Quantum gravity is based on the Theory of Realitvity.
Gravity as geometry.
Moving from $$ 2^D \rightarrow 3^D $$
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$$ same as quantum waves. Black hole = edge of the universe {Why not opposite as well?} String Theory $$\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. {This constancy is a human need} <figure style="float: left"> <img src="/posts/img/qkab/cylinder_string.svg" alt="Two black holes" width="200" height="50" /> <figcaption>String between two black holes</figcaption> </figure> Closed string moving creates a cylinder;<br /> Open string rotating creates cylinder with gravity and EM. p-banes: closed strings (p = dimensions c) o-banes: open strings