The apparent velocity and acceleration of relativistically moving objects

Abstract

Although special relativity limits the actual velocity of a particle to c, the velocity of light, the observed velocity need not be the same as the actual velocity as the observer is only aware of the position of a particle at the time in the past when it emits the detected signal. We consider the apparent speed and acceleration of a particle in two cases, one when the particle is moving with a constant speed and the other when it is moving with a constant acceleration. One curious feature of our results is that in both cases, if the actual velocity of the particle approaches c, then the apparent velocity approaches infinity when it is moving toward the observer and c/2 when it is moving away from the observer.

Gamow’s cyclist: a new look at relativistic measurements for a binocular observer

“…As the bicycle approaches the observer (with an apparent velocity greater than c [19,30,31]), it appears grossly extended with the circular wheels deformed into elongated ellipsoids. As it passes the observer, the wheels and spokes appear concave and the entire frame is contracted (receding now with apparent velocity ≤ c/2 [32]). It can also be noted that all line sections parallel to the direction of movement remain parallel, such as the cross bar of the bicycle, and the height of the bicycle remains unchanged.…”