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

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

Apr 10, 2024 243 likes •1.08k views

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

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String Theory in the LHC Era

1

J Marsano (marsano@uchicago.edu)

Thursday, April 12, 12

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SLIDE 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
  • 9. String Theory and Particle Physics
  • 5. Supersymmetry
  • 6. Einstein’s Gravity
  • 7. Why is Quantum Gravity so Hard?
  • 8. String Theory and Unification

2

Thursday, April 12, 12

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SLIDE 3

3

Electromagnetic Waves

Characterized by:

  • Intensity
  • Wavelength

Maxwell → fixed speed c |E|2 λ Wavelength λ

Frequency ν = c λ

Thursday, April 12, 12

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4

Photoelectric Effect

How does emission depend on

  • Intensity of beam?
  • Wavelength of beam?

Thursday, April 12, 12

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5

Photoelectric Effect

Robert Millikan

UChicago Professor!

← Wavelength λ

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Photoelectric Effect

At large wavelengths, no electrons emitted

→ Independent of intensity of the incident radiation

Thursday, April 12, 12

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Photoelectric Effect Electromagnetic waves have a ‘smallest piece’

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Photoelectric Effect Electromagnetic waves have a ‘smallest piece’

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Photoelectric Effect Electromagnetic waves have a ‘smallest piece’

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7

Photoelectric Effect Electromagnetic waves have a ‘smallest piece’ Smallest pieces - ‘quanta’

Photon energy is determined by its wavelength

h ∼ 6.626 × 10−34J · s

Planck constant

E = hc λ = hν

Thursday, April 12, 12

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SLIDE 11

8

Photoelectric Effect

Photon energy is determined by wavelength

Beam intensity ↔ # of photons

Electron interacts with one photon at a time

→ Ejected only if wavelength short enough

Wavelength, λ ↔ Energy of each photon

E = hc λ = hν

Incident light (photons)

Thursday, April 12, 12

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9

Two Important Points:

  • 1. ‘Particle-like’ behavior of light
  • 2. Correlation between energy and length scales

Energy Wavelength

E = hc λ

Thursday, April 12, 12

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We observe the world through scattering experiments

Wavelength of light limits distance scales that we can resolve

Thursday, April 12, 12

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We observe the world through scattering experiments

Wavelength of light limits distance scales that we can resolve

Thursday, April 12, 12

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SLIDE 15

10

We observe the world through scattering experiments

Wavelength of light limits distance scales that we can resolve

Thursday, April 12, 12

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We observe the world through scattering experiments

Wavelength of light limits distance scales that we can resolve

Thursday, April 12, 12

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datom

Need λ < datom to study atoms

↔ E > hc datom

Need λ < dnucleus to study atomic nucleus

↔ E > hc dnucleus dnucleus

Thursday, April 12, 12

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11

datom

Need λ < datom to study atoms

↔ E > hc datom

Need λ < dnucleus to study atomic nucleus

↔ E > hc dnucleus dnucleus

Thursday, April 12, 12

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SLIDE 19

11

datom

Need λ < datom to study atoms

↔ E > hc datom

Need λ < dnucleus to study atomic nucleus

↔ E > hc dnucleus dnucleus

Thursday, April 12, 12

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12

Must go to higher energies to probe small distance scales

LHC ∼ 10−18 cm (0.000000000000000001 cm) Strings: 10−33 cm?

Thursday, April 12, 12

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Waves and Particles

Sometimes light behaves like a wave.... ....and sometimes like a particle ...depends on the question we ask

Let’s examine some important wave behavior and its implications

Thursday, April 12, 12

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Waves and Uncertainty

A photon in this wave carries momentum p = h λ

λ

But where is it?

E = hc λ

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Interference Constructive Destructive

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Interference Constructive Destructive

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Interference Constructive Destructive

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Interference Constructive Destructive

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Interference Constructive Destructive Waves can ‘cancel’ one another

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∆x Waves and Uncertainty

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∆x Waves and Uncertainty

General property of waves

+ + + + ... =

∆x∆ ✓ 1 λ ◆ & 1

∆λ

Thursday, April 12, 12

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17

Heisenberg Uncertainty

Quantum Theory: Light composed of photons

∆x∆p & h

Cannot pin down position and momentum of a photon ∆x∆ ✓ 1 λ ◆ & 1

p = h λ

(more fundamental than our treatment suggests)

Thursday, April 12, 12

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So Far:

  • 1. Light waves composed of many quanta -- photons
  • Wave can behave like stream of particles
  • 2. Energy and momentum determined by wavelength
  • 3. Cannot pin down and to arbitrary precision

x

p

E

p

What about particles (eg electrons)? Do they behave like waves?

Thursday, April 12, 12

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Diffraction

Incident wave Screen Intensity Slit

I ∼ |E|2

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Diffraction

Incident wave Screen Intensity Slit

I ∼ |E|2

Interference!

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Screen Number of Electrons Slit

e− source

Electrons too!

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Screen Number of Electrons Slit

e− source

Electrons too!

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Screen Number of Electrons Slit

e− source

Electrons too!

Thursday, April 12, 12

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Screen Number of Electrons Slit

e− source

Electrons too!

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Screen Number of Electrons Slit

e− source

Electrons too!

Thursday, April 12, 12

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Screen Number of Electrons Slit

e− source

Electrons too!

Thursday, April 12, 12

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Screen Number of Electrons Slit

e− source

Electrons too!

Thursday, April 12, 12

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Screen Number of Electrons Slit

e− source

Electrons too!

Thursday, April 12, 12

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Screen Number of Electrons Slit

e− source

Electrons too!

Thursday, April 12, 12

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Screen Slit

e− source

Particle of momentum has an intrinsic wavelength

λ = h p

p

Number of Electrons

What is ‘waving’?

