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holographic_dark_energy
Course: ASTR 5770, Fall 2008School: Colorado
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Dark Holographic Energy Preety Sidhu 5 May 2006 Black Holes and Entropy Black holes are maximal entropy objects Entropy of a black hole proportional to surface area of event horizon Max entropy for volume of space goes as bounding surface area, not mass The Holographic Principle All information about a physical system in some region of space is encoded in its boundary surface, not its volume Like all the...
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Dark Holographic Energy
Preety Sidhu 5 May 2006
Black Holes and Entropy
Black holes are maximal entropy objects Entropy of a black hole proportional to surface area of event horizon Max entropy for volume of space goes as bounding surface area, not mass
The Holographic Principle
All information about a physical system in some region of space is encoded in its boundary surface, not its volume Like all the information in a room encoded in its walls
Information Entropy
Information entropy (or Shannon entropy) measure of randomness or uncertainty in a signal Thermodynamic entropy like amount of Shannon entropy missing between classical macroscopic variables and full microscopic description of systems state Entropy ultimately measured in bits or nats 1 bit = (ln 2) nats 0.69 nats 1 nat ~ 4 Planck areas Total bits related to matter/energy degrees of freedom Maximum info density, for given volume, about enclosed particle states Matter cannot be infinitely subdivided
Holographic Cosmology
Related to the (poorly understood) principles of quantum gravity Bekenstein max entropy for weakly selfgravitating physical [4D system flat spacetime]: S 2ER Taken to be max holographic entropy for universe
Sizes and Scales
In quantum field theory
UV cutoff: short wavelength, high energy bound IR cutoff: long wavelength, low energy bound Related by limits set by black hole formation
UV limit IR limit
~
Planck length
~
size of universe
Particle horizon: largest comoving distance from which light could have reached observer today Event horizon: largest comoving distance from which light will ever reach observer
Vacuum Fluctuations
Uncertainty principle for quantum vacuum energy fluctuations, with N degrees of freedom Holographic principle sets N within UV and IR cutoffs One degr...
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