A & B Clocks: Why Velocity Time Dilation is Not a Paradox

[daudaudaudau]

We have two clocks, A and B. B is moving with constant velocity with respect to A. From the reference frame of A, B is running slow. From the reference frame of B, A is running slow. Why is this not a paradox?

 

[Bob_for_short]

We have two clocks, A and B. B is moving with constant velocity with respect to A. From the reference frame of A, B is running slow. From the reference frame of B, A is running slow. Why is this not a paradox?

But it is!

 

[sylas]

We have two clocks, A and B. B is moving with constant velocity with respect to A. From the reference frame of A, B is running slow. From the reference frame of B, A is running slow. Why is this not a paradox?

Because the passage of time is not absolute. It depends on the observer. There's nothing inconsistent about having different results in different reference frames.

 

[JesseM]

We have two clocks, A and B. B is moving with constant velocity with respect to A. From the reference frame of A, B is running slow. From the reference frame of B, A is running slow. Why is this not a paradox?

I'd say it's because of the relativity of simultaneity--two events which happen at the same time-coordinate in one frame may happen at a different time-coordinates in another. If the two clocks read 0 when they departed one another, and are moving apart at 0.866c (so the time dilation factor is 0.5), then in A's rest frame, the event of clock A reading 20 years is simultaneous with the event of clock B reading 10 years; but in B's rest frame these two events are not simultaneous, instead the event of clock B reading 10 years is simultaneous with the event of clock A reading 5 years (and the event of clock A reading 20 years is simultaneous with the event of clock B reading 40 years).

 

[meopemuk]

We have two clocks, A and B. B is moving with constant velocity with respect to A. From the reference frame of A, B is running slow. From the reference frame of B, A is running slow. Why is this not a paradox?

Suppose that you and I look at each other from a distance. You say that my (angular) size is small. I say that your (angular) size is small. Is this a paradox? No, because the angular size of an object is not an intrinsic property of that object. The angular size depends on the observer as well. Einstein's big discovery was the realization of the fact that the clock rate is not an intrinsic property of the clock. The rate depends also on who is watching that clock.

 

[ernestpworrel]

There's nothing inconsistent about having different results in different reference frames.

I agree with this statement. You are not allowed to draw any conclusions about the conditions of a particular frame based solely on measurements made from a non uniformly moving frame.