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/spe

crel/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 You and your friend are playing catch in a train moving at at 60 mph in an eastward direction60 mph in an eastward direction. Your friend is at . Your friend is at the front of the car and throws you the ball at the front of the car and throws you the ball at 3 mph3 mph (according to you). What velocity does the ball have (according to you). What velocity does the ball have when you catch it, according to you?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 You and your friend are playing catch in a train moving at at 60 mph in an eastward direction60 mph in an eastward direction. Your friend is at . Your friend is at the front of the car and throws you the ball at the front of the car and throws you the ball at 3 mph3 mph (according to you). What velocity does the ball have (according to you). What velocity does the ball have when you catch it, according to you?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 You and your friend are playing catch in a train moving at at 60 mph in an eastward direction60 mph in an eastward direction. Your friend is at . Your friend is at the front of the car and throws you the ball at the front of the car and throws you the ball at 3 mph3 mph (according to you). What velocity does the ball have as (according to you). What velocity does the ball have as measured by someone at rest on the platform?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 You and your friend are playing catch in a train moving at at 60 mph in an eastward direction60 mph in an eastward direction. Your friend is at . Your friend is at the front of the car and throws you the ball at the front of the car and throws you the ball at 3 mph3 mph (according to you). What velocity does the ball have as (according to you). What velocity does the ball have as measured by someone at rest on the platform?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 Which of the following systems are notnot inertial inertial reference framesreference 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 Which of the following systems are notnot inertial inertial reference framesreference 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 frameinertial reference frame is the same as a non-accelerating reference non-accelerating reference

frameframe. Due to the circular motion of the merry-go-round, there is a

centripetal accelerationcentripetal acceleration, which means that the system is accelerating.

Therefore it is notnot 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 Which of these quantities change when you change your change your reference framereference 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 Which of these quantities change when you change your change your reference framereference 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 each

flash will take flash will take tt = = LL//c,c, which will be the samesame 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 According to an observer on the ground, 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 According to an observer on the ground, 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 still sees the light moving at speed cc. But while the light is going, the boxcar has actually But while the light is going, the boxcar has actually advancedadvanced. 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 travellonger distance to travel and takes a longer timelonger 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 t

Dtc 20

cD

t2

0

22

22

tv

Dtc

2

2

1

12

cvc

Dt

2

20

1cv

tt

½ vt

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 The period of a pendulum attached in a spaceship is 2 2 secondsseconds while the spaceship is parked on Earth. What while the spaceship is parked on Earth. What is its period for an observer on Earth when the is its period for an observer on Earth when the spaceship moves at spaceship moves at 0.60.6cc with respect to Earth? 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 The period of a pendulum attached in a spaceship is 2 2 secondsseconds while the spaceship is parked on Earth. What while the spaceship is parked on Earth. What is its period for an observer on Earth when the is its period for an observer on Earth when the spaceship moves at spaceship moves at 0.60.6cc with respect to Earth? 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 moving relative to himhim and so it takes longer to swinglonger to swing (moving clocks run slow)(moving clocks run slow) due to the effect of time dilation.

The period of a pendulum attached in a spaceship is The period of a pendulum attached in a spaceship is 2 2 secondsseconds while the spaceship is parked on Earth. 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 The period of a pendulum attached in a spaceship is 2 2 secondsseconds while the spaceship is parked on Earth. 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. t0

2

20

1cv

tt

2

2

0 1cv

tt 295.15.4

t0 = 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 to 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”

t > toTime 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