For me, time dilation is throwing up a very difficult paradox.
When one rocket is moving at 60% the speed of light or .6c relative to another rocket, an astronaut in each rocket observes time dilation effects in the other rocket. This appears contradictory. A clock in each rocket is running slow relative to a clock in the other rocket. How can both clocks run slow relative to each other?
I have set out the paradox below.
For astronaut A.
5 seconds have elapsed
Rocket B has travelled 3 light seconds at a speed of .6c
Astronaut B’s clock is reading 4 seconds
For astronaut B
4 seconds have elapsed
Rocket A has travelled 2.4 light seconds at a speed of .6c
Astronaut A’s clock is reading 3.2 seconds
Here is my problem. We started by saying that five seconds have elapsed in astronaut A’s reference frame but concluded by saying that, as far as astronaut B is concerned, 3.2 seconds have elapsed in astronaut A’s reference frame. How can this paradox be resolved
Regards
John
Answer John,
Since both rockets are in inertial frames(i.e. unaccelerated frames), it is equally correct to say that
1) A is moving with respect to B with B being stationary and
2) B is moving with respect to A with A being stationary.
Thus in case 1 if A measures a time interval of 5 seconds in his watch then B measures the same time interval to be 6.25 seconds.
For case 2 if B measures a time interval of 5 seconds , then A will measure a time interval of 6.25 seconds.
Both are right from their respective frames.
Thus there is no contradiction. You must remember that the times are measured relative to a particular reference frame and hence your argument doesn't hold.
