Question

Special Relativity:

A and B are initially a distance L apart, at rest with respect to each other. At a given time, B accelerates toward A with constant proper acceleration a. Assume aL << c^2.

a.) Working in A's frame, calculate the difference in readings on A's and B's clocks when B reaches A.

b.) Do the same by working in B's frame, and show that the result agrees (neglecting higher-order effects) with the result from a.).

Answer 1

Pease look up Classical mechanics by John. R. Taylor Example 15.11 where he solves to get the relativistic equation of motion under a constant proper acceleration. I have directly used that result and did the sum in the following image. However you are free to follow me up in case you want to kow more on how the equation of motion is coming.