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Announcements Review: Relativistic mechanics • Reading for Monday: Chapters 1 & 2! • HW 4 due Wed. Do it before the exam! • Exam 1 in 4 days. It covers Chapters 1 & 2. Room: G1B30 (next to this classroom). Relativistic momentum: p≡m Relativistic force: F≡ Total energy of a particle with mass ‘m’: dr dt propper = γ mu dp d = (γ m u ) dt dt Etot = γmc2 = K + mc2 • Practice exam available on CUlearn. (NOTE: our exam will be all multiple choice) These definitions fulfill the momentum and energy conservation laws. And for u<<c the definitions for p, F, and K match the classical definitions. But we found that funny stuff happens to the proper mass ‘m’. From last class: total energy E = γmc2 = K + mc2 v -v m m Etot = 2K + 2mc2 m m Etot = Mc2 Mc2 ≡ 2K + 2mc2 M > 2m Example: Deuterium fusion Example: Deuterium fusion Isotopes of Hydrogen: Isotope mass: Deuterium: 2.01355321270 u Helium 4: 4.00260325415 u (1 u ≈ 1.6610-27 kg) 1kg of Deuterium yields ~0.994 kg of Helium 4. Energy equivalent of 6 grams: E0 = mc2 = (0.006 kg)·(3·108 m/s )2 = 5.4·1014 J Enough to power ~20,000 American households for 1 year! Relationship of Energy and momentum Recall: = γmc2 p = γmu Total Energy: E Momentum: From the momentum-energy relation E2 = p2c2 + m2c4 we obtain for mass-less particles (i.e. m=0): Therefore: p2c2 = γ2m2u2c2 = γ2m2c4 · u2/c2 use: u2 γ 2 − 1 = 2 c2 γ p2c2 = γ2m2c4 – m2c4 E = pc , (if m=0) p=γmu and E=γmc2 p/u = E/c2 =E2 This leads us the momentum-energy relation: or: Application: Massless particles E2 = (pc)2 + (mc2)2 E2 = (pc)2 + E02 Using E=pc leads to: u=c , (if m=0) Massless particles travel at the speed of light!! C no matter what their total energy is!! Example: Electron-positron annihilation Do neutrinos have a mass? Positrons (e+, aka. antielectron) have exactly the same mass as electrons (e-) but the opposite charge: me+ = me-= 511 keV/c2 (1 eV ≈ 1.610-19J) Neutrinos are elementary particles. They come in three flavors: electron, muon, and tau neutrino (νe,νµ, ντ). The standard model of particle physics predicted such particles. The prediction said that they were mass-less. E1, p1 eBAM! e+ E2, p2 At rest, an electron-positron pair has a total energy E = 2 511 keV. Once they come close enough to each other, they will annihilate one other and convert into two photons. What can you tell about those two photons? Do neutrinos have a mass? (cont.) The fusion reaction that takes place in the sun (H + H He) produces such νe. The standard solar model predicts the number of νe coming from the sun. All attempts to measure this number on earth revealed only about one third of the number predicted by the standard solar model. Summary SR • Classical relativity Galileo transformation Bruno Pontecorvo predicted the ‘neutrino oscillation,’ a quantum mechanical phenomenon that allows the neutriono to change from one flavor to another while traveling from the sun to the earth. Why would this imply that the neutrinos have a mass? • Special relativity (consequence of 'c' is the same in all inertial frames; remember Michelson-Morley experiment) – Time dilation & Length contraction, events in spacetime Lorentz transformation – Spacetime interval (invariant under LT) – Relativistic forces, momentum and energy – Lot's of applications (and lot's of firecrackers) C Everything we have discussed to this point will be part of the first mid-term exam (including reading assignments and homework.) If you have questions ask as early as possible!! Part 2: Quantum* Mechanics Quantum Mechanics is the greatest intellectual accomplishment of human race. - Carl Wieman, Nobel Laureate in Physics 2001 To understand something means to derive it from quantum mechanics, which nobody understands. -- - unknown origin… Courtesy of IBM *We say something is quantized if it can occur only in certain discrete amounts. Part 2 of this course: 1. Basic properties of light (electromagnetic waves). 2. Photoelectric effect and how it shows light comes in quantum units of energy. When is a wave not a wave? (If it is a particle!) 