Two Novel Special Relativistic Effects: Space Dilatation and Time Contraction

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 τL (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 longer in the direction of the relative velocity ~v by a factor 1/ √ 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 faster than a similar clock at rest by the factor 1/ √ 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. PACS 03.30+p Published in: American Journal of Physics 68 (2000), 267-274.