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Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation…
Contemporary relativity theory is restricted in two points: (1) a use of the Riemannian space-time geometry and (2) a use of inadequate (nonrelativistic) concepts. Reasons of these restrictions are analysed in [1]. Eliminating these…
The model of a stationary universe and the notion of local times presented in [10] are reviewed with some alternative formulation of the consistent unification of the Riemannian and Euclidean geometries of general relativity and quantum…
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 pedagogical description of a simple ungeometrical approach to General Relativity is given, which follows the pattern of well understood field theories, such as electrodynamics. This leads quickly to most of the important weak field…
Minkowski's concept of a four-dimensional physical space is a central paradigm of modern physics. The three-dimensional Maxwellian electrodynamics is uniquely generalized to the covariant four-dimensional form. Is the (1+3) decomposition of…
We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized…
We propose a new classical theory of gravity which is based on the principle of equivalence and assumption that gravity, similarly to electrodynamics, is described by a vector field in Minkowski space-time. We show that such assumptions…
Space time cube representation is an information visualization technique where spatiotemporal data points are mapped into a cube. Fast and correct analysis of such information is important in for instance geospatial and social visualization…
We present a deductive theory of space-time which is realistic, objective, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective because it can be formulated…
We highlight the correspondence between one-dimensional Lorentz transformations, which relate events observed from two distinct inertial reference frames, and ray transfer transformations in Gaussian optics. Specifically, we identify…
We consider the timelike minimal surface problem in Minkowski spacetimes and show local and global existence of such surfaces having arbitrary dimension $\geq 2$ and arbitrary co-dimension, provided they are initially close to a flat plane.
Special Relativity is often seen as a conceptually difficult topic, which in turn is difficult to effectively teach. This work focuses on the role of visualizations as a tool in teaching Special Relativity at the secondary or university…
We discuss the most elementary properties of the hyperbolic trigonometry and show how they can be exploited to get a simple, albeit interesting, geometrical interpretation of the special relativity. It yields indeed a straightforword…
The state-of-the-art physics consists of two irreconcilable branches, i.e., the quantum theory and the general relativity, which work well in their own territories, independently. However, what are quantum and spacetime after all? The key…
Recent advances in observational cosmology are changing the way we view the nature of time. In general relativity, the freedom in choosing a time hypersurface has hampered the implementation of the theory. Fortunately, Hamilton-Jacobi…
An approach to special relativity is outlined which emphasizes the wave and field mechanisms which physically produce the relativistic effects, with the goal of making them seem more natural to students by connecting more explicitly with…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
In asymptotically Minkowski space-times, one finds a surprisingly rich interplay between geometry and physics in both the classical and quantum regimes. On the mathematical side it involves null geometry, infinite dimensional groups,…
In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is…