|MadSci Network: Physics|
Dear James, This is a great question and refers to a classic problem in Special Relativity called the “Twin Paradox”. I think you might have seen a response I wrote (perhaps to you) about the problem of simultaneity. Please take a look at Mad Science Question ID Number 1156778977.Ph and my response if you haven’t seen them, yet. Your question comes down to determining what the difference between the Earth and the rocket is, so that the twin in the rocket is younger than the twin who stays on the Earth. If the twin, or clock, in the rocket was allowed to travel on through space, there would be no way to compare the two twins, or clocks, and each one would say that the other one was aging more slowly. (See the other MadSci question.) In this case, there can be no difference, and to say one is younger would completely depend on whose frame of reference you were using. So how can we compare the ages of the two twins so that both would agree with our conclusion? Well, we would have to start them out together in the same frame (this is usually not too hard for twins, but it is something to keep in mind with clocks!), and then we would need to bring them back together at the end of the experiment to compare them again, to see which one has aged more. Thus, we begin with the twins together, let’s call them Apollo and Athena, on the Earth, for example. Then, one must blast off on a rocket, let’s say Athena. Now we come to the first difference. Apollo, who stays on the Earth, does not change his reference frame. Athena, on the other hand, starts out in the Earth’s frame of reference, and then she changes to the rocket’s frame of reference, one that is moving relative to her initial frame. Is this important? Absolutely! She experiences this shift from one frame to another as an acceleration, in other words she would know she was changing her frame because she would be feel the force from the rocket pushing her forward. (This is just like sitting in a car. If the car moves at a constant speed along a straight road, you don’t notice that you’re moving. If, however, the car starts to speed up, you can feel this because your car seat starts pushing you from behind. If the car starts to slow down, your seatbelt starts pulling you back.) Apollo feels no such acceleration. At this point, both twins would start to “see” the other twin as aging more slowly than they. Athena thinks Apollo is aging more slowly than she is, and Apollo thinks Athena is aging more slowly than he is. Half-way through her trip, when she is very far from Earth, Athena turns her ship around and starts her return. Once again she must change her frame of reference, from one moving away from the Earth to one moving toward the Earth. Why can’t we say the Earth has turned around and started heading toward the rocket? We must ask ourselves which one of the twins experiences an acceleration? Apollo or Athena? In this case, Athena is the one who would have to turn on her rockets, so she would feel the acceleration and would thus know she was the one changing reference frames. It is during this that a major change occurs in what the twins measure. Since Apollo stays in the same frame as he’s always in, he still thinks that Athena is aging more slowly than he is. Athena, on the other hand, has just changed from one frame which is moving away from the Earth at a great speed to one that is moving toward the Earth at a great speed. The clocks in these two frames are not synchronized with each other. During this turn-around, Athena sees Apollo age at a great rate. Having started out seeming younger than she is, he ages very rapidly until he seems to be much older than she is! Then, during the rest of her trip back to Earth, Apollo seems to age slowly again, but he has now started out this part of the trip older than Athena. When Athena finally gets back to Earth and greets her brother, Apollo is now older than she is. Apollo would say that this change occurred slowly during the entire trip because Athena was aging slower than he was, but Athena would say that Apollo was aging slower than she was for all of her trip except for the big age change that occurred during her turn-around, and this big change more than made up for the slowness of his aging the rest of the time. As an aside, let’s think about a perfectly symmetric problem. Let’s imagine that both Apollo and Athena blast off in rockets, but in opposite directions, then turn around and meet back at the Earth at the same time. What would each one measure? Again, Athena would say that Apollo was aging more slowly than she was, but this time, much more slowly, since he seems to be moving away from her even faster than when he was on the Earth. During the turn-around, Apollo would seem to age very quickly until he was older than Athena, again. During the return trip, Apollo would again age much more slowly than Athena, so that when they both arrived back at Earth, Athena’s age would have caught up with Apollo’s, and they would again be the same age! Of course, Apollo would say the same thing about Athena. The importance of acceleration to the differences of frames is one point that led Prof. Albert Einstein to develop his Theory of General Relativity from his Theory of Special Relativity. He showed that the acceleration due to gravity was just like the acceleration experienced by Athena when she changed from one frame to another, and so gravity could therefore have an affect on time measurement in reference frames! Well, James, I hope I have answered your question. If you would like some more information, please let us know. Sincerely, Jim Guinn
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