Physics 1161: Lecture 26
Special Relativity
Sections 29-1 – 29-6
Special Relativity
• Null result of Michelson Morley Experiment
• Relative motion of magnet and loop of wire
induces current in loop
• http://www.fourmilab.ch/etexts/einstein/spec
rel/www/
Michelson-Morley Experiment
• Designed to prove the
existence of the ether
– the still reference
frame
• Speed of light was the
same no matter the
direction relative to
the earth’s motion
Lorentz-Fitzgerald Contraction
• Length is contracted in the direction of motion
• Accounts for the null result
• Amount of shrinkage:
1 v c
2
2
You and your friend are playing catch in a train moving
at 60 mph in an eastward direction. Your friend is at
the front of the car and throws you the ball at 3 mph
(according to you). What velocity does the ball have
when you catch it, according to you?
1)
2)
3)
4)
5)
3 mph eastward
3 mph westward
57 mph eastward
57 mph westward
60 mph eastward
0%
1)
0%
0%
2)
3)
0%
0%
4)
5)
You and your friend are playing catch in a train moving
at 60 mph in an eastward direction. Your friend is at
the front of the car and throws you the ball at 3 mph
(according to you). What velocity does the ball have
when you catch it, according to you?
1)
2)
3)
4)
5)
3 mph eastward
3 mph westward
57 mph eastward
57 mph westward
60 mph eastward
0%
1)
0%
0%
2)
3)
0%
0%
4)
5)
You and your friend are playing catch in a train moving
at 60 mph in an eastward direction. Your friend is at
the front of the car and throws you the ball at 3 mph
(according to you). What velocity does the ball have as
measured by someone at rest on the platform?
1)
2)
3)
4)
5)
63 mph eastward
63 mph westward
57 mph eastward
57 mph westward
60 mph eastward
0%
1)
0%
0%
2)
3)
0%
0%
4)
5)
You and your friend are playing catch in a train moving
at 60 mph in an eastward direction. Your friend is at
the front of the car and throws you the ball at 3 mph
(according to you). What velocity does the ball have as
measured by someone at rest on the platform?
1)
2)
3)
4)
5)
63 mph eastward
63 mph westward
57 mph eastward
57 mph westward
60 mph eastward
0%
1)
0%
0%
2)
3)
0%
0%
4)
5)
Inertial Reference Frame
• Frame in which Newton’s Laws Work
• Moving is OK but….
– No Accelerating
– No Rotating
• Technically Earth is not inertial, but it’s close
enough.
Which of the following systems are not inertial
reference frames?
1) a person standing still
2) an airplane in mid-flight
3) a merry-go-round rotating
at a constant rate
4) all of the above are IRFs
5) none of the above are IRFs
0%
1)
0%
0%
2)
3)
0%
0%
4)
5)
Which of the following systems are not inertial
reference frames?
1) a person standing still
2) an airplane in mid-flight
3) a merry-go-round rotating
at a constant rate
4) all of the above are IRFs
5) none of the above are IRFs
0%
1)
0%
0%
2)
3)
An inertial reference frame is the same as a non-accelerating reference
frame. Due to the circular motion of the merry-go-round, there is a
centripetal acceleration, which means that the system is accelerating.
Therefore it is not an inertial reference frame.
0%
0%
4)
5)
Speed of Light
Checkpoint
Your friend fires a laser at you while you're standing still.
You measure the photons to be coming towards you at
the speed of light (c = 3.0 x 108 m/s). You start running
away from your friend at half the speed of light (1/2c =
1.5 x 108 m/s). Now how fast do you measure the
photons to be moving?
1. 0.5 c
2. C
3. 1.5 c
Special Theory of Relativity Postulates
• All laws of nature are the same in
all uniformly moving frames of
reference.
• The speed of light in free space
has the same measured value for
all observers, regardless of the
motion of the source or the
motion of the observer; that is, The speed of a light flash
the speed of light is a constant. emitted by the space
station is measured to be
c by observers on both
the space station and the
rocket ship.
Which of these quantities change when you
change your reference frame?
1)
2)
3)
4)
5)
position
velocity
acceleration
All of the above
Only a) and b)
0%
1)
0%
0%
2)
3)
0%
0%
4)
5)
Which of these quantities change when you
change your reference frame?
1) position
2) velocity
3) acceleration
4) All of the above
5) Only a) and b)
0%
1)
0%
0%
2)
3)
0%
0%
4)
5)
Position depends on your reference frame – it also depends on
your coordinate system. Velocity depends on the difference in
position, which also relates to the frame of reference.
