Time measured by two clocks (involves time dilation)

[songoku]

Homework Statement

A friend speeds by you in her spacecraft at a speed of 0.720c.
(a) How many seconds elapsed on your friend’s watch when 20.0 s passed on yours?
(b) How many seconds elapsed on your watch when she saw 20.0 s pass on hers?

Relevant Equations

$t=\gamma t_o$

Proper time (t_o) is the time interval between two events measured by an observer who sees the events occur at the same point in space.

I am confused how to determine which one is proper time for this question. How to know which events occur at the same point from the question sentence?

Thanks

 

[PeroK]

Homework Statement:: A friend speeds by you in her spacecraft at a speed of 0.720c.
(a) How many seconds elapsed on your friend’s watch when 20.0 s passed on yours?
(b) How many seconds elapsed on your watch when she saw 20.0 s pass on hers?
Relevant Equations:: $t=\gamma t_o$

Proper time (t_o) is the time interval between two events measured by an observer who sees the events occur at the same point in space.

I am confused how to determine which one is proper time for this question. How to know which events occur at the same point from the question sentence?

Thanks

All watches record proper time. The answer, therefore, is both.

 

[songoku]

All watches record proper time. The answer, therefore, is both.

Sorry I don't understand.

Let say I wear watch P and my friend wears watch Q.

Question (a) states my watch P records 20 s and asks for the time recorded by watch Q. By "all watches record proper time", which watch do you refer to?

Maybe my understanding is wrong but I think which watch measures proper time is related to what time interval is actually measured. If let say I want to measure the time needed for the spacecraft to move from a certain point A to another point B, then watch Q measures the proper time. But if I want to measure the time for the whole body of the spacecraft to pass through point A, then watch P is the one recording the proper time.

That's why I feel like there is missing information from the question.

Thanks

 

[PeroK]

Sorry I don't understand.

Let say I wear watch P and my friend wears watch Q.

Question (a) states my watch P records 20 s and asks for the time recorded by watch Q. By "all watches record proper time", which watch do you refer to?

All watches record proper time. That is the definition of proper time. It's equivalent to the one you gave.

 

[kumusta]

Another way to look at proper time is in terms of the relative motion between (1) the observer using a watch, and (2) the event whose duration is being measured by the observer. With zero relative motion between (1) and (2), the time obtained is the proper time.

Sorry I don't understand.
Let say I wear watch P and my friend wears watch Q ...

Let us assume instead that Q is the female friend moving relative to the other friend P.
In (a), with Q wanting to know the elapsed time in her watch after 20.0 s passed in P's watch, the 20.0 s is a proper time since in looking at his watch, the observer P and the passing of time being measured have zero relative motion. Q herself did not measure the time using P's watch.
Similarly in (b), with P wanting to know the elapsed time in his watch after 20.0 s passed in Q's watch, the 20.0 s is a proper time too since in looking at her watch, the observer Q and the passing of time being measured have zero relative motion. P himself did not measure the time using Q's watch.

 

[jbriggs444]

Homework Statement:: A friend speeds by you in her spacecraft at a speed of 0.720c.
(a) How many seconds elapsed on your friend’s watch when 20.0 s passed on yours?
(b) How many seconds elapsed on your watch when she saw 20.0 s pass on hers?
Relevant Equations:: $t=\gamma t_o$

Proper time (t_o) is the time interval between two events measured by an observer who sees the events occur at the same point in space.

I am confused how to determine which one is proper time for this question. How to know which events occur at the same point from the question sentence?

Thanks

I am not fond of the question statement. The answers depend strongly on the choice of reference frame and the relativity of simultaneity. But no reference frame is clearly specified. Welcome to real life, where questions almost always carry implicit assumptions that are not clearly communicated.

Let us assume that both clocks were zeroed at the event of your passing each other.

Rewritten for clarity:

(a) How many seconds elapsed on your friend’s watch when (according to your rest frame's standard of simultaneity), 20.0 s has passed on yours?

(a) How many seconds elapsed on your friend’s watch when (according to her rest frame's standard of simultaneity) 20.0 s passed on yours?

 

[songoku]

I am not fond of the question statement. The answers depend strongly on the choice of reference frame and the relativity of simultaneity. But no reference frame is clearly specified. Welcome to real life, where questions almost always carry implicit assumptions that are not clearly communicated.

Let us assume that both clocks were zeroed at the event of your passing each other.

Rewritten for clarity:

(a) How many seconds elapsed on your friend’s watch when (according to your rest frame's standard of simultaneity), 20.0 s has passed on yours?

(a) How many seconds elapsed on your friend’s watch when (according to her rest frame's standard of simultaneity) 20.0 s passed on yours?

I also lean more towards this approach, it is not really clear whether 20 s is proper time or dilated time

Another way to look at proper time is in terms of the relative motion between (1) the observer using a watch, and (2) the event whose duration is being measured by the observer. With zero relative motion between (1) and (2), the time obtained is the proper time.

Let us assume instead that Q is the female friend moving relative to the other friend P.
In (a), with Q wanting to know the elapsed time in her watch after 20.0 s passed in P's watch, the 20.0 s is a proper time since in looking at his watch, the observer P and the passing of time being measured have zero relative motion. Q herself did not measure the time using P's watch.
Similarly in (b), with P wanting to know the elapsed time in his watch after 20.0 s passed in Q's watch, the 20.0 s is a proper time too since in looking at her watch, the observer Q and the passing of time being measured have zero relative motion. P himself did not measure the time using Q's watch.

I understand your explanation.

But I just got the solution from the teacher :

The solution states "we find the dilated time" but the calcuation actually is for proper time.

I think I will just dismiss this question as a bad question.

Thank you very much for the help and explanation PeroK, kumusta, jbriggs444

 

[kumusta]

From 20.0 s to 15.0 s < 20.0 s is not time dilation but time deflation!
Also, the rocket was supposed to be traveling at (0.75)$c$ and not at (0.66)$c$ that you gave in the solution. The 20.0 s must be used at the right hand side of the time dilation formula because it is the proper time. Instead, you used the 20.0 s as the apparent time which is not correct.

 

[PeroK]

The solution states "we find the dilated time" but the calcuation actually is for proper time.

I think I will just dismiss this question as a bad question.

That's all very well, but it leaves you in a state of confusion over what proper time is. All clocks and watches measure their own proper time. Proper time is a personal thing!

 

[songoku]

From 20.0 s to 15.0 s < 20.0 s is not time dilation but time deflation!
Also, the rocket was supposed to be traveling at (0.75)$c$ and not at (0.66)$c$ that you gave in the solution. The 20.0 s must be used at the right hand side of the time dilation formula because it is the proper time. Instead, you used the 20.0 s as the apparent time which is not correct.

I didn't realize that the speed is wrong . I only paid attention to what 20 s is, proper time or dilated time. So it means that in my teacher point of view, 20 s is the dilated time

but it leaves you in a state of confusion over what proper time is.

It certainly is.

If you were the one doing the question, what would be your approach to solve it? Would you regard the 20 s as proper time or dilated time?

Thanks

 

[PeroK]

If you were the one doing the question, what would be your approach to solve it? Would you regard the 20 s as proper time or dilated time?

Time dilation is symmetric. Your friend's proper time is dilated in your reference frame; and your proper time is dilated in her reference frame.

Time dilation applies to proper time.

 

[songoku]

Time dilation is symmetric. Your friend's proper time is dilated in your reference frame; and your proper time is dilated in her reference frame.

Time dilation applies to proper time.

I think I understand. Your interpretation is the same as my teacher.

Thank you again kumusta and PeroK