Re: [Phys-l] twin paradox question

[John Mallinckrodt <ajm@csupomona.edu>]

Just to be a little more concrete ...

If the relative speed is 3/5 c and the turnaround point is 3 light years away in the frame of the stay at home twin, then the round trip takes 10 years according to the stay at home twin and 8 years according to the traveler (since she sees a Lorentz contracted distance of only 2.4 light years.)

How the traveler sees things:

For the first four years, while the traveler is moving away, she sees her brother aging half as fast for a total of two years of aging.  For the remaining four years, while returning, she sees her brother aging twice as fast for a total of eight more years of aging.  The overall result is that she observes him to age by ten years.

How the stay at home twin sees things:

He can calculate that his sister reaches the turnaround point in five years, but he won't SEE that event for another 3 years.  So, for the first eight years he sees his sister moving away and aging half as fast for a total of four years of aging.  For the remaining two years, he sees his sister returning and aging twice as fast for a total of four years of aging.  The overall result is that he observes her to age by eight years.


(Incidentally, note also that he SEES--again, literally SEES--his sister *apparently* moving faster than the speed of light as she *apparently* covers the three light year distance in only two years.)

John Mallinckrodt
Cal Poly Pomona

On Dec 18, 2010, at 6:14 PM, John Mallinckrodt wrote:

> ... I think it is even easier and certainly more concrete to think about it in terms of Doppler shift.  Both twins SEE (literally SEE) the other twin aging more slowly as they move away from each other because of the Doppler shift and both SEE the other aging more quickly as they move towards each other.  The traveling twin SEES equal periods of slower and faster aging because the Doppler shift changes for her immediately upon turning around.  In contrast, the stay at home twin sees a much longer period of slower aging, because he doesn't see the Doppler shift change until the light from the turnaround event gets to him.  Thus, the traveling twin is younger when she returns.
>
> See http://www.csupomona.edu/~ajm/materials/twinparadox.html for a more complete explanation and spacetime diagrams.