Who Measures Proper Time Interval in Astronaut Problem?

[IWantToLearn]

please read this problem

"An astronaut traveling in a spaceship aims his flashlight to an object inside the spaceship, the beam of light moves on the same direction as the direction of motion of the ship, he observed the time interval between the light leaves the flashlight and when it hits the object, another observer on the Earth measure the time interval between the two events, which one of them measures the proper time interval between these two events?"

i thought that the answer of this question is that the first observer measures the proper time

but the answer was "neither of them measures the proper time"

i need to know why?

 

[bcrowell]

The events are A, emission of the light, and B, the light hitting the object. Proper time between these events would be the clock time recorded by a clock that goes from A to B, and by implication the problem intends this to be a clock that moves inertially (else they wouldn't say "the proper time").

Neither of the observers referred to in the problem are present at event B, so neither has a clock that measures the proper time. The only thing that is moving inertially from A to B is the light itself. The light isn't a clock, and you can't make a clock from light. The proper time here is actually zero.

 

[someGorilla]

Proper time is measured along an object's worldline. It's the time that elapses between two events according to a clock sitting on board the object. If the astronaut turns the light on (event A) and then taps his foot on the floor (event B), the time between A and B is different according to different observers. But the proper time between A and B along the astronaut's worldline is only one, the one measured by the guy's wristwatch.
There's no such thing as "the proper time between A and B". There is the proper time between A and B along this path here or along that other path there. In the case of your problem, A and B are lightlike separated events, i.e. only light is fast enough to be in A and also in B, so there's no possible path for a (massive) object connecting them, and no sensible notion of a proper time. Unless you want to measure proper time along the light ray and say it's zero.

 

[IWantToLearn]

i got it now, Thanks for all

 

[sardar]

I can provide an explanation for why neither of the observers in this scenario measures the proper time interval. The concept of proper time is a fundamental principle in special relativity, which states that the proper time interval between two events is the time interval measured by an observer in the same frame of reference as the events. In this scenario, the astronaut and the observer on Earth are in different frames of reference, due to the relative motion of the spaceship and the Earth. Therefore, neither of them can measure the proper time interval between the events, as they are not in the same frame of reference. The proper time interval can only be measured by an observer who is at rest with respect to the events being measured. This concept is crucial in understanding the effects of time dilation and the relativity of simultaneity in special relativity.