Related papers: Coll Positioning systems: a two-dimensional approa…
If a clock, mathematically modeled by a parametrized timelike curve in a general-relativistic spacetime, is given, the radar method assigns a time and a distance to every event which is sufficiently close to the clock. Several geometric…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
This talk discusses various aspects of the structure of space-time presenting mechanisms leading to the explanation of the "rigidity" of the manifold and to the emergence of time, i.e. of the Lorentzian signature. The proposed ingredient is…
We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of…
A general approach to the problem of positioning by means of pulsars or other pulsating sources located at infinity is described. The counting of the pulses for a set of different sources whose positions in the sky and periods are assumed…
The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important…
In transformer architectures, position encoding primarily provides a sense of sequence for input tokens. While the original transformer paper's method has shown satisfactory results in general language processing tasks, there have been new…
Starting with two light clocks to derive time dilation expression, as many textbooks do, and then adding a third one, we work on relativistic spacetime coordinates relations for some simple events as emission, reflection and return of light…
Recent developments in fundamental physics (in theory as well as in technology) provide novel capabilities for geodetic applications such as refined observations of the Earth`s gravity field. We will focus on two new concepts: one applies…
A dual foliation treatment of General Relativity is presented. The basic idea of the construction is to consider two foliations of a spacetime by spacelike hypersurfaces and relate the two geometries. The treatment is expected to be useful…
Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring…
A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…
An orbiting `photon clock' is proposed to test directly the relativity of simultaneity effect of special relativity. This is done by exchanging microwave signals between two satellites in low Earth orbit carrying clocks that have previously…
The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system,…
Future lunar missions will depend on an internationally agreed upon timescale that remains accurate under the Moon's unique gravitational environment and its orbital dynamics. This thesis investigates the proposed Lunar Coordinate Time…
The advent of novel measurement instrumentation can lead to paradigm shifts in scientific research. Optical atomic clocks, due to their unprecedented stability and uncertainty, are already being used to test physical theories and herald a…
Mass redistribution on Earth due to dynamic processes such as ice melting and sea level rise leads to a changing gravitational field, observable by geodetic techniques. Monitoring this change over time allows us to learn more about our…
A natural two-metric formalism, generated by the world function of the space-time, is used. This circumstance admits one to localize the relative gravitational field, which is described by a tensor.
Several local elliptic coordinates are used to build a new polyelliptic coordinate system which is orthogonal and admits the separation of variables. Such coordinate systems can give the exact solutions of some unsolved problems in quantum…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…