When moving clocks run fast

摘要

An asymmetry in Lorentz contraction can be created with a pointlike object in uniform motion relative to another object that has a finite, linear, spatial extent along the line of motion (extended object). Let Dt be the time that elapses as the pointlike object flies by the extended object in the frame of the latter. Let Dt0 be the time that elapses as the extended object flies by the pointlike object in the frame of the latter. These elapsed times depend upon the frame of reference. However, because the extended object is Lorentz contracted and the pointlike object is not, the relationship between the elapsed times is interframe consistent according to Dt/Dt0 1/4c. In the frame of the extended object, time runs slower in the moving frame, as expected. But in the frame of the pointlike object, time runs faster in the moving frame. In both frames, the duration of the flyby is shorter in the frame of the pointlike object. The twin-type paradox is eliminated without acceleration. Cosmic ray showers provide a natural example. Analogous to measurement in quantum mechanics, an experimentalist can create a pointlike object by choosing to measure the uniform motion of an extended object relative to a point in the laboratory frame.