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String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 Thursday, April 12, 12 String Theory in the LHC Era 1. Electromagnetism and 5. Supersymmetry Special Relativity 2. The Quantum World 6. Einsteins Gravity 3. Why do we need

  1. String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 Thursday, April 12, 12

  2. String Theory in the LHC Era 1. Electromagnetism and 5. Supersymmetry Special Relativity 2. The Quantum World 6. Einstein’s Gravity 3. Why do we need the Higgs? 7. Why is Quantum Gravity so Hard? 4. The Standard Model and Beyond 8. String Theory and Unification 9. String Theory and Particle Physics 2 Thursday, April 12, 12

  3. Electromagnetic Waves Wavelength λ Frequency ν = c λ Maxwell → fixed speed c Characterized by: • Intensity | E | 2 • Wavelength λ 3 Thursday, April 12, 12

  4. Photoelectric Effect How does emission depend on • Intensity of beam? • Wavelength of beam? 4 Thursday, April 12, 12

  5. Photoelectric Effect Robert Millikan UChicago Professor! ← Wavelength λ 5 Thursday, April 12, 12

  6. Photoelectric Effect At large wavelengths, no electrons emitted → Independent of intensity of the incident radiation 6 Thursday, April 12, 12

  7. Photoelectric Effect Electromagnetic waves have a ‘smallest piece’ 7 Thursday, April 12, 12

  8. Photoelectric Effect Electromagnetic waves have a ‘smallest piece’ 7 Thursday, April 12, 12

  9. Photoelectric Effect Electromagnetic waves have a ‘smallest piece’ 7 Thursday, April 12, 12

  10. Photoelectric Effect Electromagnetic waves have a ‘smallest piece’ Photon energy is determined by its wavelength E = hc λ = h ν Planck constant Smallest pieces - ‘quanta’ h ∼ 6 . 626 × 10 − 34 J · s 7 Thursday, April 12, 12

  11. Photoelectric Effect Photon energy is Wavelength, λ ↔ Energy of each photon determined by wavelength Beam intensity ↔ # of photons E = hc λ = h ν Electron interacts with one photon at a time Incident light → Ejected only if wavelength short enough (photons) 8 Thursday, April 12, 12

  12. Two Important Points: 1. ‘Particle-like’ behavior of light 2. Correlation between energy and length scales Energy E = hc λ Wavelength 9 Thursday, April 12, 12

  13. We observe the world through scattering experiments Wavelength of light limits distance scales that we can resolve 10 Thursday, April 12, 12

  14. We observe the world through scattering experiments Wavelength of light limits distance scales that we can resolve 10 Thursday, April 12, 12

  15. We observe the world through scattering experiments Wavelength of light limits distance scales that we can resolve 10 Thursday, April 12, 12

  16. We observe the world through scattering experiments Wavelength of light limits distance scales that we can resolve 10 Thursday, April 12, 12

  17. d atom Need λ < d atom to study atoms hc ↔ E > d atom Need λ < d nucleus to study atomic nucleus hc ↔ E > d nucleus d nucleus 11 Thursday, April 12, 12

  18. d atom Need λ < d atom to study atoms hc ↔ E > d atom Need λ < d nucleus to study atomic nucleus hc ↔ E > d nucleus d nucleus 11 Thursday, April 12, 12

  19. d atom Need λ < d atom to study atoms hc ↔ E > d atom Need λ < d nucleus to study atomic nucleus hc ↔ E > d nucleus d nucleus 11 Thursday, April 12, 12

  20. Must go to higher energies to probe small distance scales LHC ∼ 10 − 18 cm (0 . 000000000000000001 cm) Strings: 10 − 33 cm? 12 Thursday, April 12, 12

  21. Waves and Particles Sometimes light behaves ....and sometimes like a like a wave.... particle ...depends on the question we ask Let’s examine some important wave behavior and its implications 13 Thursday, April 12, 12

  22. Waves and Uncertainty E = hc λ A photon in this wave carries momentum λ p = h λ But where is it? 14 Thursday, April 12, 12

  23. Interference Constructive Destructive 15 Thursday, April 12, 12

  24. Interference Constructive Destructive 15 Thursday, April 12, 12

  25. Interference Constructive Destructive 15 Thursday, April 12, 12

  26. Interference Constructive Destructive 15 Thursday, April 12, 12

  27. Interference Waves can ‘cancel’ one another Constructive Destructive 15 Thursday, April 12, 12

  28. Waves and Uncertainty ∆ x 16 Thursday, April 12, 12

  29. Waves and Uncertainty + = ∆ λ + ∆ x + + ... ✓ 1 ◆ & 1 ∆ x ∆ λ General property of waves 16 Thursday, April 12, 12

  30. Heisenberg Uncertainty p = h Quantum Theory: Light composed of photons λ ✓ 1 ◆ ∆ x ∆ p & h & 1 ∆ x ∆ λ Cannot pin down position and momentum of a photon (more fundamental than our treatment suggests) 17 Thursday, April 12, 12

