Lecture 4 Fields, Relativity

Transcription

1 The Nature of the Physical World January 7th, 00 Lecture 4 Fields, Relatiity Arán García-Bellido

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3 What is the essence of a force? Graitational Field Electric Field At each point in space, graitational Force/mass (magnitude plus direction) that would be felt by a little test mass at that point At each point in space, electric Force/charge (magnitude plus direction) that would be felt by a little test charge at that point m q+ M Q+ Graitational field F M =G m d Electric field (Newton) F Q =k q d (Coulomb) 3

4 Electric field between two charges Demo of charges and fields +Q -Q Lines of force: a isualization of the field Remember the wind map 4

5 Galilean relatiity Velocities add: it's just common sense! 4 miles/hour Speed with respect to you is 4 miles/hour 4 miles/hour miles/hour Speed with respect to you is +4=6 miles/hour Implication: If you are in an airplane that moes at constant elocity, there is no way to tell if the airplane is at rest or moing. Eerything looks the same on a plane in steady motion as it does on a plane at rest. But you can tell when the plane is accelerating or turning. 5

6 Now with light A car moes with elocity and a passenger shines a flashlight in three directions. The speed of light is greater for beam A, B or C? B C A Experiment says: the speed of light is the same in all directions!! 6

7 Michelson-Morley (887) Wanted to proe that light traels through aether : a perasie substance that carries the light Idea was to measure the speed of light traeling upwind of this aether (when Earth glides along) and then downwind (in the opposite direction): the difference should be twice the wind speed. Not easy! The speed of light is much much faster than the aether wind (Earth speed in orbit ~0 miles/second ; speed of light ~00,000 miles/second) Need to measure part in 0,000 They deised a race for two beams of light: path path Demonstration UVa site Analogy with swimmers 7

8 Enter our man Einstein! 8

9 Einstein thought experiment Consider a train moing at constant speed. A beam of light is emitted from the floor of the wagon and bounces off a mirror on the ceiling and returns to the point on the floor where it was emitted H 9

10 What do we see? Fact: Light is emitted and detected in point X This must be true no matter who makes the measurement! H X 0

11 Sam is on the train H Velocity of light = c c = distance / time Sam measures TS c = H/TS TS = H/c

12 Alice watches the train pass from the platform H Alice starts her stopwatch Light is emitted

13 Alice watches the light bounce H Light bounces on mirror 3

14 Alice measures stopwatch H X Light returns to point X Alice also sees the light return to X Visual demo 4

15 Sam and Alice: comparison Sam Alice Alice sees the light traeling further If light traels at constant speed, the same eent must seem to take longer to Alice than Sam: TA > TS Time is relatie... not absolute! 5

16 Alice's point of iew Path light takes to mirror D distance train traels while light is traeling = TA D= H T A H Path light takes from mirror to detector Makes use of Pythagoras theorem 6

17 Alice's point of iew D H c = distance/time = D/TA TA = D/c 7

18 A little algebra Sam (on train) Alice (on ground) c = D/TA H/TS = c c= H TS = TA H T A H TS = H TA TA H T A H = TS TS = H TA TA TA T A H 8

19 And finally... = TS = TS TA H TA But H=cTS ct S [ ] TA= c= c T T A S TS c 9

20 And finally... = TS = TS TA H TA c H=cTS TS But ct S [ ] TA= c= c T T A S This number is > It becomes larger as approaches c And it all started because we imposed that c, the speed of light, is the same number for Sam and Alice! 0

21 Wow! Sam and Alice measure the time interal for the same eent The only difference between Sam and Alice is that one is moing with respect to the other Yet, TAlice > TSam Alice sees Sam's clock taking more time to tick: longer path his clock runs slower The same eent takes a different amount of time depending on your reference frame Time is not absolute! It is relatie!

22 Is this true? Yes! Experiments confirm it Ground Plane

23 Is this true? Yes! Experiments confirm it Ground Plane 3

24 Is this true? Yes! Experiments confirm it Ground Plane 4

25 Twin paradox [ ] [ ] T Earth= c Tspaceship Alice remains on Earth When Sam gets back he has aged 50 years proper time T Earth= 0.98c c A spaceship leaes Earth with Sam on it and moes with speed =0.98c How much has Alice aged? 50years = [5]50years=50years 5

26 Length is relatie too Time dilation length contraction Measure the length of the wagon, when you are on it (Sam): L A = LS c And now when the wagon moes past you (Alice, at rest in the ground): 6

27 Length is relatie too Time dilation length contraction For a measurement of the length of the wagon (along the same direction of motion of the wagon): L A = c LS Smaller than Sam Alice Alice sees the wagon shorten in length (not in height): link 7

28 Einstein's special relatiity ) The Laws of Physics are the same in all Inertial Frames (Galileo) ) Thus, any measurement of the speed of light in any inertial frame will always gie 86,300 miles per second 8