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Holographic Dark Energy Preety Sidhu 5 May 2006. Black Holes and Entropy Black holes are “maximal...
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Transcript of Holographic Dark Energy Preety Sidhu 5 May 2006. Black Holes and Entropy Black holes are “maximal...
Black Holes and EntropyBlack 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 PrincipleThe 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 EntropyInformation 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 system’s 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 CosmologyHolographic Cosmology
• Related to the (poorly understood) principles of quantum gravity
• Bekenstein max entropy for weakly self-gravitating physical system [4D flat spacetime]:
S ≤ 2πER• Taken to be max
holographic entropy for universe
Sizes and ScalesSizes 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 ~ Planck length
• IR limit ~ “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 FluctuationsVacuum Fluctuations
• Uncertainty principle for quantum vacuum energy fluctuations, with N degrees of freedom
• Holographic principle sets N within UV and IR cutoffs
• One degree of freedom is a maximum entropy of one Boltzmann unit k
• Corresponds to Ω = π/4(z) = -1+(1- π/4)z
• No adjustable parameters, consistent with recent cosmological observations