Chapter 37, Problem 63P

Superluminal jets. Figure 37-29a shows the path taken by a knot in a jet of ionized gas that has been expelled from a galaxy. The knot travels at constant velocity $\stackrel{\to }{v}$ at angle θ from the direction of Earth. The knot occasionally emits a burst of light, which is eventually detected on Earth. Two bursts are indicated in Fig. 37-29a, separated by time t as measured in a stationary frame near the bursts. The bursts are shown in Fig. 37-29b as if they were photographed on the same piece of film, first when light from burst 1 arrived on Earth and then later when light from burst 2 arrived. The apparent distance D_app traveled by the knot between the two bursts is the distance across an Earth-observer’s view of the knot’s path. The apparent time T_app between the bursts is the difference in the arrival times of the light from them. The apparent speed of the knot is then V_app = D_app/T_app. In terms of v, t, and θ, what are (a) D_app and (b) T_app? (c) Evaluate V_app for v = 0.980c and θ = 30.0°. When superluminal (faster than light) jets were first observed, they seemed to defy special relativity—at least until the correct geometry (Fig. 37-29a) was understood.

Figure 37-29 Problem 63.