Hello I have some doubts about this problem which I have attached. If we assume that both the clocks are started at the time the airliner goes for a trip, then for an observer on the airliner, when the airliner comes back to the New York, the time interval would be a proper time interval since both the time measurements are done at the same place on the airliner. But the observer in New York is also not moving. So when the airliner comes back and the observer in the ground stops his clock, his measurement could also be considered proper time interval since the measurement is again done at the same place. Am I missing something ? Thanks [tex]\smile\smile\smile\smile[/tex]
I'm not sure what you mean by a proper time interval, but both the time intervals seen on the plane and on the ground are correct within their own reference frames. The plane was in a moving reference frame so time will have dilated(1 second on the plane takes more than one second on the ground), relative to the ground. But both clocks are correct, or proper. The velocity of the plane actually meant that the distance it traveled was shorter according to the clock on the ground (length contraction). Try to reconcile this with what the plane sees the clock on the ground doing and check that the clock on the ground still sees 4 hours.
Proper time interval is defined as the interval between two events which occur at the same position in a given inertial frame. In this sense, time interval measurements by both these persons seem to be proper time interval.
Yes, both times are the proper time interval IN THEIR OWN FRAME OF REFERENCE. But since they are not in the same frame of reference, they do not show the same amount of time.
Apologies, the last time I studied relativity in any real depth was over a year ago and I forget the terminology for things.......I think my answer is still valid though, despite not using proper properly!
I think part which is confusing is that the airliner comes back to New York. If it has landed at some other place like San Francisco, then for clock on the airliner we have proper time interval and for the clock on the ground we don't have a proper time interval.
There's not just one proper time between two events in space-time, if that's what you were thinking. The proper time measured between two events also depends on the motion of the clock.
vela, yes that's what I was thinking. But instead of airliner coming back to NY , I can imagine airliner going equal distance forward from the point of return and landing in some location we can all NY2. I think we get the same solution but conceptually its easier. Am I right ?
Yeah, if all you're looking to do is calculate the effect of time dilation, that scenario would be easier. But perhaps one of the purposes of the problem was to get you to think about exactly what you did.
It's more likely that clocks run a bit faster on the plane, assuming gravitational dilation is greater that velocity dilation.