I think I am going to reverse my earlier position and conclude one of two
situations.
(1) The problem is okay if a couple reasonable assumptions are made.
(2) The problem is totally unreasonable.
I also conclude that the first part of what John Mallinckrodt said about
Peter thinking Jane reads 0.46 is not quite properly worded.
Foremost, we have to remember John Denker's point 3 in his original post in
which he warns us to speak of an event in both time and space as opposed to
thinking of it just in time or just in space.
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. If we cannot assume this there is nothing we can do. We'll
assume Jane is moving in Peter's positive x direction and Jane is moving in
Peter's negative x direction. We do that only to get agreement on the +-
signs for position.
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), and she observes he is located at -6.19x10^8 m when he
reads 1.00 minute on his clock, and she sees her clock reads 2.29 minutes.
I have just described the second half of what John M. said; I think this is
correct; and it is probably what the question writer intended.
However, 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.
If the writer does not intend such assumptions then I conclude the problem
is totally messed up because the writer is trying to imply Jane reads some
time simultaneously to Peter reading some time, and this is something that
cannot be done.
I suppose I could conclude the event being referenced is Jane reading her
clock at t=0.46 min and x=0 m, and Peter observes her doing this at t=1.00
min on his clock and she is located at x=+2.85x10^8 m on his coordinate
system. But I would probably not conclude this because I think the problem
is referring to the event of Peter reading his clock.
In any event I would definitely not say "Jane reads xyz WHEN Peter reads
abc" because this type of wording is inappropriate. That's where the
problem went awry. We have to assume the writer meant to say "When Jane
sees Peter is reading 1.00 min on his clock, what is she reading on her
clock."
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817