Related papers: 25 years ago: the official farewell to the meter

Explicit expressions and computational approaches are given for the Fortet-Mourier distance between a positively weighted sum of Dirac measures on a metric space and a positive finite Borel measure. Explicit expressions are given for the…

This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…

The most powerful tool for measuring distances within our Galaxy is the annual parallax. We carried out phase-referencing VLBI observations of H$_{2}$O masers in the star forming region W3(OH) with respect to the extragalactic continuum…

Since its discovery in 1993, we witness an intensive theoretical and experimental effort centered on teleportation. Very recently it was claimed in the press that ``quantum teleportation has been achieved in the laboratory'' (T. Sudbery,…

The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…

A test is suggested for whether the obtaining of certain information, and then deleting it too quickly to be retained, constitutes a quantum measurement of that information.

We study the Wasserstein (or earthmover) metric on the space $P(X)$ of probability measures on a metric space $X$. We show that, if a finite metric space $X$ embeds stochastically with distortion $D$ in a family of finite metric trees, then…

The Hipparcos satellite was launched in 1989. It was the first, and remains to date the only, attempt at performing large-scale astrometric measurements from space. Hipparcos marked a fundamentally new approach to the field of astrometry,…

This is a partial account of the fascinating history of Distance Geometry. We make no claim to completeness, but we do promise a dazzling display of beautiful, elementary mathematics. We prove Heron's formula, Cauchy's theorem on the…

A masure (a.k.a affine ordered hovel) I is a generalization of the Bruhat-Tits building that is associated to a split Kac-Moody group G over a non-archimedean local field. This is a union of affine spaces called apartments. When G is a…

The present paper deals with the life and some aspects of the scientific contributions of the mathematician Ren\'e Gateaux, killed during World War 1 at the age of 25. Though he died very young, he left interesting results in functional…

In the context of earlier work, we investigate the emergence of a "distance" in the physical world. For this we consider a Cantor ternary like process, but much more general: properties like perfectness and disconnectedness are not invoked,…

We present a 0.16% precise and 0.27% accurate determination of R0, the distance to the Galactic Center. Our measurement uses the star S2 on its 16-year orbit around the massive black hole Sgr A* that we followed astrometrically and…

In 1955, an international conference took place in Berne at which the state of relativity theory and its possible generalizations were presented and critically discussed. I review the most important contributions to that conference and put…

The revised International System of Units (SI), expected to be approved late in 2018, has implications for physics pedagogy; the ampere definition which dates from 1948 will be replaced by a definition that fixes the numerical value of the…

This article deals with empty spacetime and the question of its physical reality. By "empty spacetime" we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric…

In this short review I present the status of the global 21-cm signal detected by EDGES in March 2018. It is organized in three parts. First, I present the EDGES experiment and the fitting procedure used by the collaboration to extract the…

21cm Intensity Mapping (IM) has been proposed about 15 years ago as a cost effective method to carry out cosmological surveys and to map the 3D distribution of matter in the universe, over a large range of post EoR redshifts, from z=0 to…

We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…

We obtained two astronomical values, the Earth-Venus distance and Venus diameter, by means of a geometrical treatment of photos taken of Venus transit in June of 2012. Here we presented the static and translational modelsthat were…