here - Department of Physics, HKU

CHAPTER 5. PARADOXES 36
B
v ∆t
θ
To Earth
A
C
Figure 5.5: An illusion of superluminal motion.
two doors simultaneously. We know that this depends on observers. In fact,
both views are correct, Fig. 5.4. The stationary observer will see that the
two doors are closed for a brief moment, but an observer moving with the
pole will not see that the two doors are closed at the same time. The moving
observer will see that the back door is closed before the front end of the pole
reaches it. Then, the back door opens for the pole to pass through. And
then, the front door closes after the back end of the pole completely is inside
the barn. The readers could work out the space-time diagram for the whole
process.
5.3 An Illusion of Superluminal Motion
We very often see jets associated with black holes and quasars. The jets will
produce gas clouds, which move in a very high speed. We did observe that
the gas clouds appear to be moving with speed greater than the speed of
light, called superluminal motion. This is an illusion. How can we explain
it?
Usually, the velocity of the gas cloud will make an angle θ with our line
of sight, Fig. 5.5. Let the distance between point B or C from the Earth be
L, and the time at which the gas cloud was at point A be t 1 . Also, assume
that the gas cloud will move from point A to point B in time ∆t with speed
v. Then, the time that we see the gas cloud at point B is
t 1 + ∆t + L/c . (5.1)
However, the light emitted when the cloud was at point A will take a bit
more time to reach Earth. Because the distance between point A and C is
v∆t cosθ, the time that we see the gas cloud at point A is
t 1 + (v∆t cosθ + L)/c . (5.2)
Because point A and C are on the same line of sight, we cannot distinguish
between the two points. Thus, from our point of view, the time taken for the