arXiv subjects

Thomas B. Bahder

Publications and source records attributed to Thomas B. Bahder.

27 records · Page 2Linked to original sources

arXiv2004

Clock Synchronization and Navigation in the Vicinity of the Earth

Clock synchronization is the backbone of applications such as high-accuracy satellite navigation, geolocation, space-based interferometry, and cryptographic communication systems. The high accuracy of synchronization needed over satellite-to-ground and satellite-to-satellite distances requires the use of general relativistic concepts. The role of geometrical optics and antenna phase center approximations are discussed in high accuracy work. The clock synchronization problem is explored from a general relativistic point of view, with emphasis on the local measurement process and the use of the tetrad formalism as the correct model of relativistic measurements. The treatment makes use of J. L. Synge's world function of space-time as a basic coordinate independent geometric concept. A metric is used for space-time in the vicinity of the Earth, where coordinate time is proper time on the geoid. The problem of satellite clock syntonization is analyzed by numerically integrating the geodesic equations of motion for low-Earth orbit (LEO), geosynchronous orbit (GEO), and highly elliptical orbit (HEO) satellites. Proper time minus coordinate time is computed for satellites in these orbital regimes. The frequency shift as a function of time is computed for a signal observed on the Earth's geoid from a LEO, GEO, and HEO satellite. Finally, the problem of geolocation in curved space-time is briefly explored using the world function formalism.

gr-qc↗

arXiv2003

Clock Synchronization based on Second-Order Quantum Coherence of Entangled Photons

We present an algorithm for synchronizing two clocks based on second-order quantum interference between entangled photons generated by parametric down-conversion. The procedure is distinct from the standard Einstein two-way clock synchronization method in that photon correlations are used to define simultaneous events in the frame of reference of a Hong-Ou-Mandel (HOM) interferometer. Once the HOM interferometer is balanced, by use of an adjustable optical delay in one arm, arrival times of simultaneously generated photons are recorded by each clock. Classical information on the arrival times is sent from one clock to the other, and a correlation of arrival times is done to determine the clock offset.

quant-ph↗

arXiv2003

Relativity of GPS Measurement

The relativity of Global Positioning System (GPS) pseudorange measurements is explored within the geometrical optics approximation in the curved space-time near Earth. A space-time grid for navigation is created by the discontinuities introduced in the electromagnetic field amplitude by the P-code broadcast by the GPS satellites. We compute the world function of space-time near Earth, and we use it to define a scalar phase function that describes the space-time grid. We use this scalar phase function to define the measured pseudorange, which turns out to be a two-point space-time scalar under generalized coordinate transformations. Though the measured pseudorange is an invariant, it depends on the world lines of the receiver and satellite. While two colocated receivers measure two different pseudoranges to the same satellite, they obtain correct position and time, independent of their velocity. We relate the measured pseudorange to the geometry of space-time and find corrections to the conventional model of pseudorange that are on the order of the gravitational radius of the Earth.

gr-qc↗

arXiv2003

Force on an Asymmetric Capacitor

When a high voltage (~30 kV) is applied to a capacitor whose electrodes have different physical dimensions, the capacitor experiences a net force toward the smaller electrode (Biefeld-Brown effect). We have verified this effect by building four capacitors of different shapes. The effect may have applications to vehicle propulsion and dielectric pumps. We review the history of this effect briefly through the history of patents by Thomas Townsend Brown. At present, the physical basis for the Biefeld-Brown effect is not understood. The order of magnitude of the net force on the asymmetric capacitor is estimated assuming two different mechanisms of charge conduction between its electrodes: ballistic ionic wind and ionic drift. The calculations indicate that ionic wind is at least three orders of magnitude too small to explain the magnitude of the observed force on the capacitor. The ionic drift transport assumption leads to the correct order of magnitude for the force, however, it is difficult to see how ionic drift enters into the theory. Finally, we present a detailed thermodynamic treatment of the net force on an asymmetric capacitor. In the future, to understand this effect, a detailed theoretical model must be constructed that takes into account plasma effects: ionization of gas (or air) in the high electric field region, charge transport, and resulting dynamic forces on the electrodes. The next series of experiments should determine whether the effect occurs in vacuum, and a careful study should be carried out to determine the dependence of the observed force on gas pressure, gas species and applied voltage.

