Related papers: Coordinate time and proper time in the GPS
In this paper we deduce a quite general formula which allows the relation of clock rates at two different space time points to be discussed. In the case of a perturbed Robertson-Walker metric, our analysis leads to an equation for the…
In this paper we establish a generally and globally valid coordinate system in curved space-time with the simultaneous hypersurface orthogonal to the time coordinate. The time coordinate can be preseted according to practical evolving…
Although the effects of solar (and lunar) gravitational potentials on the frequencies of orbiting Global Positioning System (GPS) clocks are actually no more than a few parts in 10^(15), a na\"ive calculation appears to show that such…
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…
Some authors have defended the claim that one needs to be able to define 'physical coordinate systems' and 'observables' in order to make sense of general relativity. Moreover, in Rovelli (Physical Review D, 65(4), 044017 2002), Rovelli…
The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild space-time. The results are used to construct analytic expressions for the source terms in the Regge-Wheeler and…
Clock synchronization between the ground and satellites is a fundamental issue in future quantum telecommunication, navigation, and global positioning systems. Here, we propose a scheme of near-Earth orbit satellite-based quantum clock…
In General Relativity, the rotation of a gravitating body like the Earth influences the motion of orbiting test particles or satellites in a non-Newtonian way. This causes, e.g., a precession of the orbital plane known as the Lense-Thirring…
The precision of optical atomic clocks is approaching a regime where they resolve gravitational time dilation on smaller scales than their own extensions. Hence, an accurate description of quantum clocks has to take their spatial extension…
Time delay in Schwarzschild spacetime for null and timelike signals with arbitrary velocity $v$ is studied. The total travel time $t_\mathrm{if}$ is evaluated both exactly and approximately in the weak field limit, with the result given as…
We survey the role of stable clocks in general relativity. Clock comparisons have provided important tests of the Einstein Equivalence Principle, which underlies metric gravity. These include tests of the isotropy of clock comparisons…
We show how a suitably prepared set of clocks can be used to determine all components of the gravitational field in General Relativity. We call such an experimental setup a clock compass, in analogy to the usual gravitational compass.…
We present an alternate formula for calculating gravitational time delay. We use this formula to reduce geodetic Very Long Baseline Interferometry (VLBI) data, taking into account gravitational effects within the solar system, and to test…
In order to test the Einstein gravitation theory (EGT) we compare their predictions with the measured results in the following phenomena: the perihelion advance of planets, deflection of light, radar echo delays around the Sun and an…
General relativity predicts that clocks run more slowly near massive objects. The effect is small---a clock at sea level lags behind one 1000 m above sea level by only 9.4 ns/day. Here, we demonstrate that a measurement of this effect can…
In the global positioning system (GPS) satellites, the earth-centered, earth-fixed (ECEF) reference frame is used for calculations. In the application of the theory of special relativity to GPS satellites, one must use the ECEF reference…
Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation…
This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…
Starting from the description of space-time as a curved four-dimensional manifold, null Gaussian coordinates systems as appropriate for relativistic positioning will be discussed. Different approaches and strategies will be reviewed,…
A satellite-based scheme to perform clock synchronization between ground stations spread across the globe using quantum resources was proposed in [Phys. Rev. A 107, 022615 (2023)], based on the quantum clock synchronization (QCS) protocol…