String Theory in the LHC Era

Transcription

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

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

3 Start our story with the original unified theory... Electric force between charged objects Detectable in simple pith ball experiments How to measure precisely? 3

4 q q r 4

5 Inverse Square Law E = q 4 0 r 2 permittivity of free space C2 Nm 2 q q r 4

6 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

7 Magnetism Bar Magnet Magnetic field lines Iron filings 6

8 Magnetism Bar Magnet Magnetic field lines Iron filings Very important magnetic field 6

9 Relation of Electricity and Magnetism I: Magnetic Fields from Currents Electric current causes compass deflection Current in Ring Electric current generates magnetic field 7 Compass

10 Relation of Electricity and Magnetism I: Magnetic Fields from Currents B = µ 0I 4 r 2 permeability of free space µ N A 2 Determines strength of magnetic field induced by a current Can measure in a simple lab experiment 8

11 Relation of Electricity and Magnetism II: Electromagnetic Induction Changing magnetic field induces an electric field Many applications including electric generators, motors, etc 9

12 Maxwell s Electromagnetic Theory r E = 0 Charge density generates electric field r B =0 No magnetic analog of electric point charge r Changing magnetic field generates electric field r B = µ 0 J + µ Changing electric field and moving charges generate magnetic field 10

13 Maxwell s Electromagnetic Theory r E = 0 Depends on only 2 parameters r B =0 r 0, µ 0 which can be measured in the lab r B = µ 0 J + µ 11

14 Prediction of Maxwell Theory: Electromagnetic Waves! r Changing electric field generates magnetic field 12 r B = µ Changing magnetic field generates electric field

15 Prediction of Maxwell Theory: Electromagnetic Waves! Propagate with speed 1 p 0 µ 0 r Changing electric field generates magnetic field 12 r B = µ Changing magnetic field generates electric field

16 Maxwell s theory predicts the speed of light, c c = 1 p 0 µ 0 300, 000, 000 meters/second in terms of simple quantities we can measure in the lab 13

17 Maxwell s theory predicts the speed of light, c = 1 p 0 µ 0 300, 000, 000 meters/second This simple fact turns classical physics on its head 14

18 Crazy driver going 120 mph Me standing on side of road Normal driver going 70 mph I see the crazy driver going 120 mph The normal driver sees the crazy driver going =50 mph 15

19 Light ray going 671,000,000 mph Me standing on side of road Normal driver going 70 mph I see the light ray going 671,000,000 mph The normal driver sees the light ray going 671,000, mph? 16

20 Light ray going 671,000,000 mph Crazy driver going 120,000,000 mph Me standing on side of road Normal driver going 70 mph I see the light ray going 671,000,000 mph The normal driver sees the light ray going 671,000, mph? The crazy driver sees the light ray going 671,000, ,000,000 mph? 16

21 Light ray going 671,000,000 mph Crazy driver going 120,000,000 mph Me standing on side of road Normal driver going 70 mph I see the light ray going 671,000,000 mph The normal driver sees the light ray going 671,000, mph? The crazy driver sees the light ray going 671,000, ,000,000 mph?... but we all measure 0, µ 0 and find c 671, 000, 000 mph 16

22 Light ray going 671,000,000 mph Crazy driver going 120,000,000 mph Me standing on side of road Normal driver going 70 mph Two possibilities: Everyone sees the light ray going 671,000,000 mph 17 Maxwell s laws of electromagnetism different for each observer

23 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

24 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

25 Michelson Interferometer If light speed depends on direction......detect interference pattern in recombined beam 20

26 Michelson Interferometer If light speed depends on direction......detect interference pattern in recombined beam 20

27 Michelson Interferometer If light speed depends on direction......detect interference pattern in recombined beam 20

28 Michelson Interferometer If light speed depends on direction... Founded UChicago Physics Department! Albert Michelson First American Nobel Laureate...detect interference pattern in recombined beam 20

29 Michelson-Morley Interferometer 5 m Interferometer arms 21

30 Michelson-Morley Interferometer 5 m Interferometer arms 4 km Interferometer arms! 21

31 Light ray going 671,000,000 mph Crazy driver going 120,000,000 mph Me standing on side of road Normal driver going 70 mph Two possibilities: Everyone sees the light ray going 671,000,000 mph 22 Maxwell s laws of electromagnetism different for each observer

32 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

33 Your clock You (driving fast) Flips on at time t Me x Me Me My clock Expect: x You = x Me vt Me You see a shorter distance to the bulb than I do because you are moving toward it t You = t Me Our clocks agree on the time that the bulb flips on 24

34 Your clock You (driving fast) Flips on at time t Me x Me Me My clock Expect: x You = x Me t You = t Me vt Me Actually: x You = x Me q t You = t Me q vt Me 1 v 2 c 2 vx Me c 2 1 v 2 c 2 24

35 Your clock You (driving fast) Flips on at time t Me x Me Me My clock Expect: Actually: x You = x Me t You = t Me vt Me Our clocks don t even agree on the time that the bulb goes off! 24 x You = x Me q t You = t Me q vt Me 1 v 2 c 2 vx Me c 2 1 v 2 c 2

36 Special Relativity Complicated rules to relate what different observers see x You = x Me q vt Me 1 v 2 c 2 t You = t Me vx Me c 2 q 1 v 2 c 2 Many odd phenomena and potential paradoxes 25 Length contraction Time dilation Causality (and issues with superluminal speeds)...

