Related papers: OPERA and the GPS
A 4-dimensional relativistic positioning system for a general spacetime is constructed by using the so called "emission coordinates". The results apply in a small region around the world line of an accelerated observer carrying a Fermi…
I tell about different mathematical tool that is important in general relativity. The text of the book includes definition of geometrical object, concept of reference frame, geometry of metric-affinne manifold. Using this concept I learn…
A reference frame consists of: a reference space, a time scale and a spatial metric. The geometric structure induced by these objects in spacetime is developed. The existence of a class of spatial metrics that are rigid, have free mobility…
A reference frame in event space is a smooth field of orthonormal bases. Every reference frame is equipped by anholonomic coordinates. Using anholonomic coordinates allows to find out relative speed of two observers and appropriate Lorentz…
We introduce an operational approach to the use of pulsating sources, located at spatial infinity, for defining a relativistic positioning and navigation system, based on the use of four-dimensional bases of null four-vectors, in flat…
We generalize to higher dimension results of Birkhoff and Mather on the existence of orbits wandering in regions of instability of twist maps. This generalization is strongly inspired by the one already proposed by Mather. However, its…
Recent modern space missions deliver invaluable information about origin of our universe, physical processes in the vicinity of black holes and other exotic astrophysical objects, stellar dynamics of our galaxy, etc. On the other hand,…
We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the…
A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to…
IAU 2000 resolutions on the reference frames set up a solid theoretical foundation for implementing general relativity in astronomical data processing algorithms and for unambiguous interpretation of measured relativistic effects. We…
Adaptive Optics is a prime example of how progress in observational astronomy can be driven by technological developments. At many observatories it is now considered to be part of a standard instrumentation suite, enabling ground-based…
The notion of optical geometry, introduced more than twenty years ago as a formal tool in quantum field theory on a static background, has recently found several applications to the study of physical processes around compact objects. In…
In a recent article [1] we have explored alternative decompositions of the Lorentz transformation by adopting the synchronization convention of the target frame at the end and alternately at the outset. In this note we develop the…
Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many…
The Palatini formulation is used to develop a genuine connection theory for general relativity, in which the gravitational field is represented by a Lorentz-valued spin connection. The existence of a tetrad field, given by the Fock-Ivanenko…
I here investigate what is arguably the most significant residual challenge for the proposal of phenomenologically viable "DSR deformations" of relativistic kinematics, which concerns the description of composite particles, such as atoms.…
One of geodesy's main tasks is to determine the gravity field of the Earth. High precision clocks have the potential to provide a new tool in a global determination of the Earth's gravitational potential based on the gravitational redshift.…
A generalization of the coadjoint orbit action describes the dynamics of an observer (or instrument). We consider how this fits in with the view of observables in field theory being correlations of read-outs of instruments and show how one…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
Over the last decade of the 20th century and the first few years of the 21st, the uncertainty of atomic clocks has decreased by about two orders of magnitude, passing from the low 10^-14 to below 10^-16, in relative frequency . Space…