String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 Tuesday, April 3, 12
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 Tuesday, April 3, 12
Start our story with the original ‘unified’ theory..... Electric force between charged objects Detectable in simple ‘pith ball’ experiments How to measure precisely? 3 Tuesday, April 3, 12
q q r 4 Tuesday, April 3, 12
Inverse Square Law q E = 4 ⇡✏ 0 r 2 ‘permittivity of free space’ ✏ 0 ∼ 8 . 854 × 10 − 12 C 2 N m 2 q q r 4 Tuesday, April 3, 12
Aside: Cavendish Study gravitational interaction Basic idea still in use today (tests of equivalence principle, fifth forces, etc) “Eot-Wash” group at UW and others 5 Tuesday, April 3, 12
Magnetism Bar Magnet Magnetic field lines Iron filings 6 Tuesday, April 3, 12
Magnetism Bar Magnet Magnetic field lines Iron filings Very important magnetic field 6 Tuesday, April 3, 12
Relation of Electricity and Magnetism I: Magnetic Fields from Currents Electric current causes compass deflection Current in Ring → Electric current generates magnetic field Compass 7 Tuesday, April 3, 12
Relation of Electricity and Magnetism I: Magnetic Fields from Currents B = µ 0 I 4 π r 2 ‘permeability of free space’ µ 0 ∼ 1 . 257 × 10 − 6 N A 2 → Determines strength of magnetic field induced by a current → Can measure in a simple lab experiment 8 Tuesday, April 3, 12
Relation of Electricity and Magnetism II: Electromagnetic Induction Changing magnetic field induces an electric field Many applications including electric generators, motors, etc 9 Tuesday, April 3, 12
Maxwell’s Electromagnetic Theory r · E = ⇢ ✏ 0 Charge density ρ generates electric field r · B = 0 No magnetic analog of electric point charge r ⇥ E = � ∂ B ∂ t Changing magnetic field generates electric field @ E r ⇥ B = µ 0 J + µ 0 ✏ 0 @ t Changing electric field and moving charges generate magnetic field 10 Tuesday, April 3, 12
Maxwell’s Electromagnetic Theory r · E = ⇢ Depends on only 2 ✏ 0 parameters ✏ 0 , µ 0 r · B = 0 which can be measured in the lab r ⇥ E = � ∂ B ∂ t @ E r ⇥ B = µ 0 J + µ 0 ✏ 0 @ t 11 Tuesday, April 3, 12
Prediction of Maxwell Theory: Electromagnetic Waves! r ⇥ E = � ∂ B @ E r ⇥ B = µ 0 ✏ 0 ∂ t @ t Changing electric field generates Changing magnetic field generates magnetic field electric field 12 Tuesday, April 3, 12
Prediction of Maxwell Theory: Electromagnetic Waves! 1 Propagate with speed √ ✏ 0 µ 0 r ⇥ E = � ∂ B @ E r ⇥ B = µ 0 ✏ 0 ∂ t @ t Changing electric field generates Changing magnetic field generates magnetic field electric field 12 Tuesday, April 3, 12
Maxwell’s theory predicts the speed of light, c 1 c = ∼ 300 , 000 , 000 meters/second √ ✏ 0 µ 0 in terms of simple quantities we can measure in the lab 13 Tuesday, April 3, 12
Maxwell’s theory predicts the speed of light, 1 c = ∼ 300 , 000 , 000 meters/second √ ✏ 0 µ 0 This simple fact turns classical physics on its head 14 Tuesday, April 3, 12
Crazy driver going 120 mph Normal driver going 70 mph Me standing on side of road • I see the crazy driver going 120 mph • The normal driver sees the crazy driver going 120-70=50 mph 15 Tuesday, April 3, 12
Light ray going 671,000,000 mph Normal driver going 70 mph Me standing on side of road • I see the light ray going 671,000,000 mph • The normal driver sees the light ray going 671,000,000 - 70 mph? 16 Tuesday, April 3, 12
Crazy driver going 120,000,000 mph Light ray going 671,000,000 mph Normal driver going 70 mph Me standing on side of road • I see the light ray going 671,000,000 mph • The normal driver sees the light ray going 671,000,000 - 70 mph? • The crazy driver sees the light ray going 671,000,000 - 120,000,000 mph? 16 Tuesday, April 3, 12
Crazy driver going 120,000,000 mph Light ray going 671,000,000 mph Normal driver going 70 mph Me standing on side of road • I see the light ray going 671,000,000 mph • The normal driver sees the light ray going 671,000,000 - 70 mph? • The crazy driver sees the light ray going 671,000,000 - 120,000,000 mph? . . . but we all measure ✏ 0 , µ 0 and find c ∼ 671 , 000 , 000 mph 16 Tuesday, April 3, 12
