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

摘要

Space-time coordinate transformations valid for arbitrarily long coordinate time are derived from global Minkowski coordinates to the Fermi coordinates of an observer moving in a circle in three-dimensional space. The metric for the Fermi coordinates is calculated directly from the tensor transformation rule. The Fermi coordinates are used in an examination (from the observer's reference frame) of the detailed behavior of ideal clocks. 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. For portable clocks that orbit the Fermi coordinate origin, an orbital Sagnac-like effect exists. The coordinate speed of light is isotropic but is periodic in time and varies with Fermi coordinate position. In a numerical illustration of the magnitudes of these kinematic effects, this report uses parameters relevant to clocks carried aboard satellites orbiting the Earth.