As you pilot your space utility vehicle at a constant speed toward the moon, a r

Question

As you pilot your space utility vehicle at a constant speed toward the moon, a race pilot flies past you in her spaceracer at a constant speed of 0.800c relative to you. At the instant the spaceracer passes you, both of you start timers at zero. (a) At the instant when you measure that the spaceracer has traveled 1.20 X 10^8m past you, what does the race pilot read on her timer? (b) When the race pilot reads the value calculated in part (a) on her timer, what does she measure to be your distance from her? (c) At the instant when the race pilot reads the value calculated in part (a) on her timer, what do you read on yours?

Please no calculus. I'll rate high!

Explanation / Answer

Question (c) is a VERY poorly worded question. It indicates that your teacher does not understand Relativity. There is NO SUCH THING as "the instant when the pilot reads part (a) on her timer" in any absolute sense. What people consider to be "that instant" is RELATIVE. It depends on who you ask. In other words, if it is "that instant" according to the pilot, it will be one answer and if it is "that instant" according to you, then it will be a different answer.

Part (a) suffers from the same problem, but it is doable because both you and the pilot agree that she does pass a mile marker marked "1.2*10^8 meters," and when she does, there is a graduate student sitting on that marker with a clock synchronized with yours, who can look at the pilot's clock for you. Both the pilot and the graduate student agree on the meaning of "instant" because they are right next to each other. But In Part (c), there is no such kluge you can set up. Part (c) attempts to make two distant observers agree on simultaneous events (race pilot passing the mile marker, and time read out on YOUR watch), and that is NOT POSSIBLE.

If "the instant" means an instant as measured by you, then you are correct: the time is simply from d=rt in part (a). If "the instant" is measured by the race pilot, then she observes your clock going too slow by a factor of gamma. It was zero when she was next to you, and the time found in part (a) has elapsed since then on her watch. Therefore, your clock reads what you found in part (a) (race pilot's time), REDUCED by a factor of gamma, because your clock (as measured by the race pilot) runs too slow.

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