Relativity Lite

ATrip to Alpha Centauri | 33 At 11.648 years (figure 8), the fourth ( yellow-green ) return pulse from the outbound trip reaches Earth (count 4). You can see that the next ( blue-green ) one comes close on its heels, following in 0.728 years . We see the frequency blue-shifted to twice the emitting frequency as the saucer now approaches the Earth. The first three pulses from the inbound trip arrive at 12.376 years ( blue-green ) in figure 9 (count 1); 13.104 years ( cyan ), next in line in figure 9 (count 2); and 13.832 years ( blue ), seen having passed the Earth in figure 10 (count 3). At 14.56 years , the saucer reaches Earth and would have emitted its fourth pulse had it been needed at this point (count 4). Figure 9. At 12.376 years into the trip, the first ( blue-green ) saucer pulse from the return trip reaches Earth. One sees the next saucer pulse ( cyan ) from the inbound trip following in about 3/4 of the 1 c year grid: more precisely 0.728 years . Figure 10. At 14.56 years into the trip, the saucer reaches Earth. Let us sum up what we know. Your twin on Earth sees four pulses from the outbound trip at 2.912 years between pulses for a subtotal of 11.648 years . She also sees four pulses from the inbound trip at 0.728 years between pulses for a subtotal of 2.912 years . Thus, the total trip took 11.648 + 2.912 = 14.56 years , as we expected. What about you? You sent eight pulses at 1.456-year intervals for a total of 11.648 years . Note that if we multiply your proper-time interval by γ = 1.25 , we get the 14.56 years that your twin experienced! All this seems to work! One may account for the time in a third way. The ( blue ) saucer pulse having just passed the Earth in figure 10 is the seventh and last (the eighth “pulse” not being emit- ted because the saucer has returned). The corresponding seventh ( blue ) Earth-pulse is also shown in figure 10 just arriving at Alpha Centauri. Concentric and inward from that one are two more pulses—colored purple and lavender , respectively—together accounting for an