Let us assume that there are two astronauts A and B who are floating in space. A sees B passing by and vice versa. A sends signals to B every minute. According to A since B is moving his clock will be slower. So B will receive the signals prior to the appointed minute. The same argument can be applied for B who will conclude A's clock is running slow. Who is right?
Answer
Both are right. Any moving clock is slower than a clock at rest, from the perspective of the frame at rest.
Maybe this simplified freehand graphic (apologies for its lack of precision) helps to see that both A and B feel the same about each other's time dilation:
Let's say that the red axis represents A and its proper time measured in minutes (first eight minutes are showed). Green axis and its numbers represents B observer.
Light or radio signals from A to B, represented in red oblique lines, are fired on a minute basis. Six of them are showed, that took six minutes of A proper time. However, these six signals from A to B take some eight minutes in B proper time. B concludes that A clock is slower. The same holds if we invert the situation (green lines from B to A). Well, almost the same (the last green line is intended to go from green 6 to red 8, blame my trembling fingers).
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