Time Slows Down

1
Time Slows Down
t
t

x
The x axis marks all the places where t 0.
x
2
t
t

x
x
3
Consider the point where the stationary frames
time hits the t axis. We cant assume that t
t. Lets assume for now that t g t.
t
t

x
x
4
Consider the point where the moving frames
time hits the t axis. Well label the two times
as t1 and t2. All frames are equivalent, so t
g t1.
t

t2
x
t1
x
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t2 g t
How are t1 and t2 related?
t g t1
t2 g2 t1
t

t2
x
t1
x
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t2 g2 t1 What does that tell you about g
? What does that tell you about time?
g is greater than one.
t
t

x
t
Each observer sees the other moving observer
with their time ticking more slowly.
x
7
We can find the formula for g by considering a
light clock, which sends light up and down
between mirrors once every time t.
8
Suppose that this clock is on a rocket ship
moving at a speed v to the right.
We observe that the light travels farther in our
frame. To keep c constant, it must also take more
time, c Dx/Dt. Therefore, our time interval is
larger than the rockets. Their clock runs
slower..
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c2 t2 v2 t2 c2 t2
(c2 - v2 ) t2 c2 t2
How much more slowly can be found by applying
Pythagoras theorem to the diagram below. Write
the equation and solve for t.
ct
ct
vt
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This formula does not depend on the fact that we
used a light clock. Anything that ticks will
do.
If you were on a rocket ship and sent a signal to
Earth every time your heart beat, doctors on
Earth would say that your pulse was slow.
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If the Earth doctor sent you a signal every time
that her heart beat, you would say that her pulse
was
a) faster b) normal c) slower
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Hint All inertial frames are equivalent.
a) faster b) normal c) slower
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What is g, if the relative speed of the two
frames is 3/5 c?
t
t

x
t
x
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• 5/4

t
t

8
x
x
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t is shorter but it looks longer.
t
t

x
x
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Reality Check3 Muons at CERN were accelerated
to high speeds and lived 20 times longer than
normal.