How can she reconcile a picture of the clock reading 4 seconds with her assertion that at the
instant she took the photograph the clock was registering 6.4 seconds?
The answer is that she can if she knows her relativity!
First point: length contraction
. To Jill, the clock
C
1
is actually only 4/5 x 18 x 10
8
meters away
(she sees the distance
C
1
C
2
to be Lorentz contracted!).
Second point: The light didn’t even have to go that far!
In her frame, the clock
C
1
is
moving
away
, so the light arriving when she’s at
C
2
must have left
C
1
when it was closer—at distance
x
in the figure below.
The figure shows the light in her frame moving from the clock towards her at
speed
c
, while at the same time the clock itself is moving to the left at 0.6
c
.
It might be helpful to imagine yourself in her frame of reference, so you are at rest, and to think
of clocks
C
1
and
C
2
as being at the front end and back end respectively of a train that is going
past you at speed 0.6
c
. Then, at the moment the back of the train passes you, you take a picture
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 Fall '10
 DavidJudd
 Physics, Special Relativity, Speed of light, Time Dilation, Lorentz, 2.4 seconds

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