Answer to Question #274901 in Mechanics | Relativity for JMD

Question

Assuming 2 objects, A & B, connected together, so sitting still in relationship to one another, then a force is applied to B causing it to accelerate through space away from A, and then the accelerating force is removed leaving B to continue away from A at a constant velocity.

Since we know that the accelerating force was applied to B, can we say that a clock in B, that had been initially synchronized with a clock in A, will tick slower than the clock in A, and would read, at some lapsed time, less than A?

And if the two objects returned to rest in regards to one another, (at some distance apart from each other) either by a reverse force being applied to B until it slows to a stop in regards to A, or a force being applied to A accelerating it in the direction of B until it reaches the velocity of B, can we say that the two clocks will again tick in unison but that the clock in B will read behind the clock in A?

Answer 1

After compensating for varying signal delays due to the changing distance between an observer and a moving clock (i.e. Doppler effect), the observer will measure the moving clock as ticking slower than a clock that is at rest in the observer's own reference frame. In addition, a clock that is close to a massive body (and which therefore is at lower gravitational potential) will record less elapsed time than a clock situated further from the said massive body (and which is at a higher gravitational potential).