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A space explorer A sets off at a steady 0.95c to a distant
Chapter 15, Problem 15.5(choose chapter or problem)
A space explorer A sets off at a steady 0.95c to a distant star. After exploring the star for a short time, he returns at the same speed and gets home after a total absence of 80 years (as measured by earth-bound observers). How long do A's clocks say that he was gone, and by how much has he aged as compared to his twin B who stayed behind on earth?
[Note: This is the famous "twin paradox." It is fairly easy to get the right answer by judicious insertion of a factor of \(\gamma\) in the right place, but to understand it, you need to recognize that it involves three inertial frames: the earth-bound frame \(\mathcal{S}\), the frame \(\mathcal{S}^{\prime}\) of the outbound rocket, and the frame \(\mathcal{S}^{\prime \prime}\) of the returning rocket. Write down the time dilation formula for the two halves of the journey and then add. Notice that the experiment is not symmetrical between the two twins: A stays at rest in the single inertial frame \(\mathcal{S}\), but B occupies at least two different frames. This is what allows the result to be unsymmetrical.]
Questions & Answers
QUESTION:
A space explorer A sets off at a steady 0.95c to a distant star. After exploring the star for a short time, he returns at the same speed and gets home after a total absence of 80 years (as measured by earth-bound observers). How long do A's clocks say that he was gone, and by how much has he aged as compared to his twin B who stayed behind on earth?
[Note: This is the famous "twin paradox." It is fairly easy to get the right answer by judicious insertion of a factor of \(\gamma\) in the right place, but to understand it, you need to recognize that it involves three inertial frames: the earth-bound frame \(\mathcal{S}\), the frame \(\mathcal{S}^{\prime}\) of the outbound rocket, and the frame \(\mathcal{S}^{\prime \prime}\) of the returning rocket. Write down the time dilation formula for the two halves of the journey and then add. Notice that the experiment is not symmetrical between the two twins: A stays at rest in the single inertial frame \(\mathcal{S}\), but B occupies at least two different frames. This is what allows the result to be unsymmetrical.]
ANSWER:Step 1 of 3
With \(\beta=0.95\), the \(\gamma\) factor for both the outward and return trips is \(\gamma=1 / \sqrt{1-\beta^{2}}=3.20\).