Crazy driver going 120,000,000 mph Light ray going 671,000,000 mph Normal driver going 70 mph Me standing on side of road Two possibilities: • Everyone sees the light ray • Maxwell’s laws of going 671,000,000 mph electromagnetism different for each observer 17 Tuesday, April 3, 12
Einstein: Laws of physics are the same for all (inertial) observers → Everyone must measure the same speed of light → We must change the way we relate what different observers see 18 Tuesday, April 3, 12
How do we know? If light only moves at 631,000,000 mph in a ‘preferred’ reference frame then the speed we measure depends on the direction 19 Tuesday, April 3, 12
Michelson Interferometer If light speed depends on direction.... ...detect interference pattern in recombined beam 20 Tuesday, April 3, 12
Michelson Interferometer If light speed depends on direction.... ...detect interference pattern in recombined beam 20 Tuesday, April 3, 12
Michelson Interferometer If light speed depends on direction.... ...detect interference pattern in recombined beam 20 Tuesday, April 3, 12
Michelson Interferometer Founded UChicago Physics If light speed depends on Department! direction.... → First American Nobel Laureate Albert Michelson ...detect interference pattern in recombined beam 20 Tuesday, April 3, 12
Michelson-Morley Interferometer 5 m Interferometer arms 21 Tuesday, April 3, 12
Michelson-Morley Interferometer 5 m Interferometer arms 4 km Interferometer arms! 21 Tuesday, April 3, 12
Crazy driver going 120,000,000 mph Light ray going 671,000,000 mph Normal driver going 70 mph Me standing on side of road Two possibilities: • Everyone sees the light ray • Maxwell’s laws of going 671,000,000 mph electromagnetism different for each observer 22 Tuesday, April 3, 12
Einstein: Laws of physics are the same for all (inertial) observers → Everyone must measure the same speed of light → We must change the way we relate what different observers see 23 Tuesday, April 3, 12
Your clock You (driving fast) Flips on at time t Me x Me My clock Me Expect: You see a shorter distance to the bulb than I do because you are moving toward it x You = x Me − vt Me t You = t Me Our clocks agree on the time that the bulb flips on 24 Tuesday, April 3, 12
Your clock You (driving fast) Flips on at time t Me x Me My clock Me Expect: Actually: x You = x Me − vt Me x You = x Me − vt Me q 1 − v 2 c 2 t You = t Me − vx Me t You = t Me c 2 q 1 − v 2 c 2 24 Tuesday, April 3, 12
Your clock You (driving fast) Flips on at time t Me x Me My clock Me Expect: Actually: x You = x Me − vt Me x You = x Me − vt Me q 1 − v 2 c 2 t You = t Me − vx Me t You = t Me c 2 q 1 − v 2 Our clocks don’t even agree on the time c 2 that the bulb goes off! 24 Tuesday, April 3, 12
Special Relativity Complicated rules to relate what different observers see x You = x Me − vt Me t You = t Me − vx Me c 2 q q 1 − v 2 1 − v 2 c 2 c 2 • Length contraction Many odd phenomena • Time dilation and potential paradoxes • Causality (and issues with superluminal speeds) • ... 25 Tuesday, April 3, 12
Your clock You (driving fast) My clock Flips on at time t Me = 0 Me x Me x You = x Me − vt Me q 1 − v 2 c 2 t You = t Me − vx Me c 2 q 1 − v 2 c 2 26 Tuesday, April 3, 12
Your clock You (driving fast) My clock Flips on at time t Me = 0 Me x Me x You = x Me − vt Me Your ‘worldline’ Your ‘worldline’ q 1 − v 2 My ‘worldline’ c 2 t Me Light rays t You = t Me − vx Me c 2 q 1 − v 2 c 2 t Me = 2 t Me = 1 t Me = 0 x Me t Me = − 1 My constant time slices 26 Tuesday, April 3, 12
Your clock You (driving fast) My clock Flips on at time t Me = 0 Me x Me x You = x Me − vt Me Your ‘worldline’ q 1 − v 2 My ‘worldline’ c 2 t Me t You t You = t Me − vx Me c 2 q 1 − v 2 c 2 t Me = 2 t Me = 1 t Me = 0 t You = 2 x Me t Me = − 1 t You = 1 x You t You = 0 My constant t You = − 1 time slices Your constant time slices 27 Tuesday, April 3, 12
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