Relativity Lite

40 | Relativity Lite Pause the movie again at 1:11, when the clock shows 6.5 years . Now pulses are 6.5 grid lines apart, and there are two additional ( orange and  yellow ) Earth-pulse emissions, show- ing that an additional 2.9 Earth years have elapsed during the 3/4-year saucer deceleration. The saucer reverses direction, and we should pause the movie again at 1:19, when the clock shows 7.2 years and we have returned to coasting, shown in figure 20. The pulses have continued to bunch up with the relativistic Doppler shift and are now 3 grid lines apart, 1/4 of the 12.2 spacing on the outbound coast, just as expected. Back the movie up to 5.8 years , and note that two pulses of light are in flight from the Earth since the saucer left (the orange one has yet to reach the saucer). Run the movie up to 7.2 years again, and note that six pulses of light are now in flight from the Earth since the saucer left, a difference of four ( yellow  , green , cyan , and blue ). The Earth was due to send pulses at 1.58-year intervals, so about 4 × 1.58 yr = 6.3 yr have passed on Earth during the deceleration, and reacceleration phase, which took 1.4 saucer years . Over the 5 years that the saucer saw the Earth moving away at a constant v = 0.6 c , after the initial acceleration, it would see Earth clocks slow down, showing that only 4 Earth years would have passed. But during the deceleration and reacceleration phase near Alpha Centauri, 6.3 years passed on Earth while the saucer experienced only 1.4 years . Combining these two eras shows that 10.3 Earth years pass for every 7.7 saucer years , for a ratio of 1.3. This is quite close to the 1.22 overall time-dilation factor for the trip given by our crude counting of rings on a grid. (As with the earlier trip using instantaneous jumps from stillness to motion, and the reverse, the initial acceleration-induced time ef- fects at the beginning of the trip and the final deceleration-induced time effects at the end of the trip will essentially cancel the time-dilation effects of the unaccelerated por- tion of the trip.) Figure 20. At 7.2 years into the trip, where the saucer has returned to coasting.