| MadSci Network: Physics |
Hello Carl
Thank you for your interesting question. Let's start with your first example, in which traveler B accelerates out, comes to a rest, accelerates in the opposite direction, and comes back. You state that "Put another way, when Twin A decelerates, it is the same thing as Twin B accelerating". Now, if this were true, you'd indeed have a point, as there would be no way of telling which would be the twin that accelerates and which would be the other twin. However, one can fairly easily see that the two twins are not quite doing the same: the one that is accelerating is the one that fires (presumably) his rocket engine. This increases his kinetic energy. Clearly, the situation of the twins is not symmetrical. There is more technical explanation available involving inertial frames of reference - basically, the "observer" in a relativistic experiment is not supposed to be accelerating, as then, he would not be in an inertial frame of reference. This is discussed in [1,2].
Your second example involves twin B traveling to Alpha Centauri and twin A on Earth. Twin A will then go to Alpha Centauri, while twin B waits. However, the difference here with the original twin paradox is that there, twin B is doing all the traveling, while here, both twins are traveling, and, assuming the distance between the Earth and Alpha Centauri does not change and they take a direct route, will travel just as much. If they all travel at the same speed , there will be no time difference. This situation is however not identical to the situation in the twin paradox, so this conclusion does not invalidate it.
In short, who is accelerating and who is not is not amigos in the twin paradox, as acceleration always involves an expenditure of energy. I hope this clarifies matters, and answers your question.
Bart Broks
Try the links in the MadSci Library for more information on Physics.