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Experiment --> 1 2 3 4 5 6 7 8 9 Experiment 3
We now have the same set up except that the railroad car is now moving to the
left with a velocity v.
Answer:
From Mr. Einstein's perspective, the beam of light keeps going up and down
between the mirrors, but from Mrs. Einstein's perspective, the light now has to
travel a diagonal path from one mirror to the other. Since Mrs. Einstein still
measures the speed of light as c, she is now going to observe Mr. Einstein's
light clock as ticking slower than hers since the light now has a longer
distance to travel. However, since Mr. Einstein still experiences his watch as
being synchronized with his clock, Mrs. Einstein will see his watch slow down
along with his clock! Conclusion:
If someone moves in a straight line with velocity v with respect to you, then
you will observe time passing more slowly for them. With
a little algebra we can compute exactly how much time will slow down. Let, L=
length or height of the light clocks
We
will make frequent use of the formula distance = rate x time. We now
compute the distance that the light travels in two ways.
Hence,
ct´ =
which
implies that c2t´2 = 4L2 + v2t´2
, Since
t = (2L)/c (i.e. t = d/r), this gives us t´
=
Therefore,
if t is the time between ticks on Mrs. Einstein's watch, then she will observe a
longer interval of t´
=
between ticks on Mr. Einstein's watch! Notice that this difference is not very much unless one is traveling at an extremely fast velocity.
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