# proper time interval

We have two frames s and s' , s' moves with a constant velocity 'v' with respect to s in positive x direction, a particle B is thrown downwards from s' , and it collides with a particle A , the point which i don't get is when the author of the book(modern physics by arthur beiser) says that the time interval for the collision measured by observer in frame s' is the proper time. But here there is relative motion between the observer in s' and the objects A and B , then how can it be the proper time. My understanding of proper time is built upon the idea of meon decay, where the proper lifetime of meon is that time which an observer would record if it traveled with the same velocity as that of meon along its journey.

• Is that Concepts of Modern Physics by Arthur Beiser? If so, what page is this on? – John Rennie Oct 27 '15 at 16:05
• In the first edition its on page 32 and in the sixth edition its on page 22 . The wording in my question isn't exactly the same as that of the book, i have presented gist of the point, which i am doubtful about. – Mohammad Nayef Oct 27 '15 at 16:21

## 1 Answer

In the book is said that the time required for B to make its round trip is $T_0$ as seen from the S' reference frame and $T$ as seen from the S frame, with the following relation connecting them: $T=\frac{T_0}{\sqrt{1-\frac{u^2}{c^2}}}$. The events, start and end of the trajectory of B happen in the same place for S' and in a different one for S. So the proper time between these two events is measured by S' and the above relation is correct.

Also there is no inconsistency with the muon case, since the observer moving with the muon measures the lifetime of it in the same place , i.e the origin of the frame.