Related papers: The generally covariant meaning of space distances
The measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as non-extensibility, curvature constraints, and non-crossing become central…
Distances play important roles in cosmological observations, especially in gravitational lens systems, but there is a problem in determining distances because they are defined in terms of light propagation, which is influenced…
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…
In the standard cosmological theory one uses the Einstein concepts of space and time as were originally introduced for the special theory of relativity and the general relativity theory. According to this approach all physical quantities…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
In this paper we apply the symmetry principle in order to search for an alternative unified explanation of several cosmological puzzles such as the present stage of accelerated expansion of the Universe and the Hubble tension issue, among…
The geometric foundations of General Relativity are revisited, with particular attention to its gauge invariance, as a key to understanding the true nature of spacetime. Beyond the common image of spacetime as a deformable 'fabric' filling…
The degree to which subjects differ from each other with respect to certain properties measured by a set of variables, plays an important role in many statistical methods. For example, classification, clustering, and data visualization…
In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…
Distance covariance is a measure of dependence between two random variables that take values in two, in general different, metric spaces, see Sz\'ekely, Rizzo and Bakirov (2007) and Lyons (2013). It is known that the distance covariance,…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
The use of time--like geodesics to measure temporal distances is better justified than the use of space--like geodesics for a measurement of spatial distances. We give examples where a ''spatial distance'' cannot be appropriately determined…
We explore extensions of domain theoretic concepts, replacing transitive relations with general non-symmetric distances. These lead to a generalization of Smyth completeness which we characterize in various ways analogous to our previous…
Several recent studies have been devoted to investigating the limitations that ordinary quantum mechanics and/or quantum gravity might impose on the measurability of space-time observables. These analyses are often confined to the…
We provide a gauge-invariant theory of gravitation in the context of Weyl Integrable Space-Times. After making a brief review of the theory's postulates, we carefully define the observers' proper-time and point out its relation with…
The concept of a horizon known from general relativity describes the loss of causal connection and can be applied to non-gravitational scenarios such as out-of-equilibrium condensed-matter systems in the laboratory. This analogy facilitates…
This contribution is an introduction to the metric aspect of noncommutative geometry, with emphasize on the Moyal plane. Starting by questioning "how to define a standard meter in a space whose coordinates no longer commute?", we list…
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…
This paper defines the spacetime geometry attached with observor as vacuum geometry (it defines the idea physical measurement geometry) and the spacetime geometry attached with matter as spacetime geometry. The initial spacetime geometry…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…