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Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…
This is an informal review of the formulation of canonical general relativity and of its implications for quantum gravity; the various versions are compared, both in the continuum and in a discretized approximation suggested by Regge…
Theories based on General Relativity or Quantum Mechanics have taken a leading position in macroscopic and microscopic Physics, but fail when used in the other extremity. Thus, we try to establish a new structure of united theory based on…
Although General Relativity (GR) is a very successful theory of gravity, it cannot explain every observational phenomenon. People have tried many kinds of modified gravity theory to explain these phenomena which GR cannot explain very well,…
The Principle of Relativity has so far been understood as the {\it covariance} of laws of Physics with respect to a general class of reference frame transformations. That relativity, however, has only been expressed with the help of {\it…
We derive the pure spin connection and constraint-free BF formulations of real four-dimensional Lorentzian vacuum General Relativity. In contrast to the existing complex formulations, an important advantage is that they do not require the…
A local conception is proposed to reconcile quantum theory with general relativity, which allows one to avoid some difficulties --- as e.g. vacuum catastrophe --- of the global approach.
This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the fact that the quantum theory is based on…
Relativistic mechanics on an arbitrary manifold is formulated in the terms of jets of its one-dimensional submanifolds. A generic relativistic Lagrangian is constructed. Relativistic mechanics on a pseudo-Riemannian manifold is particularly…
Currently, string theory represents the only advanced approach to a unification of all interactions, including gravity. In spite of the more than thirty years of its existence it did not make any empirically testable predictions. And it is…
The high accuracy of modern space astrometry requires the use of General Relativity to model the propagation of stellar light through the gravitational field encountered from a source to a given observer inside the Solar System. In this…
A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta…
Theory of Relativity (Special and General) is one of the most influential theories of the 20th century and has changed the way we view the world. It is part of many undergraduate curriculums and it is often suggested that it should be…
We show that the local and deterministic mode of description is not only in conflict with the quantum theory, but also with relativity. We argue that elementary relativistic properties of spacetime lead to the emergence of a…
The problem of the referring of space and time relationships between physical objects in a curved space-time is discussed. The basic notions of column and weak column that could constitute the basis for consistent general relativistic…
Post-relativistic gravity is a hidden variable theory for general relativity. It introduces the pre-relativistic notions absolute space, absolute time, and ether as hidden variables into general relativity. Evolution is defined by the…
The notion of ``fundamental constant'' is heavily theory-laden. A natural, fairly precise formulation is possible in the context of the standard model (here defined to include gravity). Some fundamental constants have profound geometric…
String theory has been the dominating research field in theoretical physics during the last decades. Despite the considerable time elapse, no new testable predictions have been derived by string theorists and it is understandable that…
The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion…
It is shown that Einstein gravity in four dimensions with small cosmological constant and small extra dimensions can be obtained by spontaneous compactification of Lovelock gravity in vacuum. Assuming that the extra dimensions are compact…