Katie Thorne,

1
Special and General Relativity

• By
• Katie Thorne,
• Ben Gookin Bob Niffenegger

2
Outline

• The Beginning
• Newton relativity
• Galileo
• Special Relativity
• Train paradox
• Gamma factor
• Lorentz
• Invariance
• Transformations
• Maxwells Invariance
• Einsteins Famous equation
• The Math

3
Newtonian Relativity

• Space and time were absolute
• Light propagate through aether
• Regulate speed like air for planes
• Light travels at different speeds
• 1881 Albert Michelson tried to measure this
• Used Michelson Interferometery
• Found no variance

4
Galilean Invariance

• All fundamental laws of physics are the same in
  all inertial frames of reference
• Applied to mechanics, we get Galilean
  transformations

5
Special Relativity

• What is special relativity?
• Einsteins laws of physics in the absence of
  gravity.
• It describes how objects move through space and
  time

6
This brings up an interesting concept.
Time is not a universal quantity which exists on
its own, separate from space.
This means that time is not the same in all
reference frames.
7
Mirror
Reference point Platform that is stationary
Light source
Reference point Train moving at speed of light
The Train Paradox
8
This gives us the equation for time dilation

The gamma factor appears in other relativistic
expressions
9
An example
Length Contraction
10
Lorentz Invariance

• All non-gravitational laws must give same
  predictions when given
• Two different reference frames
• Moving relative to each other
• All fundamental equations of physics must be
  Lorentz invariant

11
Lorentz Transformations

• Speed of light the same in all reference frames
• Transform space-time coordinates (x,y,z,t) in one
  reference frame A, to another A moving at
  velocity V relative to A

12
Maxwells Equations

• When Lorentz transformations are applied to
  Maxwells equations, the remain the same.
• Thereby showing that they are invariant
• This in essential for General Relativity
• Speed of light is the same in all reference frames

13
Where does Einsteins famous equation come into
play?

• Newtonian definitions of momentum, energy, and
  mass are not conserved in Special Relativity
• We can make small modifications to account for
  relativistic velocities

14
"Matter tells spacetime how to bend and spacetime
returns the complement by telling matter how to
move." -John Wheeler
15
Quick Math Overview

• Tensor
• Vector (X) which under transformation (T) obeys
  this rule
• Metric Tensor
• Geodesic
• Curved Geometry
• (Riemann Geometry)
• Energy Momentum Tensor

16
Einsteins Equation
These equations appeared so complicated that
when first formulated them in 1915, he did not
believe that a solution would ever be found. He
was therefore quite surprised when, only a year
later, Karl Schwarzschild created the
Schwarzschild solution.
17
The End
18
Bibliography

• A Serious but Not to Ponderous Book About
  Relativity. Sheider, Walter. Cavendish Press.
  Ann Arbor, MI. 1996
• Lecture Notes from Intro to Gravitation,
  Alexander B. Kostinski, Michigan Technological
  University
• Lecture Notes from Honors Physics III , Bryan H.
  Suits, Michigan Technological University
• Scienceworld.Wolfram.com
• Lorentz Covariance. Wikipedia
• Lorentz Transformations. Wikipedia
• Galilean Transformations. Wikipedia
• Special Relativity. Wikipedia