Related papers: How to measure spatial distances?
We develop the spacetime approach to gravitational lensing by spherically symmetric perturbations of flat, cosmological constant-dominated Friedman-Robertson-Walker metrics. The geodesics of the spacetime are expressed as integral…
The performance of optical clocks has strongly progressed in recent years, and accuracies and instabilities of 1 part in 10^18 are expected in the near future. The operation of optical clocks in space provides new scientific and…
Overview of the determination of astronomical distances from a metrological standpoint. Distances are considered from the Solar System (planetary distances) to extragalactic distances, with a special emphasis on the fundamental step of the…
The geometric concept of geodesic completeness depends on the choice of the metric field or "metric frame". We develop a frame-invariant concept of "generalised geodesic completeness" or "time completeness". It is based on the notion of…
Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…
We consider the geometry of spacetime based on a non-metric, Finslerian, length measure, which, in terms of physics, represents a generalized clock. Our defnition of Finsler spacetimes ensure a well defined notion of causality, a precise…
Separate constituents of extended systems measure proper-times on different world-lines. Relating and comparing proper-time measurements along any two such world-lines requires that common simultaneity be possible, which in turn implies…
This paper is about similarity between objects that can be represented as points in metric measure spaces. A metric measure space is a metric space that is also equipped with a measure. For example, a network with distances between its…
Some ideas aimed to understand that time is one-dimensional are briefly reviewed. Some attempts to construct theories in varieties with more spatial and temporal components are presented. It is discussed, from the epistemological point of…
The geodesic deviation equation (GDE) describes the tendency of objects to accelerate towards or away from each other due to spacetime curvature. The GDE assumes that nearby geodesics have a small rate of separation, which is formally…
Classical geometry can be described either in terms of a metric tensor $g_{ab}(x)$ or in terms of the geodesic distance $\sigma^2(x,x')$. Recent work, however, has shown that the geodesic distance is better suited to describe the quantum…
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…
Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate…
Einstein's Equivalence Principle is used with the electromagnetic spectrum to translate meters and seconds into radians and seconds. Based on a unique geometric relationship, a new transformation of velocities and a changed Lorentz…
We discuss the problem of how to calculate the distance between two cosmological objects given their redshifts and angular separation on the sky. Although of a fundamental nature, this problem and its solution seem to lack a detailed…
The existence of a global time is often taken for granted but should instead be considered as a matter of investigation. By using the tools of global Lorentzian geometry I show that, under physically reasonable conditions, the impossibility…
This paper discusses the extent to which one can determine the space-time metric from a knowledge of a certain subset of the (unparametrised) geodesics of its Levi-Civita connection, that is, from the experimental evidence of the…
Astronomers measure cosmic distances to objects beyond our own galaxy using standard candles: objects of known intrinsic brightness, whose apparent brightnesses in the sky are then taken as an indication of their distances from the…
Despite the growing popularity of human mobility studies that collect GPS location data, the problem of determining the minimum required length of GPS monitoring has not been addressed in the current statistical literature. In this paper we…
Spacetimes have conventionally been described by a global Lorentzian metric on a differentiable four-manifold. Herein we explore the possibility of spacetimes defined by a connection, which is locally but not globally Levi-Civita. The…