Space Time Measurements in Special Relativity

Abstract

The conventional discussion of apparent distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations of : (i) moving objects of limited lifetime in their own rest frame (`transient luminous objects') and (ii) a moving extended array of synchronised `equivalent clocks' in a common inertial frame. Application of the Lorentz Transformation to (i) shows that such objects, viewed with coarse time resolution, appear to be longer in the direction of the relative velocity $\vec{v}$ by a factor $1/\sqrt{1-(v/c)^2}$ (Space Dilatation) and to (ii) that the moving equivalent clock that appears at any fixed position in the rest frame of an inertial observer appears to be running faster than a similar clock at rest by the factor $1/\sqrt{1-(v/c)^2}$ (Time Contraction). The actual appearance of moving objects and clocks, taking into account light propagation time delays, as well as the effect of the Lorentz Transformation, is also discussed.