多普勒频移
我们来看另一个旅行的双胞胎,但这一次约翰将12个小时,12小时,以他的时钟。每小时他将无线电信号发送给猎人告诉他。无线电信号只是另一种形式的电磁辐射;因此,它也以光速传播。我们得到约翰的旅行离开猎人吗?当约翰的时钟读取“1小时”他发出的第一个信号。因为他是远离猎人光速的60%,相对论多普勒效应会导致½猎人观察约翰的传播源值。从上面的讨论中,½意味着时间频率的两倍长,因此,猎人收到约翰的“1小时”当他的时钟信号读取“两小时”。约翰给他的“2小时”信号时,猎人收到在4小时。所以你可以看到发展的关系。 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.
我们将仔细审视双重悖论在接下来的部分。
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