physics.hist-ph↗

arXiv2002

Attitude Determination from Single-Antenna Carrier-Phase Measurements

A model of carrier phase measurement (as carried out by a satellite navigation receiver) is formulated based on electromagnetic theory. The model shows that the phase of the open-circuit voltage induced in the receiver antenna with respect to a local oscillator (in the receiver) depends on the relative orientation of the receiving and transmitting antennas. The model shows that using a {\it single} receiving antenna, and making carrier phase measurements to seven satellites, the 3-axis attitude of a user platform (in addition to its position and time) can be computed relative to an initial point. This measurement model can also be used to create high-fidelity satellite signal simulators that take into account the effect of platform rotation as well as translation.

physics.ins-det↗

arXiv2002

Transformation Properties of the Lagrangian and Eulerian Strain Tensors

A coordinate independent derivation of the Eulerian and Lagrangian strain tensors of finite deformation theory is given based on the parallel propagator, the world function, and the displacement vector field as a three-point tensor. The derivation explicitly shows that the Eulerian and Lagrangian strain tensors are two-point tensors, each a function of both the spatial and material coordinates. The Eulerian strain is a two-point tensor that transforms as a second rank tensor under transformation of spatial coordinates and transforms as a scalar under transformation of the material coordinates. The Lagrangian strain is a two-point tensor that transforms as scalar under transformation of spatial coordinates and transforms as a second rank tensor under transformation of the material coordinates. These transformation properties are needed when transforming the strain tensors from one frame of reference to another moving frame.

physics.class-ph↗

arXiv2002

Stress in Rotating Disks and Cylinders

The solution of the classic problem of stress in a rotating elastic disk or cylinder, as solved in standard texts on elasticity theory, has two features: dynamical equations are used that are valid only in an inertial frame of reference, and quadratic terms are dropped in displacement gradient in the definition of the strain. I show that, in an inertial frame of reference where the dynamical equations are valid, it is incorrect to drop the quadratic terms because they are as large as the linear terms that are kept. I provide an alternate formulation of the problem by transforming the dynamical equations to a corotating frame of reference of the disk/cylinder, where dropping the quadratic terms in displacement gradient is justified. The analysis shows that the classic textbook derivation of stress and strain must be interpreted as being carried out in the corotating frame of the medium.

physics.ed-ph↗

arXiv2001

Navigation in Curved Space-Time

A covariant and invariant theory of navigation in curved space-time with respect to electromagnetic beacons is written in terms of J. L. Synge's two-point invariant world function. Explicit equations are given for navigation in space-time in the vicinity of the Earth in Schwarzschild coordinates and in rotating coordinates. The restricted problem of determining an observer's coordinate time when their spatial position is known is also considered.

gr-qc↗

arXiv1998

Fermi Coordinates of an Observer Moving in a Circle in Minkowski Space: Apparent Behavior of Clocks

Coordinate transformations are derived from global Minkowski coordinates to the Fermi coordinates of an observer moving in a circle in Minkowski space-time. The metric for the Fermi coordinates is calculated directly from the tensor transformation rule. The behavior of ideal clocks is examined from the observer's reference frame using the Fermi coordinates. A complicated relation exists between Fermi coordinate time and proper time on stationary clocks (in the Fermi frame) and between proper time on satellite clocks that orbit the observer. An orbital Sagnac-like effect exists for portable clocks that orbit the Fermi coordinate origin. The coordinate speed of light is isotropic but varies with Fermi coordinate position and time. The magnitudes of these kinematic effects are computed for parameters that are relevant to the Global Positioning System (GPS) and are found to be small; however, for future high-accuracy time transfer systems, these effects may be of significant magnitude.

gr-qc↗