String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 - - PowerPoint PPT Presentation
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. Einsteins Gravity 3. Why do we need
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J Marsano (marsano@uchicago.edu)
Tuesday, April 3, 12
Special Relativity
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Start our story with the original ‘unified’ theory.....
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r
q q
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‘permittivity of free space’
✏0 ∼ 8.854 × 10−12 C2 N m2
Inverse Square Law
r
q q
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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
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Bar Magnet
Iron filings Magnetic field lines
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Tuesday, April 3, 12
Bar Magnet
Iron filings Magnetic field lines
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Current in Ring Compass
Electric current causes compass deflection
→ Electric current generates magnetic field
Relation of Electricity and Magnetism I: Magnetic Fields from Currents
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Relation of Electricity and Magnetism I: Magnetic Fields from Currents
‘permeability of free space’
µ0 ∼ 1.257 × 10−6 N A2
→ Determines strength of magnetic field induced by a current → Can measure in a simple lab experiment
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Changing magnetic field induces an electric field
Many applications including electric generators, motors, etc
Relation of Electricity and Magnetism II: Electromagnetic Induction
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r · E = ⇢ ✏0 r · B = 0 r ⇥ E = ∂B ∂t r ⇥ B = µ0J + µ0✏0 @E @t
Charge density ρ generates electric field
Changing magnetic field generates electric field
No magnetic analog of electric point charge
Changing electric field and moving charges generate magnetic field
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r · E = ⇢ ✏0 r · B = 0 r ⇥ E = ∂B ∂t r ⇥ B = µ0J + µ0✏0 @E @t
Depends on only 2 parameters which can be measured in the lab
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r ⇥ E = ∂B ∂t r ⇥ B = µ0✏0 @E @t
Changing electric field generates magnetic field Changing magnetic field generates electric field
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Tuesday, April 3, 12
r ⇥ E = ∂B ∂t r ⇥ B = µ0✏0 @E @t
Changing electric field generates magnetic field Changing magnetic field generates electric field
1 √✏0µ0
Propagate with speed
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c = 1 √✏0µ0 ∼ 300, 000, 000 meters/second
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Tuesday, April 3, 12
c = 1 √✏0µ0 ∼ 300, 000, 000 meters/second
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Tuesday, April 3, 12
Crazy driver going 120 mph Normal driver going 70 mph Me standing on side of road
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Tuesday, April 3, 12
Normal driver going 70 mph Me standing on side of road
Light ray going 671,000,000 mph
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Tuesday, April 3, 12
Crazy driver going 120,000,000 mph Normal driver going 70 mph Me standing on side of road
Light ray going 671,000,000 mph
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Tuesday, April 3, 12
Crazy driver going 120,000,000 mph Normal driver going 70 mph Me standing on side of road
Light ray going 671,000,000 mph
. . . but we all measure ✏0, µ0 and find c ∼ 671, 000, 000 mph
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Tuesday, April 3, 12
Crazy driver going 120,000,000 mph Normal driver going 70 mph Me standing on side of road
going 671,000,000 mph
Light ray going 671,000,000 mph
electromagnetism different for each observer
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→ Everyone must measure the same speed of light → We must change the way we relate what different observers see
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If light only moves at 631,000,000 mph in a ‘preferred’ reference frame then the speed we measure depends on the direction
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...detect interference pattern in recombined beam If light speed depends on direction....
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Tuesday, April 3, 12
...detect interference pattern in recombined beam If light speed depends on direction....
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Tuesday, April 3, 12
...detect interference pattern in recombined beam If light speed depends on direction....
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Tuesday, April 3, 12
...detect interference pattern in recombined beam If light speed depends on direction....
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Albert Michelson
→ First American Nobel Laureate
Tuesday, April 3, 12
5 m Interferometer arms
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5 m Interferometer arms
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Crazy driver going 120,000,000 mph Normal driver going 70 mph Me standing on side of road
going 671,000,000 mph
Light ray going 671,000,000 mph
electromagnetism different for each observer
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→ Everyone must measure the same speed of light → We must change the way we relate what different observers see
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You (driving fast) Me Your clock
My clock Flips on at time
xYou = xMe − vtMe tYou = tMe
Expect:
xMe
Our clocks agree on the time that the bulb flips on You see a shorter distance to the bulb than I do because you are moving toward it
tMe
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You (driving fast) Me Your clock
My clock Flips on at time
xYou = xMe − vtMe tYou = tMe
Expect: Actually:
xYou = xMe − vtMe q 1 − v2
c2
tYou = tMe − vxMe
c2
q 1 − v2
c2
xMe tMe
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Tuesday, April 3, 12
You (driving fast) Me Your clock
My clock Flips on at time
xYou = xMe − vtMe tYou = tMe
Expect: Actually:
xYou = xMe − vtMe q 1 − v2
c2
tYou = tMe − vxMe
c2
q 1 − v2
c2
xMe
Our clocks don’t even agree on the time that the bulb goes off!