37 Your clock You (driving fast) Flips on at time t Me =0 x Me Me My clock x You = x Me q vt Me 1 v 2 c 2 t You = t Me q vx Me c 2 1 v 2 c 2 26

38 Your clock You (driving fast) Flips on at time t Me =0 x Me Me My clock t Me =2 t Me =1 Your worldline t Me My worldline Light rays x You = x Me q t You = t Me q vt Me 1 v 2 c 2 vx Me c 2 1 v 2 c 2 t Me =0 t Me = 1 x Me My constant time slices 26

39 Your clock You (driving fast) Flips on at time t Me =0 x Me Me My clock Your worldline t You t Me My worldline x You = x Me q vt Me 1 v 2 c 2 t Me =2 t Me =1 t You = t Me q vx Me c 2 1 v 2 c 2 t Me =0 t Me = 1 x Me x You t You =2 t You =1 My constant time slices Your constant time slices 27 t You =0 t You = 1

40 Your clock You (driving fast) Flips on at time t Me =0 x Me Me My clock Your worldline t You t Me My worldline x You = x Me q vt Me Your clock reads -1 when the bulb flips on 1 v 2 c 2 t Me =2 t Me =1 t Me =0 t Me = 1 My constant time slices x Me x You Your constant time slices 27 Mine reads 0 t You =2 t You =1 t You =0 t You = 1 t You = t Me q vx Me c 2 1 v 2 c 2

41 Your clock Both flip on at time t Me =0 x Me You (driving fast) My clock Me 28

42 Your clock Both flip on at time t Me =0 x Me You (driving fast) My clock Me Your worldline t You t Me My worldline I think the blue and yellow bulbs flip on at the same time t Me =2 t Me =1 You think the yellow bulb flips on first t Me =0 t Me = 1 x Me x You t You =2 t You =1 My constant time slices Your constant time slices 28 t You =0 t You = 1

43 Special Relativity x You = x Me q vt Me 1 v 2 c 2 t You = t Me vx Me c 2 q 1 v 2 c 2 The order of events can look different to different observers Causality: If any observer sees event A happening before event B, then B cannot have any influence on A 29

44 If is outside the light cone of, there are observers that see them in either order t Light Cone x and are spacelike separated not in causal contact 30

45 If is outside the light cone of, there are observers that see them in either order t t Light Cone x x and are spacelike separated not in causal contact 30

46 If is outside the light cone of, there are observers that see them in either order t t Light Cone x x and are spacelike separated not in causal contact 30

47 If is inside the light cone of, then happens first for all observers t Light Cone x and are timelike separated can affect 31

48 If is inside the light cone of, then happens first for all observers t t Light Cone x x and are timelike separated can affect 31

49 If is inside the light cone of, then happens first for all observers t t Light Cone x x and are timelike separated can affect 31

50 Can know about what happens at t Light Cone Cannot know about what happens at x Cannot send information faster than speed of light, c 32

51 Send beam of superluminal neutrinos Encode signal in beam commanding second bulb to light up yellow or green Superluminal neutrino beam t Light Cone x 33

52 Send beam of superluminal neutrinos Encode signal in beam commanding second bulb to light up yellow or green Superluminal neutrino beam t Light Cone x 33

53 Send beam of superluminal neutrinos Encode signal in beam commanding second bulb to light up yellow or green Superluminal neutrino beam t Light Cone x Fast-moving observer sees: 1. Second bulb light up yellow 2. Neutrino beam propagate back towards me 3. Me hitting the switch to initiate the beam 33

54 Superluminal speeds Information moving backward in time Loss of causality 34

55 Oscillation Project with Emulsion-tRacking Apparatus arxiv:

56 Oscillation Project with Emulsion-tRacking Apparatus arxiv: Appeared on Friday, September 23, 2011 Cited by 44 preprints by Friday, September 30, 2011 (now over 220 citations) 36

57 CERN Neutrino beam travels ~ 730 km Would take about 2-3 ms at speed of light Gran Sasso Mine OPERA result: neutrinos arrived about 57 ns ( seconds) too early 37

58 Not completely crazy... MINOS reported superluminal result for lower energy neutrinos (~3 GeV) v c c =(5.1 ± 2.9) 10 5 Big uncertainty 38

59 Objections: Bound from SN1987A v c c < But these were neutrinos of much lower energy (10 MeV) 39

60 Objections: Bound from SN1987A v c c < But these were neutrinos of much lower energy (10 MeV) Cohen and Glashow: arxiv: Superluminal neutrinos will radiate energy in flight 39 If moving at OPERA speeds, would lose too much energy to be seen

61 This is a very difficult measurement Many intricate details that could be sources for error GPS Timing issues Subtle (gravitational) time dilation effects Slow-down of satellite signals by atmosphere Satellite motion during neutrino flight Pulse shape degradation emerged as a likely candidate early on 40

62 From arxiv:

63 But OPERA responded... From arxiv: and superluminality persisted! 42

64 Recently two new sources of error Problem with an optical fiber connecting GPS timer to the OPERA master clock (can reduce measured time of flight by up to 100 ns) Miscalibrated oscillator (can increase measured time of flight...by 10 s of ns?) Net effect is????? More data later this year 43

65 Meanwhile, the ICARUS experiment in the same mine has reported Neutrinos from CERN do not lose energy as they should if moving faster than light (Cohen and Glashow) Very recently (March 15, 2012) reported a direct measurement of neutrino velocities consistent with travel at or just below the speed of light 44

66 Looks like Einstein wins again... 45

67 SUMMARY Maxwell s theory unifies electricity and magnetism Predicts electromagnetic waves -- light Speed of light determined by 2 numbers that can be measured in the lab Light moves at the same speed for all observers Must change the way we relate the physics that different observers see Many novel effects: length contraction, time dilation, no notion of simultaneity Information cannot move faster than the speed of light without losing causality and allowing travel backward in time Light barrier recently challenged by OPERA experiment Extremely difficult measurement No evidence for superluminal neutrinos at present 46

68 Next time: The Quantum World 47