1April 21, 2005 Physics for Scientists&Engineers 2 1Physics for Scientists &Physics for Scientists &EngineersEngineers 22Spring Semester 2005Lecture 47April 21, 2005 Physics for Scientists&Engineers 2 2RelativityRelativity Common wisdom: “everything is relative …” Is this really what the theory of relativitytells us? Absolutely not!April 21, 2005 Physics for Scientists&Engineers 2 3Interference in a NutshellInterference in a Nutshell Path length difference of λ (n + 1/2):destructive interference Path length difference of nλ:constructive interference Interferometer: can be used to measure very smallpath length differences between light-”beams”• Appearance of fringes (light and dark)April 21, 2005 Physics for Scientists&Engineers 2 4InterferometerInterferometer Simplified Michelson-Morley interferometer2April 21, 2005 Physics for Scientists&Engineers 2 5Waves in a Nutshell (fromWaves in a Nutshell (from PHY183)PHY183) The equation for all wave motion: Solutions: with Y = arbitrary function! Sinusoidal waves:• Moving to “right”:• Moving to “left”: Wave speed:!2!t2y(x,t) " v2!2!x2y(x,t) = 0y1(x, t ) = Y (x ! vt)y2(x, t ) = Y (x + vt)y(x,t) = Asin!t "#x +$0( )y(x,t) = Asin!t +"x +#0( )v =!"=#fApril 21, 2005 Physics for Scientists&Engineers 2 6Wave in Medium:Wave in Medium:Doppler EffectDoppler Effect Physical reason for Doppler Effect:• Stationary sound source emits sphericalsound waves, spreading with vs• Movement of sound source with vtowards observer bunches up waves,causing more waves to move past theobserver in a given time interval• => perceived higher frequencyApril 21, 2005 Physics for Scientists&Engineers 2 7Doppler Effect (2)Doppler Effect (2) General formula for observed frequency of sound fo as a function ofemitted frequency of sound f :• vs = sound velocity• vo = velocity of observer• v = velocity of source +- signs for the following cases:• Source moves away from observer: +• Source moves towards observer: -• Observer moves away from source: -• Observer moves towards source: + All velocities are relative to the medium (air), which isassumed to be at restfo= fvs± vovs± vApril 21, 2005 Physics for Scientists&Engineers 2 8Electromagnetic WavesElectromagnetic Waves The speed of an electromagnetic wave can be expressed in terms oftwo fundamental constants related to electric fields and magneticfields, the magnetic permeability and the electric permittivity of thevacuum For an electromagnetic wave, the wavelength and frequency of the waveare related to the speed of light Traveling electromagnetic wavesc =1µ0!0c =!f E(!r ,t ) = Emaxsin kx !"t( )B(!r ,t ) = Bmaxsin kx !"t( )3April 21, 2005 Physics for Scientists&Engineers 2 9Electromagnetic SpectrumElectromagnetic SpectrumApril 21, 2005 Physics for Scientists&Engineers 2 10EtherEther So far we have not answered what medium lightwaves propagate in• Air? Not needed, because light from outside theatmosphere reaches us, too (sun, stars, moon)• Now we know: light can propagate in vacuum• Around 1900 this was not known, and the medium thatlight propagates in was postulated to be the “ether” Can one see something similar to the DopplerEffect for light, since the Earth moves relative tothe ether?• Michelson&Morley built their interferometer to find outApril 21, 2005 Physics for Scientists&Engineers 2 11Michelson & MorleyMichelson & Morley’’s Results Result If there is motion of Earth relative to ether, thenthe observed speed of light should be differentfor light in different directions Michelson & Morley used their interferometer andfound … NOTHING Light speed is the same in any direction ~300,000 km/sApril 21, 2005 Physics for Scientists&Engineers 2 12EinsteinEinstein1879 Born in Ulm, Germany (March 14)1902 Begins work at Swiss patent office1905 Publishes the three seminalpapers on theoretical physics1916 Proposes general theory ofrelativity1919 General relativity is proved correctduring a solar eclipse1922 Awarded Nobel Prize in Physics1933 Emigrates to US (Princeton, N.J.)1939 Urges F.D.R. to develop atom bomb1955 Dies in his sleep (April 18)4April 21, 2005 Physics for Scientists&Engineers 2 13EinsteinEinstein’’s Miracle Year, 1905s Miracle Year, 1905 Three seminal papers:• A paper explaining the so-called photoelectric effect asdue to the quantum nature of light. This earned him theNobel Prize in 1922. Light a quantum particle (more onthis in modern physics).• A paper explaining the effect of Brownian motion, themotion of very small particles in water or other solutions,as due to collisions with molecules and atoms, thusproving that atoms really exist. (This was not at all clearbefore his work.) This would have also been worth aNobel Prize.• Theory of special relativity.• 2005: Celebrate 100th anniversaryApril 21, 2005 Physics for Scientists&Engineers 2 14EinsteinEinstein’’s Postulatess Postulates Postulate 1:• The laws of physics are the samein each reference frame,independent of the motion of thisreference frame. Postulate 2:• The speed of light, c, is the samein every reference frame.April 21, 2005 Physics for Scientists&Engineers 2 15Reference FrameReference Frame What is a reference frame? It is any frame in which an observation can bemade. Any point on Earth is a reference frame Reference frames can move with respect to eachother Let’s go back to moving reference frames, anotherreview from PHY183April 21, 2005 Physics for Scientists&Engineers 2 16Moving Reference Frame - ClassicalMoving Reference Frame - Classical Person walking with a velocity vw, as measured byan observer moving along with him on the walkway. Walkway surface moveswith vwt relative toterminal. Two velocities add asvectors Velocity of person asmeasured by someonestanding in the terminal: vt = vwt + vw5April 21, 2005 Physics for Scientists&Engineers 2 17Galilean TransformationGalilean Transformation Two coordinate systems x,y,z and x’,y’,z’ that have theiraxes parallel to each other and coincide at t=0. Origin of x’,y’,z’ moves withconstant velocity relativeto x,y,z After some time t, the originof x’,y’,z’ is located at Vector addition gives us thetransformation between frames !vT !rT=!vTt !r =!r '+!rT=!r '+!vTtApril 21, 2005 Physics for Scientists&Engineers 2 18Galilean Transformation
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