Related papers: Clarifying spatial distance measurement
This paper develops a conditional framework for understanding the emergence of measurable physical structure from a pre-metric domain. Contemporary physics provides powerful and precise descriptions of relations among already-defined…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
A metric measure space is a metric space with a Borel measure. In Gromov's theory of metric measure spaces, there are important invariants called the partial diameter and the observable diameter. We obtain the result that the partial…
In Gedankenexperiment mentioned in the title, the imprecision in space-time measurement is related to the spreading of clock's wave-function with the passage of time required for the measurement. Special relativity puts a bound on the…
We formulate a spatial extension of the Leggett-Garg inequality by considering three distant observers locally measuring a many-body system at three subsequent times. The spatial form, in particular, is specially suited to analyze…
We develop a perturbation theory for surfaces confining photons and massive particles in static spherically symmetric spacetimes in terms of two parameters: the mass-to-energy ratio and the deviation of metric functions from a given form,…
To study the processes and mechanisms of the correlation between space and time, particularly between lengths and durations in human perception, a special method (device and procedure) to conduct this experiment was designed and called LDR…
In [M. Zych et al., Nat. Commun. 2, 505 (2011)], the authors predicted that the interferometric visibility is affected by a gravitational field in way that cannot be explained without the general relativistic notion of proper time. In this…
The continuation of the Schwarzschild metric across the event horizon is almost always (in textbooks) carried out using the Kruskal-Szekeres coordinates, in terms of which the areal radius r is defined only implicitly. We argue that from a…
The Landau-Lifshitz decomposition of spacetime, or (1+3)-split, determines the three-dimensional velocity and acceleration as measured by static observers. We use these quantities to analyze the geodesic particles in Schwarzschild and Kerr…
3D scatterplots are a well-established plotting technique that can be used to represent data with three or more dimensions. On paper and computer monitors they are essentially two-dimensional projections of the three-dimensional Cartesian…
The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of…
We introduce a new method for studying length spectrum rigidity problems based on a combination of ideas from dynamical systems and geometric group theory. This allows us to compare the marked length spectrum of metrics and distance-like…
It is well known that observers will be accelerated when they approach the planets. Thus, discussing the properties of accelerating observers in the Schwarzschild space is of sense. For the sake of simplicity, we can construct these…
In the realm of target tracking, performance evaluation plays a pivotal role in the design, comparison, and analytics of trackers. Compared with the traditional trajectory composed of a set of point-estimates obtained by a tracker in the…
We consider an evaporating Schwarzschild black hole in a framework in which the spectral dimension of spacetime varies continuously from four at large distances to a number smaller than three at small distances, as suggested by various…
Two different forms of time dilation, namely, the kinematical time dilation of special relativity and gravitational red shift are coupled during observations of systems moving through a gravitational field. In the particular situation of…
We introduce in the explicit form the tetrads of arbitrary observers in spacetimes with spherical and axial symmetries. The observers confined to the equatorial plane are parametrized by the pair of functions. We apply this description in…
It is shown by very simple arguments that the observed 3+1 dimensionality of spacetime may be understood on the basis of four fundamental principles of physics namely, Causality, General Covariance, Gauge Invariance and Renormalizability.…
The geometry of a light wavefront evolving in the 3--space associated with a post-Newtonian relativistic spacetime from a flat wavefront is studied numerically by means of the ray tracing method. For a discretization of the bidimensional…