Relativity Lite

ATrip to Alpha Centauri | 35 Figure 12 shows the two stars and their planets having moved to the left for a span of 1.6 years and the emission of the first pulse expanding almost two months after the agreed-­ upon time of 1.456 years . You were not lying after all about sending the pulses on time! But what about your twin left on Earth? Why did she not send off a pulse? Figure 13 shows the configuration 1.92 years into the trip. We see a small expanding ring of ( red ) light that was emitted by the Earth a little over a month prior at 1.82 years . From an omnipotent observer at rest relative to the saucer, the Earth appears to have sent its first pulse late. What could cause this? Time dilation would seem to be the cause, since 1.25 × 1.456 yr = 1.82 yr . But that would mean that the saucer at rest sees the moving Earth clocks slowed and the Earth at rest sees the moving saucer clocks slowed by the same time-dilation factor. This is why Einstein called this a theory of “relativity.” Despite the fact that one’s view is relative in this case, somehow the twin on the saucer experiences less time for the overall round trip than does the twin on the Earth. This is called the Twin Paradox. Read on for its resolution. Figure 13. At 1.92 years into the trip, about a month after the first ( red ) pulse was emitted by the Earth at 1.82 years . Figure 14. At 2.912 years into the trip, as the first ( red ) pulse emitted by the receding Earth reaches saucer. Figure 14 shows the configuration at 2.912 years . The receding Earth has its ( red ) pulse received by the saucer at a half the emission frequency, as one would expect with a relativis- tic red shift: count 1 of Earth-pulses received in the outward interval.