Related papers: Special Relativity and its Newtonian Limit from a …
Symmetries and transformations are explored in the framework of entropic quantum dynamics. Two conditions arise that are required for any transformation to qualify as a symmetry. The heart of this work lies in the application of these…
Classical gravity can be described as a relational dynamical system without ever appealing to spacetime or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles…
In this work, we use real quaternions and the basic concept of the final speed of light in an attempt to enhance the standard description of special relativity. First, we demonstrate that it is possible to introduce a quaternion time domain…
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
Solutions of vacuum Einstein's field equations describing uniformly accelerated particles or black holes belong to the class of boost-rotation symmetric spacetimes. They are the only explicit solutions known which represent moving finite…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
The book is based largely on the author's researches presented at conferences in the period 1992 onwards. It is a historically based exposition and an extension of the hyperbolic version of special relativity first proposed by Vari\'cak…
We present a mathematical model for a physical theory that is compatible with Einstein's Special Relativity Theory. Our model consists of three pseudo-complex dimensions, representing three real dimensions of space, dual to what could be…
A Newtonian approach to quantum gravity is studied. At least for weak gravitational fields it should be a valid approximation. Such an approach could be used to point out problems and prospects inherent in a more exact theory of quantum…
We lay down the foundations of particle dynamics in mechanical theories that satisfy the relativity principle and whose kinematics can be formulated employing reference frames of the type usually adopted in special relativity. Such…
We propose an approximation to general relativity that captures the main gravitational effects of dynamical importance in supernovae. The conceptual link between this formalism and the Newtonian limit is such that it could likely be…
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by…
In order to avoid the difficulties encountered by relativistic quantum theory of single particles, we pursue a deductive development of the theory from physical principles, without canonical quantization, by making use of group-theoretical…
Solutions of the sourceless Einstein's equation with weak and strong cosmological constants are discussed by using In\"on\"u-Wigner contractions of the de Sitter groups and spaces. The more usual case corresponds to a weak…
Earlier, we had presented \cite{heuristic} heuristic arguments to show that a {\em natural unification} of the ideas of the quantum theory and those underlying the general principle of relativity is achievable by way of the measure theory…
Based on a tentative interpretation of gravity as a pressure force, a scalar theory of gravity was previously investigated. It assumes gravitational contraction (dilation) of space (time) standards. In the static case, the same Newton law…
The conceptual definition and understanding of the nature of time, both qualitatively and quantitatively is of the utmost difficulty and importance, and plays a fundamental role in physics. Physical systems seem to evolve in paths of…
With special relativity, we seem to be facing a conundrum. It is a very well-tested theory; in this way, the Minkowski spacetime must be "capturing" essential features of space and time. However, its geometry seems to be incompatible with…
Using the differential calculus on discrete group, we study the general relativity in the space-time which is the product of a four dimensional manifold by a two-point space. We generalize the usual concept of frame and connection in our…
In this review, we have reached from the most basic definitions in the theory of groups, group structures, etc. to representation theory and irreducible representations of the Poincar'e group. Also, we tried to get a more comprehensible…