In the twin paradox, twin A remains on Earth while twin B travels a distance L, measured in the Earth's inertial frame, at a velocity v to a very distant solar system. In turning around for the return trip, the rocket malfunctions somewhat and achieves only a velocity ½ v. Find formulas for the number of cycles counted by A and B from the two clocks, NA, NB, N'A, and N'B.

#3)
In the twin paradox, twin A remains on Earth while twin B travels a distance L, measured in the Earth's inertial frame, at a velocity v to a very distant solar system. In turning around for the return trip, the rocket malfunctions somewhat and achieves only a velocity ½ v. Find formulas for the number of cycles counted by A and B from the two clocks, NA, NB, N'A, and N'B.

Solution: Here we can take the number of cycles counted equal to the time measured in respective clocks. NA is the time measured by A's clock during onward journey, NB is the time measured by B's clock during onward journey, N'A is the time measured by A's clock during return journey and N'B is the time measured by B's clock during return journey.

When twin A observes the space craft (onward journey):
Let us consider twin A observes the space craft and measures the time taken by the space craft to travel 'L' distance. Given that the velocity of space ...

Solution Summary

With very thorough explanations and calculations, the problem is solved. The number of cycles from two clocks in modern physics are determined.

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The fully formatted problem is in the attached file.

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Problem 1. Bob is watching Anna ﬂy by in her high-speed plane, which Anna knows
to be 70 m in length. As a greeting, Anna turns on two lights simultaneously, one in front
and one at the tail. According to Bob, the lights come on at different times, 45 ns apart.
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