Transcript Paradox PowerPoint

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.
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
The second part looks like this. During the
second half they each see the other
person’s time run slowly.
Ali
t
Brenda
t’
x
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
t’
10
5
Brenda accelerates when she turns
around. This can be detected.
x
You are in a closed room.
What tests could you do to tell if you were
accelerating?
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
x
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
t’
x’
x
During the turnaround.
t
t’
x’
x
This marks all the times that are simultaneous with
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
What would happen if Brenda stopped
and remained at the star? She would be
A) 6years younger.
B) 4 years younger.
C) 2 years younger
D) 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 matter
D) 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.
t
t’
How long must Ali wait
for her to get back?
How long does Brenda
think the trip took?
x
Ali sends Brenda a radio message every year. How
many messages does she receive? Draw them.
t
t’
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.