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 τL (their “luminous proper time”) in their rest frame; these may be called “transient luminous objects” and (ii) a moving, extended, array of synchronized “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.