Re: SR examination question

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Thu, 17 May 2001, Michael Edmiston wrote:

> ... I also conclude that the first part of what John
> Mallinckrodt said about Peter thinking Jane reads 0.46 is not
> quite properly worded.

A minor point, but before this goes any further, allow me to
correct a genuine error:  The number is 0.44.

> ... 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.

I don't see why this is necessary other than for nitpicking
reasons which I have already chosen not to indulge in.  I am
willing to concede a number of things including

 1 the intent that the relative motion be linear

 2 the intent that "observation" takes on its usual, somewhat
   unfortunate meaning in special relativity--that is, that we
   correct for the literal "appearances" of things and actually
   "determine" when and where things happen within our own
   reference frame.

Since we are not interested in the actual readings of the clocks
but simply "how many revolutions they make during some (poorly
specified) time period," we need not concern ourselves with
synchronization processes.

> ... 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),

Hmm.  So do you *really* mean "observe?"  I think not, but the
introduction of that telescope does serve as pretty powerful
misdirection. If you do, it vastly complicates matters and I
sincerely doubt that it was the author's intent.

> ... 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.

I disagree.  The question (as I wrote it) explicitly states that
Jane is observing her watch.  It asks *what* *Peter* says Jane
observes *when* *Peter* observes his watch to have completed one
revolution.

I can agree that the question could have been made less unwieldy
by simply referring to what Jane's watch reads (rather than to
what Jane *observes* her watch to read), but there is no ambiguity
here:  Every observer agrees that what Jane *observes* her watch
to read (at *any* instant according to *any* observer) is what
Jane's watch *does* read at that same instant.

Pheww!

> 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.

Of *course* that is the event both people are observing; about
this fact there is absolutely no ambiguity.  But the question is
what *Jane's* watch reads "at the time of that event" and the
question is completely ambiguous about whether "*the* time" of
that event is to be determined by Jane or by Peter.

>  In that case Jane observes this event at x=-6.19x10^8 meters
> and t=2.19 minutes.

Right (almost.)  Jane says the time of the event, "Peter's clock
reads 1.00 minute," is 2.29 minutes.  Peter, of course, says the
time of that same event is 1.00 minute.  They disagree on what
time it is, but they certainly agree on what Peter's watch reads
(and what Peter *observes* his watch to read) since that *is* the
event they are watching.

But what do they each say *Jane's* watch reads (which is the same
thing as asking what do they each say Jane *observes* her watch to
read) at "*the* time" of the event, "Peter's watch reads 1.00
minute"?  Jane, of course, says her watch reads 2.29 minutes at
"that time."  But Peter says Jane's watch reads 0.436 minutes at
"that time."

I still see no way of resolving the ambiguity.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm