Lectures on String Theory

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Lectures on String Theory
Music of the Spheres
Jan Pieter van der Schaar
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Pythagoras Music of the Spheres

• 569 475 BC, ancient Greece
• Mathematics, astronomy
• Pythagoreans
• Everything related to numbers
• Positive integers
• Discovered musical harmonics
• Planets, cosmic harmony
• Music of the Spheres

String theory everything is made out of string
harmonics
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Outline of the series

• Why do we need string theory
• What is string theory
• Latest developments

Quantum mechanics vs. Einstein

• Quantum mechanics and particle physics
• General relativity
• Quantum gravity

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Goals

• I hope to show that theoretical (string)
  physicists are not boring
• Give you a sense of the wonderful, beautiful but
  strange world described by fundamental
  theoretical physics
• Show you the basics, the why, what and how of
  string theory
• Get across some of our excitement
• To have fun

R.P. Feynman Poets say science takes away from
the beauty of the stars - mere globs of gas
atomsFor far more marvelous is the truth than
any artists of the past imagined!What men are
poets who can speak of Jupiter if he were like a
man, but if he is an immense spinning sphere of
methane and ammonia must be silent?
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Goals of fundamental physics

• Find the basic rules of the game (nature)

Principle of Science the test of all knowledge
is experiment Source of knowledge experiment,
imagination and guesses Division of labor
experimental and theoretical
To see complete nature as different aspects of
one set of phenomena and unify our understanding

• Heat and mechanics
• Electricity, magnetism and light
• Special relativity and gravity

R.P. Feynman
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Unification
Picasso A painter should work with as few
elements as possible
String Theory
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The Correspondence Principle
Most and perhaps all laws of nature are only an
approximation, valid up to a certain scale. Even
though corrections can be extremely small, in
terms of our ideas behind the laws of nature
(philosophically) we are completely wrong.
So very small effects sometimes require profound
changes in our ideas.

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The large and small

• What is the world made off ?
• Elementary particles
• What holds it together ?
• Forces

Physical laws of motion and forces

• The Standard Model of elementary particles
• Quantum mechanics and special relativity
• Gravity
• General relativity

Small
Large
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Quantum Mechanics
A. Einstein
M. Planck

• Black body radiation and the photo-electric
  effect
• Particles are waves and waves are particles!
• Light rays become photon bundles (energy quanta)
• Electron bundles become electron rays (electron
  waves)
• Apparent when probing very short distances,
  typical scale is the size of atoms, 0.00000001 cm

M. Planck ... the whole procedure was an act of
despair because a theoretical interpretation had
to be found at any price, no matter how high that
might be
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Quantum fuzziness

• Heisenbergs uncertainty principle

W. Heisenberg
Nothing can sit still, which is what we mean with
quantum fuzziness, or the jittery nature of the
quantum world
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Quantum interference and probability

• QM only predicts probabilities
• Wavelike interference of amplitudes
• If it can happen, it will happen
• Identical particles FERMIONS and BOSONS
• Half integer and integer SPIN respectively

W. Pauli
Pauli exclusion principle
Fermions
Bosons
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Probing matter

• Accelerate and collide particles
• Particle/wave duality, wavelength h/p
• Distance/energy relation

L. De Broglie
Moral to gather the most information about an
object, use the smallest possible probe, visible
light 0.00005 cm (cell)
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Special relativity

• Speed of light is the same for all observers!
• Confirmed experimentally Michelson-Morley (1887)
• Consequences moving clocks run slower and moving
  sticks are shorter
• Mass is just a form of energy Emc2
• Space and time become space-time
• Apparent at velocities that are a significant
  fraction of the speed of light

A. Einstein
H. Minkowski Space of itself, and time of
itself will sink into mere shadows, and only a
kind of union between them shall survive
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Special relativity in a nutshell
Space-Time
Mass-Energy
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Quantum field theory

• Matter and forces are all quantum relativistic
  fields
• Particles are lumps (quanta) of the fields, e.g.
  photons, electrons, gluons and quarks
  many-particle theory !
• General prediction anti-matter, matter
  anti-matter force field lumps (e.g. photons)
• Interactions matter and force fields due to
  exchange of messenger particles, the lumps of the
  force field
• Feynman diagrams

P.A.M. Dirac
Yang, Mills Feynman Gell-Mann Schwinger t
Hooft Veltman Weinberg Dyson, and Many others
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Feynman diagrams

• Calculates the probability that something happens
  
• Interactions at space-time points, called
  vertices
• Quantum corrections correspond to loops
• If it can happen, it will happen
• Because e 1/137 is a small number we can make
  consecutive approximations using Feynman diagrams

e
e
e
e
e
e



INFINITE !
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The Standard Model
Range Infinite 10-16 cm Infinite
10-13 cm
Strength 10-40 10-3 1
10-100
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The Standard Model poster
http//particleadventure.org
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Beyond the Standard Model

• Strength of electromagnetic, weak and strong
  interactions (almost) meet when extrapolated to
  higher energies
• Unification interactions 1016 GeV, Grand
  Unified Theory (GUT)
• Explaining 21 parameters masses, charges etc.
• Dark matter in our universe
• Inclusion of gravitational interaction

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Experimental sites

• CERN (Geneve) electron/positron
• SLAC (San Francisco) electron/positron
• FERMILAB (Chicago) proton/anti-proton

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Accelerator scales

• Today (25 km) 10-17 cm or 104 GeV
• Earth (40,000 km) 10-21 cm or 108 GeV
• Universe 1022 km
• Proton mass 1 GeV, electron mass 0.5 MeV

Mega 106 Giga 109 1 GeV 10-24 grams
TERRA INCOGNITA !
String scale
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General relativity

• Equivalence acceleration and gravitational fields
  
• Equivalence inertial and gravitational mass
• Space-time is curved by presence of energy
• Test objects follow the shortest paths in curved
  space-time (geodesics)
• Experiment
• Bending of light
• Shifting of perihelion in orbit Mercury
• Stage of physics is no longer fixed, rather it
  has become a treacherous swamp !

A. Einstein
J. Wheeler Mass grips space by telling it how
to curve, space grips mass by telling it how to
move
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Curved space-time

• Test objects follow shortest paths
• Positive and negative curvature
• Singularities are points of infinite curvature
  our stage breaks down !
• Source is any energy
• Analogy the rubber sheet

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Gravity, particles and QM

• General relativity is a classical theory
  describing classical space-time
• Gravity is weak, but always acts in the same
  direction (clumps)
• Describes large scale physics very accurately
• Can be neglected for elementary particles
• More energy means stronger gravity
• Planck scale is 10-33 cm, where quantum gravity
  effects are thought to become important
• Space-time foam and quantum gravity

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When large meets small

• Space-time singularities (points of infinite
  curvature)
• Big Bang
• Inside black holes
• Vacuum energy in quantum field theory
• Particle physics near the Planck length 10-33 cm
  or 1018 GeV

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QFT and GR dont mix

• Gravitational waves, lumps of GR gravitons
• Quantizing GR gives untamable infinities
• What does it mean to quantize space and time ?
• Interactions in QFT are point-like
• We have to be more creative !

Point-like and smeared interactions
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String theory
J. Schwarz
M. Green

• Points replaced by loops of string
• Q loops of what ? A stuff or energy
• Two-dimensional Feynman diagrams tubes or pants
• Gravitons included finite quantum corrections !

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To summarize
String theory
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Come back next week

• String modes and elementary particles
• Open and closed strings
• Extra space-time dimensions
• Supersymmetry
• Consistent superstring theories

Anonymous It is all string theory to me