Special Relativity

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/specrel/www/

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:

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

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.

Which of the following systems are notinertial 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 notinertial 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 Aninertial reference frameis the same as anon-accelerating reference frame. Due to the circular motion of the merry-go-round, there is acentripetal acceleration, which means that the system is accelerating. Therefore it isnotan inertial reference frame.

Speed of LightCheckpoint 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 thesamein 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.

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? • theblueflash • thegreenflash • 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? • theblueflash • thegreenflash • 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). Soeach flash will take t = L/c,which will be thesamefor each one.

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? • theblueflash • thegreenflash • 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? • theblueflash • thegreenflash • both the same The ground observerstill 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 alonger distance to traveland takes alonger time.

Twin ParadoxCheckpoint 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 • http://www.youtube.com/watch?v=KHjpBjgIMVk&feature=related

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

L=v Dt D D ½ vDt Time Dilation 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? • it would be faster • it would be slower • it wouldn’t change • 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.

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

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 ismoving relative to himand so it takeslonger 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? • 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 ContractionCheckpoint • 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

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

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

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

In the speeder’s reference frame Lo > L In your reference frame Always <1 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

Time seems longer from “outside” Dt > Dto Length seems shorter from “outside” Lo > L 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.

Relativistic Momentum 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

Special Relativity