# Physics 1161: Lecture 26 Special Relativity Sections 29-1 – 29-6.

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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

Michelson-Morley Experiment
Null Result 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 Interferometer

Lorentz-Fitzgerald Contraction
Length is contracted in the direction of motion Accounts for the null result Amount of shrinkage:

3 mph eastward 3 mph westward 57 mph eastward 57 mph westward
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? 3 mph eastward 3 mph westward 57 mph eastward 57 mph westward 60 mph eastward

3 mph eastward 3 mph westward 57 mph eastward 57 mph westward
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? 3 mph eastward 3 mph westward 57 mph eastward 57 mph westward 60 mph eastward

63 mph eastward 63 mph westward 57 mph eastward 57 mph westward
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? 63 mph eastward 63 mph westward 57 mph eastward 57 mph westward 60 mph eastward

63 mph eastward 63 mph westward 57 mph eastward 57 mph westward
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? 63 mph eastward 63 mph westward 57 mph eastward 57 mph westward 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. Small distance gives quantum mechanics. High speed gives relativity

Which of the following systems are not inertial reference frames?
a person standing still an airplane in mid-flight a merry-go-round rotating at a constant rate all of the above are IRFs none of the above are IRFs

Which of the following systems are not inertial reference frames?
a person standing still an airplane in mid-flight a merry-go-round rotating at a constant rate all of the above are IRFs 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.

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? 0.5 c C 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 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?
position velocity acceleration All of the above Only a) and b)

Which of these quantities change when you change your reference frame?
position velocity acceleration All of the above 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 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 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? v the blue flash the green flash both the same

A boxcar moves to the right at a very high speed
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? v the blue flash the green flash both the same 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 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? v the blue flash the green flash both the same

A boxcar moves to the right at a very high speed
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? v the blue flash the green flash 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.

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: Younger than you Older than you The same age as you are

Time Dilation

Time Dilation D t0 is proper time Because it is rest frame of event

Time Dilation L=v Dt D D ½ vDt t0 is proper time
Because it is rest frame of event

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? it would be faster it would be slower it wouldn’t change no pulse - the astronaut died a long time ago

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? 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.

Less than 2 seconds 2 seconds 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? Less than 2 seconds 2 seconds More than 2 seconds

Less than 2 seconds 2 seconds 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? Less than 2 seconds 2 seconds 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.

Less than 2 seconds 2 seconds 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? Less than 2 seconds 2 seconds More than 2 seconds

Less than 2 seconds 2 seconds 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? Less than 2 seconds 2 seconds More than 2 seconds

Space Travel Example 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 Example 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? People on ship have ‘proper’ time they see earth leave, and Alpha Centauri arrive. Dt0 Dt0 = 1.4 years Physics 1161: Lecture 28, Slide 34

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: Longer than your ship Shorter than your ship Exactly the same as your ship

Length Contraction Gifs
v=0.1 c v=0.8 c v=0.95 c

Length Contraction Example
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 Length in moving frame Length in object’s rest frame

Length Contraction Example
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: Sue:

Length Contraction Example
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) Length in moving frame Length in object’s rest frame Physics 1161: Lecture 28, Slide 39

Your spaceship is parked outside an interstellar cafe
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: Longer than your ship Shorter than your ship Exactly the same as your ship

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: Longer than your ship Shorter than your ship Exactly the same as your ship Lo > L In the speeder’s reference frame In your reference frame Always <1

Comparison: Time Dilation vs. Length Contraction
Dto = 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. Dt > Dto Time seems longer from “outside” Lo > L Length seems shorter from “outside”

Relativistic Momentum
Note: for v<<c p=mv Note: for v=c p=infinity Relativistic Energy Note: for v=0 E = mc2 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

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