Elements of Physics II

Transcription

1 Physics 132: Lecture 21 Elements of Physics II Agenda for Today Special Theory of relativity Inertial vs. non-inertial reference frames Postulates of SR Consequences of SR Simultaneity Time dilation Physics 201: Lecture 1, Pg 1

2 Maxwell s Theory of Electromagnetic Waves A changing electric field creates a magnetic field, which then changes in just the right way to recreate the electric field, which then changes in just the right way to again recreate the magnetic field, and so on. This is an electromagnetic wave. Physics 201: Lecture 1, Pg 2

3 Speed c Relative to What? Maxwell's equations show that light and other electromagnetic waves propagate in vacuum at the speed of light, c. But with respect to what? 19th-century physicists thought that light waves were like other waves, which required a material medium in which to propagate. They called that medium the ether. Then Maxwell's equations would be strictly correct only in a reference frame at rest with respect to the ether. Because only in such a frame would the prediction of waves propagating at speed c be correct. So a logical question for 19th century physics was What is Earth's motion relative to the ether? Physics 201: Lecture 1, Pg 3

4 The Michelson-Morley Experiment The Michelson-Morley experiment used wave interference to test for differences in the speed of light in different directions. Those differences e should result from Earth's motion o through the ether. e In its 1887 version, the experiment was far more sensitive than needed to detect motion at Earth's orbital speed. The experiment was conducted in different orientations and at different times of year to account for different directions of Earth's motion relative to the ether. There was never any significant change in the interference pattern. Conclusion: Earth isn't moving relative to the ether! Physics 201: Lecture 1, Pg 4

5 Galilean-Newtonian Relativity Reference frame: The place of reference that one can make measurement of distance velocity etc from. Inertial reference frame: A reference frame that is not undergoing an acceleration (moving at constant velocity) Relativity Principle The laws of mechanics are the same for all inertial reference frames. Physics 201: Lecture 1, Pg 5

6 Reference Frames The figure shows two reference frames called S and S. The coordinate axes in S are x, y, z and those in S are x, y, z. Frame S moves with velocity v relative to S. Physics 201: Lecture 1, Pg 6

7 Galilean Transformations Physics 201: Lecture 1, Pg 7

8 Clicker Question 1: Which of these quantities change when you change your inertial reference frame? a) position b) velocity c) acceleration d) all of the above e) only a) and b) Physics 201: Lecture 1, Pg 8

9 Inertial Reference Frames Physics 201: Lecture 1, Pg 9

10 Galilean-Newtonian relativity The laws of physics are the same for all inertial reference frames. There is no preferred or more correct frame When you are in a constantly moving object (that travels smoothly) you can not tell if you are still or moving. (No experiment can either) Lengths of objects and time that passes between events are constant t (absolute) meter sticks are always a meter If a ball drop it takes 6 s for it to fall in all frames Physics 201: Lecture 1, Pg 10

11 IRF Physics 201: Lecture 1, Pg 11

12 Trouble Maxwell predicted EM waves will travel with a velocity of c. His theory did not account for relative velocity. People were perplexed. Physics 201: Lecture 1, Pg 12

13 Airplanes Two planes travel To the bottom plane the 500 mph top plane is travelling 300 mph v T = = 300 mph To an observer on the ground who is not moving the top plane goes 500 mph 200 mph Physics 201: Lecture 1, Pg 13

14 Chewbacca here sees the EM wave travelling at a speed of c = m/s EM (Light) waves v = c This is bad for physics! EM wave Using Newton s and Gallileo s way Luke would measure: v L = c - c/2 = c/2 However this is not correct v = c/2 Chewbacca s frame is better than Luke s frame because it correctly figures the speed of the wave Physics 201: Lecture 1, Pg 14

15 Postulates of Special Relativity 1) The laws of Physics have the same form in all inertial reference frames. (Moving with constant velocity) 1B) The speed of light (in a vacuum) is always c, independent of the observer. Physics 201: Lecture 1, Pg 15

16 Pre-Class Quiz/Clicker 2 Teenagers Sam and Tom are playing chicken in their rockets. As figure shows, an experimenter on earth sees that each is traveling at 0.95 as he approaches the other. Sam fires a laser beam toward Tom. What is the speed of the laser beam relative to Sam? A) 0.95 c B) 0 C) c D) 1.95 c E) 0.05 c What is the speed of the laser beam relative to Tom? Physics 201: Lecture 1, Pg 16

17 Clicker Question 3: It is said that Einstein, in his teenage years, asked the question: What would I see in a mirror if I carried it in my hands and ran with the speed of light? How would you answer this question? a) the mirror would be totally black b) you would see the same thing as if you were at rest c) the image would be distorted d) none of the above Physics 201: Lecture 1, Pg 17

18 Consequences This may not seem to be revolutionary In order to measure c = m/s, different frames must measure distance and time intervals differently! v distance time Physics 201: Lecture 1, Pg 18

19 Relativity Solving relativity problems in relativity is as much an art as a science Physics 201: Lecture 1, Pg 19

20 Clicker Question 4: A boxcar moves right at a very high speed. A green ball is thrown from left to right, and a blue ball is thrown from right to left with the same speed. According to an observer on the ground, which ball takes longer to hit the student at the center of the car? a) the blue ball b) the green ball c) both the same v Physics 201: Lecture 1, Pg 20

21 Clicker Question 4: v Physics 201: Lecture 1, Pg 21

22 Simultaneity The two events are simultaneous in Ryan s reference frame. Physics 201: Lecture 1, Pg 22

23 Simultaneity As seen in Ryan s reference frame. Right flash reaches Peggy first! Physics 201: Lecture 1, Pg 23

24 Simultaneity As seen in Peggy s reference frame. The two events are not simultaneous in Peggy s reference frame! This is called the relativity it of simultaneity. Right flash reaches Peggy first! Physics 201: Lecture 1, Pg 24

25 Clicker Question 5: The figure below shows a rocket traveling from left to right. At the instant it is halfway between two trees, lightning simultaneously (in the rocket's frame) hits both trees. Do the light flashes reach the rocket pilot simultaneously? If not, which reaches her first? (a) The light flashes reach the rocket pilot simultaneously. (b) The left flash reaches the rocket pilot first. (c) The right flash reaches the rocket pilot first. Physics 201: Lecture 1, Pg 25

26 Clicker Question 5: Physics 201: Lecture 1, Pg 26

27 Clicker Question 6: The figure below shows a rocket traveling from left to right. At the instant it is halfway between two trees, lightning simultaneously (in the rocket's frame) hits both trees. A student was sitting on the ground halfway between the trees as the rocket passed overhead. According to the student, were the lightning g strikes simultaneous? If not, which tree was hit first? (a) The lightning strikes were simultaneous. (b) The left tree was hit first. (c) The right tree was hit first. Physics 201: Lecture 1, Pg 27