PH 103

1. PH 103 Dr. Cecilia Vogel Lecture 14

2. Review • Einstein’s relativity • 1st and 2nd postulates of special relativity • equivalence principle of general relativity • Consequences of Einstein’s postulates • time dilation • simultaneity Outline

3. Some Consequences Can be derived from constancy of speed of light: • Time interval between two events is different measured by different observers. • Order of events may be different measured by different observers. • Length of object or length of a trip is different measured by different observers.

4. Recall Classical Relativity • Suppose two observers time the pretzel you throw and catch. One observer on plane, one on Earth. Same pretzel. Go-stop. t=5 s Go------------------------------stop. t =?

5. Recall Classical Relativity • At any point, let the velocity of the pretzel measured by the plane observer be vp. • The velocity measured by Earth observer is vplane + vp. Earth observer measures faster speed: • pretzel goes farther, faster, but same time (5s) Compared to this frame, in this frame, the pretzel goes... farther

6. Now Einstein’s Relativity • That worked for pretzels, what about light? • Person on super-plane shines light at mirror. • Suppose two observers time the light that shines and reflects. One observer on plane, one on Earth. Same light. Go-------------stop. t=? Go-stop. to=5 ms

7. Now Einstein’s Relativity • At any point, the velocity of the light measured by the plane observer is c • And the velocity measured by Earth observer is c, so Earth observer measures: • Light goes farther, same speed→ in this frame, light goes... Compared to this frame, farther t>5ms longer time!

8. Time Dilation • Generalize result: • Dt and Dto are both the time between same events • measured by different observers • v is relative speed of the two observers • Notice that if v<<c, the two times are . • Hard part: which time is which?

9. Time Dilation • Units comment • If velocities are given as a fraction of c, • then the “c”units cancel. • Example: • If v= 0.8 c, • then (v/c) =(0.8c/c) = 0.8 (no units)

10. Proper time • What’s the difference between Dt and Dto? • Dto is the “proper time” • It is always less than any other measured time. • Definition: proper time is time in frame in which the two events occur at same place • Events are • single instant in time, single point in space, • Events don’t move. • They don’t have reference frame. Occur in all frames • Time interval is time between two events • One event makes you start your timer • other even makes you stop you timer.

11. Proper time • What’s the difference between Dt and Dto? • Dto is the “proper time” • Definition: proper time is time in frame in which events occur at same place • For example • If the two events happen to someone or something,their frame measures proper time • your heartbeat • particle’s lifetime • If someone is at both events, (or same Dx away) their frame measures proper time • person taking trip • you and the clock on the wall

12. Time Trip • Nikos travels to a planet 12 light-years away at a speed of 0.6 c. Juan stays on Earth. Each measures the trip to take a different amount of time. Note: • A light-year is distance light travels in a yr • 1 light-year = (c)(1yr) = 1c-yr • Consistent units: distance in light-years, speed as fraction of c, time in years Ex: 12c-yr/24yr = 0.5c • The values in example are relative to Earth • In that frame (in any one frame), the laws of physics hold, including d = vt

13. More Example • If Nikos makes a 12 light-year trip at 0.6c, Juan sees him moving at 0.6c for 20 years. • d = vt = (0.6c)(20 y) = 12c-yr. • Nikos sees himself moving at • Nikos sees the planet getting closer at 0.6c for 16 years. • d = vt = (0.6c)(16y) = 9.6 c-yr • Both are measuring the distance between Earth and planet, yet the distances are different!

14. Proper Length • What’s the difference between the two lengths? • One is the “proper length” • It’s always longer than any other measured length. • Def: proper length is length in frame in which object (or ends of trip) is at rest • For example • Object, or anyone at rest relative to it, measures object’s proper length. • Your own height • Length of ship you are riding on • Someone measures the proper length between two objects, if both are at rest relative to them • person on either planet, for a trip between planets

15. Just How Proper is it? If there is a proper time and a proper length, is there a proper reference frame? • NO!!!!!!! • Proper time of trip in example: Nikos • Proper length of trip in example: Juan • Proper time of astronaut’s heartbeat: Astronaut • Astronaut’s heartbeat looks SLOW to you. • Proper time of your heartbeat: You • Your heartbeat looks SLOW to astronaut.

16. Simultaneity • How do we know whether 2 events are simultaneous? • If signals coming from events arrive at the same time, the events might not have been simultaneous • how long did it take the signal to get here? demo

17. If tarrive, d, and v the same, conclude tevent same

18. Veraser-vthrower veraser+vthrower If tarrive, is smaller and d/v also smaller, can conclude tevent same

19. SIMULTANEITY IS NOT ABSOLUTE If tarrive is earlier and d/v is same, must conclude tevent is earlier! one observer says two events are simultaneous, other says they are not!!