2. Atomic spectra- quantized energy of electrons in atoms. 3. Bohr model of the atom. Where it works. Why it is wrong. 4. de Broglie idea- wave-particle duality of electrons etc. When is a particle not a particle? (when it’s a wave). 5. Schrodinger Equation and quantum waves. 6. What they are, how to use. 7. Applications: chemistry, electronics, lasers, MRI, C Properties of light Interaction with matter Rest of today (and next class): Basic properties of light (aka. electromagnetic waves): – How to generate light – Wave-like properties of light – Next week: Particle-like properties of light Disclaimer: A very exciting part of this course is the particle-wave duality of light (and matter!) However, do not get confused with when to use the wave or the particle representation of the very same physical entity. It actually depends on the experiment (‘question’ or ‘measurement’)! We will see several experiments that should help you understand this concept. Strap in and enjoy the ride! The sun produces lots of light Electric fields exert forces on charges (e’s and p’s in atom) + + + + + + + + E + _ F=qE E F=qE - Why? How? Force = charge • electric field F= qE + + + Light is an oscillating E(and B)-field. It interacts with matter by exerting forces on the charges – the electrons and protons in atoms. + Surface of sun- very hot! Whole bunch of free electrons whizzing around like crazy. Equal number of protons, but heavier so moving slower, less EM waves generated by protons. Light is an oscillating E (and B)-field • Oscillating electric and magnetic field • Traveling at speed of light (c) Snap shot of E-field in time: At t=0 A little later in time E c Emax Remember this one? Electromagnetic radiation E-field (for a single color): E(x,t) = E0 sin(2πx/λ ─ ωt + This symbolizes a local disturbance of the electric field E(x,t) Light source E λ φ) λ = 2πc/ω, ω = 2πf = 2π/T E0 x x φ Wavelength λ of visible light is: λ ~ 350 nm C 750 nm. E The E-field is a function of position (x) and time (t): E(x,t) = Emaxsin(ax+bt) sin(ax-bt) , (here: b/a=c) x B Electromagnetic Spectrum Making sense of the Sine Wave Spectrum: All EM waves. Complete range of wavelengths. Wavelength (λ) = Frequency (f) = distance (∆x) until wave repeats # of times per second E-field at λ point changes through complete Blue light cycle as wave passes λ Red light λ Cosmic rays CQ: What does the curve tell you? -For Water Waves? -For Sound Wave? -For E/M Waves? SHORT Electromagnetic waves carry energy Emax=peak amplitude c Emax X E(x,t) = Emaxsin(ax-bt) Light shines on black tank full of water. How much energy absorbed? LONG Maxwell’s Equations: Describes EM radiation dΦ m Qin • = − E d s E • d A = ∫ ∫ dt ε0 ∫B•ds = µ I ∫B•d A= 0 0 through Intensity = Power = energy/time α (Emax)2 α (amplitude of wave)2 area area B Intensity only depends on the E-field amplitude but not on the color (or frequency) of the light! E + ε 0 µ0 dΦ e dt Maxwell’s Equations: Describes EM radiation Qin ∫E •d A= ε0 ∫B•d A= 0 In 3-D: ∫E •ds = − ∫B•ds = µ I 1 ∂2E ∇E= 2 2 c ∂t 2 dΦ m dt 0 through In 1-D: Show that E(x,t) = Emaxcos(ax+bt) + ε 0 µ0 dΦ e dt ∂2E 1 ∂2E = ∂x 2 c 2 ∂t 2 How can we see that light really behaves like a wave? During 1600-1800s: lot’s of debate about what light really is. After ~1876 (Maxwell): Light = EM radiation viewed as a wave. How can it be tested? What is most definitive observation we can make that tells us something is a wave? is a solution (in 1-D) with b/a=c. EM radiation is a wave What is most definitive observation we can make that tells us something is a wave? EM radiation is a wave What is most definitive observation we can make that tells us something is a wave? Constructive interference:(peaks are lined up and valleys are lined up) c Destructive interference: (peaks align with valleys E-fields cancel each other) c Two slit interference Light is a wave interference! The definite check that light IS a wave Observe interference! wave interfarence online wave-interference_en.jar wave-interference_en.jar