Relativity visualized

Space Time Travel

Apparent superluminal motion

jet of quasar 3C273
Fig. 4: A bright component in the jet of quasar 3C273 moves away from the quasar at a rate of three quarters of a milliarcsecond per year. The figure shows contour levels of brightness for the radio emission of the quasar and its jet. The tick marks on the axes are in units of two milliarcseconds (1 milliarcsecond = 1 degree / (3.6 x 106). Image after [3].

If approaching rulers look longer than they are (Fig. 1, left), then they must also appear to be faster than they are: Imagine that we take a second picture, on which all rulers have advanced by one place in the line. Then the approaching rulers appear to have moved a longer distance than the receding ones, therefore, they must appear to be faster. The different apparent velocities are best appreciated in the movie, see the supplement on the first page of this paper.

So, we see rulers with different velocities, although their measured velocities are the same. The reason for this phenomenon is once more the travel time of the light signals. When the object is approaching, a signal emitted at a later time has a shorter way to go which makes up for some of the delay. More time has passed between the emission of the signals than the observer thinks and the object's velocity is overestimated. Conversely, the velocity of a receding object is systematically underestimated because a signal emitted at a later time has a longer way into the bargain. Just as the apparent length can be arbitrarily large for a sufficiently fast ruler, the apparent velocity can be arbitrarily high - and even exceed the speed of light.

Apparent superluminal speeds of this kind are in fact being observed. In 1973, in the quasar 3C279 a luminous component was found that apparently moves away from the quasar core at ten times the speed of light. At the present time, a number of these so called superluminal quasars is known, among them 3C273 shown in Fig.  4. The figure shows how a component in the jet of this quasar moves away from the quasar core at a rate of about three quarters of a milliarcsecond per year. The redshift of the quasar indicates a distance of about 2.6 billion light years [3]. A path at this distance that extends over three quarters of a milliarcsecond in the sky, is more than nine light years long. Thus, the component appears to traverse 9 light years in the course of a single year. This would make it nine times as fast as light. In addition, the motion that we observe is only the transverse part. There is an additional (unobserved) velocity component of unknown size in the direction of the line of sight.

If the unknown velocity component in the direction of the line of sight is nearly equal to the speed of light, then the light travel times come into play as described above. The velocity is overestimated and even the (smaller) transverse component may appear to exceed the speed of light. The observed superluminal motion in the jet of 3C273 can be explained by a jet that moves at more than 99 percent of the speed of light and approaches us almost along our line of sight.

 
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Authors: Ute Kraus, Date: July 14, 2005
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