The definition of the proper time

[shallod]

Homework Statement

An observer in the rest frame sees a train go by at 0.99c and a clock on the train counts 2.0s.How much time has elapsed in the observers frame of reference？

Relevant Equations

t=dt*(1-v^2/c^2)^0.5

I wonder what is the proper time, the time passed on the train or the time of the observer?
If there is another people on the train, we see the train as a frame, so is the time on the train the proper time or the time of rest frame?

 

[etotheipi]

I wonder what is the proper time, the time passed on the train or the time of the observer?
If there is another people on the train, we see the train as a frame, so is the time on the train the proper time or the time of rest frame?

I'm conscious that I'm still a beginner in this topic too (so please take this with a grain of salt!), however as far as I am aware the proper time between two events on a worldline is defined as the time measured by a clock moving along that worldline; in other words $\Delta x$, $\Delta y$ and $\Delta z$ are zero in the spacetime interval expression. In this case, the two events could be the second hand of the clock in the train reaching $0\text{s}$ and the second hand reaching $2\text{s}$ - so which frame measures proper time?

Edit: Please see Orodruin’s answer

 

[Orodruin]

The problem statement is not entirely well written. Supposedly you are being asked for the coordinate time difference in the observer’s rest frame between the events where the clock shows t and t+2 s. Proper time is not related to any frame, it is the time measured by a clock following a particular world line. However, the coordinate time difference between two events on an observer’s world line in that observer’s rest frme is by definition equal to the proper time between the events.

 

[etotheipi]

Proper time is not related to any frame

I learned something as well today!