wasser_1@viking.DEC (John A. Wasser) (06/03/85)
The Twin Paradox occurs because of the contraction along the
direction of travel of objects moving at high speed relative
to the observer. Lets take a trip from Earth to a star 10
light-years away at a speed where the contraction is 1/2.
Lets call this speed .5c (which is wrong). (V would realy
be 211,985,280m/s or c/sqrt(2) or about .707c) The ship leaves
Earth at this speed, goes to the star and instantly reverses
direction (this will simplify the example).
Observer on the ship moving relative to the Earth/Star system:
Due to the contraction, the distance from the Earth to
the star looks like 5 light years. Traveling 5 light
years at .5c takes ten years. Reversing direction and
traveling the other way also takes 10 years so the total
trip time (measured in the ship) is 20 years.
Observer on the Earth/Star system moving relative to the ship:
Due to the contraction, the length of the ship seems
to be half its normal length. The distance to the
star is still 10 light-years because the observer is
not moving along the vector between the Earth and the
star. The Earth/Star system move past the ship for
20 years at .5c. At this time the star end of the
Earth/Star system has reached the (stationary) ship.
The system now reverses direction and moves past the
ship in the opposite direction. In another 20 years
of moving at .5c, the Earth has once again reached
the ship. The total trip time (measured on the Earth)
is 40 years.
Much of this I derived for my own edification after reading
"Einstein for Beginners". It explains why the speed limit
on light implies contraction.
-John A. Wasser
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