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by: Mrs. Peter Toy


Mrs. Peter Toy

GPA 3.96


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Class Notes
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This 7 page Class Notes was uploaded by Mrs. Peter Toy on Friday October 30, 2015. The Class Notes belongs to PHYS 2130 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 10 views. For similar materials see /class/232113/phys-2130-university-of-colorado-at-boulder in Physics 2 at University of Colorado at Boulder.




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Date Created: 10/30/15
Announcements Reading for Friday TZD 15110 Homework 1 will be posted today due next Wednesday in Class First midterm is on Tuesday Oct 7 730pm900pm Contact us immediately if you cannot make this date Need special accommodations See us Office hours Mon and Wed 1pm 2pm Physics tower F527 Today Galilean relativity cont lnertial frames in classical physics Motivation for special relativity Strange things about Speed of light Every class Swap clicker code to DC Wait for 13 1 clicker question to open Hold down OnOff Switch 4 seconds Flashing blue light 9 hit D C light turns solid blue If not Try it again Type in Answer you39re set for rest of class period DO NOT TURN OFF CLICKER FOR CLASS ow repeat above for any new clicker question Please setup your clicker Q1 Quiz about last class An inertial reference frame is one a that is not moving b that is not accelerating c in which objects are a fixed distance apan d in which observers are a fixed distance apart e in which nothing is moving Last class Comparing inertial frames 3 2 1 O 1 2 3 gt 3 2 1 0 1 2 3 Here are two inertial reference frames moving with respect to one another According to S S is moving to the right with v 1 ms According to S S is moving to the left with v 1 ms Comparing inertial frames At time t 0 the two frames coincide A ball is at rest in frame S Its position is x 2minS x 2minS Comparing inertial frames Frame 8 is moving to the right relative to S at v1 ms At time t 3 sec the position of the ball is Important conclusion Where something is depends on when you check on it and on the movement of your own reference frame Time and space are not independent quantities they are related by velocity Definition An event is a measurement of where something is and when it is there 39 s L ml sv xyzt 02 Comparing inertial frames Galilean position transformation 8 is moving with speed v in the positive x direction 0 relative to S then its coordinates in S are l l l l l l V re 72 rt 0 l a X Vt l l l l l V a 2 r 0 l 2 a z39z At time 0 the ball was at x x At time t later the ball is 39 7 still at x in S but where is it in S at the same tImet ax x bx xvt cx xvt Note In Galilean relativity time is measured the same in both reference frames why wouldn t it e Galilean velocity transformation L l l l l l l l x rsrzrioizs v l l l l l l X srzioizs If an object has velocity u in frame 8 and if frame 8 is moving with velocity v relative to frame 8 then the position of object in S is x x vt Velocity of the object is therefore d u39iix vti vu v dt dt dt Q3 Galilean velocity transformation U lt o l l l l l V 73 72 rl 0 l S l l l l l l S 2 r 0 l 2 S Same thing as on monday but now the ball is moving in 8 too wit velocty 2 ms Is the ball faster or slower as measured in Frame 8 A faster B slower C same speed Important conclusion Two observers in different reference frames can give a different description of the same physical fact in this case the velocity of the ball And they re both right Dynamics Dynamics In inertial frame 8 we have in Xdirection say F 2 ma How about in inertial frame 8 Well F 39 F since you re still applying the same forces and dv d du 61 u v a dt dt dt since there s no additional acceleration in an inertial frame S 339 239 l V S l l l l l 3 2 1 O 1 2 3 Galilean relativity Thelawsof mechanics good old Fma are the same in any inertial frame of reference Einstein s First Postulate of Relativity If S is an inertial frame and if a second frame 8 moves with constant velocity relative to S then S is also an inertial frame Peculiar lightwaves A sound wave propagates through air with velocity relative to the air 330 m sec A water wave propagates in water with velocity relative to the water 1 100 m sec The wave propagates through a crowd in a stadium with velocity relative to the stadium An electromagnetic wave propagates through Answer 19th century physics The Iuminiferous ether Ideas behind Einstein s relativity Is there an ether There where various other motivations for special relativity but for simplicity we will