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 Jim
is in a train car without any windows. Because the car has no windows
it is dark, so Jim decides to turn on his flashlight. From the end
of his flashlight to the wall is 100 meters. Because Jim always
measures the speed of light to be constant at 3.00 x 10^8 m/sec
and because Jim knows that the wall is 100 meters away, Jim discovers
that the light took only 1/3 x 10^-8 seconds to go from his flashlight
to the wall.
What Jim
doesn't know (because there are no windows) is that the train car
he is in is traveling along a track at 98% of the speed of light
in relation to Bob. Bob knows this because Bob is on the side of
the track. In fact, Bob can actually see inside the train car and
knows that Jim has a flashlight (trust me). Bob sees when Jim turns
his flashlight on, and notices when the light reaches the far wall
of the traincar.
He
measures the distance the train traveled from the time Jim turned
on the flashlight till the time the light hit the wall and discoveres
that the light traveled 994.98 meters. Bob, knowing that the speed
of light is constant at 3.00 x 10^-8 m/sec, calculates the time
it took the light to go from Jim's flashlight to the wall of the
car to be 3.317 x 10^-6 seconds.
When Jim
and Bob meet back up again, they decide to compare notes. They noticed
that:
- both of them measured
the speed of light to be the same, even though Jim was moving
in relation to Bob.
- both of them measured
the time it took the light to go from the flashlight to the wall.
- since Jim measured
the time it took the light to go from the flashlight to the wall
to be shorter than Bob's time, Jim must have experienced the event
faster than Bob; Jim's clock must have measured fewer clock ticks
and so run slower than Bob's.
- Bob knew that he could
find out the distance Jim's flashlight was to the wall by subtracting
how far Jim's train car traveled from how far the light traveled
(which he already measured to be 994.98 meters). Since Bob know's
Jim was going 98% of the speed of light, or 2.940 x 10^8 m/sec,
and the light traveled for 3.317 x 10^-6 seconds, the car must
have traveled 975.20 meters. 994.98 - 975.20 = 19.78 meters long.
Jim's length actually decreased as observed by Bob!
At this point Jim rose
up in frustration, exclaiming that he's quite sure the distance
was at least 5 times that measured by Bob. But what Jim failed to
realize was that Bob did not observe the light hit the end of the
wall at the same time Jim did. Bob noticed the light hit the wall
before Jim did, thus Bob measured the car's length as shorter.
Thinking quickly, Bob tried to explain this to Jim, but Jim soon
became tired of playing around with train cars and got into his
spaceship to explore the galaxies, thus demonstrating the Twin
Paradox.
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