QUESTION: Dear Mr. Nelson,
This question has bothered me for a long time. The famous "twin paradox" does not exist because only people on earth can make the relativistic prediction--- time dilation on spaceship, because earth is an inertial reference frame and the spaceship is not. But what will happen if the spaceship eventually stopping accelerating and flying at constant velocity close to speed of light? During this period the spaceship becomes an inertial reference frame again, can the space twin use the time dilation formula to calculate the earth time? Will the times for both earth and spaceship be same because they are both inertial reference frames now?
Looking forward to your explanation. Thanks for your time!
ANSWER: That simply continues the existence of the spaceship in that inertial reference frame. The difference you're looking for is that it's not the same inertial reference frame at all, but one that started (this is the origin of the re-setting of the clock that goes with relativity). Then it re-accelerates to an inertial reference frame that comes from the other direction and, if you calculate it, has a clock set to the time that would properly account for the time difference between Earth and the time traveler.
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QUESTION: Thank you Steve for your answer and your time.
I do not understand the explanation very well. Do you mean the time difference is still there but will remain unchanged before the spaceship re-accelerates?
The atomic clock flying with plane is slower than the other atomic clock on earth. Does the "time loss" happen only during acceleration? If so, the magnitude of the acceleration will affect the time dilation or not?
looking forward to your explanation.
Thanks a lot!
You do understand it, "time loss" happens when you join a new inertial reference frame which is behind us in time by being approaching or receding in velocity Acceleration is just how you reach that new reference frame. The magnitude of acceleration will of course affect time dilation, just as gravitation (acceleration) affects time dilation. Of course you don't have a mathematical understanding of it any more than I had one before I took a serious graduate course on the subject...but still, you have the basics.