Relativity Lite

32 | Relativity Lite Note that this is one pulse per 5.824 yr − 5.096 yr = 0.728 yr , so the saucer pulses ar- rive at Alpha Centauri at twice the frequency they were supposed to be emitted, one per 1.456 years . * This is the relativistic Doppler shift. The relativistic Doppler shift can also be seen by measuring the distance between the wave front of this pulse and the one just emit- ted by the saucer. It is about 3/4 of the one-light-year grid. (We can also double-check that the travel time of Earth’s first [ red ] pulse was t = d/v = 4.37 c yr/c = 4.37 yr , which, since it was emitted at 1.456 years , gives us an arrival time of 5.826 years .) This increase in the frequency of the light waves is called a blue shift because visual colors shifted to higher frequencies move toward the blue end of the visual spectrum from their emis- sion frequencies. For instance, red light might be blue-shifted to orange, orange light to yellow, yellow to green, green to blue, and blue to violet. One would also say that infrared light that is seen as ultraviolet light is extremely blue-shifted. (Please note that the colors in the figures are labels for the sequence of pulses and not the actual colors [shifted or not] of the pulses of light.) The left edge of the third ( yellow ) pulse of light just emitted by the saucer in figure 5 can be measured to be about 2.9 c years away from the left edge of the second ( orange ) return pulse emitted by the saucer, which has incidentally also just reached Earth (count 2). Thus, the Earth sees the light from the saucer at half the frequency the pulses were supposed to be emitted— one per 2.912 years instead of one per 1.456 years , which is the relativistic Doppler red shift. At 7.28 years , you reach Alpha Centauri and immediately turn around (figure 6). At 8.736 years , the third ( yellow ) saucer pulse reaches Earth (count 3), as seen in figure 7. * Formally, the relativistic Doppler shift is given by f f v c v c f f f = + − = + + = = 0 0 0 0 1 1 5 5 3 5 5 5 3 5 8 5 2 5 2 / / / / / / / / , where f 0 is the emission frequency of light from the spaceship or star. We get the reciprocal one-half f 0 if we change the signs of the velocities. Figure 7. At 8.736 years into the trip, the third ( yellow ) saucer pulse reaches Earth. Figure 8. At 11.648 years into the trip, the fourth ( yellow-green ) saucer pulse reaches Earth.