"Androcles" wrote in message
. uk...
"The Ghost In The Machine" wrote in
message
news
| In sci.physics.relativity, Jeckyl
|
| wrote
| on Sat, 2 Feb 2008 17:41:55 +1100
| :
| "snapdragon31" wrote in message
|
...
| The measurement is always on the distance between the Earth and the
| star 10c away.
|
| Relative to whom?
|
| Presumably, S.
|
|
| Twin S can predict what twin M measures based on S's information.
| But twin M cannot predict what twin S measures based on M's
| information.
|
| Yes .. they can .. its exactly the same math .. the problem is only
that
| *you* can't
|
| Predict? With a sufficiently large radiotelescope one can
| easily observe (in theory) the other twin, and the slowdown
| and speedup are symmetric in frequency but not in duration.
|
| Briefly put, M sees S slowed down for half of his trip,
| and sped up for the other half.
|
| Elapsed time (M) Observed ticks (S)
| L/(vg) sqrt(1-v/c)/sqrt(1+v/c)*L/(vg)
| L/(vg) sqrt(1+v/c)/sqrt(1-v/c)*L/(vg)
| --------------------------------------------------------
| 2L/(vg) ((1-v/c)+(1+v/c))*L/(vg*sqrt(1-v^2/c^2)
| = 2L/v
|
| For his part S sees
|
| Elapsed time (S) Observed ticks (M)
| sqrt(1+v/c)/sqrt(1-v/c)*L/(vg) L/(vg)
| sqrt(1-v/c)/sqrt(1+v/c)*L/(vg) L/(vg)
| --------------------------------------------------------
| 2L/v 2L/(vg)
|
| as one might expect. The problem is perfectly symmetrical in many
| respects, except that M has to turn around at the midway point.
Interesting.
So M gets fewer (emailed by radio) birthday cards than S, or do they
(being siblings) both send and receive the same number?
vice versa, actually, if we are talking about a full two-way twins-paradox
situation. M will end up getting way too many from S, and S will get very
few from M. The rate of arrival of cards will be quite different for the
two legs of the twins-paradox trip. Have a look at a Doppler analysis of
the twins paradox.
Now all I need to know is what a distance of 10c is...
Indeed .. but we being generous and are assuming that it is the distance
light would travel in 10 units of time (the units of time being implicit
there).