  The fluxon dynamics in a long Josephson junction with a ferromagnetic
insulating layer is investigated. It is found that the Josephson phase obeys a
double sine-Gordon equation involving a bound pi fluxon solution, and the
internal oscillations of the bound pair acting as a clock exhibit Lorentz
reductions in their frequencies regarded as a relativistic effect in the time
domain, i.e., time dilation. This is the complement to the Lorentz contraction
of fluxons with no clock. A possible observation scheme is also discussed.
