Angular Momentum

**String Theory**

**The Theory of Everything**

Let's start with the Big Picture...

String Theory... generalized:

Everything in the entire Universe - all matter, all energy, and literally everything in every dimension - is made up of one dimensional 'strings'

The string's properties and it's motion determine what it is

Now we can begin our Journey to Understanding String Theory...

Strings Are:

Different Lengths

Open / Closed

torus

This Theory's goal is to connect General Relativity with Quantum Theory

Vibrating

Provides for different characteristics

Applications

Wavelength and Frequency

Gravitation

Centripetal Force of a String

F = mV /r

c

t

2

If 2 oscillating strings are interpreted as quarks, and those quarks, each with a mass of 3.559 x 10 kg, are held together as a meson via gravity, and that meson has a radius of 6.626 x 10 m and a tangential velocity is 2.6 x 10 , what is the Centripetal Force?

-30

-32

7

F = 2 x (3.559 x 10 ) x (2.6 x 10 ) / 6.626 x 10

-30

7

-32

c

Meson

m

V

r

2

What would the new Centripetal Force be if the tangential velocity was doubled?

Answer: 7.262 x 10 N

16

Answer: 2.905 x 10 N

17

Angular Momentum of a String

L

=

m

x

v

x

r

Meson

If 2 oscillating strings are interpreted as quarks, and those quarks, each with a mass of 3.559 x 10 kg, are held together as a meson via gravity, and that meson has a radius of 6.626 x 10 m, a tangential velocity of 2.6 x 10 m/s, what is the Angular Momentum of one quark?

-30

-32

7

L = 3.559 x 10 x 2.6 x 10 x 6.626 x 10

-30

7

-32

m

v

r

Answer: 6.131 x 10 J s

-54

What is the Angular Momentum if the tangential velocity is halved?

Answer: 3.066 x 10 J s

-54

Wavelength and Frequency of a String

ν = c / λ

If a string acting as a photon of light has a wavelength of 6.00 x 10 m, what is its frequency?

-8

ν = 3.0 x 10 m/s / 6.00 x 10 m

ν = c / λ

8

-8

Answer: 5.0 x 10 Hz

What would the frequency be if the wavelength doubled?

Gravitation of Strings

F = G x (m x m ) / r

g

1

2

2

r = 6.626 x 10

-32

m = 3.559 x 10

-30

Two strings are seen as quarks, and those quarks, each with identical mass, are held together via gravity. Using the diagram pictured, what is the Force of gravitation between the two quarks?

F = 6.67 x 10 x ( 3.559 x 10 ) / (6.626 x 10 )

g

-11

-30

-32

2

2

Answer: 1.924 x 10 N

-7

What would the Force of gravitation be if the radius was twice as long?

Answer: 4.810 x 10 N

-8

(4x weaker)

(1/2x frequency)

(1/2x Momentum)

(4x Force)

What you will learn:

Centripetal Force

Angular Momentum

Wavelength and Frequency

Gravity

How

Applies to Strings

Tangential Velocity and Force have a Direct Exponential Relationship

Tangential Velocity and Angular Momentum have a Direct Relationship

Radius and Gravitational Force have an Inverse Exponential Relationship

History:

1921: Kaluza-Klein Theory

1970: String Theory

1971: Supersymmetry

1974: Gravitons

1976: Supergravity

1980: Superstrings

1984: The Big Year

1991-1995: Duality Revolution

1996: Black Hole Entropy

-15

Answer: 2.5 x 10 Hz

-15

Wavelength and Frequency are Inversely Proportional