I'm wondering if this is indeed correct. As you have described the thought experiment, clock 1 moves quickly from point A to point B, but it then it has to stop and wait for clock 2 to catch up, so that we can compare them. So for a period of time clock 1 is the faster moving clock, but then it stops and clock 2 becomes the faster moving clock. Do these two effects cancel each other out such that the two clocks will actually read the same time when clocks 1 and 2 reach point B? Or is the effect of increased time dilation exponentially greater as speed increases such that the faster moving clock will have actually experienced less time when both clocks ultimately reach point B?A------------------------------B
Let's say that you have two identical atomic clocks with identical readings at point A. Now clock 1 is moved fast from A to B, and clock 2 is moved slowly from A to B. Then you compare the two clocks at B and you will find that clock 1 is behind on clock 2. In other words, the clock that moved slower will have recorded more units of time than the clock that moved fast.