1. Chapter 27 Wave/Particle Exp. Chapter 26 Relativity Intro.

3. Hint: Be able to do the homework (both the problems to turn in AND the recommended ones) you’ll do fine on the exam! Monday, May 10, 1999 10:30am - 11:20am Chs. 20, 26, and 27 You may bring one 3”X5” index card (hand-written on both sides), a pencil or pen, and a scientific calculator with you. Same format!

4. Hint: Review notes from my review lectures! Try to do some of the old homework recommended homework, and exam problems. Monday, May 10, 1999 11:30am - 12:30pm everything we’ve covered You may bring one 8.5”X11” sheet (hand-written on both sides), a pencil or pen, and a scientific calculator with you.

5. Monday, December 15, 1997 11:30am - 12:30pm everything we’ve covered Format: 5 problems, pick 4. 1 problem on each of the following topics: ElectrostaticsCircuitsMagnetism Optics Modern

6. Which says that it is impossible to know both the position and momentum of a particle with infinite accuracy.

7. In fact, if you know the position of a particle precisely, you have no clue as to its momentum! And if you know its mass and velocity precisely, you have no clue as to where it is!

8. There is an alternate form of the uncertainty principle, one relating time and energy. It says: Where  t is the time required to make a measurement and  E is the uncertainty in a particle’s energy.

9. Consider the following system: electron The reflected photon allows us to determine the location of the electron. In the collision, momentum is transferred between the photon and the electron, however!

10. If particles really have wave properties, I should be able to observe interference effects. So, let’s redo Young’s Experiment using electrons instead of light and see what happens….

11. electron gun photographic plate electrons When you develop the plate, what do you see??? Gun fires exactly one electron at a time

12. Zeroth order maximum 1 st 2 nd 0011 dark fringes The familiar 2-slit interference pattern!!! REMEMBER, only one electron passes through the slits at a time! So the electron is interfering with itself!!

13. You’re saying to yourself, “That electron has got to pass through one slit or the other!” Okay, let’s change the experiment to find out!

14. electron gun photographic plate electrons Gun fires exactly one electron at a time Detector will tell us when the electron passes through the bottom slit.

15. Now we know which path each electron takes on its journey to the photographic plate. So what do we see when we develop the plate? Bright spots behind the slits! No interference!

16. By observing this system, we’ve changed the system and the results indicated on the photographic plate! We leave behind the world of quantum physics… for now! Thanks for visiting Quantum World. Hope you enjoyed your stay!

17. Essentially in parallel with the entirely separate development of quantum mechanics, Einstein developed relativity:

18. Developed in 1905 handles the comparison of measurements made in different inertial reference frames. An inertial reference frame is a frame not that is not being accelerated. A frame that is not being accelerated must be at rest or moving with a constant velocity.

19. Developed in 1915 handles non-inertial reference frames (i.e. accelerating reference frames) and gravity. Problems in general relativity require the use of sophisticated mathematical techniques. We won’t attempt to cover general relativity here.

20. We already have a notion of relativity. Newtonian mechanics told us that the laws of mechanics worked equally well standing still on the surface of the Earth as riding a train (provided, of course, that the train was moving with a constant velocity). Such a train provides an example of an inertial reference frame!

21. GM R/R Physics Rules u Here, a woman juggles on a moving train car. Our friend, “The Shadow,” stands still and watches the train (and the juggler) go by.

22. When asked to describe the motion of the juggling balls, these two people will have very different things to say!

23. To the woman juggling on the train, she is unable to detect the motion of the train, so long as the train does not accelerate. The juggling balls will follow a simple, parabolic path to the right from her left hand to her right hand across a distance, d. d

24. In fact, if you sat in a soundproof boxcar, with no windows, you could not tell the difference between the train moving at a constant speed of 100 m.p.h. or the train standing still! It’s only the fact that the train goes up and down hills, speeding up and slowing down, hitting bumps, that allows you to know the difference between motion and rest!

25. What will our friend, the shadow say? Things seem quite different to him...

26. GM R/R Physics Rules u GM R/R Physics Rules u The Shadow sees the red ball released from the juggler’s left hand at point A. AB A short time later, the ball is caught by the juggler’s right hand at point B. The shadow would say that the ball moved to the right in a parabolic path from A to B.

27. Notice that we have a seeming contradiction! “The balls move from my left to my right.” “The balls move from my left to my right.”

28. How did classical mechanics handle this? GM R/R Physics Rules u S The “lab” frame. It’s the one “at rest.” S’ u the moving frame Moves with a velocity v relative to frame S.

29. Well, the position of the ball in the frame S’ is given by: x’ = x - ut And the x-direction velocity of the ball in the frame S’ is given by: v’ = v - u where v is the apparent velocity in the lab frame.

30. With this simple transformation (named for its inventor), we can reconcile the apparently contradictory observations of our two observers. There is no preferred inertial reference frame in which to describe the laws of mechanics. These laws are invariant.

31. The stationary observer measures the velocity of the juggling ball to be 19 m/s to the right and the Velocity of the train to be 20 m/s to the right. What is the velocity of the ball relative to the train? v’ = v - u GM R/R Physics Rules 20 m/s 19 m/s v’ = 19 - 20 v’ = -1 m/s On the boxcar, the ball moves toward the back!

32. Two cars, each driving 50 mph, travel in opposite directions on a 2-lane road. You ride in one car. How fast does the other car appear to be approaching? 50 mph You’re in this car S’ 50 mph v’ = v - u v’ = -50 - 50 v’ = -100 mph

33. This classical theory of relativity works well for juggling balls and railroad cars, but what happens when we try to apply it to electromagnetic waves (i.e., light)? The solution to Maxwell’s equations, which describe light waves, doesn’t obey these classical principles! The solution to his equations always travels at the speed of light in free space! What would happen if light did obey the classical theory?

34. You’re in a spaceship travelling away from the Sun at 0.9c. How fast does light from the Sun fly past you? Well, according to classical theory v’ = v - u v’ = c - 0.9c = 0.1c

35. An electron is accelerated across an electrical potential of 100 million volts. What is the final speed of the electron? PE = qV = (1.6 X 10 -19 C)(10 8 V) Initially, the electron’s energy is all potential energy... = 1.6 X 10 -11 J electron

36. When the electron reaches the opposite plate, all the energy will be kinetic electron KE = 1/2 mv 2 = 1.6 X 10 -11 J m = 9.1 X 10 -31 kg v = 5.9 X 10 9 m/s = 19.7c !!!!