The Twin Paradox

1


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.
2
The first part looks like this. During this
half, Ali sees Brendas clock run slowly and
Brenda sees Alis clock run slowly.

Brenda
Ali
t
x
3
The second part looks like this. During the
second half they each see the other persons time
run slower.

Brenda
Ali
t
x
4
Suppose Ali ages 10 years during the trip. How
much did Brenda age?

What is v?
t
v is 4/5 c. What is g?

• is 5/3.
• What is the time in the middle of the trip?

3
Brenda has only aged 6 years.
x
5
If Brenda always sees Alis time ticking more
slowly and Ali always sees Brendas time ticking
more slowly. Why dont they age by the same
amount?

t
Brenda turns around. Her frame is not inertial
and therefore not equivalent.
x
6
If Brenda always sees Alis time ticking more
slowly and Ali always sees Brendas time ticking
more slowly. When does Ali pick up the extra 4
years?

t
x
7
During the turnaround.

t
x
8
This is Brendas time at the start of the turn

t
x
9
... in the middle

t
x
10
and at the end.

t
x
11
Almost no time passed for Brenda during the
turnaround, while a lot passed for Ali.

t
x
12
Reality Check 4 GPS satellites are constantly
turning around.
13
This makes their time run slower than ours by
8.99 x 10-11s every second.
14
If the GPS failed to adjust for the different
times, then they would be out by 2.5 km after one
day!