Special Relativity II Twominute movie Quiz Breakdown of

Special Relativity II Two-minute movie Quiz Breakdown of simultaneity Length Contraction Time Dilation (Some clicker examples here after derivation) 1

Simultaneity Movie https: //www. youtube. com/watch? v=wteiuxyqto. M

Breakdown of Simultaneity Example A. Lightning at same time B. At different times C. On the train no-one can hear you scream Lightening bolts appear to be simultaneous to Stanley. What does Mavis see ? 3

Breakdown of Simultaneity Example A. Lightning at same time B. At different times C. On the train no-one can hear you scream Lightening bolts appear to be simultaneous to Stanley. What does Mavis see ? 4

Q 9. 1 As a high-speed spaceship flies past you at half the speed of light, a strobe light fires at the center of a room aboard the spaceship. As measured by you, the light from the strobe A. reaches point A before it reaches point B. B. reaches point B before it reaches point A. C. reaches points A and B simultaneously. D. not enough information given to decide 5

Q 9. 1 As a high-speed spaceship flies past you at half the speed of light, a strobe light fires at the center of a room aboard the spaceship. As measured by you, the light from the strobe A. reaches point A before it reaches point B. B. reaches point B before it reaches point A. C. reaches points A and B simultaneously. D. not enough information given to decide The wavefronts arrive from the bulb arrive at B first with respect to the earth observer 6

Q 9. 2 An astronaut on the spaceship is also viewing this event. What does she see? A. reaches point A before it reaches point B. B. reaches point B before it reaches point A. C. reaches points A and B simultaneously. D. not enough information given to decide 7

Q 9. 2 An astronaut on the spaceship is also viewing this event. What does she see? A. reaches point A before it reaches point B. B. reaches point B before it reaches point A. C. reaches points A and B simultaneously. D. not enough information given to decide This must be true for the speed of light to be the same in all inertial reference frames 8

Breakdown of Simultaneity Going back to Mavis and Stanley (again) Note that both sets of wavefronts from A’ and B’ (as well as from A and B) are moving at c 9

Breakdown of Simultaneity Example N. B. that both sets of wavefronts from A’ and B’ are moving at c in Mavis’ frame of reference. The first wavefront reaches Mavis early Mavis says that the lightening hit the front of the train first and the back of the train later. The two events are not simultaneous. 10

Breakdown of Simultaneity Example Stanley says that the lightening hit the front of the train and the back of the train at the same time (simultaneously). Stanley and Mavis do not agree simultaneity has broken down (depends on frame of reference) 11

Pole Vaulter “classic” problem à 1. 6 m barn, 2 m pole à Run “really fast” through barn à Back door initially closed à Pole (and vaulter) entirely inside and Front door closed 12

Pole Vaulter (ladder and garage) Paradox à What we see observing the barn (garage) à Ladder shorter when However our pole vaulter (ladder bearer) sees pole/ladder as same length! How can this be? Think about “events” !! 13

Pole Vaulter Resolution à Pole longer than barn, what a fly on pole sees 14

Some places where Special Relativity is needed Particle accelerator: electrons and positrons moving at 99. 99% c Supernova in a distant galaxy. Remember the universe is expanding ! GPS satellite in orbit (v~3. 9 km/sec, 7μs/day SR correction) 15

Review from Friday: Einstein’s postulates • Einstein’s first postulate: The laws of physics are the same in all inertial reference frames • Einstein’s second postulate is that the speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source. • We must modify determination of space and time intervals when a frame of reference is moving relative to us at high velocity. (Today’s class: tough deep material, please slow me down if I start going too fast. Reread the textbook when you go home). • Another consequence: it is impossible for an inertial observer to travel at c, the speed of light in the vacuum. We will do two derivations (time dilations and length contraction) These are quite deep (not just algebra). 16

Relativity of time intervals and Time Dilation • The two observers (Mavis and Stanley) measure different time intervals due to their relative motion. Let’s work out this important example in full detail. 17

Relativity of time intervals and Time Dilation • The two observers (Mavis and Stanley) measure different time intervals due to their relative motion. Let’s work out this example. Mavis in reference frame S’ fires a light source at a mirror and measures the time interval. What does she find ? This is a “proper time interval” – a time interval between events at the same space point. 18

Relativity of time intervals and Time Dilation • Stanley in reference S measures this time interval. What does he find ? What length does Stanley measure ? 19

Relativity of time intervals and Time Dilation The time intervals measured by Mavis (frame S’) and Stanley (frame S) are different ! Let’s compare the two results 20

Relativity of time intervals and Time Dilation The time intervals measured by Mavis (frame S’) and Stanley (frame S) are different ! Let’s work out how they are related. Now square this and collect Δt terms 21

Relativity of time intervals and Time Dilation Question: does Stanley measure a longer or shorter time interval ? Stanley measures a longer round trip time than Mavis ! This is called relativistic time dilation 22

Time dilation vs velocity (let’s plot the “gamma factor”) Introduce the γ factor. 23

Time dilation vs velocity (let’s plot the “gamma factor”) At what speed is γ = 2 ? (in other words, twice the time) A. 0. 5 c B. 0. 75 c C. 0. 866 c D. 0. 913 c 24

Time dilation vs velocity (let’s plot the “gamma factor”) At what speed is γ = 2 ? (in other words, twice the time) A. 0. 5 c B. 0. 75 c C. 0. 866 c D. 0. 913 c 25

Do muons produced in cosmic rays make it to ground level ? Flux of muons at ground level ~1/cm 2/min Apparent Paradox ? The lifetime of the muon is 2. 2 microseconds. It is moving close to the speed of light (3 x 108 m/s). Therefore it will travel about 6. 6 x 102 m before decaying. But the earth’s atmosphere is over 20 km high. So no muons will be found at ground level. 26

Time dilation example A muon decays into other particles with a mean lifetime of 2. 20 μs = 2. 20 x 10 -6 sec as measured in a reference frame in which it is at rest. If a muon is moving at 0. 990 c relative to the earth, what will an observer on earth measure its mean lifetime to be ? Reference frame S’ of the muon, proper lifetime Δt 0= 2. 20 μs Reference frame S of the earth; relative speed of S’ and S is u=0. 990 c A. B. C. D. E. What is the gamma factor here ? 7. 1 8. 2 9. 3 10. 4 11. 5 27

Time dilation example A muon decays into other particles with a mean lifetime of 2. 20 μs = 2. 20 x 10 -6 sec as measured in a reference frame in which it is at rest. If a muon is moving at 0. 990 c relative to the earth, what will an observer on earth measure its mean lifetime to be ? Reference frame S’ of the muon, proper lifetime Δt 0= 2. 20 μs Reference frame S of the earth; relative speed of S’ and S is u=0. 990 c Question: What is the gamma factor here ? 7. 1 ! 28

For next time • Relativity continues Ø Read and study in advance (37. 3 -37. 5) Ø Concepts require wrestling with material 29