physics 102: lecture 28, slide 1 special relativity physics 102: lecture 28 make sure your grade...

Physics 102: Lecture 28, Slide 1

Special Relativity

Physics 102: Lecture 28

•Make sure your grade book entries are correct

•Bring ID to Final EXAM!!!!

• Today’s Lecture will cover chapter 26.1 – 26.7

• Take a look at Special Relativity in 14 Easy (Hyper)lessons:http://web.hep.uiuc.edu/home/g-gollin/relativity/

http://web.hep.uiuc.edu/home/g-gollin/relativity/








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.


Postulates of Relativity

• Laws of physics are the same in every inertial frame– Perform experiment on train going east gives

same results as on train going west.

• Speed of light in vacuum is c for everyone– Measure c=3x108 m/s if you are on train going

east or on train going west, even if light source isn’t on the train.


Postulates of Relativity

• Laws of physics are the same in every inertial frame– Perform experiment on train going east gives

same results as on train going west.

• Speed of light in vacuum is c for everyone– Measure c=3x108 m/s if you are on train going

east or on train going west, even if light source isn’t on the train.

Weird!


Relative Velocity (Ball)

• ______ throws ball 30 mph. How fast do I think it goes when I am:– Standing still?

– Running 15 mph towards?

– Running 15 mph away?

(Review Lecture 14 for help with Relative Velocities)


Relative Velocity (Light)• _____ throws photon (3x108 m/s). How fast

do I think it goes when I am:– Standing still

– Running 1.5x108 m/s towards

– Running 1.5x108 m/s away

Preflight 28.1


Relative Velocity (Light)• _____ throws photon (3x108 m/s). How fast

do I think it goes when I am:– Standing still

– Running 1.5x108 m/s towards

– Running 1.5x108 m/s away

Strange but True!

3x108 m/s

3x108 m/s

3x108 m/s

Preflight 28.1


Simultaneous?

At Rest

Moving

A flash of light is emitted from the exact center of a box. Does the light reach all the sides at the same time?


Simultaneous?

At Rest

Moving

YES

NO

Simultaneous depends on frame!

A flash of light is emitted from the exact center of a box. Does the light reach all the sides at the same time?


Simultaneous?

http://web.hep.uiuc.edu/home/g-gollin/relativity/p112_relativity_8.html




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


Time Dilation

2

20

1cv

tt

You and a friend are having a drinking contest. Your friend is on a train traveling at speed v=0.9 c. By her watch, she finishes her drink in 5 seconds. Determine the time you measure, if you are standing still at the train station.


Time Dilation

2

20

1cv

tt

You and a friend are having a drinking contest. Your friend is on a train traveling at speed v=0.9 c. By her watch, she finishes her drink in 5 seconds. Determine the time you measure, if you are standing still at the train station.

2

2)9.0(1

5

cc

81.1

5

seconds 5.11

Since drinking is happening on the train, that is the “proper” time.


Time Dilation 2Now it is your turn to drink. According to your watch you finish your drink in 5 seconds. How long does your friend think it took you to finish the drink?

2

20

1cv

tt


Time Dilation 2Now it is your turn to drink. According to your watch you finish your drink in 5 seconds. How long does your friend think it took you to finish the drink?

Now drinking is happening at the station, so that is the “proper” time.

2

20

1cv

tt

2

2)9.0(1

5

cc

81.1

5

seconds 5.11

Both people think they won!


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?


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


Twin ParadoxPreflight 28.2

Twins decide that one will travel to Alpha Centauri and back at 0.95c, while the other stays on earth. Compare their ages when they meet on earth.


Twin ParadoxPreflight 28.2

Twins decide that one will travel to Alpha Centauri and back at 0.95c, while the other stays on earth. Compare their ages when they meet on earth.

Earth twin thinks it takes 2 x 4.5 = 9 years

Traveling twin thinks it takes 2 x 1.4 = 2.8 years

Traveling twin will be younger!

Note: Traveling twin is NOT in inertial frame!


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


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


Preflight 28.3

You’re eating a burger at the interstellar café 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


Preflight 28.3

You’re eating a burger at the interstellar café 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

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


Gook Luck on the Exam!

physics 102: lecture 28, slide 1 special relativity physics 102: lecture 28 make sure your grade...

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