Proper Time Interval: A Puzzler

[cdenne]

Hello. I'm having trouble figuring out from which perspective to measure the proper time interval for Special Relativity. In the textbook, the definition says it's "the time interval between two events measured by an observer who sees the events occur at the same point in space." But in the derivation of the formula for time dilation, the authors use an example with two observers, one on a moving train, one stationary on Earth. The observer on the train measures the proper time interval as being the time it takes for a beam from a flashlight to go up (directly vertical), bounce off a mirror on the ceiling directly above the observer and return to the flashlight. But as I see it, the observer is not viewing the two events (the light leaving the flashlight and the light returning to the flashlight) at the same point in space because they've moved down the track and are in a different position from when the light left the flashlight. If anyone can help me with this, I'd appreciate it. Thanks.

 

[Nathanael]

I don't know much Special Relativity, so sorry if I'm wrong.

because they've moved down the track and are in a different position from when the light left the flashlight.

They've only "moved down the track" from the perspective of someone outside of the train. Within the train perspective, though, the flashlight's "position" is the same.

 

[cdenne]

Thank you for your response. I thought about that as I was typing the post. "The same position in space" probably refers to the reference frame in which the two events take place. From that perspective, the observer on the train is still in the same position on the train when both events occur whereas the observer outside the train has moved by the time the second event occurs.

 

[phinds]

In the textbook, the definition says it's "the time interval between two events measured by an observer who sees the events occur at the same point in space." .

Yes, you have figured it out (in post#3). It should say "by an observer who sees the events occur at the same point in space IN HIS FRAME OF REFERENCE".

There is no such thing as a "point in space" except as referenced against some OTHER point. That is "point in space" is frame dependent.

 

[cdenne]

Great. Thank you.