Option H: Relativity H2 Concepts/postulates special relativity

1. Option H: RelativityH2 Concepts/postulates special relativity This part of Option H has already been covered in Option D2 Concepts and postulates of special relativity. It is replicated here without any changes.

2. Option H: RelativityH2 Concepts/postulates special relativity H.2.1 Describe what is meant by an inertial frame of reference. H.2.2 State the two postulates of special relativity. H.2.3 Discuss the concept of simultaneity.

3. y y x x Option H: RelativityH2 Concepts/postulates special relativity Describe what is meant by an inertial frame of reference. A frame of reference is a coordinate system (cs) with respect to which we measure motion. We can set up a cs with respect to a dirt road: But we can also set up a cs with respect to a wagon on the road.

4. y y y x x x Option H: RelativityH2 Concepts/postulates special relativity Describe what is meant by an inertial frame of reference. Suppose the wagon, traveling at a constant speed, has a bowling ball fall from it. The x-coordinate of the ball doesn’t change. This is because vx,ball= vx,wagon for the whole fall. The observer in the non-accelerating wagon sees that the bowling ball is accelerating downward at g. EXPECTED.

5. y y y x x x Option H: RelativityH2 Concepts/postulates special relativity Describe what is meant by an inertial frame of reference. Now suppose the wagon is decreasing its speed while the ball is falling. Note that in this case the x-coordinate of the ball does change (it increases). This is because vx,wagon decreases during the drop. The observer in the decelerating wagon sees that the bowling ball is accelerating FORWARD! UNEXPECTED.

6. y y x x Option H: RelativityH2 Concepts/postulates special relativity Describe what is meant by an inertial frame of reference. The two scenarios bear comparison. When the cs was not accelerating (as in the first example) the observer noted that the ball had but a single downward acceleration of g. When the cs was accelerating (decelerating, as in the second example) the observer noted that the ball not only accelerated downward at g, but it accelerated forward as well. v = CONST v  CONST Non-accelerating reference frame. Accelerating reference frame. Inertial reference frame Non-inertial reference frame

7. y y x x a g g Option H: RelativityH2 Concepts/postulates special relativity Describe what is meant by an inertial frame of reference. In both reference frames the observers would discover that the acceleration in the y-direction is g. In this respect, both frames yield the correct physical result. However, in the non-inertial frame, the observer “discovers” another acceleration in the x-direction! v = CONST v  CONST Non-accelerating reference frame. Accelerating reference frame. Inertial reference frame Non-inertial reference frame

8. y y x x a g g Option H: RelativityH2 Concepts/postulates special relativity Describe what is meant by an inertial frame of reference. Given that in the non-inertial frame the observer has “discovered” a in the x-direction, he would, knowing the laws of physics, state that there must be a force acting in that direction causing the ball to pick up speed! There is indeed no such force, demonstrating that the preferred reference frame is an inertial reference frame (IRF). v = CONST v  CONST Non-accelerating reference frame. Accelerating reference frame. Inertial reference frame Non-inertial reference frame

9. Option H: RelativityH2 Concepts/postulates special relativity State the two postulates of special relativity. Einstein, in the publication of his special theory of relativity, stated the following two postulates: (1)The laws of physics are the same in all inertial reference frames. (2)The speed of light is the same in all inertial reference frames. His first postulate is the product of his philosophical beliefs (and probably yours, as well). His second postulate is the product of the most famous of all null-experiments, the Michelson-Morley experiment.

10. Option H: RelativityH2 Concepts/postulates special relativity State the two postulates of special relativity. Before looking in detail at special relativity we must look at Maxwell’s theory of electromagnetism and the Michelson-Morley experiment. First Maxwell. James Clerk Maxwell formulated his theory in the late 1800s, just prior to Einstein’s special theory. One of the parts of Maxwell’s theory that we have studied is that moving charges produce and thus respond to magnetic fields, and, stationary charges do neither. The scenario on the next slide baffled scientists before special relativity: Typical college nerd tee-shirt!

11. y y x x Option H: RelativityH2 Concepts/postulates special relativity State the two postulates of special relativity. EXAMPLE: Consider two charges Q at rest in the cs of the road. Since they are at rest they exert no magnetic force on each other. But in the cs of the moving wagon they each have a velocity, and thus each feels a magnetic force! This conundrum violates Einstein’s first postulate of relativity. Why? The magnetic force isn’t the same! Special relativity resolves this conundrum.

12. Vat of liquid mercury Option H: RelativityH2 Concepts/postulates special relativity State the two postulates of special relativity. The next driving force behind special relativity was the Michelson-Morley experiment. A large vat was filled with liquid mercury on which was floated a slab of stone. On the slab was an interferometer which could be freely rotated with the slab. The interferometer used a beam- splitter which insured that the two beams were coherent. Michelson Mirrors Floating table of heavy marble Detector Beam splitter Source FYI The mercury allowed easy rotation and absorbed vibrations from road traffic outside the lab.

