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You should now have a good sense of what George and Gracie would see during the twin paradox scenario. Let’s now determine what each would conclude, after post-processing their observations, regarding the passage of time for the other. That is, let’s work out what will each measure regarding the other’s rate of aging. Take Gracie’s speed to be $v = \frac{12}{13} c$ and the distance according to George to the turnaround point to be 12 lt-yrs. Assume both George and Gracie emit a flash each time their own clock shows that a year has elapsed.
Module 40: The Twins Communicate, Quantitative – Problem 2
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Question 1 of 4
1. Question
Based on George’s observations, the time that elapses on his own clock between the reception of each of Gracie’s flashes, and his full knowledge about Gracie’s flight, what will he conclude about the rate at which Gracie emits flashes? Quote your answer in terms of the number of years that George says elapses on his clock between each flash that Gracie emits. (Hint: In all these problems, you can figure the answer from a space-time diagram with little calculation.)
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Question 2 of 4
2. Question
Based on Gracie’s observations, the time that elapses on her own clock between the reception of each of Georges’s flashes, and her full knowledge regarding her flight, what will she conclude about the rate at which George emits flashes during the portion of her journey before the turnaround? Quote your answer in terms of the number of years, as measured on Gracie’s clock, between each flash that George emits.
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Question 3 of 4
3. Question
Based on Gracie’s observations, the time that elapses on her own clock between the reception of each of Georges’s flashes, and her full knowledge regarding her flight, what will she conclude about the rate at which George emits flashes during the portion of her journey after the turnaround? Quote your answer in terms of the number of years, as measured on Gracie’s clock, between each flash that George emits.
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Question 4 of 4
4. Question
Based on Gracie’s observations, the time that elapses on her own clock between the reception of each of Georges’s flashes, and her full knowledge regarding her flight, what will she conclude about the number of flashes George emits during the moment she turned around to head back to Earth?
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