Special Relativity Physics 1161: Lecture 35 Sections 29-1 – 29-6.
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Transcript of Special Relativity Physics 1161: Lecture 35 Sections 29-1 – 29-6.
Special RelativityPhysics 1161: Lecture 35
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
Inte
rfer
omet
er
• 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
Null Result
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)
0% 0% 0%0%0%
1) 3 mph eastward2) 3 mph westward3) 57 mph eastward4) 57 mph westward5) 60 mph eastward
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)
0% 0% 0%0%0%
1) 3 mph eastward2) 3 mph westward3) 57 mph eastward4) 57 mph westward5) 60 mph eastward
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)
0% 0% 0%0%0%
1) 63 mph eastward2) 63 mph westward3) 57 mph eastward4) 57 mph westward5) 60 mph eastward
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)
0% 0% 0%0%0%
1) 63 mph eastward2) 63 mph westward3) 57 mph eastward4) 57 mph westward5) 60 mph eastward
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) 2) 3) 4) 5)
0% 0% 0%0%0%
1) a person standing still 2) an airplane in mid-flight 3) a merry-go-round rotating
at a constant rate4) all of the above are IRFs 5) none of the above are IRFs
Which of the following systems are not inertial reference frames?
1) 2) 3) 4) 5)
0% 0% 0%0%0%
1) a person standing still 2) an airplane in mid-flight 3) a merry-go-round rotating
at a constant rate4) all of the above are IRFs 5) none of the above are IRFs
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.
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 light is a constant.
The speed of a light flash 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)
0% 0% 0%0%0%
1) position2) velocity3) acceleration4) All of the above5) Only a) and b)
Which of these quantities change when you change your reference frame?
1) 2) 3) 4) 5)
0% 0% 0%0%0%
1) position2) velocity3) acceleration4) All of the above5) Only a) and b)
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
• http://sq.netlog.com/go/explore/videos/videoid=sq-18174
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) 2) 3)
0% 0%0%
1) the blue flash2) the green flash3) both the same v
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) 2) 3)
0% 0%0%
1) the blue flash2) the green flash3) 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.
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) 2) 3)
0% 0%0%
1) the blue flash2) the green flash3) both the same v
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) 2) 3)
0% 0%0%
1) the blue flash2) the green flash3) both the same
v
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 blue flash, and the front wall is moving away from the green flash. Thus, the green flash has a longer distance to travel and takes a longer time.
Time Dilation
• http://www.youtube.com/watch?v=KHjpBjgIMVk&feature=related
Time Dilation
D
Dtc 20
cD
t2
0
t0 is proper time
Because it is rest frame of event
Time Dilation
D D
L=v Dt
Dtc 20
cD
t2
0
22
22
tv
Dtc
2
2
1
12
cvc
Dt
2
20
1cv
tt
½ vDt
t0 is proper time
Because it is rest frame of event
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)
0% 0%0%0%
1) it would be faster2) it would be slower3) it wouldn’t change4) no pulse - the astronaut
died a long time ago
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)
0% 0%0%0%
1) it would be faster2) it would be slower3) it wouldn’t change4) 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.
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) 2) 3)
0% 0%0%
1) Less than 2 seconds2) 2 seconds3) More than 2 seconds
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) 2) 3)
0% 0%0%
1) Less than 2 seconds2) 2 seconds3) 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.
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) 2) 3)
0% 0%0%
1) Less than 2 seconds2) 2 seconds3) More than 2 seconds
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) 2) 3)
0% 0%0%
1) Less than 2 seconds2) 2 seconds3) More than 2 seconds
Space TravelAlpha 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?
Physics 1161: Lecture 28, Slide 32
Space TravelAlpha 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.?
vd
t c 95.0years-light 3.4 years 5.4
How long do people on the ship think it takes?
People on ship have ‘proper’ time they see earth leave, and Alpha Centauri arrive. Dt0
2
20
1cv
tt
2
2
0 1cv
tt 295.15.4
Dt0 = 1.4 years
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 = v t
2
2
0 1cv
LL
Length in moving frame
Length in object’s rest frame
Length ContractionSue 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:
2
2
0 1cv
LL
Sue:
2
2
0 1cv
LL
Physics 1161: Lecture 28, Slide 35
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 (4.3 light years)
Ship d = v t = .95 (3x108 m/s) (1.4 years)
= 1.25x1016m (1.3 light years)
2
2
0 1cv
LL
Length in moving frame
Length in object’s rest frame
Length Contraction Gifs
v=0.1 c
v=0.8 c
v=0.95 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) 2) 3)
0% 0%0%
1) Longer than your ship2) Shorter than your ship3) Exactly the same as your ship
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) 2) 3)
0% 0%0%
1) Longer than your ship2) Shorter than your ship3) Exactly the same as your ship
2
2
0 1cv
LL
Always <1
Lo > L
In the speeder’s reference frame
In your reference frame
Comparison:Time Dilation vs. Length Contraction
• to = time in same reference frame as event – i.e. if event is clock ticking, then Dto is in the reference frame of
the clock (even if the clock is in a moving spaceship).
• Lo = length in same reference frame as object – length of the object when you don’t think it’s moving.
2
2
0 1cv
LL
2
2
0 1cv
tt
Lo > L Length seems shorter from “outside”
Dt > DtoTime seems longer
from “outside”
Relativistic Momentum
Relativistic Momentum2
2
1cv
mvp
Note: for v<<c p=mv
Note: for v=c p=infinity
Relativistic Energy2
2
2
1cv
mcE
Note: for v=0 E = mc2
Objects with mass can’t go faster than c!
Note: for v<<c E = mc2 + ½ mv2
Note: for v=c E = infinity (if m<> 0)
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