13. vorb Mirrors Detector Vat of liquid mercury Beam splitter Source Option H: RelativityH2 Concepts/postulates special relativity State the two postulates of special relativity. The basic idea behind the device was that as the floating table was rotated, the beam parallel to the earth's orbital velocity would squish. The beam perpendicular to the earth's orbital velocity would act as the control - it would not be squished. In the region where the beams rejoined, interference would be detected. Destructive interference would result in seeing dark in the eyepiece of the detector while rotating. Constructive interference would result in seeing bright in the eyepiece of the detector. Squished beam Control beam Region of interference

14. Option H: RelativityH2 Concepts/postulates special relativity State the two postulates of special relativity. The null results showed that there was no interference. Thus the light waves did not squish in the direction of motion. Thus the speed of light is constant in a stationary reference frame (the control one) or a reference frame moving at vorbital. This result baffled scientists who thought that being a wave, light must travel through a medium. They gave this particular medium the name ether and assumed that the ether permeated all of space, and even matter itself. The MM experiment was really a method to determine how Earth was moving through the ether, and thus of establishing an absolute frame of reference, that of the ether.

15. 0.5c c 0.5c c Option H: RelativityH2 Concepts/postulates special relativity State the two postulates of special relativity. Einstein capitalized on the Michelson-Morley experiment in his second postulate. PRACTICE: Two trains approach each other each at a speed of 0.5c. How fast does the light travel in each of the reference frames according to the Galilean transformations? SOLUTION: For someone on the ground the speed of each beam would be 1c + .5c = 1.5c. For someone in a locomotive his own beam would have a speed of 1c and the beam from the other locomotive would be 0.5c + (0.5c + 1c) = 2c. The beams approach each other at 2(1.5c) = 3c.

16. Postulate 2) The speed of light is the same in all inertial reference frames. 0.5c c 0.5c c Option H: RelativityH2 Concepts/postulates special relativity State the two postulates of special relativity. Einstein capitalized on the Michelson-Morley experiment in his second postulate. PRACTICE: Two trains approach each other each at a speed of 0.5c. How fast does the light travel in each of the reference frames according to Einstein’s second postulate? SOLUTION: For someone on the ground the speed of each beam would be 1c! For someone in a locomotive his own beam would have a speed of 1c and the beam from the other locomotive would be 1c! The beams approach each other at 1c!

17. Lorentz- FitzGerald contraction L = L0 1 – v2/c2 Option H: RelativityH2 Concepts/postulates special relativity State the two postulates of special relativity. An Irish physicist by the name of George FitzGerald proposed that if the length of an object contracted in the direction of motion by a factor that was dependent on the speed of the object then the null result could be explained. At the same time a mathematician by the name of H. A. Lorentz determined much the same thing. The Lorentz-FitzGerald contraction was determined to be given by where L0 is the restlength of the object.

18. Lorentz- FitzGerald contraction L = L0 1 – v2/c2 L = 601 – (.5c)2/c2 60 m v = 0 L = 601 – .25c2/c2 52 m v = 0.5c L = 601 – .25 L = L0 1 – v2/c2 L = 600.75 Option H: RelativityH2 Concepts/postulates special relativity State the two postulates of special relativity. PRACTICE: According to the Lorentz-FitzGerald contraction, what would be the length of a rocket ship which was traveling at 0.5c in the direction of its length, if its rest length were 60 m? SOLUTION: Simply substitute values into : This represents a 15% reduction in length! L = 52 m

19. Option H: RelativityH2 Concepts/postulates special relativity Discuss the concept of simultaneity. Consider a village clock tower that is just on the verge of striking noon. Consider two observers: One a man standing on the village green, and one an alien in a rocket skimming the green at high speed, both at exactly the same distance from the clock. At the stroke of noon, light from the clock reflects to both the man and the alien: Note that the alien sees noon a little later than the man! Why?

20. Option H: RelativityH2 Concepts/postulates special relativity Discuss the concept of simultaneity. Consider a man centered on a moving flatcar and being observed by another man standing on the ground. At precisely the instant the two observers are opposite each other lightening bolts strike both ends of the flatcar. Note that the stationary observer saw the bolts simultaneously, but the moving one did not!

21. Option H: RelativityH2 Concepts/postulates special relativity Discuss the concept of simultaneity. We call the lightening strike an event. The event occurred in the frame of the man who is at rest. We call the frame of reference that is at rest with respect to an event the proper frame of reference. PRACTICE: In the village clock example who was in the proper frame? Was it the man on the green, or the alien in the rocket? SOLUTION: The man on the green was in the proper frame of reference since the event of the clock striking noon occurred in the man’s rest frame, not the alien’s

22. Option H: RelativityH2 Concepts/postulates special relativity Discuss the concept of simultaneity. Miguel is in the proper frame of reference. Why? Since he is “midway” the light will reach him simultaneously from both matches.

23. Option H: RelativityH2 Concepts/postulates special relativity Discuss the concept of simultaneity. Carmen’s is not the proper frame of reference. Why? She will see light from A before light from B because her reference frame is “moving” toward A.

24. Option H: RelativityH2 Concepts/postulates special relativity Discuss the concept of simultaneity. Simon will not see simultaneity but will see bird B first since he is approaching its light and receding from bird A’s light.