Re: Special Relativity

[John Clement <clement@HAL-PC.ORG>]

> The key point is that when the traveller transfers his
> timekeeping from the outbound observer to the inbound
> observer, there is a radical disagreement as to
> what they think the "current" time is back home.  We
> can understand this just by glancing at the spacetime
> diagram:  Look at the the red line (toward 8:00) from
> the turnaround point and see where it crosses the
> green vertical axis (which is the worldline of the
> stay-at-home twin).  Then look at the blue line (toward
> 10:00) from the turnaround point and see where it
> crosses the the green axis. These two crossing points
> are radically different.
>
> Note that we do not need to worry about what Gee forces
> the traveller is subjected to during the turnaround.
> That doesn't matter.  No matter how he accomplishes
> the turnaround, he must transfer from one timekeeping
> system to the other, and must therefore incur the
> disgreement as to the "current" time back home.
>
> To complete the analysis, you need to take into account
> the time dilatation of the red and blue observers
> relative to the green observer, but that's relatively
> routine.
While correct it requires that you ignore what happens during the
turnaround.  In other words the solution is not complete.  To complete the
solution requires GR.  The fact that SR will not change the results
significantly does not alter the incompleteness of the SR solution.  It
seems simple to say that one must change timekeeping to the new frame, but I
suspect from the point of view of the beginning student this is a large
leap.  Indeed just understanding a spacetime diagram would be a large leap
for such a student.  As a result they might still tend to see it as
paradoxical.  One can certainly speculate as to what the moving twin
observes during the acceleration, but this is not properly predicted by SR.

Whether or not we call the twin problem paradoxical is in a sense irrelvant.
Historically it has been called the "twin paradox" and when students first
encounter the idea they instinctively think of it as being paradoxical.
Acknowledging the apparent paradox might be helpful when teaching the
problem.  This is similar to PER methods of teaching which have students
bring up their misconceptions in order to dispel them.

John M. Clement
Houston, TX

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.