Two Novel Special Relativistic Effects: Space Dilatation and Time Contraction

Abstract

The conventional discussion of the observed distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations, from a stationary frame, of : (i) objects moving with constant velocity and uniformly illuminated during a short time $\tau_L$ (their `Luminous Proper Time') in their rest frame; these may be called `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, observed from the stationary frame with coarse time resolution in a direction perpendicular to their direction of motion are seen to be at rest but {\it 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 at any fixed position in the rest frame of the stationary observer is seen to be running {\it faster} than a similar clock at rest by the factor $1/\sqrt{1-(v/c)^2}$ (Time Contraction). All four space-time `effects' of Special Relativity are simply classified in terms of the projective geometry of space-time, and the close analogy of these effects to linear spatial perspective is pointed out.