Re: SR examination question

[Rick Tarara <rtarara@SAINTMARYS.EDU>]

How many Ph.D. Physicists does it take to......

While all the nit-piks that have been stated are arguably true, I think it
is quite clear what the question intends.  Jane's second hand makes 2.29
revolutions while Peter's makes one.  The watches don't need to be
synchronized to observe this and the observation is a 'God's Eye View' as is
often the case when talking about time dilation.  The assumption that Jane
is at rest and Peter is moving in a straight line are also common to such
problems.  At the intended level of the problem, I see nothing that should
confuse the students.  Any who could come up with all of our nit-piks should
also be wise enough to understand the intent of the question.

Rick

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Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556
rtarara@saintmarys.edu

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----- Original Message -----
From: "John S. Denker" <jsd@MONMOUTH.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Thursday, May 17, 2001 9:35 AM
Subject: Re: SR examination question


> 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.