no doubt that both the special and general theories of relativity capture the imagination. The anti-intuitive properties of the special theory of relativity and its deep philosophical implications, the bizzare and dazzling predictions of the general theory of relativity: the curvature of spacetime, the exotic characteristics of black holes, the bewildering prospects of gravitational waves, the discovery of astronomical objects as quasers and pulsers, the expansion and the (possible) recontraction of the universe..., are all breathtaking phenomena. In this paper, we give a philosophical non-technical treatment of both the special and the general theory of relativity together with an exposition of some of the latest physical theories. We then give an outline of an axiomatic approach to relativity theories due to Andreka and Nemeti that throws light on the logical structure of both theories. This is followed by an exposition of some of the bewildering results established by Andreka and Nemeti concerning the foundations of mathematics using the notion of relativistic computers. We next give a survey on the meaning and philosophical implications of the the quantum theory and end the paper by an imaginary debate between Einstein and Neils Bohr reflecting both Einstein's and Bohr's philosophical views on the quantum world. The paper is written in a somewhat untraditional manner; there are too many footnotes. In order not to burden the reader with all the details, we have collected the more advanced material the footnotes. We think that this makes the paper easier to read and simpler to follow. The paper in full is adressed more to experts.Comment: 40 pages, LaTeX-fil

Albert Einstein's 1916 Review Article on General Relativity

The first comprehensive overview of the final version of the general theory of relativity was published by Einstein in 1916 after several expositions of preliminary versions and latest revisions of the theory in November 1915. A historical account of this review paper is given, of its prehistory, including a discussion of Einstein's collaboration with Marcel Grossmann, and of its immediate reception.Comment: 27 pages, 1 jpg imag

Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity?

Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical interpretation of their quantum analogues is ambiguous. In particular, can we assume that `quantisation commutes with reduction' and treat the promotion of these constraints to operators annihilating the wave function, according to a Dirac type procedure, as leading to a Hilbert space equivalent to that reached by quantisation of the problematic reduced space? If not, how should we interpret Hamiltonian constraints quantum mechanically? And on what basis do we assert that quantisation and reduction commute anyway? These questions will be refined and explored in the context of modern approaches to the quantisation of canonical general relativity.Comment: 18 Page