Superstring Theory

1
Superstring Theory

• Symmetry and the Unification of Forces

2
Overview

• Covariance and Special Relativity
• Four Major Forces
• Field Theory
• General Relativity
• Quantum Field Theory and the Standard Model
• Kaluza and Klein
• Superstring Theory
• Plan For Research

3
Covariance and Special RelativityChasing Light
Beams

• Covariance- laws of physics must be the same
  everywhere
• Problem with Newtonian Mechanics at high speeds
• Einstein- time is actually a dimension traveled
  by an object in motion
• spacetime
• Maintains the constancy of the speed of light in
  all frames of reference
• time dilation and length contraction

4
Four Fundamental Forces
Strong Force
Electromagnetic Force
Gravity
Weak Force

• Big bang theory claims all forces were one
• Separated when universe cooled and expanded
• Theory of Everything would describe all forces

5
Field Theory

• Began with Faradays electromagnetic field
• New way to describe forces
• Defined at every point in space
• Maxwells equations provide a mathematical
  representation
• Einstein applies field theory and special
  relativity to gravity

6
General Relativity

• Provides a geometric description of the force of
  gravity
• 4 dimensional spacetime is curved by the presence
  of mass
• Curvature alters the path of neighboring objects
• Equations involve Riemanns metric tensor to
  quantify curvature

7
Quantum Field Theory and the Standard ModelThe
Theory of Almost Everything

• Based on Quantum Mechanics
• Energy is quantized
• Available in packets, or integral multiples of
  Planks constant, h
• Properties such as position and momentum are
  known by probability
• Uncertainty principle

8
Quantum Field Theory and the Standard ModelThe
Theory of Almost Everything

• 3 families of matter particles (fermions)
• Differ only by particle mass
• Force is caused by the exchange of quanta, or
  bosons

9
Quantum Field Theory and the Standard ModelThe
Theory of Almost Everything

• Successfully describes non-gravitational forces
• Symmetry
• Quantum chromodynamics
• Electroweak Theory
• Gravity cannot be quantized

10
Kaluza and KleinAnother dimension?

• Proposed the existence of a 4th curled up
  spatial dimension
• Exist at every point in space
• Too small to detect
• Unified electromagnetic and gravitational forces
• 5 x 5 matrices describe symmetry

11
Superstring Theory

• Vibrational patterns produce the particles of the
  standard model
• 10 dimensions unify
• the forces
• Calabi Yau spaces
• Lower limit of space
• Plank length 10-33cm

12
Plan for Research

• I. Main Focus- Added dimensions and field
  theory
• a. Kaluzas theory unifying light and gravity
  in 5 dimensions
• i. Riemanns metric tensor
• ii. relativistic electromagnetic field theory
• b. Einsteins gravitational field in terms of
  the metric tensor
• c. Gauge symmetry--Lie groups
• d. Symmetry of 10 dimensional spacetime
• II. Additional topic- String collisions and the
  elimination of infinities
• a. Feynman diagrams and attempts to quantize
  the graviton
• b. Particle decay
• c. Worldsheets and string collisions