Related papers: Relativistic Distance
The development of both special and general relativity is accomplished in a series of 6 papers using a simple approach. The purpose is to explain the how and why of relativity to a broad public, and to be useful for students of physics by…
We investigate the representation of the geometrical information of the universe in terms of the eigenvalues of the Laplacian defined on the universe. We concentrate only on one specific problem along this line: To introduce a concept of…
The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose,…
Quantum measurement predictions are consistent with relativity for macroscopic observations, but there is no consensus on how to explain this consistency in fundamental terms. The prevailing assumption is that the relativistic structure of…
For a given real number $\alpha$, let us place the fractional parts of the points $0, \alpha, 2 \alpha,$ $ \cdots, (N-1) \alpha$ on the unit circle. These points partition the unit circle into intervals having at most three lengths, one…
We present three natural but distinct formalisations of Einstein's special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made…
Although special relativity limits the actual velocity of a particle to $c$, the velocity of light, the observed velocity need not be the same as the actual velocity as the observer is only aware of the position of a particle at the time in…
The M-relative distance, denoted by \rho_M is a generalization of the p-relative distance, which was introduced by Ren-Cang Li. We establish necessary and sufficient conditions under which \rho_M is a metric. In two special cases we derive…
Formulae for the line-of-sight and transverse comoving distances, proper motion distance, angular diameter distance, luminosity distance, k-correction, distance modulus, comoving volume, lookback time, age, and object intersection…
There are many books on the classical subject of special relativity. However, after having spent a number of years, both in relativistic engineering and research with relativity, I have come to the conclusion that there exist a place for a…
Earlier, we had presented \cite{heuristic} heuristic arguments to show that a {\em natural unification} of the ideas of the quantum theory and those underlying the general principle of relativity is achievable by way of the measure theory…
Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional…
The quantum relative entropy is frequently used as a distance measure between two quantum states, and inequalities relating it to other distance measures are important mathematical tools in many areas of quantum information theory. We have…
The new approach of the regular spacing of planetary orbits and planet mass distribution in the Solar system is considered. The relative planetary distances will be represented as the inverse composite probabilities of two discrete…
Let $\mathcal{S}$ be a finite set of integer points in $\mathbb{R}^d$, which we assume has many symmetries, and let $P\in\mathbb{R}^d$ be a fixed point. We calculate the distances from $P$ to the points in $\mathcal{S}$ and compare the…
Distance transformation is an image processing technique used for many different applications. Related to a binary image, the general idea is to determine the distance of all background points to the nearest object point (or vice versa). In…
Despite its mathematical complexity, the multiple gravitational lens can be studied in detail in every situation where a perturbative approach is possible. In this paper, we examine the caustics of a system with a lens very far from the…
By taking into account both quantum mechanical and general relativistic effects, I derive an equation that describes limitations on the measurability of space-time distances as defined by a material reference system.
Many authors noted that the principle of relativity, together with space-time symmetries, suffices to derive Lorentz-like coordinate transformations between inertial frames. These contain a free parameter, $k$, (equal to $c^{-2}$ in special…
We present a derivation of the relativistic length-contraction formula based on Lorentz space-time transformations on non-simultaneous events. Our derivation avoids the disputable story about the stationary observer and its simultaneous…