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... I also conclude that the first part of what John
Mallinckrodt said about Peter thinking Jane reads 0.46 is not
quite properly worded.
... I will assume the question writer wanted us to assume
Peter's clock and Jane's clock were synchronized at t=0 when
their coordinate origins overlapped.
... The act of Peter reading his clock is an event occurring in
both time and space. He observes a particular time, and he is
somewhere in space when this occurs. In his reference frame
t=1.00 minute and his location is x=0 meters. We assume Jane
can also witness this event (with a sufficiently good
telescope),
... the first half of what John M. said is: "When Peter
observes the second hand on his watch to have made one
complete revolution, how many revolutions will Peter say Jane
observes the second hand of her watch to have made?"
This is a question we cannot ask because the question does not
specifying what event Jane is observing. If Jane is observing
Peter's clock reading 1.00, then she reads her clock as 2.29.
If Peter is observing Jane reading 0.46 on her clock , then he
reads 1.00 on his clock, but he cannot conclude she is reading
0.46 at the same time he is reading 1.00.
Therefore I conclude the problem is basically okay by assuming
Peter reading his clock at 1.00 minute is the event both
people are observing.
In that case Jane observes this event at x=-6.19x10^8 meters
and t=2.19 minutes.