Quantum gravity is based on the Theory of Realitvity.
Gravity as geometry.
Moving from $2^D \rightarrow 3^D$
$2^D = \triangle = 180^o$
$3^D = \triangle = 270^o$
In curved space, the sum of the angles of the triangle are $720^o$, which is too many.

Equations that produce metric from metric have angle.
Geometry: A recipe to measure lengths.
Straight lines in curved surfaces seem to interact (if || they will come together)
Particles move on shortest path possible (geodesic)

Quantum Field Theory

$3^D$ : we can use $2^D$ calculations to calculate where particle is and where it will be (classical physics).

Probability Theory

Laplace: Philosophical essay on probability
Paradox:

• conflict between reality and what
• forces arise from particle exchange
• occurs at well-defined place in spacetime
• leads to divergences (infinities) $\rightarrow$ not fundamental, but emergent.
• not good for gravity

Quantum Electrodynamics

"lines" - particles
"vertices" - intersection

Macro: Force in gravity: general relativity: geometry
Micro: Force in QFT: particle exchange: cannot violate gravity; lots of parameters, conceptually challenging.

{Driven by belief in G-d, or disbelief too.}
Waves in water $\rightarrow$ same as quantum waves.
Black hole = edge of the universe

String Theory $\rightarrow$ point like particles like little loops.
Inherent in the description of the the string is its interactions.
Strings sing: pluck a string, produce different notes.
Closed string = gravity (9 space dimensions + 1 time dimension) $\rightarrow$ super-gravity.
Open string = other 3 forces; more symmetric version of EM. (Yang-Mills)
QFT: no gravity
String theory needs to incorporate gravity.
$L = 10^{-34}m$ ( $\lt 10^{-18}$ ) which is the smallest we can see. {Not with the naked eye, but with the correct equipment. So what is it that we are "seeing"?}
Only with the above constraints (super-gravity & super-symmetry) is the tension of the string as it is stretched constant.

Closed string moving creates a cylinder;
Open string rotating creates cylinder with gravity and EM. p-banes: closed strings (p = dimensions c) o-banes: open strings