Related papers: Relativistic Distance
We motivate and construct a mathematical theory for the separation of space and time in general relativity. The formalism only requires a single observer and an optional choice of reference frame at each instant. As the splitting is done…
In this note, we discuss the significance of the general principle of relativity for a physical theory that abandons the newtonian concept of force and, hence, uses an entirely different conception for the ``cause'' behind motions of…
Despite the extraordinary successes the two great bastions of $20^{th}$ century science (Quantum Theory and General Relativity) are troubled with serious conceptual and mathematical difficulties. As a result, further growth of fundamental…
Rovelli's relational interpretation of quantum mechanics tells us that the description of a system in the formalism of quantum mechanics is not an absolute, but it is relative to the observer itself. The interpretation goes further and…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
In an apparently unexplored region of relativistic spacetime, a simple thought experiment demonstrates that conjoined Lorentz transformations predict a proper clock at rest will run backwards and that prediction violates the logical…
Recent astronomical observations verify the new scenario resulting from new conservation laws and a new relativity principle fixed either by dual properties of light or by new gravitational (G) tests and the Einstein's equivalence…
The high accuracy of modern space astrometry requires the use of General Relativity to model the propagation of stellar light through the gravitational field encountered from a source to a given observer inside the Solar System. In this…
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…
We note that Einstein's relativistic Doppler formula presents a strange aspect. For incident light received under a fixed non zero angle, the Doppler shift will change from blueshift to redshift (or vice-versa) for some critical relative…
Let P_1 and P_2 be two sets of points in the plane, so that P_1 is contained in a line L_1, P_2 is contained in a line L_2, and L_1 and L_2 are neither parallel nor orthogonal. Then the number of distinct distances determined by the pairs…
Order of magnitude reasoning - reasoning by rough comparisons of the sizes of quantities - is often called 'back of the envelope calculation', with the implication that the calculations are quick though approximate. This paper exhibits an…
In the present paper we investigate the Gromov--Hausdorff distances between a bounded metric space $X$ and so called simplex, i.e., a metric space all whose non-zero distances are the same. In the case when the simplex's cardinality does…
Nature succeeds in accelerating extended and massive objects to relativistic velocities. Jets in Active Galactic Nuclei and in galactic superluminal sources and gamma-ray bursts fireballs have bulk Lorentz factors from a few to several…
According to the Special Theory of Relativity, there should be no resting frame in our universe. Such an assumption, however, could be in conflict with the Standard Model of cosmology today, which regards the vacuum not as an empty space.…
In this paper, we study the distance problem in the setting of finite p-adic rings. In odd dimensions, our results are essentially sharp. In even dimensions, we clarify the conjecture and provide examples to support it. Surprisingly,…
We show that there exists an absolute positive constant $b (\geq \frac{1}{48})$ so that any set of $n$ points in $\mathbb{R}^d$ that is $d$-dimensional determines at least $bdn$ lines with pairwise distinct directions. As a consequence we…
I review the current state of determinations of the Hubble constant, which gives the length scale of the Universe by relating the expansion velocity of objects to their distance. There are two broad categories of measurements. The first…
Satellite conjunctions involving "near misses" of space objects are becoming increasingly likely. One approach to risk analysis for them involves the computation of the collision probability, but this has been regarded as having some…
Uniform fields are one of the simplest and most pedagogically useful examples in introductory courses on electrostatics or Newtonian gravity. In general relativity there have been several proposals as to what constitutes a uniform field. In…