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The Twin Paradox
Brenda goes off at 4/5 c to a distant
star and then returns. Her twin brother
Ali stays on Earth. When she gets back
she is no longer the same age as Ali.
The first part looks like this. During this
half, Ali sees Brenda’s clock run slowly
and Brenda sees Ali’s clock run slowly.
Ali
t
Brenda
t’
x’
x
The second part looks like this. During the
second half they each see the other
person’s time run slower.
Ali
t
Brenda
t’
x’
x
Suppose Ali ages 10 years during the trip.
How much did Brenda age?
What is v?
v is 4/5 c.
t
What is g?
10
g is 5/3.
What is
the time
in the
middle of
the trip?
5
t’
x’
3
Brenda has only
aged 6 years.
x
If Brenda always sees Ali’s time ticking more slowly
and Ali always sees Brenda’s time ticking more
slowly. Why don’t they age by the same amount?
t
t’
x’
Brenda turns around.
Her frame is not
inertial andx therefore
not equivalent.
If Brenda always sees Ali’s time ticking more slowly
and Ali always sees Brenda’s time ticking more
slowly. When does Ali pick up the extra 4 years?
t
t’
x’
x
During the turnaround.
t
t’
x’
x
This is Brenda’s time at the start of the turn…
t
t’
x’
x
... in the middle …
t
t’
x’
x
… and at the end.
t
t’
x’
x
Almost no time passed for Brenda during the
turnaround, while a lot passed for Ali.
t
t’
x’
x
Reality Check #4: GPS satellites are
constantly turning around.
This makes their time run slower than ours
by 8.99 x 10-11s every second.
If the GPS failed to adjust for the different times,
then they would be out by 2.5 km after one day!