Relativity Lite

36 | Relativity Lite Figure 15. At 5.824 years into the trip, as the second ( orange ) pulse emitted by the moving Earth reaches the saucer, as does Alpha Centauri. Figure 16. At 5.8240001 years into the trip, 3 seconds later, as the two stars reverse their course. Figure 15 shows the configuration at 5.824 years when Alpha Centauri just reaches the saucer: count 2 on the outbound trip. This matches the time, t = d/v , that the saucer thinks is required for Alpha Centauri to move a distance of 3.496 light-years (to reach the saucer) at speed v = 0.6 c . Note that the second ( orange ) pulse emitted by the moving Earth reaches the saucer simultaneously with Alpha Centauri, a simultaneity also seen in the other refer- ence frame in figure 6. As we move forward by just 3 seconds (10 −7 years), notice the huge shift in perspective of figure 16. From the point of view of the saucer at rest, the Sun and Alpha Centauri have instantaneously screeched to a halt from a velocity leftward (which we write as v = −0.6 c ), reversed course, and instantaneously ramped their velocity up to v = +0.6 c (rightward at the same speed). But—and this is the crucial clarification—however much you on the saucer may assert the privilege of claiming to be at rest while the universe moves back and forth around you, no one on the Earth feels any acceleration as they stop moving leftward and start moving rightward. On the other hand, your body does feel acceleration. What we see in our omniscient perspective in figure 15 is that in the saucer’s outgoing rest frame, there is a ( red ) Earth-pulse having been received by the saucer and having moved on to the right, an ( orange ) Earth-pulse currently being received, and a ( yellow ) Earth- pulse in flight yet to be received, having barely left the Earth. In the saucer’s incoming rest frame 3 seconds later, our omniscient perspective in figure 16 shows the same ( red ) Earth- pulse having been received, and having moved on to the right, and the same ( orange ) Earth-pulse currently being received just as in figure 15. But it also shows four Earth-pulses