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In the frame of multifractal theory of time and space (in this model our universe is consisting of real time and space fields and is the multifractal universe) in the works [1]-[16] some problems were analyzed: how the fractional dimensions…
In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate…
There is now overwhelming observational evidence that our Universe is accelerating in its expansion. I discuss how modified gravitational models can provide an explanation for this observed late-time cosmic acceleration. We consider…
What does it mean to ``add'' velocities relativistically -- clarification of the conceptual problems, new derivations of the related formulas, and identification of the source of the non-associativity of the standard vector version of the…
A challenge in teaching about special relativity is that a number of the theory's effects are at odds with the intuition of classical physics, as well as student's everyday experience. The relativity of simultaneity, time dilation and…
In this methodological note we discuss some details and peculiarities of the cosmic expansion as viewed by a realistic observer. We show that the velocity $v_\Theta$ related to a change (measured by observer's clock) of the angular…
This paper presents an approach to the creation of a variant of Extended Special Relativity that takes into consideration the existence of limiting relativistically invariant quantities (Planck parameters). It shows the possibility of…
In this contribution we assess the current experimental status of Special and General Relativity. Particular emphasis is put on putative extensions of these theories and on how these could be detected experimentally.
The acceleration of a light buoyant object in a fluid is analyzed. Misconceptions about the magnitude of that acceleration are briefly described and refuted. The notion of the added mass is explained and the added mass is computed for an…
There are three goals of this thesis. First: to present a concise yet accessible description of basic mathematical logic and model theory. Second: to develop an axiomatization of special relativity using only two undefined predicates.…
The discovery that the cosmic expansion is accelerating has been followed by an intense theoretical and experimental response in physics and astronomy. The discovery implies that our most basic notions about how gravity work are violated on…
In this paper Einstein's field equations, for static spherically symmetric perfect fluid models with a linear barotropic equation of state, are recast into a 3-dimensional regular system of ordinary differential equations on a compact state…
Astronomers measure distances to faraway galaxies and their velocities. They do that in order to determine the expansion rate of the Universe. In Part I of these lectures the foundations of the theory of the expansion of the Universe was…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
This paper constitutes a background to the paper 'Quantum mechanics as "space-time statistical mechanics"?', arXiv:quant-ph/0501133, presented previously by the author. But it is also a free-standing and self-contained paper. The purpose of…
We consider a Hubble expansion law modified in the infra-red by distance-dependent terms, and attempt to enforce homogeneity upon it. As a warm-up, we re-derive the basic kinematics of a Friedman Robertson Walker universe without using…
The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…
We consider the linear kinematics of large-scale peculiar motions in a perturbed Friedmann universe. In so doing, we take the viewpoint of the "real" observers that move along with the peculiar flow, relative to the smooth Hubble expansion.…
The paper offers general technical facts on the kinematics of a moving continuum involved in research on robotic following of flexible extended objects.
General relativistic corrections to the expansion rate of the Universe arise when the Einstein equations are averaged over a spatial volume in a locally inhomogeneous cosmology. It has been suggested that they may contribute to the observed…