focus here on the quest for detecting the ether Q4 The ether Suppose the earth moves through the fixed eth39er with speed v A light wave traveling at speed c with respect to the ether is heading in the opposite direction According to Galilean relativity what is the speed of the light wave as viewed from the earth Further assume the earth is not accelerating a c b cv c cv Michelson and Morley Performed a famous experiment that effectively measured the speed of light in different directions with respect to the ether wind g mm 1552 193 Frame of reference Observer on the sun Ether V Ether viewed in the laboratory on the earth Ether in the laboratory frame v L v 335 How can we measure the speed v of the ether If the ether would be a river we could measure the speed of the water using a boat that travels at a known speed u u is the relative velocity between the boat and the water If the boat travels the distance L within the time t then we know v Luvt therefore v u Llt Very difficult in practice u c 9 t 10ns and v 00001c 9 We would have to measure twith an absolute precision of 00000000000001s and we have to know 0 very precisely Michelson and Morley Michelson and lMorley Irrors Semitransparent 39 39 mirror Compare the roundtrIp tImes tA and tB for paths A and B This has the great benefit that we do not have to measure the absolute times tA and tB which are only a Light source few ns and we are less sensitive to uncertainties in the speed of light Interferometer The detector measures differences in the position of the maxima or minima of the lightwaves of each of the two beams Yes light is a wave l I 4 i 397 139 I l rquot Sod 139 Sod m Iun39t lu r L39gh soume 1 A I quot 39BI gt r LIghtSourca 1 1I 3 a i v t x I I 1 A 39 n lEl A El i I j I I I v 1 l39 v V 39 r V I I 50mmquot waves m I sodium waves oul 50mmquot WBVGS m I sodium waves out phase 2 I or phase Phase l r39 I 0 phase L 3 I t L 3 l 1 r 2 39 7 a g l quotAJ err 13 f l em r r3 3939I I392 39 r I 2 D F o F I o F D F 1 I M r39 39veluclly cl Ilgm lnru me Iurrtlntlewusaetrter Arm ltl39 ll l39h l d Izttm39 39zvaloclty otIIglttInru inelamlrtllerous aetrter Arrtn hl llI39ivvtl lulur 139 velocity at MtohetsmMcrlay Interferometer In Its Earth transit orbit t39 velouty al Mtctselsm Marley Interferometer In Its Earth transit orbit Il longitudinal arm moving unnome in a rectilinear oIrectIun I longlludlnal arm moving unrlorme In a rectilinear direction I r The historic setup 1887 EZE39WE C Homework L L 2L 1 6 1 12 c v cv C 1 72 L 2 2 At t1 2 v 2 Msz 2 6 c c MichelsonMorley experimental results Over a period of about 50 years the MichelsonMorley experiment was repeated with growing levels of sophistication The overall result is a high level of confidence that the wavelength shift is consistent with zero L cm Calc Meas Ratio Michelson 1881 120 004 002 2 Michelson amp Morley 1887 1100 040 001 40 Morley amp Miller 190204 3220 113 0015 80 llingworth 1927 200 007 00004 175 Joos1930 2100 075 0002 375 Shankland et al Rev Mod Phys 27 167 1955 Michelson and Morley They thought that the experiment was a complete failure because no effect was found Michelson was awarded the Nobel Prize in 1907 5391am L amwmg Speed of light IS the 239 539 M 9 same in all directions True result Homework part of your reading assignment Work out the math for this experiment TDZ Chapter 15 Yes but Q What if the ether is dragged alongquot the surface of the earth like air flowing around a tennis ball A If so this would require a viscosity of the ether and would require re writing Maxwell s equations Remark Lots of effort tried to save the idea of the ether but none held up There is no ether J 39 The Electric and Magnetic Fields Electromagnetic waves are special A timechanging electric field induces a magnetic field and viceversa A medium ether is not necessary 05 Quiz on MichelsonMorley The MichelsonMorley Experiment tests if in all inertial frames the speed of light A is the same in air and in vacuum B is not the same in air and in vacuum C is the same in all directions D does not depend on the wavelength E does not depend on the color Einstein s Second Postulate of Relativity The speed of light is the same in all inertial frames of reference This was new in 1905 when Einstein proposed it Now it has been experimentally tested lots of times Answers to clicker questions Assrgnments 89889 For Friday Please study TZD 15110 Written homework1 due next Wednesday Homework assignments are posted on the course web page httpwwwcooradoeduphysicsphys2130 phys21307fa08homeworkhtm TZD problems 14 16 110 111 112 114115116


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