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Physics 115 “Physics for FUTURE LEADERS” Prof. Paul Steinhardt Princeton in the Nation’s Service Woodrow Wilson, 1896 Take out you’re A-B-C-D card Quantum Weirdness Relativity Weirdness Waves in water versus Electromagnetic waves in vacuum ETHER? Maxwell’s Equations (1873) 1831-1879 A B •Alice is in the Dinky. Bob is by the side of the tracks. •The Dinky has velocity vAB = 5 m/s to the right. •Alice, travelling in the Dinky, throws the ball with velocity vA = 5 m/s relative to herself. A) 0 m/s B) 5 m/s C) 10 m/s D) more information needed A 0 5 B 0 5 10 12:00:00 TIMEX A 0 5 B 0 5 10 12:00:01 TIMEX •Alice, standing on the train, sees the ball move 5 m in one sec •Bob, standing on the ground next to the tracks, sees Alice move 5 m AND the ball move 5 m ahead of her •So Bob see balls move 10 m in one second, or 10 m/s VELOCITIES ADD Imaginary speed-of-light measurement device. incoming pulse ruler of light stopwatch 0 5 00:00:00 light detectors A flashlight 5 m/s B A flashlight in the train makes a pulse of light. Alice (in the train) measures light’s speed to be 300,000,000 m/s relative to her. Bob (standing still) measures the same pulse of light. What does he get? 300,000,000 m/s + 5 m/s = 300,000,005 m/s So say Newton and Galileo… Maxwell’s equations say: No! speed should be the same. Special Relativity If the speed of light is the same, then the clocks and rulers used to measure velocities must measure different times and distances! Worksheet mirror d mirror Alice is now in a spaceship. Two mirrors are separated by distance d. Time for a pulse of light to go from floor to ceiling is ? d = tA c v L d Bob •Bob is outside the spaceship, which moves by with speed v. •He sees the light pulse take the path shown above, which is longer than the path seen by Alice. v L d v tB 1 2 2 d 2 2 2 x L = d + (v tB) tB = v c2 [1 – c2] 1 2 2 tB = L/c = c d + (v tB) tA 2 1 2 2 t = 2 [d + (v t ) ] t = 1 B c B B x d 2 v2 d2 1 –(v/c)2 c tB [1 – c2] = c 2 Relativity: Time Dilation “Rest clocks run slowest”* time measured in rest g 1 frame of clock = 2 1− v c 2 tMOVING = g tREST time measured by observer who sees clock move at speed v *least time elapsed Is time dilation important in everyday life? Typical jet airplane speed is v = 300 m/s. Plug into formula, get g= 1.000 000 000 000 5. Time between takeoff and landing measured by a passenger would be about one-trillionth less than that measured by someone on the ground. (0.000 02 sec difference in 1 year.) ==> Not significant. (...but it has been measured, using atomic clocks.) Is time dilation important to interstellar space travelers? war & peace • Spacecraft moving at 99% the speed of light. (v = 0.99c = 297,000,000 m/s) •g= 7 • 7 years of rocket travel measured by someone on Earth would only be 1 year for the astronaut. • This is REAL. In 7 years of space travel (according to Bob) at 0.99 c, ---Alice’s watch would show only 1 year of elapsed time ---Alice would age only 1 year Handy Dandy Chart • g = 1 v = 0 • g = 2 v = 0.866 c • g = 2.5 v = 0.92 c • g = 7 v = 0.99 c • g = 10 v = 0.995 c • g = 100 v = 0.99995c Alice v Bob A Seinfeld episode normally lasts 30 minutes. Alice watches a tape of a Seinfeld show on her VCR as her spacecraft passes Bob with speed v = 0.995 c. The Lorentz factor is g=10. How long does the show last, according to Alice? A. 3 minutes B. 30 minutes C. 300 minutes Alice v Bob A Seinfeld episode normally lasts 30 minutes. Alice watches a tape of a Seinfeld show on her VCR as her spacecraft passes Bob with speed v = 0.995 c. The Lorentz factor is g=10. How long does the show last, according to Bob? A. 3 minutes B. 30 minutes C. 300 minutes Alice v people Bob Now consider things in Alice’s frame of reference. According to Alice, her rocket is standing still, while Bob is flying off at speed v = 0.995 c. (g=10.). If Bob takes 30 minutes to read a magazine article (according to his watch), how long does it take according to Alice? A. 3 minutes B. 30 minutes C. 300 minutes Puzzler : Suppose Alice only shows a 3 minute videotape. According to Bob, this takes 30 minutes – Precisely the same time it takes for him to read his magazine! So, according to him, he can start and stop reading his magazine simultaneous with the start and stop of the tape. Yet Alice, who sees the tape last 3 minutes, measures that Bob takes 300 minutes to read his magazine. How can that be? If they start and end simultaneously according to Bob, doesn’t it have to be simultaneous according to Alice?? Special Relativity If the speed of light is constant, then the clocks and rulers used to measure velocities must not be constant! What about Distance? Add a rocket to the Dinky so it moves at v = 260 000 km/s = 0.866 c g=2 The Dinky trip viewed by Bob: v Princeton Princeton Junction LB=5 km Same events observed in the Alice’s reference frame; Here the earth is moving at speed v. v Princeton Princeton Junction LB LA tB = = γ t = γ v A v Princeton Princeton Junction L L LA B = γ A RULER MOVING at REST Time dilation Time duration longer in the frame that sees a clock moving tmoving = g trest Length contraction Ruler shorter in a frame that sees a ruler moving -- but only along the direction of motion 1 Lmoving= g Lrest.
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