# Proper time problem

## Main Question or Discussion Point

"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?

## Answers and Replies

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bcrowell
Staff Emeritus
Gold Member
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.

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.

i got it now, Thanks for all