多普勒移位
让我们与双胞胎再次旅行，但是这次约翰将在他的时钟衡量的情况下旅行12小时和12小时。每小时，他都会向亨特发出无线电信号，告诉他小时。无线电信号只是电磁辐射的另一种形式。因此，它也以光速行进。当约翰从亨特离开猎人时，我们会得到什么？当约翰时钟读“ 1小时”时，他发送了第一个信号。由于他以光速的60％的速度离开了猎人，因此相对论的多普勒效应使猎人观察到约翰的传播是量的½。从上面的讨论中，½的频率意味着所花费的时间是两倍的时间，因此，当他的时钟读写“ 2小时”时，亨特会收到约翰的“ 1小时”信号。当约翰发出“ 2小时”信号时，亨特在4小时为他收到它。因此，您可以看到这种关系的发展。 For every 1-hour signal by John's watch, the elapsed time for Hunter is 2 hours. When John's clock reads "12 hours" he has sent 12 signals. Hunter, on the other hand, has received 12 signals, but they were all 2 hours apart … thus 24 hours have passed for Hunter. Now John turns around and comes back sending signals every hour in the same manner as before. Since he is approaching Hunter, the Doppler shift now causes Hunter to observe the frequency to be twice the source value. Twice the frequency is the same as ½ the time, so Hunter receives John's "1 hour" signals at 30min intervals. When the 12-hour return trip is over, John has sent 12 signals. Hunter has received 12 signals, but they were separated by 30 minutes, thus 6 hours have passed for Hunter. If we now total up the elapsed time for both twins, we see that 24 hours (12 + 12) have elapsed for John, but 30 hours (24 + 6) have elapsed for Hunter. Thus, Hunter is now older than his identical twin, John. If John had traveled farther and faster, the time dilation would have been even greater. Look at the twins again, but this time let John travel 84 hours out and 84 hours back (by his clock) at 80% the speed of light. The total trip for John will be 168 hours, and the total time elapsed for Hunter will be 280 hours; John was gone for 1 week by his clock, but Hunter waited for 1 week 4 days and 16 hours by his clock. Remember that Hunter will receive John's outgoing signals at half the frequency which means twice the time. Therefore, Hunter receives John's 84 hourly signals every 3 hours for a total of 252 hours (3 is the Relativistic Doppler shift for 80% the speed of light). Likewise, Hunter receives John's return trip 84 hourly signals every 20 minutes for a total of 28 hours (20 minutes is the 1/3 Relativistic Doppler shift for the return). Now you know the total round trip from Hunter's perspective, 252 + 28 = 280 hours or 1 week 4 days and 16 hours. John, on the other hand, traveled 84 hours out and 84 hours back for a total of 168 hours or 1 week.
我们将在下一部分中仔细查看双胞胎悖论。
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