Relativistic Reference Frames Research Articles

Universal transformation of displacement operators and its application to homodyne tomography in differing relativistic reference frames

In this paper, we study how a displacement of a quantum system appears under a change of relativistic reference frame. We introduce a generic method in which a displacement operator in one reference frame can be transformed into another reference frame. It is found that, when moving between non-inertial reference frames there can be distortions of phase information, modal structure and amplitude. We analyse how these effects affect traditional homodyne detection techniques. We then develop an in principle homodyne detection scheme which is robust to these effect, called the ideal homodyne detection scheme. We then numerically compare traditional homodyne detection with this in principle method and illustrate regimes when the traditional homodyne detection schemes fail to extract full quantum information.

On a Self-Consistency Thermodynamical Criterion for Equations of the State of Gases in Relativistic Frames

More than three decades ago, Tykodi and Hummel proposed a procedure to investigate the self-consistency thermodynamical criterion for equations of the state of gases. The main criterion used by these authors consists of requiring that an equation of state must not be inconsistent with certain thermodynamical identities from the first and second laws of thermodynamics. This paper explores the possibility of another self-consistency method based on relativistic transformations of the thermodynamical variables. It is shown that the virial coefficients have to be corrected by a relativistic factor if the equation of state is considered in a moving relativistic reference frame. Some relativistic and non-relativistic equations of state are analyzed.

General relativistic observables of the GRAIL mission

We present a realization of astronomical relativistic reference frames in the Solar System and its application to the Gravity Recovery and Interior Laboratory (GRAIL) mission. We model the necessary space-time coordinate transformations for light-trip time computations and address some practical aspects of the implementation of the resulting model. We develop all the relevant relativistic coordinate transformations that are needed to describe the motion of the GRAIL spacecraft and to compute all observable quantities. We take into account major relativistic effects contributing to the dual one-way range observable, which is derived from one-way signal travel times between the two GRAIL spacecrafts. We develop a general relativistic model for this fundamental observable of GRAIL, accurate to $1\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. We develop and present a relativistic model for another key observable of this experiment, the dual one-way range rate, accurate to $1\text{ }\text{ }\ensuremath{\mu}\mathrm{m}/\mathrm{s}$. The presented formulation justifies the basic assumptions behind the design of the GRAIL mission. It may also be used to further improve the already impressive results of this lunar gravity recovery experiment after the mission is complete. Finally, we present transformation rules for frequencies and gravitational potentials and their application to GRAIL.

Accelerating relativistic reference frames in Minkowski space-time

We study accelerating relativistic reference frames in Minkowski space-time under the harmonic gauge. It is well-known that the harmonic gauge imposes constraints on the components of the metric tensor and also on the functional form of admissible coordinate transformations. These two sets of constraints are equivalent and represent the dual nature of the harmonic gauge. We explore this duality and show that the harmonic gauge allows presenting an accelerated metric in an elegant form that depends only on two harmonic potentials. It also allows reconstruction of the spatial structure of the post-Galilean coordinate transformation functions relating inertial and accelerating frames. The remaining temporal dependence of these functions together with corresponding equations of motion are determined from dynamical conditions, obtained by constructing the relativistic proper reference frame of an accelerated test particle. In this frame, the effect of external forces acting on the observer is balanced by the fictitious frame-reaction force that is needed to keep the test particle at rest with respect to the frame, conserving its relativistic linear momentum. We find that this approach is sufficient to determine all the terms of the coordinate transformation. The same method is then used to develop the inverse transformations. The resulting post-Galilean coordinate transformations extend the Poincaré group on the case of accelerating observers. We present and discuss the resulting coordinate transformations, relativistic equations of motion, and the structure of the metric tensors corresponding to the relativistic reference frames involved.

Numerical simulations of laser wakefield accelerators in optimal Lorentz frames

The simulation of laser wakefield accelerators with particle-in-cell codes in relativistic reference frames is described, with emphasis on the computational speed-ups, which may potentially exceed three orders of magnitude in comparison with laboratory frame configurations. The initialization of laboratory quantities in a relativistically moving frame is depicted, and the method for result comparison with the plasma rest frame is described. Benchmarks with laboratory frame simulations and experimental data where gains of ∼20 times were obtained are discussed, and potential numerical issues are analyzed. This method enables numerical simulations with shorter turnaround times required for parameter scanning, and for one-to-one three-dimensional experimental modeling of current and next generation laser wakefield experiments.

Relativistic reference frames including time scales: Questions and answers

The subject of relativistic reference frames in astronomy is discussed with respect to the problems and needs of the various user groups. For didactical reasons the discussion is presented in form of a sequence of questions and answers.

Spacetime coordinates in the geocentric reference frame

A geocentric relativistic reference frame is established which is close to the conventional non-relativistic equatorial frame of reference. Within post-Newtonian approximation the worldline of the geocentre is used to connect points by spacelike geodesics on the equal proper time hypersurface and to establish a properly chosen tetrad reference frame. Points on the earth surface and near the earth-space are coordinated making use of the Frobenius matrix of integrating factors which connects the geocentric orthonormal tetrad with the tangent spacetime of relativistic pseudo-Riemann geometry. The gravity field of the earth and its relative velocity with respect to the solar system barycentre cause coordinate effects of the order of 10 cm for topocentric point positioning.

The rotation and precession of relativistic reference frames

The Clifford algebra of three- and four-vectors is reviewed and used to examine the nature of the rotation and precession of accelerating reference frames in Minkowskian space-time, and freely falling reference frames in general relativity. It is shown that the usual interpretation of Thomas precession must be modified because in space-time three-vectors in one frame of reference cannot be related to three-vectors in another.