The Appearance, Apparent Speed, and Removal of Optical Effects for Relativistically Moving Objects

Because various parts of an object are different distances from an observer, and light takes a finite time to reach the observer, the appearance of a relativistically moving object will be very different from that given by the Lorentz contraction. We derive equations that can be applied to a photographic image so that the Lorentz contraction can still be observed. We also give equations that quantify the apparent deformation of the object and plots that show the apparent speed of the object as a function of time. In particular, as an object approaches, its apparent speed can be much greater than the speed of light. In addition, we derive equations that can be applied to photographic images to show how a relativistically moving image will appear. This transformation is applied to photographic images that demonstrate the changes in appearance of a relativistically moving object. The dominate effect is that of appearing to be rotated, that is, the Terrell effect. (c) 2005 American Association of Physics Teachers.