|All Roads Lead to String Theory (Polchinski)|
Prior to the First Superstring Revolution
|Early History|| S-Matrix Theory|
|Bosonic String Theory|| Worldsheet|
Bosonic String Theory
String Perturbation Theory
|Supersymmetric Revolution|| Supersymmetry|
|First Superstring Revolution|| GSO Projection|
Type II String Theory
Type IIB String Theory
Type IIA String Theory
Type I String Theory
Type H String Theory
Type HO String Theory
Type HE String Theory
|Second Superstring Revolution|| T-Duality|
Horava-Witten String Theory
N=4 Super-Yang-Mills Theory
BFSS Matrix Theory
Matrix String Theory
Twistor String Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
|Phenomenology|| String Theory Landscape|
Minimal Supersymmetric Standard Model
The Holographic Principle is a principle that states that all the information within a reigon is completely encoded onto it's boundary.
Motivating examplesEdit this section
In other words, the flux through the surface is equal to the work along the boundary. This means that something on the surface has an alternate description on its boundary.
Stokes' TheoremEdit this section
The Stokes-Navier Theorem is merely a special case of the more general, all-intuitive theorem, known as [[Stokes' Theorem]. It can be stated as:
Again, on the left - hand - side, the integral is taken along , but, whereas, on the right - hand - side, it is taken along , which means that it relates a property on a surface or manifold to an alternate description of that on it's boundary.
Gauss's TheoremEdit this section
The Gauss's Theorem statesj thaty:
This again means that some information about the region has an alternate description on the boundary.
A Schwarzschild Black HoleEdit this section
For a Schwarzschild Metric, this becomes at the event horizon, so that this in - falling observer would appear to an external observer as stopping at the event horizon.
Therefore, all activities that happen to this in - falling observer would appear to the external observer as appearing at the event horizon; where - as the in - falling observer itself would perceive it as happening within the event horizon of the black hole.
Again, something in a reigon, has an alternate description on the boundary of this reigon.
Black Hole EntropyEdit this section
In the framework of Semi-Classical Gravity, Hawking Radiation is the radiation emitted from black holes due to Quantum Mechanicsal processes. The entropy associated with Hawking Radiation is given by (in a convinient system of natural units):
This thus means that the entropy of the (three-dimensional) black hole can be expressed in terms of an alternative description, on it's boundary; the area.
Statement of the theoremEdit this section
From these observations, we can thus state that:
The information in a region is can be completely be described by the information on its boundary.
This statement is known as the Holographic Principle.
Applications in PhysicsEdit this section
A word of caution about the motivating examplesEdit this section
Most of the motivating examples mentioned, except for the one on black holes is not the same sort of the Holographic Principle as that which is used in Physics, but merely just "Holographic Statements", as they relate the information about a region to information on it's boundary.