What is the definition of proper time interval according to the book?

[joryboy]

Hi guys, I'm having trouble understanding the definition of proper time interval, according to my book (Physics for scientists and engineers with modrn physics 10th edition serway jewett) the proper time interval "is the time interval between two events measured by an observer who sees the events occur at the same point in space/is always the time interval measured by an observer for whom the two events take place at the same position". What do they mean by "events taking place at the same point/position"? For example if event 1 happens at point A and event 2 happens at point A as well, then an observer in the same inertial frame of reference as those two events is the one that can measure the proper time interval? Is that what they mean? Also they give an example about observer O' carrying a watch at rest, being in a train moving at constant velocity, and pointing a flashlight upwards to a mirror and another observer O being on the ground at rest and watching the same pair of events. According to the book observer O' measures the proper time, now from what I've seen online proper time is measured by a clock that is in the same inertial frame of reference where the events are happening, which agrees with the example of the book. But they have a second example where they ask which of the two observers would measure the proper time interval if observer O' aims the flashlight at the far end of the train and turns it on and off, sending a pulse of light toward the far wall of the train. Both O and O' measure the time interval between when the pulse leaves the flashlight and when it hits the far wall. This time the book says neither of them would measure the proper time interval, but does not explain why. My answer would be that O' can measure the proper time interval since he is in the train. Can somebody please help me clarify the idea of proper time interval in simple english? Thanks

 

[Chestermiller]

If an observer is physically present at the two events, the time interval he measures on his watch is the "proper time interval." As reckoned by observers in other frames of reference, these two events can occur at different spatial locations. However, in the frame of reference of the "proper time observer," the spatial coordinates of the two events are the same.