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Intensity

I ∼ |E|2

Slit

e− source

Number of Electrons

Intensity ⬌ # of photons Intensity profile ⬌

probability for an individual photon to hit a particular spot on the screen

Associate an abstract ‘wave function‘ to each electron

Ψ |Ψ|2 ↔ probability

Thursday, April 12, 12

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What is waving? Probability!

....it is a wave so we can get interference effects

Classical EM Wave ‘Electron wave’

E |E|2 Ψ |Ψ|2

Intensity Probability

Thursday, April 12, 12

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Double Slit Experiment

Incident wave Screen Intensity

I ∼ |E|2

Thursday, April 12, 12

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Double Slit Experiment

Incident wave Screen Intensity

I ∼ |E|2

Interference

Thursday, April 12, 12

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Double Slit Experiment

Incident wave Screen Intensity

I ∼ |E|2

Interference

Thursday, April 12, 12

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What about Electrons?

Screen

Interference

e− source

Probability ∼ |Ψ|2

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What about Electrons?

Screen

Interference

e− source

Probability ∼ |Ψ|2

Detectors

Thursday, April 12, 12

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What about Electrons?

Screen

e− source

Probability ∼ |Ψ|2

Detectors

Thursday, April 12, 12

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e− source

Detectors

Electrons passing through different slits do not interfere with one another after we add the detectors

How can we understand this?

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Slits Electron probability

Before measurement

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Slits Electron probability

After measurement

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Slits Electron probability

Measurement causes ‘Wave function collapse’

‘Copenhagen Interpretation’

Niels Bohr

Thursday, April 12, 12

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About ‘wave function collapse’.....

Wave from top slit Wave from bottom slit Direction of ‘waving’ ‘Detector state space’

Detectors

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About ‘wave function collapse’.....

Wave from top slit Wave from bottom slit Direction of ‘waving’ ‘Detector state space’

Detectors

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About ‘wave function collapse’.....

Wave from top slit Wave from bottom slit Direction of ‘waving’ ‘Detector state space’

Detectors

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About ‘wave function collapse’.....

Wave from top slit Wave from bottom slit Direction of ‘waving’ ‘Detector state space’

Detectors

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Electron passing through each slit becomes ‘entangled’ with its detector

Spoils cancellation that caused interference pattern

→ ‘Decoherence’

Detectors

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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’

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Detectors

Explains why detectors destroy the interference pattern ...but not the whole story

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  • 1. Particles exhibit wave-like behavior
  • Waves describe ‘probabilities’
  • 2. Particle wavelength determined by momentum
  • 3. We disturb the system when we make observations

p

Particles as Waves:

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‘Wave-particle duality’ forces us to take a probabilistic view

  • f nature

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What about relativity??? Quantum mechanics + Relativity Quantum field theory Language of particle physics

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What about relativity??? Sidney Coleman

(Illinois Institute of Technology alumnus!) http://www.physics.harvard.edu/about/Phys253.html http://arxiv.org/abs/1110.5013 Lecture notes: Videos:

Quantum mechanics + Relativity Quantum field theory Language of particle physics

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Suppose we could trap an electron... ....and then we release it

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Suppose we could trap an electron... ....and then we release it Light Cone

t

x

Nonzero probability to detect it here!

Quantum mechanics doesn’t care about the speed of light

Release trapped particle

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∆x∆p & h

∆x → 0 = ⇒ ∆p → ∞! Significant probability of huge momenta and energies in the box Enough to create new particles

  • ut of the vacuum

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∆x∆p & h

∆x → 0 = ⇒ ∆p → ∞! Significant probability of huge momenta and energies in the box Enough to create new particles

  • ut of the vacuum

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Light Cone

t

x

New particles interfere to give zero probability of detection here

Sometimes one particle comes out..... ...and sometimes several do

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Effect of adding relativity: Particle number is not conserved Even in vacuum!!!

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e− e− γ

Interaction of electron with photon

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e− e− γ

Interaction of electron with photon

  • r
  • r .....

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Must sum over all possibilities weighted by their ‘probability amplitudes’ + + + ... ...sum over histories

Richard Feynman

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+ + ... Quantum Electrodynamics

These diagrams determine the ‘anomalous magnetic moment’ of the electron

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+ + ... Quantum Electrodynamics

These diagrams determine the ‘anomalous magnetic moment’ of the electron = 1 159 652 180.73(2.8) × 10−12 = 1 159 652 175.86(8.48) × 10−12 g − 2 2 (theory) g − 2 2 (exp)

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Quantum Electrodynamics (QED) works incredibly well

Richard Feynman Julian Schwinger Sin-Itiro Tomonoga

L ∼ ¯ ψ (iγµDµ − m) ψ − 1 4e2 FµνF µν

Photon Electron Charge Electron mass

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L ∼ ¯ ψ (iγµDµ − m) ψ − 1 4e2 FµνF µν

Photon Electron Charge Electron mass

Mass without Higgs...... so why all the fuss......

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Next time: Why do we need the Higgs?

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SUMMARY

  • Electromagnetic waves can behave like streams of particles
  • Energy of ‘smallest piece’ (photon) determined by wavelength
  • Fundamental relation between energy and distance scales
  • Particles can behave like waves
  • Each particle has a Broglie wavelength determined by momentum
  • The quantity that ‘waves’ is probability
  • We are forced to take a probabilistic view of nature!
  • When we add relativity, particle number is not conserved
  • Vacuum not empty--particles popping in and out of existence
  • Must sum over all histories (Feynman diagrams)
  • Observation cannot be separated from the act of measurement
  • Measurement entangles the system we observe with our detectors

Thursday, April 12, 12