1. RelativityEinsteins solution: Two principlesPrinciple of Relativity:All of the laws of physics are thesame for any two observersmoving at constant relative speedPrinciple of Constancy of Speed of Light:All observers see the same speed of light, no matter their relativevelocities. Requires re-thinking of basic physics from the ground up Requires re-thinking of nature of time and spaceTime moves at different rates for different observers

2. Quantum MechanicsThe other great theory of modern physics Deals with very small objects Electrons, atoms, moleculesGrew out of problems that seemed simple Black-body radiation Photoelectric Effect Atomic SpectraProduces some very strange results 3. Blackbody RadiationLight emitted by hot objectDepends only on temperatureCharacteristic spectrum of light 4. Blackbody RadiationMax Planck, 1900 Developed mathematical formula for spectrumProblem: Derivation of formula required a mathematical trick Introduced idea of quantum of energy Completely overturned classical physics 5. Blackbody ModelImagine object as box with oscillators in wallsSmall amount of light leaks out blackbody spectrum What radiation exists in box? Standing wave integer number of half-wavelengths fit across the length of the boxDivide thermal energy of object among possible modes Add up all allowed modes to get total spectrum (Rayleigh-Jeans approach; slightly different than Planck, but simpler) 6. Standing Waves 7. Ultraviolet CatastropheProblem: Lots and lots of ways to get short wavelengths 120200 modes, 0.02L bins Predicts huge 100 80amount of light at very short wavelengthsNumber 60 40 200 0.0 0.20.40.6 0.8 1.0 Wavelength (box length) 8. Quantum HypothesisPlancks trick: Each mode has a minimum energy depending on frequencyCan only contain an integer multiple of fundamental energyModes with very short wavelength would need more than theirshare of thermal energy Amount of radiation drops off very sharply at short wavelength 9. Energy Partition6 quanta3 quanta2 quanta1 quanta0 quanta 10. Blackbody Spectrum 11. Photoelectric EffectShine light on some object,electrons come outDiscovered by Heinrich Hertz, 1887Simple model: Shaking electrons Predict: 1) Number of ejected electrons depends on intensity2) Energy of ejected electrons depends on intensity3) No obvious dependence on frequency 12. Photoelectric Effect: ExperimentObservations:1) Number of electronsdepends on intensity2) Energy of electrons DOESNOT depend on intensity3) Cut-off frequency:minimum frequency to getany emission4) Above cut-off, energy increases linearly with frequency 13. Photoelectric Effect: EinsteinEinstein, 1905: Heuristic Model of PE EffectParticle model: Light quanta with energySome minimum energy to remove electron:Work FunctionEnergy of emitted electron:Takes Plancks trick seriously, runs with the idea 14. Photoelectric Effect: EinsteinObservations:1) Number of electrons depends on intensity Higher intensity More quanta2) Energy of electrons DOES NOT dependon intensity Only one photon to eject3) Cut-off frequency: minimum frequencyto get any emissionEinstein in 1921Nobel Prize portrait4) Above cut-off, energy increases linearly Cited for PE Effectwith frequency 15. Atomic SpectraAtoms emit light at discrete, characteristic frequenciesObserved in 1860s, unexplained until 1913 16. Bohr Model1913: Neils Bohr comes up with solar system model1) Electrons orbit nucleus in certain allowed states2) Electrons radiate only when moving between allowed states3) Frequency of emitted/absorbed light determined by Planck rule Works great for hydrogen, but no reason for ad hoc assumptions 17. Matter WavesLouis de Broglie: Particles are WavesElectrons occupy standing wave orbitsOrbit allowed only if integral number ofelectron wavelengthsh Wavelength determined by momentum p Same rule as for light 18. Matter Waves de Broglie Waves: h pWhy dont we see this?Plancks Constant is tinyh = 6.626 10 34 J-s More significant for single atoms145 g baseball, 40 m/s 87Rb, 200 m/s = 1.1 10 34 m = 0.02 nm Insignificant for macroscopic objects Still small, but canstart to see effects 19. Electron DiffractionSend electrons at two slits in a barrier:Image and video from Hitachi:http://www.hitachi.com/rd/research/em/doubleslit.html 20. Fullerene Diffractionhttp://commons.wikimedia.org/wiki/File:Fullerene-C60.png Fig. 7 in the paper, "Quantum interference experiments with large molecules," by Nairz, Arndt, and Zeilinger (Am. J. Phys 71, 319 (2003)). 21. Big Molecules430 ATOMS 22. Light as a ClockLight: Electromagnetic waveExtremely regular oscillationNo moving partsUse atoms as a reference: Performance: Lose 1s in 100,000,000 years