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The relativity of Global Positioning System ͑GPS͒ 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 the 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 the pseudorange that are on the order of the gravitational radius of the Earth.

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.

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy-momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Rather than construct a total momentum from the Abraham momentum or the Minkowski momentum, we define a thermodynamically closed system consisting of a propagating electromagnetic field and a negligibly reflecting dielectric and we identify the Gordon momentum as the conserved total momentum by the fact that it is invariant in time. In the formalism of classical continuum electrodynamics, the Gordon momentum is therefore the unique representation of the total momentum in terms of the macroscopic electromagnetic fields and the macroscopic refractive index that characterizes the material. We also construct continuity equations for the energy and the Gordon momentum, noting that a time variable transformation is necessary to write the continuity equations in terms of the densities of conserved quantities. Finally, we use the continuity equations and the time-coordinate transformation to construct an array that has the properties of a traceless, symmetric energy-momentum tensor.

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The lifetime of the lowest quasibound state localized between the barriers of a GaAs/AlGaAs double-barrier structure is calculated as a function of barrier and well dimensions. The results are consistent with high-frequency experiments.