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PHY3221
Detweiler
Lecture #3
Relativity
A surprising consequence of length contraction:
Simultaneity is relative
In the search for a logical contradiction to the special relativity idea that the speed of
light
c
is always measured to be the same value, we look at the consequences of length
contraction.
The train that Alice rides on is 200 m long. Bob’s platform is actually inside the train
station, and is 175 m long. The station also has doors that lower over the tracks at either
end.
Here is a description of the experiment that Alice and Bob try. Alice’s train moves with
a speed
v
= 0
.
6
c
= 3
c/
5 so
p
1

v
2
/c
2
= 4
/
5 = 0
.
8
.
Bob knows that the
proper length
of
the train is
L
train
0
= 200 m, so at that speed if Bob measures the length of the train it will
only be
L
train
B
=
L
train
0
p
1

v
2
/c
2
= 4
/
5
×
200 m = 160 m
.
So Bob arranges to have two of his assistants put themselves at the doors at either end
of the station. The assistants are instructed to lower the doors when the train is inside
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 Spring '08
 CHAN
 mechanics, Special Relativity, Light

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