Pass the (A)Ether, Albert?

Transcription

1 PH0008 Quantum Mechanics and Special Relativity Lecture 1 (Special Relativity) Pass the (A)Ether, Albert? Galilean & Einstein Relativity Michelson-Morley Experiment Prof Rick Gaitskell Department of Physics Brown University Main source at Brown Course Publisher background material may also be available at Gaitskell

2 Special Relativity [Lecture #] Galilean Relativity [1] Relativistic Dynamics [7] o Problem - Maxwell s Eqns o Waves on an Aether Speed of Light Michelson Morley Experiment Einstein s Special Relativity [2] o Time Dilation o Lorentz Contraction [3] Lorentz Transformation [4] o A twist due to momentum conservation, mass variance with velocity o Rewriting Newton s 2nd Law & KE [8] Massless Particles Energy-momentum invariant o Energy-mass equivalence o Relativistic Collisions Compton Effect o Examples: Time Dil., Lorentz Cont., Relativity of Simultaneity o Reciprocity of Time Dilation [5] Intervals, space time and world lines o Addition of Velocities [6] Rel. Doppler Effect Transverse Doppler Effect

3 Section: Special Relativity First Week Homework 3 (hand in now) Previous hw#1 & hw#2 available outside by office Rm 516 Reading 4 (Prepare for short week 2/20) o SpecRel (also by French) Ch2 Light Propagation Ch3 Einstein & Lorentz Transforms Homework 4 (hand in M 2/25) (see Assignments on web pages) Pretty modest this time to allow revision for Mid-Term I Lecture 10 (W 2/20) o Galilean Relativity o Michelson-Morley Experiment

4 Homework #3 Homework o Due Now Homework #1 & #2 will be available outside my office B&H 516 o Now

5 Exam I: Waves (See Class Schedule for diary) Exam I on classical wave phenomena will be on Friday 1 March o This is two days later than originally scheduled to give you time to benefit from two conferences that week. Conferences on Tues & Wed that week o Note early start time 8.30 am am (Room T.B.A) To help you prepare o Previous Exam Questions are posted in Homework Assignments page on web

6 Review Section

7 Question Who made the first quantitative measurement of the speed of light? o(1) Kepler & Brahe o(2) Fresnel & Young o(3) Hugens & Roemer o(4) Michelson & Morley

8 Question How was it made? o(1) Bouncing light off moon o(2) Sending light between a ship & light house o(3) Observing Jupiter s Moons o(4) Observing Earth s shadow across the Sun

9 Question At which position # is Stellar Aberration most noticeable (assume star at typical distance)? o(1) 1 3 o(2) o(3) 3 1 o(4) 4

10 Question Assuming you are standing on top of earth looking at star (as we view schematic here) how would you describe the motion of aberration (assume star is above extended line 2-4)? o(1) Left-right waggle - 1 cycle per year o(2) Left-right waggle - 2 cycles per year 3 o(3) Up-down waggle - 1 cycle per year o(4) None of above 4 1 2

11 Question What was Fizeau trying to do with this apparatus? o(1) Measure the properties of Perrier o(2) Measure Fresnel s drag coefficient o(3) Measure Aether drag of light o(4) Measure velocity of light in water?

12 Question What was Michelson trying to do with this apparatus? o(1) Measure the properties of Perrier o(2) Measure Fresnel s drag coefficient o(3) Measure Aether drag of light o(4) Measure velocity of light in water?

13 Question What is the purpose of C? o Oral

14 Lecture Section

15 Galilean Relativity Inertial Frames o A ball rolling in inside a train carriage ($20 fine) o Observers in train and (if it is an open carriage) on the ground Can agree on Mass Acceleration Force Time Disagree on Position Velocity o What s wrong with this train as an inertial frame?

16 Frames of reference S and S Galilean Transformation r = r - R r t = t r R = u r t y y' u Here u x x = x - ut y = y z = z t = t r v = v r - u r R r r' x x' r a = r a

17 What about light? Consider a circular wave front o Speed of light appears to depend on frame of reference Newton s Laws seem to be invariant x = ct x = x - ut = ( c - u )t c = c - u y y' u c? r F = m a r r r F = F m = m r a = d r 2 r dt = d r 2 ( 2 r + R r ) = a r dt 2 x x'

18 Problems? Do we need an Aether-tizing Maxwell s Equations o Velocity of light appears explicitly o So they are not invariant under Galilean Transformation o Require a unique (absolute) frame in which Maxwell holds - this is the Aether Speed of Light o Sound or water waves propagate in a material medium, so the observed velocities depend on which coordinate frame used. (Consider Asymmetry in Doppler Effect) o Does light propagate in a medium? Consider light making round trip A-B-A in an instrument that is moving at u relative to an aether A B l u c = t 1 = t 2 = l c - u l c + u 1 m0e 0 Ê Dt = t 1 + t 2-2 Á l ˆ Ë c = l Ê 1 c 1- u c + 1 Á Ë 1+ u c - 2 ˆ Ê = 2l c Á 1 Ë 1- u c ( ) 2-1 ˆ ª 2l c 1+ u c ( ) 2-1 ( ) ª 2l c Ê u Á ˆ Ë c 2

19 Problems? Do we need an Aether-tizing (2) Speed of Light o Does light propagate in a medium? Consider light making round trip A-B-A in an instrument that is moving at u relative to an aether o The change in the propagation time due to earth s orbital velocity This is a reasonable minimum for velocity relative to aether? o Consider Values Light ~1 ft/ns = 0.3 m/ns u/c ~10-4 Time difference impossible to measure Ê Dt = t 1 + t 2-2 Á l ˆ Ë c ª 2l Ê u Á ˆ 2 c Ë c If u ~ m/s l ~ 1 m Dt ~ s A B l u

20 Video

21 Michelson-Morley Experiment Measure difference in transit times of two beams l T 1 = c - u + l c + u ª 2l Ê u2 ˆ Á 1+ c Ë c 2 l = l 2 + u 2 t 2 = ct t = l c 1 1- u 2 c 2 T 2 = 2t ª 2l Ê c 1+ 1 u 2 ˆ Á Ë 2 c 2 T 2 ut T 1 In frame of aether l DT = T 1 - T 2 ª l u 2 c c 2 u Moving through Aether

22 Michelson-Morley Experiment (2) Interference Pattern seen by slightly tilting M1 or M2 o A change in time delay will shift interference pattern o Rotate apparatus by 90 degrees DT -> -DT Fringe pattern changes by DN Note: time delay of l/c shifts pattern by one fringe DT = T 1 - T 2 ª l u 2 c c 2 So for 90 degree rotation DN fringe = 2DT ( l c ) = 2l u 2 l c 2 T 2 T 1 l ~ 20 m l ~ 600 nm u c ~ 10-4 DN fringe = 0.4

23 Aether Investigations

24 Material For Next Lecture

25 -ENDS-

26 Double Slits

27 Old Material