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. Sketch her trip on a spacetime diagram.

x

t

The first part looks like this. During this half, Ali sees Brenda’s clock run slowly and Brenda sees Ali’s clock

run slowly.

t’Ali Brenda

x

t

The second part looks like this. During the second half they each see the other person’s time run slowly.

t’Ali Brenda

x

t

Doesn’t relativity say their ages should be the same?

A)Yes, all frames are equivalent.B)Yes, all inertial frames are equivalent,C)No, only inertial frames are equivalent.

t’

10

5

Brenda accelerates when she turns around. This can be detected.

You are in a closed room. What tests could you do to tell if you were

accelerating?

x

t

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

t’

x’10

5

What is v?

v is 4/5 c.

What is ?

is 5/3.

What is the time in the middle of the trip?

3

x

t

If Brenda always sees Ali’s time ticking more slowly and Ali always sees Brenda’s time

ticking more slowly. When does he pick up the extra 4 years?

t’

x’

x

t

During the turnaround.

t’

x’

x

t

This marks all the times that are simultaneous with Brenda’s time at the start of the turn…

t’

x’

x

t

... in the middle …

t’

x’

x

t

… and at the end.

t’

x’

x

t

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

t’

x’

What would happen if Brenda stopped and remained at the star?

She would beA) 6years younger.B) 4 years younger.C) 2 years youngerD) the same age.

The GPS satellites are moving relative to us at 3874 m/s. This speed means that

A) we think their clocks are slow and the GPS thinks our clocks are slow.B) we think their clocks are slow and the GPS thinks our clocks are fast.C) nothing because the speed too small to matterD) nothing because gravity has a stronger effect.

Brenda goes on another long voyage at ½ c, to a star 2.5 light-years away and back.

Draw her path.

x

t’t How long must Ali wait for her to get

back?

How long does Brenda think the trip

took?

t’t

Ali sends Brenda a radio message every year.

How many messages does she receive? Draw them.

How many does she get on the way out? How many does she get on the way back?.

t’t

Brenda also sends Ali messages every year. How many will he receive compared

to Brenda?

A) the same number B) fewer

C) more

x

She sends fewer because less time has passed for her, so Ali receives

fewer.

t’t

Ali and Brenda agree on their relative speed but not on the time or distance for the trip. What is the proper distance and what is the

proper time?

t’t

Periodic signals carried by light show a Doppler shift if the source is moving

relative to the receiver. The formula for the relativistic Doppler shift is ,

fr/fs = sqrt( (1-v/c)/(1+v/c) )

How does this compare to the Doppler shift for sound? Why is it different?

fr/fs = (1-vr/u)/(1+vs/u)

Why do astronomers

think that there was a

Big Bang?

Use the data to calculate when it

occurred.