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The Twin Paradox
We should state from the very beginning that the twin paradox is actually no paradox at all. The "paradox" can be clarified as follows: A pair of twins, Adam and Eve, are thinking of what will happen to their ages if one of them will go away from Earth on a space journey. Will Eve for example be younger, older, or have the same age as her brother if she leaves Earth with a space-ship and then returns after some time?
Actually, Eve will be younger than her brother when she returns to Earth. The reason is that Eve is not in the same inertial frame all the time.
Assume that Adam and Eve are equipped with two watches (one each) that are synchronized before Eve leaves on her space journey. When Eve returns to Earth and Adam, the time has passed according to Adam's watch, but only the time according to Eve's watch. Thus, Eve is younger than Adam, when the two twins meet again after Eve's space journey.
However, can you not turn the discussion around and say that Eve has been at rest in her space-ship while Adam has been on a "space journey" with planet Earth? In that case, Adam must be younger than Eve at the reunion!
If these discussions were both correct, then Adam should be both older and younger than Eve at the same time. But both these discussions are not correct. Adam is at rest all the time on Earth, i.e., he is in the same inertial frame all the time, but Eve is not (as was stated above). Eve will feel forces when her space-ship accelerates and retards, and Adam will not feel such forces.