1
PHY3221
Detweiler
Lecture #2
Relativity
Length Contraction
The effect of time dilation, discussed in the previous lecture, seems selfcontradictory?
How can Alice say that Bob’s clock runs too slowly, while Bob is saying that Alice’s clock runs
too slowly given a situation between the two which appears to be completely symmetrical?
This conundrum brings us to what is commonly called the twin paradox which we will
discuss later.
First let’s look at an apparent paradox caused by having Alice’s and Bob’s clocks running
at different rates.
Alice is still in the train going through Bob’s station.
Assume that Alice’s speed is
v
= 3
c/
5 = 0
.
6
c
so that
p
1

v
2
/c
2
=
√
1

0
.
36 =
√
0
.
64 = 0
.
8 = 4
/
5
.
This makes the arithmetic work out nicely.
Alice and Bob have arranged the following experiment ahead of time. When Alice reaches
the front of the platform she starts her clock and also leans out the train window with a
paint brush and marks the front of the platform. Call this event #1. Exactly 1
×
10

6
s later
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 Spring '08
 CHAN
 mechanics, Special Relativity, Alice, platform

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