GaitskellPH0008Quantum Mechanics and Special RelativityLecture 3 (Special Relativity)Transformations! Lorentz-Einstein TransformationProf Rick GaitskellDepartment of PhysicsBrown UniversityMain source at Brown Course Publisherbackground material may also be available at http://gaitskell.brown.eduPH0008 Gaitskell Class Spring2002Rick GaitskellVideo• “The Mechanical Universe” Video Serieso (See Gerry’s list on web site - I am using boiled down versions for time being)o 41 - Michelson-Morley Experimento 42- The Lorentz Transformation• Lanou Fall ‘94 Tapeo I won’t use this edit (see Lanou #2)• Jim Valles ‘96 Tapeo Not useful• From “The Mechanical Universe” Video Series (Lanou #2 Tape)o This is useful - see my edits on next pagePH0008 Gaitskell Class Spring2002Rick GaitskellVideo (2)• Michelson-Morley Material• From “The Mechanical Universe” Video Series (Lanou #2 Tape)o Nodeso 02:30 “Just as Newton was born…”[See Maxwell]o 03:15 [Queen Victoria * 1887]• GOOD PLACE TO STARTo 4:15 “Many physicists believe it is all over …”o 4:40 Michelson & Morleyo 8:26 Detailed technical discussion of M&M Experimento 15:46 “Light apparently doesn’t need an Aether”• [STOP HERE]o 15:58 “For next 50 years tried to …”o 16:50 “In one attempt after another …”PH0008 Gaitskell Class Spring2002Rick GaitskellVideo (3)- Lorentz Transformation• From “The Mechanical Universe” Video Series(Lanou #2 Tape)o 00:16:50 “In one attempt after another “• START - Good place (bit of preamble, but allow themto get used to video)o 00:17:20 [FitzGerald] introduced, then onto[Lorentz]• These theories were alternative to Einstein’s finalview/theoryo 00:19:35 [Big Train - discuss observers on..]o 00:20:30 “Consider 2 observers in relative motion…” (SIMULTANEITY )• SIMULTANEITY (2:10)• 22:38 “This is not semantics of a petty debate…”o 00:22:40 [Poincaret] Laws same in all frames• Lorentz developed formula that showed how muchdx and dt would be needed to keep c constanto BREAKo START AGAINo 00:24:12 [Light Clocks] - Henry & Albert ride withclocks• USE THIS - To show idea of clockso SKIPo 00:26:40 [Examples of contractions on Earth]• NOT USE - Examples of length contraction on Earth(too verbose to be useful)o START AGAINo 00:28:14 [Lorentz Equations - explicit derivation]• Lorentz’s Equations - but he uses them to sayelectrons shrink• Can’t talk about a time, without mentioning apositiono 00:30:30o BREAK FOR DISCUSSIONo 00:30:30 [Space - Time Diagrams]• Detailed graphics of Space-Time Diagramso 00:37:50 [S-T End]PH0008 Gaitskell Class Spring2002Rick GaitskellVideo (4)• From “The Mechanical Universe” Video Series (Lanou #2 Tape)o Nodes hh:mm:ss (The times may differ slightly because I used different video decks)o 00:37:50 [Twins] - Which tape does this material come from?o 00:43:14 [Space Billiards]• Kinematics - Mass also depends on frame of referenceo 00:49:50 [E=mc^2]• Show how E=mc2 drops outo 00:55:20 [ENDS]PH0008 Gaitskell Class Spring2002Rick GaitskellExam I: Waves (See “Class Schedule” for diary)• Exam I on classical wave phenomena will be on Friday 1 Marcho Note early start time 8.30 am - 9.50 am (Room 168 - lecture theatre)o Will those who requested exam at rescheduled time please see me after this lecture• To help you prepare …o Conferences on Tues & Wed this weeko Previous Exam Questions and Solutions are posted in Homework ‘Assignments’page on webPH0008 Gaitskell Class Spring2002Rick GaitskellSection: Special Relativity Week 2• Homework 4 (hand in M 2/25)• (see”Assignments” on web pages)• Pretty modest this time to allowrevision for Mid-Term I• Reading (Prepare for 2/25)o SpecRel (also by French)• Ch3 Einstein & Lorentz Transforms• Ch4 Realtivity: Measurement of Length andTime Inetrvals• Lecture 3 (M 2/25)o Lorentz Transformation• Examples:— Time Dil.,— Lorentz Cont.,— Relativity of Simultaneity• Lecture 4 (W 2/27)o Reciprocity of Time Dilation• No Lecture (F 3/1)o (Exam Mid-Term I)• Reading (Prepare for 3/4)o SpecRel (also by French)• Ch5 RelativisticKinematics• Ch6 Relativistic Dynamics: Collisions andConservation Laws• Homework (None schedule M 3/4)o This is because of exam on previousFridayo However - I strongly suggest you startHomework #7(see web “Assignments”)PH0008 Gaitskell Class Spring2002Rick GaitskellReview SectionReview SectionPH0008 Gaitskell Class Spring2002Rick GaitskellQuestion SpecRel L03-Q1•How much longer does an airplane (v=300 m/s=10-6c)get to due to special relativistic effects viewed fromground?(Order of magnitude estimate fine)o(1) ~1 Åo(2) ~1 µmo(3) ~1 mmo(4) None of above (within factor 10)PH0008 Gaitskell Class Spring2002Rick GaitskellQuestion SpecRel L03-Q2•How much shorter does an airplane (v=300 m/s=10-6c)get to due to special relativistic effects viewed fromground? (Order of magnitude estimate fine)o(1) ~1 Åo(2) ~1 µmo(3) ~1 mmo(4) None of above (within factor 10)PH0008 Gaitskell Class Spring2002Rick GaitskellLorentz TransformationsLorentz Transformations•Also referred to as Einstein Lorentz TransformationsPH0008 Gaitskell Class Spring2002Rick GaitskellRecapRecap•Attempts to explain negative aether drag resultsPH0008 Gaitskell Class Spring2002Rick GaitskellTheoretical Explanation (1892)•Does M-M mean that Aether doesn’t existoWhat if aether exerts some kind of influence on arms ofinterferometer?oFitzGerald & Lorentz propose that arm || to motion through aether iscompressed by factor (1-v2/c2)-1/2• Why would this help?PH0008 Gaitskell Class Spring2002Rick GaitskellMichelson-Morley Experiment (Calculation in Detail)† We won't make final approximations this timeTime for round trip in Arm 1 t1t1=lc - v+lc + v=lc11- v c+11+ v cÊ Ë Á ˆ ¯ ˜ =2lc11- v2c2Ê Ë Á Á ˆ ¯ ˜ ˜ Time for round trip in Arm 2 t2Using path length in aether frame¢ l = l2+ v2t2= ctfi l2+ v2t2= c2t2fit2=l2c2- v2fi t2= 2t=2lc11- v2c2Ê Ë Á Á ˆ ¯ ˜ ˜ Time for roundtrip t1Time forroundtrip t2vtlIn frame of aetherApparatus is moving through aether with velocity vSourceImagel’020225.2.rjgPH0008 Gaitskell Class Spring2002Rick GaitskellTheoretical Explanation (1892)• Does this mean that Aether doesn’t existo What if aether exerts some kind of influence on arms of interferometer?o FitzGerald & Lorentz propose that arm || to motion through aether is