tMe
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Complicated rules to relate what different observers see
Many odd phenomena and potential paradoxes
superluminal speeds)
xYou = xMe − vtMe q 1 − v2
c2
tYou = tMe − vxMe
c2
q 1 − v2
c2
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Tuesday, April 3, 12
You (driving fast) Me Your clock
My clock Flips on at time
xMe
xYou = xMe − vtMe q 1 − v2
c2
tYou = tMe − vxMe
c2
q 1 − v2
c2
tMe = 0
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Tuesday, April 3, 12
You (driving fast) Me Your clock
My clock Flips on at time
xMe
xYou = xMe − vtMe q 1 − v2
c2
tYou = tMe − vxMe
c2
q 1 − v2
c2
xMe
Light rays
My ‘worldline’
tMe
My constant time slices
tMe = 2 tMe = 1 tMe = 0 tMe = −1
Your ‘worldline’ Your ‘worldline’
tMe = 0
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Tuesday, April 3, 12
My ‘worldline’
xMe tMe
My constant time slices
tMe = 2 tMe = 1 tMe = 0 tMe = −1
Your ‘worldline’
You (driving fast) Me Your clock
My clock Flips on at time
xMe
xYou = xMe − vtMe q 1 − v2
c2
tYou = tMe − vxMe
c2
q 1 − v2
c2
tYou xYou
Your constant time slices
tYou = 0 tYou = 1 tYou = 2 tYou = −1
tMe = 0
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Tuesday, April 3, 12
My ‘worldline’
xMe tMe
My constant time slices
tMe = 2 tMe = 1 tMe = 0 tMe = −1
Your ‘worldline’
You (driving fast) Me Your clock
My clock Flips on at time
xMe
xYou = xMe − vtMe q 1 − v2
c2
tYou = tMe − vxMe
c2
q 1 − v2
c2
tYou xYou
Your constant time slices
tYou = 0 tYou = 1 tYou = 2 tYou = −1
tMe = 0
Your clock reads ‘-1’ when the bulb flips on Mine reads ‘0’
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You (driving fast) Me Your clock
My clock Both flip on at time
xMe
tMe = 0
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Tuesday, April 3, 12
You (driving fast) Me Your clock
My clock Both flip on at time
xMe
tMe = 0
My ‘worldline’
xMe tMe
My constant time slices
tMe = 2 tMe = 1 tMe = 0 tMe = −1
Your ‘worldline’
tYou xYou
Your constant time slices
tYou = 0 tYou = 1 tYou = 2 tYou = −1
I think the blue and yellow bulbs flip on at the same time You think the yellow bulb flips on first
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The order of events can look different to different observers
xYou = xMe − vtMe q 1 − v2
c2
tYou = tMe − vxMe
c2
q 1 − v2
c2
If any observer sees event A happening before event B, then B cannot have any influence on A
Causality:
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Light Cone
If is outside the light cone
see them in either order t x and are ‘spacelike’ separated
→ not in causal contact
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Tuesday, April 3, 12
Light Cone
If is outside the light cone
see them in either order t x t x and are ‘spacelike’ separated
→ not in causal contact
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Tuesday, April 3, 12
Light Cone
If is outside the light cone
see them in either order x t t x and are ‘spacelike’ separated
→ not in causal contact
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Light Cone
If is inside the light cone
all observers t x and are ‘timelike’ separated
→ can affect
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Tuesday, April 3, 12
Light Cone
If is inside the light cone
all observers t x t x and are ‘timelike’ separated
→ can affect
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Tuesday, April 3, 12
Light Cone
If is inside the light cone
all observers x t t x and are ‘timelike’ separated
→ can affect
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Light Cone
t x
Can know about what happens at Cannot know about what happens at
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Light Cone
t x
Superluminal neutrino beam
neutrinos
commanding second bulb to light up yellow or green
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Tuesday, April 3, 12
Light Cone
t x
Superluminal neutrino beam
neutrinos
commanding second bulb to light up yellow or green
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Tuesday, April 3, 12
Light Cone
t x
Superluminal neutrino beam
neutrinos
commanding second bulb to light up yellow or green
Fast-moving observer sees:
towards me
the beam
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Oscillation Project with Emulsion-tRacking Apparatus arXiv:1109.4897
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Oscillation Project with Emulsion-tRacking Apparatus arXiv:1109.4897
Appeared on Friday, September 23, 2011 Cited by 44 preprints by Friday, September 30, 2011
(now over 220 citations)
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Neutrino beam travels ~ 730 km Would take about 2-3 ms at speed of light
OPERA result: neutrinos arrived about 57 ns (0.000000057 seconds) too early
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MINOS reported superluminal result for lower energy neutrinos (~3 GeV)
Big uncertainty
v − c c = (5.1 ± 2.9) × 10−5
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|v − c| c < 2 × 10−9
But these were neutrinos of much lower energy (10 MeV)
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Tuesday, April 3, 12
|v − c| c < 2 × 10−9
But these were neutrinos of much lower energy (10 MeV)
Cohen and Glashow:
Superluminal neutrinos will radiate energy in flight
If moving at OPERA speeds, would lose too much energy to be seen
arXiv:1109.6562
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From arXiv:1109.4897
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From arXiv:1109.4897
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the OPERA master clock (can reduce measured time of flight by up to 100 ns)
flight...by 10’s of ns?)
Net effect is ????? More data later this year
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Meanwhile, the ICARUS experiment in the same mine has reported
they should if moving faster than light (Cohen and Glashow)
direct measurement of neutrino velocities consistent with travel at or just below the speed of light
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the lab
‘simultaneity’
losing causality and allowing travel backward in time
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