Unit 10: Relativity Hewitt Chapters Brent Royuk Phys-109 Concordia University

Transcription

1 Unit 10: Relativity Hewitt Chapters Brent Royuk Phys-109 Concordia University

2 The Correspondence Principle 2

3 Relativity What s relative about relativity? 3

4 Relativity Billy-Bob s Pickup Truck Galilean Relativity Inertial Rest Frames A place where Newton s Laws work. A lab on a pickup truck? A boxcar? The space shuttle? Earth s surface? What is light s reference frame? c = 3 x 10 8 m/s The search for the luminiferous ether. 4

5 Relativity 5

6 Michelson-Morley Experiment 6

7 Einstein s Two Postulates 1. The Principle of Relativity: The laws of physics are the same in all inertial frames of reference. Galilean relativity There s no way you can tell you re moving. 2. The Principle of Constancy of Lightspeed: The speed of light is the same in all IRFs, independent of relative motion. This is the surprising one. Special vs. General Any objections? 7

8 Gedanken Billy-Bob and a flashlight. So if Sammy the Spaceman flies past you at a speed of c/2 and turns on his laser (shooting straight ahead) just as he passes, to what position has it traveled 1 microsecond later? Simultaneity 8

9 Gedanken The Relativity of Simultaneity 9

10 Time Dilation The Light Clock Why dilation? Is this a change in measured time or actual time? So which observer is right? 10

11 Time Dilation How much does time slow down? The Gamma Factor: γ = 1 1 v 2 c 2 11

12 The proverbial atmospheric muon (p. 233): Their brief lifetimes actually lengthen. Time Dilation 12

13 Time Dilation Example: Hafele and Keating, 1972: atomic clocks on commercial airplanes Time dilation was verified within 5-10% Observed time differences: east: -40 ns, west: +275 ns. (compared to ground) When atomic clocks are transported, they get out of sync. GPS satellites have to be synchronized with time dilation effects accounted for NOVA Episode #2612: On a plane trip to London, a clock gained 40 ns. Joe Hafele: Suppose you were to live for 100 years and you would spend your entire life on one of these aircraft, flying around the world, you could expect to be younger than people who did not do that by about one ten-thousandth of a second. 13

14 Length Contraction Measured lengths shrink by the gamma factor for different reference frames. This occurs only along the direction of relative motion. This is not just something that happens to fast meter sticks. Length is really relative to the observer. 18

15 Length Contraction 19

16 Length Contraction Visual Appearance: Antony Searle, 20

17 Length Contraction Visual Appearance: Antony Searle, 21

18 Relativistic Time Travel How long would it take to go 100 ly at v = 0.99 c? The Twin Paradox Bobby and Ricky are twins. When they are 20 years old, Bobby leaves on a space flight to a star that is 20 light years away, traveling very close to the speed of light. At this extreme speed, the gamma factor for time dilation is equal to 20. What happens? 24

19 Relativistic Mass Moving masses get heavier by the gamma factor. So what happens as objects move closer and closer to the speed of light? What if v = c? Rest Mass 25

20 Relativistic Mass Einstein: When you accelerate a mass, you increase its mass, and thus its kinetic energy. Energy and mass go hand-in-hand. Any time you add energy to an object, you increase its mass. Lift a rock, stretch a rubber band, etc. The connection: E = mc 2 How much energy is contained in a one-kilogram rock? Is it possible to release this energy? Matter-antimatter annihilations Nuclear processes 26

21 The Relativistic Universe What does this all mean? Well, mass is energy. And what is energy? The visible world is neither matter nor spirit but the invisible organization of energy. Heinz Pagels Science has found no things, only events. The universe has no nouns, only verbs. R. Buckminster Fuller There are no things, only processes. David Bohm So atoms are not what makes change and motion happen, change and motion make atoms happen. 32

22 The Correspondence Principle 33