1. 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/

2. Physics 102: Lecture 28, Slide 2 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.

3. Physics 102: Lecture 28, Slide 3 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=3x10 8 m/s if you are on train going east or on train going west, even if light source isn’t on the train.

4. Physics 102: Lecture 28, Slide 4 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=3x10 8 m/s if you are on train going east or on train going west, even if light source isn’t on the train. Weird!

5. Physics 102: Lecture 28, Slide 5 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)

6. Physics 102: Lecture 28, Slide 6 Relative Velocity (Light) _____ throws photon (3x10 8 m/s). How fast do I think it goes when I am: –Standing still –Running 1.5x10 8 m/s towards –Running 1.5x10 8 m/s away Preflight 28.1

7. Physics 102: Lecture 28, Slide 7 Relative Velocity (Light) _____ throws photon (3x10 8 m/s). How fast do I think it goes when I am: –Standing still –Running 1.5x10 8 m/s towards –Running 1.5x10 8 m/s away Strange but True! 3x10 8 m/s Preflight 28.1

8. Physics 102: Lecture 28, Slide 8 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?

9. Physics 102: Lecture 28, Slide 9 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?

10. Physics 102: Lecture 28, Slide 10 Simultaneous? http://web.hep.uiuc.edu/home/g- gollin/relativity/p112_relativity_8.html

11. Physics 102: Lecture 28, Slide 11 Time Dilation D t 0 is proper time Because it is rest frame of event

12. Physics 102: Lecture 28, Slide 12 Time Dilation D D L=v  t ½ v  t t 0 is proper time Because it is rest frame of event

13. Physics 102: Lecture 28, Slide 13 Time Dilation 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.

14. Physics 102: Lecture 28, Slide 14 Time Dilation 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. Since drinking is happening on the train, that is the “proper” time.

15. Physics 102: Lecture 28, Slide 15 Time Dilation 2 Now 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?

16. Physics 102: Lecture 28, Slide 16 Time Dilation 2 Now 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. Both people think they won!

17. Physics 102: Lecture 28, Slide 17 Space Travel 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?

18. Physics 102: Lecture 28, Slide 18 Space Travel 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.  t 0  t 0 = 1.4 years

19. Physics 102: Lecture 28, Slide 19 Twin Paradox Preflight 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.

20. Physics 102: Lecture 28, Slide 20 Twin Paradox Preflight 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!

21. Physics 102: Lecture 28, Slide 21 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 d 0 = v t Ship d = v t Length in moving frame Length in object’s rest frame

22. Physics 102: Lecture 28, Slide 22 Length Contraction 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:

23. Physics 102: Lecture 28, Slide 23 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 d 0 = v t=.95 (3x10 8 m/s) (4.5 years) = 4x10 16 m (4.3 light years) Ship d = v t=.95 (3x10 8 m/s) (1.4 years) = 1.25x10 16 m (1.3 light years) Length in moving frame Length in object’s rest frame

24. Physics 102: Lecture 28, Slide 24 Length Contraction Gifs v=0.1 c v=0.8 c v=0.95 c

25. Physics 102: Lecture 28, Slide 25 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

26. Physics 102: Lecture 28, Slide 26 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 Always <1 L o > L In the speeder’s reference frame In your reference frame

27. Physics 102: Lecture 28, Slide 27 Comparison: Time Dilation vs. Length Contraction  t o = time in same reference frame as event –i.e. if event is clock ticking, then  t o is in the reference frame of the clock (even if the clock is in a moving spaceship). L o = length in same reference frame as object –length of the object when you don’t think it’s moving. L o > L Length seems shorter from “outside”  t >  t o Time seems longer from “outside”

28. Physics 102: Lecture 28, Slide 28 Relativistic Momentum Note: for v<<c p=mv Note: for v=c p=infinity Relativistic Energy Note: for v=0 E = mc 2 Objects with mass can’t go faster than c! Note: for v<<c E = mc 2 + ½ mv 2 Note: for v=c E = infinity (if m<> 0)

29. Physics 102: Lecture 28, Slide 29 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

30. Physics 102: Lecture 28, Slide 30 Gook Luck on the Exam!