  31. So Far: 1. Light waves composed of many quanta -- photons • Wave can behave like stream of particles 2. Energy and momentum determined by wavelength E p 3. Cannot pin down and to arbitrary precision x p What about particles (eg electrons)? Do they behave like waves? 18 Thursday, April 12, 12

  32. Diffraction Incident wave Slit Intensity I ∼ | E | 2 Screen 19 Thursday, April 12, 12

  33. Diffraction Interference! Incident wave Slit Intensity I ∼ | E | 2 Screen 19 Thursday, April 12, 12

  34. Electrons too! e − source Slit Number of Electrons Screen 20 Thursday, April 12, 12

  35. Electrons too! e − source Slit Number of Electrons Screen 20 Thursday, April 12, 12

  36. Electrons too! e − source Slit Number of Electrons Screen 20 Thursday, April 12, 12

  37. Electrons too! e − source Slit Number of Electrons Screen 20 Thursday, April 12, 12

  38. Electrons too! e − source Slit Number of Electrons Screen 20 Thursday, April 12, 12

  39. Electrons too! e − source Slit Number of Electrons Screen 20 Thursday, April 12, 12

  40. Electrons too! e − source Slit Number of Electrons Screen 20 Thursday, April 12, 12

  41. Electrons too! e − source Slit Number of Electrons Screen 20 Thursday, April 12, 12

  42. Electrons too! e − source Slit Number of Electrons Screen 20 Thursday, April 12, 12

  43. e − source Slit Number of Electrons Screen λ = h Particle of momentum p has an intrinsic wavelength p What is ‘waving’? 21 Thursday, April 12, 12

  44. Intensity ⬌ # of photons Intensity profile ⬌ probability for an individual photon to hit a particular spot on the screen Intensity I ∼ | E | 2 Associate an abstract ‘wave function‘ to each Ψ e − electron source | Ψ | 2 ↔ probability Slit Number of 22 Electrons Thursday, April 12, 12

  45. Classical EM ‘Electron E What is waving? Wave wave’ Ψ | E | 2 Probability! | Ψ | 2 Intensity Probability ....it is a wave so we can get interference effects 23 Thursday, April 12, 12

  46. Double Slit Experiment Incident wave Intensity Screen I ∼ | E | 2 24 Thursday, April 12, 12

  47. Double Slit Experiment Incident wave Interference Intensity Screen I ∼ | E | 2 24 Thursday, April 12, 12

  48. Double Slit Experiment Incident wave Interference Intensity Screen I ∼ | E | 2 24 Thursday, April 12, 12

  49. What about Electrons? Interference e − source Probability ∼ | Ψ | 2 Screen 25 Thursday, April 12, 12

  50. What about Electrons? Detectors Interference e − source Probability ∼ | Ψ | 2 Screen 25 Thursday, April 12, 12

  51. What about Electrons? Detectors e − source Probability ∼ | Ψ | 2 Screen 25 Thursday, April 12, 12

  52. Detectors e − source Electrons passing through different slits do not interfere with one another after we add the detectors How can we understand this? 26 Thursday, April 12, 12

  53. Before measurement Electron probability Slits 27 Thursday, April 12, 12

  54. After measurement Electron probability Slits 27 Thursday, April 12, 12

  55. Measurement causes Electron probability ‘Wave function collapse’ Slits ‘Copenhagen Interpretation’ Niels Bohr 28 Thursday, April 12, 12

  56. About ‘wave function collapse’..... Detectors Wave from top slit ‘Detector state space’ Wave from bottom slit Direction of ‘waving’ 29 Thursday, April 12, 12

  57. About ‘wave function collapse’..... Detectors Wave from top slit ‘Detector state space’ Wave from bottom slit Direction of ‘waving’ 29 Thursday, April 12, 12

  58. About ‘wave function collapse’..... Detectors Wave from top slit ‘Detector state space’ Wave from bottom slit Direction of ‘waving’ 29 Thursday, April 12, 12

  59. About ‘wave function collapse’..... Detectors Wave from top slit ‘Detector state space’ Wave from bottom slit Direction of ‘waving’ 29 Thursday, April 12, 12

  60. Electron passing through each slit becomes ‘entangled’ with its detector Detectors Spoils cancellation that caused interference pattern → ‘Decoherence’ 30 Thursday, April 12, 12

  61. Decoherence is not ‘wave function collapse’.... Explains why the wave function ‘seems’ to collapse Detectors Interaction with environment spoils quantum ‘cancellations’, leading to ‘classical behavior’ 31 Thursday, April 12, 12

  62. Explains why detectors destroy the interference pattern Detectors ...but not the whole story 32 Thursday, April 12, 12

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