Re: SR examination question

["John S. Denker" <jsd@MONMOUTH.COM>]

At 12:27 PM 5/17/01 +0200, Mark Sylvester wrote:
> Am I correct in thinking that the following simple question is inadequately
> specified?
>
> Peter and Jane are each wearing a wristwatch with a second hand that takes
> one minute to make one complete revolution and Peter is moving at a speed
> of 0.9c with respect to Jane. When Peter observes the second hand on his
> watch to have made one complete revolution, how many revolutions will Jane
> observe the second hand of her watch to have made?

Yes, it's broken, in several small ways and one big way.

0) We are entitled to assume that watches run at the right rate (in their
proper frame).  That is, any second-hand takes one minute to make a
complete revolution.  Restating this in the question is harmless but
weird.  Let's delete the first half of the first sentence and see what's left.

1) To be generous, let's assume straight-line motion.  This is probably
what the questioner intended, but is certainly not the general case;  Peter
and Jane could have a constant relative speed of 0.9c while they orbit a
black hole.

2) To be very generous, let's also assume that Peter and Jane choose a
common origin of coordinates (0,0,0,0) and they start out there, with
synchronized watches.  This is probably what the questioner intended, but
it is a totally nontrivial assumption.  I don't know about you, but I have
to set my watch every so often.  If we don't assume the watches are
initially synchronized, the question is unanswerable, even in the absence
of relativistic complications.

3) Relativity implies breakdown of simultaneity-at-a-distance.  You can't
safely speak of "when" Peter observes this or that;  you need to speak of
when-and-where he observes something.  "When" one second of Peter-time has
elapsed, Jane's watch will be ahead or behind, depending on whether we
transfer that notion of "when" to Jane's location using Peter's
constant-time contours or Jane's constant-time contours.

I have no idea what the questioner intended as to item (3).  The question
is essentially symmetric.