I just saw a question about time dilation, and thought I could ask a similar question I never really found an answer for on my own, hoping that some of you bright heads here might be able to provide an answer.
Since speed is relative, how does one determine which time is slowing down?
Let’s take a very simplified example, and make this assumption:
– Assume that it is possible to move away from earth in an arbitrary direction in 0.1 c (relative to earth) for a given time or distance, then turn around and travel back for the same time or distance, and arrive back at earth. (effectively ignoring that earth is experiencing acceleration during this time, or assuming that the spaceship experiences the same).
If my brother leaves on a spaceship and travels for 1 hour (in his time) away from the earth at 0.1 c, then turns around and travels back to earth for 1 hour at 0.1 c, while I remain at earth, will our experienced time differ in this scenario?
And how is this affected by the relativity of speed? Does it change if we instead assume that earth is travelling at 0.1 c through space, and my brothers spaceship decelerates essentially to a “stop”, then accelerates up to 0.2 c in order to “catch up” to earth again?
If my assumption in this question is absurd, I am sorry for that, I just don’t really know how to properly set up an example that describes my question good enough.
In: Physics
You seam to have a grasp of special relativity. This is a simplified version of general relativity that works as long as there is no acceleration. In your scenario one of the spaceships turns around which means you can not use special relativity for that spaceship. Time behaves very differently when accelerating and this is when your times will sync up.
Acceleration. The person who accelerated can sense that he is/has changed into a higher speed, so he knows that he’s the one “speeding up” compared to a relative stationary position.
I’m going to focus on your initial question.
The model of special relativity includes the prediction that given an observer A sitting in their own inertial frame of reference, any measurement that A makes to determine the rate at which time is passing for an entity B moving at constant velocity relative to the reference frame of A, will indicate that B experiences time more slowly than A. However, special relativity makes a symmetric prediction. Measurements made by an observer in the inertial reference frame of such an entity B, of the rate at which time passes for A as it moves relative to the frame of B, will indicate that A experiences time more slowly than B.
In such a case, neither of the observers are ‘wrong’. They’re just living in different inertial frames of reference, so their measurements are predicted to yield different results. These predictions have been verified by many different experimental observations, so they are thought to be quite reliable. They are analogous to the prediction of galilean relativity that in the inertial frame of a hypothetical observer standing on the ground next to a train track, a passing train has non-zero velocity, whereas from the perspective of a passenger standing at a fixed location within a particular train car, it is instead the observer standing on the ground next to the tracks who is moving with a different, non-zero velocity. Neither observer is ‘wrong’; ie there is no ‘true’ velocity for either observer. Their measurements are both correct for their own reference frame. Special relativity extends this notion to time as well as velocity, predicting discrepancies between the time, in addition to the velocity, that different observers measure certain entities to experience, depending on the relation between the inertial frames of reference that each observer inhabits. This is why the time that one observer B experiences as measured in the inertial reference frame of another observer A is just as ‘true’ as the different time that B measures themselves as experiencing in their own inertial reference frame.
It is a strange and highly counterintuitive prediction, but it has matched the results of many rigorous experiments designed to test it.
If you could observe each other, you would indeed both think the other is slowing down as you fly away from each other. However, velocity isn’t the only thing that causes time dilation. Acceleration also slows down time. When the brother in the rocket slows down, turns around, and speeds up towards home, they are the ones who accelerate.
Unlike velocity, acceleration isn’t relative. Both brothers will agree that during the period of acceleration, time slows down for the brother in the rocket.
So, both brothers observe the other as slowing down while they are moving at a constant speed, but the brother who is accelerating gets some extra additional slow down which then makes for the age difference both can agree on.
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