Two novel special relativistic effects: Space dilatation and time contraction

The conventional discussion of the observed distortions of space and time i n special relativity (the Lorentz-Fitzgerald contraction and time dilatatio n) 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; thes e may be called "transient luminous objects" and (ii) a moving, extended, a rray of synchronized "equivalent clocks" in a common inertial frame. Applic ation of the Lorentz transformation to (i) shows that such objects, observe d from the stationary frame with coarse time resolution in a direction perp endicular to their direction of motion, are seen to be at rest but longer i n the direction of the relative velocity v by a factor 1/root 1-(v/c)(2) (s pace 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/root 1-(v/c)(2) (time contraction). All four space-time "effects" of special relativity are simpl y classified in terms of the projective geometry of space-time, and the clo se analogy of these effects to linear spatial perspective is pointed out. ( C) 2000 American Association of Physics Teachers.