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

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lectures on string theory
Lectures on String Theory

Music of the Spheres

Jan Pieter van der Schaar

Saturday Morning Physics

pythagoras music of the spheres
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

Saturday Morning Physics

outline of the series
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

Saturday Morning Physics

  • 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 atoms…For 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?”

Saturday Morning Physics

goals of fundamental physics
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

Saturday Morning Physics


Picasso: “A painter should work with as few elements as possible”

String Theory

Saturday Morning Physics

the correspondence principle
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.

Saturday Morning Physics

the large and small
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



Saturday Morning Physics

quantum mechanics
Quantum Mechanics

A. Einstein

  • 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

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”

Saturday Morning Physics

quantum fuzziness
Quantum fuzziness
  • Heisenberg’s uncertainty principle

W. Heisenberg

Nothing can sit still, which is what we mean with quantum fuzziness, or the jittery nature of the quantum world

Saturday Morning Physics

quantum interference and probability
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:



Saturday Morning Physics

probing matter
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)

Saturday Morning Physics

special relativity
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: E=mc2
  • 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”

Saturday Morning Physics

special relativity in a nutshell
Special relativity in a nutshell



Saturday Morning Physics

quantum field theory
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




‘t Hooft



Dyson, and

Many others

Saturday Morning Physics

feynman diagrams
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











Saturday Morning Physics

the standard model
The Standard Model

Range: Infinite 10-16 cm Infinite 10-13 cm

Strength: 10-40 10-3 1 10-100

Saturday Morning Physics

the standard model poster
The Standard Model poster


Saturday Morning Physics

beyond the standard model
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

Saturday Morning Physics

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

Saturday Morning Physics

accelerator scales
Accelerator scales

Mega = 106

Giga = 109

1 GeV ~ 10-24 grams

  • 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


String scale

Saturday Morning Physics

general relativity
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”

Saturday Morning Physics

curved space time
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

Saturday Morning Physics

gravity particles and qm
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

Saturday Morning Physics

when large meets small
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

Saturday Morning Physics

qft and gr don t mix
QFT and GR don’t 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 smearedinteractions

Saturday Morning Physics

string theory
String theory
  • 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 !

M. Green

J. Schwarz

Saturday Morning Physics

to summarize
To summarize:

String theory

Saturday Morning Physics

come back next week
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”

Saturday Morning Physics