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Glashow and Cohen claim that many results of special theory of relativity (SR) like time dilation, relativistic velocity addition, etc, can be explained by using certain proper subgroups, of the Lorentz group, which collectively form the…
We present a relativistic space-time diagram that displays in true magnitudes the readings (daytimes) of two inertial reference frames clocks. One reference frame is the rest frame for one clock. This diagram shows that two events…
In homogeneous isotropic turbulence, slender rods are known to align with the Lagrangian stretching direction. However, how the degree of alignment depends on the aspect ratio of the rod is not understood. Moreover, many flows of practical…
Contextuality is a central property in comparative analysis of classical, quantum, and supercorrelated systems. We examine and compare two well-motivated approaches to contextuality. One approach ("contextuality-by-default") is based on the…
Let us have in S^2, R^2 or H^2 a pair of convex bodies, for S^2 different from S^2, such that the intersections of any congruent copies of them are centrally symmetric. Then our bodies are congruent circles. If the intersections of any…
A gaze-fixating robot perceives distance to the fixated object and relative positions of surrounding objects immediately, accurately, and robustly. We show how fixation, which is the act of looking at one object while moving, exploits…
This paper is a brief overview of a more extensive article recently published in Found. Phys. Lett. [2]. Apparent disagreement with experiment as well as internal inconsistencies found in the traditional analysis of relativistically…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
For a fixed set $X$, an arbitrary \textit{weight structure} $d \in [0,\infty]^{X \times X}$ can be interpreted as a distance assignment between pairs of points on $X$. Restrictions (i.e. \textit{metric axioms}) on the behaviour of any such…
In this paper I argue for a reassessment of special relativity. The fundamental theory of relativity applicable in this Universe has to be consistent with the existence of the massive Universe, and with the effects of its gravitational…
According to Aristotle "time is the number of change with respect to the before and after". That's certainly a vague concept, but at the same time it's both simple and satisfying from a philosophical point of view: things do not change…
Angular equivalence is introduced and shown to be an equivalence relation among the norms on a fixed real vector space. It is a finer notion than the usual (topological) notion of norm equivalence. Angularly equivalent norms share certain…
Conformal Ricci and conformal matter collineations for the combination of two perfect fluids in General Relativity are investigated. We study the existence of timelike and spacelike conformal Ricci and matter collineations by introducing…
Continuous clocks, i.e. the clocks that measure time in a continuous manner, are regarded as an essential component of sensing technology. Precision and recurrence time are two basic features of continuous clocks. In this paper, in the…
The kinematics of particles refer to events and tangent vectors, while that of waves refer to dual gradient planes. Special relativity [1-3] applies to both objects alike. Here we show that spacetime exchange symmetry [7] implicit in the…
Relativistic kinematics is usually considered only as a manifestation of pseudo-Euclidean (Lorentzian) geometry of space-time. However, as it is explicitly stated in General Relativity, the geometry itself depends on dynamics, specifically,…
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
We illustrate the various ways in which the algebraic framework of noncommutative geometry naturally captures the short-distance spacetime properties of string theory. We describe the noncommutative spacetime constructed from a vertex…
Barbour's formulation of Mach's principle requires a theory of gravity to implement local relativity of clocks, local relativity of rods and spatial covariance. It turns out that relativity of clocks and rods are mutually exclusive. General…
A fundamental description of time can be consistent not only with the usual monotonic behavior but also with a periodic physical clock variable, coupled to the degrees of freedom of a system evolving in time. Generically, one would in fact…