However, since acceleration relates to the difference in
velocity, this will actually be the same in all reference frames.
Simultaneity
• two events are simultaneous if they occur at the
same time.
From the point of view of the observer who travels with
the compartment, light from the source travels equal
distances to both ends of the compartment and
therefore strikes both ends simultaneously.
Simultaneity
• Two events that are simultaneous in one frame of
reference need not be simultaneous in a frame moving
relative to the first frame.
Because of the
ship's motion, light
that strikes the
back of the
compartment
doesn't have as far
to go and strikes
sooner than light
strikes the front of
the compartment.
A boxcar moves to the right at a very high speed. A
green flash of light moves from right to left, and a blue
flash from left to right. For someone with sophisticated
measuring equipment in the boxcar, which flash takes
longer to go from one end to the other?
1) the blue flash
2) the green flash
3) both the same
v
0%
1)
0%
2)
0%
3)
A boxcar moves to the right at a very high speed. A
green flash of light moves from right to left, and a blue
flash from left to right. For someone with sophisticated
measuring equipment in the boxcar, which flash takes
longer to go from one end to the other?
1) the blue flash
2) the green flash
3) both the same
v
The speed of light is c inside the boxcar, and the distance
that each flash must travel is L (length of boxcar). So each
flash will take t = L/c, which will be the same for each one.
0%
1)
0%
2)
0%
3)
A boxcar moves to the right at a very high speed. A
green flash of light moves from right to left, and a blue
flash from left to right. According to an observer on the
ground, which flash takes longer to go from one end to
the other?
1) the blue flash
2) the green flash
3) both the same
v
0%
1)
0%
2)
0%
3)
A boxcar moves to the right at a very high speed. A
green flash of light moves from right to left, and a blue
flash from left to right. According to an observer on the
ground, which flash takes longer to go from one end to
the other?
1) the blue flash
2) the green flash
v
3) both the same
The ground observer still sees the light moving at speed c.
But while the light is going, the boxcar has actually
advanced. The back wall is moving toward the green flash,
and the front wall is moving away from the blue flash.
Thus, the blue flash has a longer distance to travel and
takes a longer time.
0%
1)
0%
2)
0%
3)
Twin Paradox
Checkpoint
You discover that you have a long-lost twin
who's been on a high-speed spaceship for the
last 10 years. When your twin returns to Earth,
he or she will be:
1. Younger than you
2. Older than you
3. The same age as you are
Time Dilation
• http://www.youtube.com/watch?v=KHjpBjgI
MVk&feature=related
Time Dilation
D
ct0  2 D
2D
t0 
c
t0 is proper time
Because it is rest frame of
event
Time Dilation
L=v t
D
D
½ vt
ct0  2 D
2D
t0 
c
t0 is proper time
Because it is rest frame of
event
vt 

ct  2 D  

 2 
2D 1
t 
c
v2
1 2
c
2
t0
t 
v2
1 2
c
2
An astronaut moves away from Earth at close to the
speed of light. How would an observer on Earth
measure the astronaut’s pulse rate?
1)
2)
3)
4)
it would be faster
it would be slower
it wouldn’t change
no pulse - the astronaut
died a long time ago
0%
1)
0%
2)
0%
3)
0%
4)
An astronaut moves away from Earth at close to the
speed of light. How would an observer on Earth
measure the astronaut’s pulse rate?
1)
2)
3)
4)
it would be faster
it would be slower
it wouldn’t change
no pulse - the astronaut died a
long time ago
The astronaut’s pulse would function like a
clock. Since time moves slower in a moving
reference frame, the observer on Earth
would measure a slower pulse.
0%
1)
0%
2)
0%
3)
0%
4)
The period of a pendulum attached in a spaceship is 2
seconds while the spaceship is parked on Earth. What
is its period for an observer on Earth when the
spaceship moves at 0.6c with respect to Earth?
1) Less than 2 seconds
2) 2 seconds
3) More than 2 seconds
0%
1)
0%
2)
0%
3)
The period of a pendulum attached in a spaceship is 2
seconds while the spaceship is parked on Earth. What
is its period for an observer on Earth when the
spaceship moves at 0.6c with respect to Earth?
1) Less than 2 seconds
2) 2 seconds
3) More than 2 seconds
To the Earth observer, the
pendulum is moving relative to
him and so it takes longer to swing
(moving clocks run slow) due to
the effect of time dilation.
0%
1)
0%
2)
0%
3)
The period of a pendulum attached in a spaceship is 2
seconds while the spaceship is parked on Earth. What
would the astronaut in the spaceship measure the
period to be?
1) Less than 2 seconds
2) 2 seconds
3) More than 2 seconds
0%
1)
0%
2)
0%
3)
The period of a pendulum attached in a spaceship is 2
seconds while the spaceship is parked on Earth. What
would the astronaut in the spaceship measure the
period to be?
1) Less than 2 seconds
2) 2 seconds
3) More than 2 seconds
0%
1)
0%
2)
0%
3)
Space Travel
Alpha Centauri is 4.3 light-years from earth. (It takes light 4.3
years to travel from earth to Alpha Centauri). How long
would people on earth think it takes for a spaceship traveling
v=0.95c to reach A.C.?
How long do people on the ship think it takes?
Space Travel
Alpha Centauri is 4.3 light-years from earth. (It takes light 4.3
years to travel from earth to Alpha Centauri). How long
would people on earth think it takes for a spaceship traveling
v=0.95c to reach A.C.?
d 4.3 light - years
 4.5 years
t  
v
0.95 c
How long do people on the ship think it takes?
People on ship have ‘proper’ time they see earth
leave, and Alpha Centauri arrive. t0
t0
t 
v2
1  Slide
Physics 1161: Lecture 28, 2
c
34
v2
t0  t 1  2  4.5 1  .952
c
t0 = 1.4 years
Length Contraction
Checkpoint
You're eating a burger at the interstellar cafe in
outer space - your spaceship is parked outside. A
speeder zooms by in an identical ship at half the
speed of light. From your perspective, their ship
looks:
1. Longer than your ship
2. Shorter than your ship
3. Exactly the same as your ship
Length Contraction Gifs
v=0.1 c
v=0.8 c
v=0.95 c
Length Contraction
People on ship and on earth agree on relative velocity v = 0.95 c. But they disagree on
the time (4.5 vs 1.4 years). What about the distance between the planets?
Earth/Alpha
d0 = v t
Ship
d=vt
Length in moving
frame
Length in object’s rest
frame
v2
L  L0 1  2
c
Length Contraction
Sue is carrying a pole 10 meters long. Paul is on a barn which is 8
meters long. If Sue runs quickly v=.8 c, can she ever have the
entire pole in the barn?
Paul:
v2
L  L0 1  2
c
Sue:
v2
L  L0 1  2
c
Length Contraction
People on ship and on earth agree on relative velocity v = 0.95 c. But they disagree on
the time (4.5 vs 1.4 years). What about the distance between the planets?
Earth/Alpha
d0 = v t
= .95 (3x108 m/s) (4.5 years)
= 4x1016m
Ship
d=vt
(4.3 light years)
= .95 (3x108 m/s) (1.4 years)
= 1.25x1016m (1.3 light years)
Length in moving
frame
Length in object’s rest
Physics 1161: Lecture 28, Slide
frame
39
v2
L  L0 1  2
c
Your spaceship is parked outside an interstellar cafe. A
speeder zooms by in an identical ship traveling at half
the speed of light. From your perspective, their ship
looks:
1) Longer than your ship
2) Shorter than your ship
3) Exactly the same as your ship
0%
1)
0%
2)
0%
3)
Your spaceship is parked outside an interstellar cafe. A
speeder zooms by in an identical ship traveling at half
the speed of light. From your perspective, their ship
looks:
1) Longer than your ship
2) Shorter than your ship
3) Exactly the same as your ship
0%
0%
1)
v2
L  L0 1  2
c
Always <1
In the speeder’s reference frame
Lo > L
In your reference frame
2)
0%
3)
Comparison:
Time Dilation vs. Length Contraction
• to = time in same reference frame as event
– i.e. if event is clock ticking, then to is in the reference frame of
the clock (even if the clock is in a moving spaceship).
v2
t0  t 1  2
c
t > to
Time seems longer
from “outside”
• Lo = length in same reference frame as object
– length of the object when you don’t think it’s moving.
v2
L  L0 1  2
c
Lo > L
Length seems shorter
from “outside”
Relativistic Momentum
Relativistic Momentum
Note: for v<<c p=mv
Note: for v=c
mv
p
v2
1 2
c
p=infinity
Relativistic Energy
Note: for v=0 E = mc2
mc 2
E
v2
1 2
c
Note: for v<<c E = mc2 + ½ mv2
Note: for v=c E = infinity (if m<> 0)
Objects with mass can’t go faster than c!
Summary
• Physics works in any inertial frame
– Simultaneous depends on frame
• Proper frame is where event is at same place, or
object is not moving.
– Time dilates
– Length contracts
– Energy/Momentum conserved
• For v<<c reduce to Newton’s Laws