Wednesday, December 12, 2007

Theory of the Holographic Universe

Holographic principle

From Wikipedia, the free encyclopedia

The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard 't Hooft and improved and promoted by Leonard Susskind, claiming that all of the information contained in a volume of space can be represented by a theory which lives in the boundary of that region. In other words, if you have a room, you can model all of the events within that room by creating a theory which only takes into account what happens in the walls of the room. The holographic principle also states that at most there is one degree of freedom (or 1 Boltzmann constant k unit of maximum entropy) for every four Planck areas in that theory, S\le A/4.

Reasons for the holographic principle

Given any finite, compact region of space (e.g. a sphere), this region will contain matter and energy within it. If this energy surpasses a critical density then the region collapses into a black hole.

A black hole is known theoretically to have an entropy[1] which is directly proportional to the surface area of its event horizon. Black holes are maximal entropy objects [2], so the entropy contained in a given region of space cannot be larger than the entropy of the largest black hole which can fit in that volume.

A black hole's event horizon encloses a volume, and more massive black holes have larger event horizons and enclose larger volumes. The most massive black hole which can fit in a given region is the one whose event horizon corresponds exactly to the boundary of the given region.

Greater mass entails greater entropy. Therefore the maximal limit of entropy for any ordinary region of space is directly proportional to the surface area of the region, not its volume. This is counter-intuitive to physicists because entropy is an extensive variable, being directly proportional to mass, which is proportional to volume (all else being equal, including the density of the mass).

If the entropy of ordinary mass (not just black holes) is also proportional to area, then this implies that volume itself is somehow illusory: that mass occupies area, not volume, and so the universe is really a hologram which is isomorphic to the information "inscribed" on its boundaries [3].

Limit on information density

Entropy, if considered as information (see information entropy), can ultimately be measured in bits or nats. One nat corresponds to about 1.44 bits, and 1 nat corresponds to four Planck areas [3]. The total quantity of bits is related to the total degrees of freedom of matter/energy. The bits themselves would encode information about the states which that matter/energy is occupying.

In a given volume, there is an upper limit to the density of information about the whereabouts of all the particles which compose matter in that volume, suggesting that matter itself cannot be subdivided infinitely many times; rather there must be an ultimate level of fundamental particles, i.e. were a particle composed of sub-particles, then the degrees of freedom of the particle would be the product of all the degrees of freedom of its sub-particles; were these sub-particles themselves also divided into sub-sub-particles, and so on indefinitely, then the degrees of freedom of the original particle must be infinite, violating the maximal limit of entropy density. The holographic principle thus implies that the subdivisions must stop at some level, and that the fundamental particle is a bit (1 or 0) of information.

Some scientists may argue that the most rigorous realization of the holographic principle is the correspondence by Juan Maldacena. However, J.D. Brown and Marc Henneaux[4] rigorously proved already in 1986, that the asymptotic symmetry of 2+1 dimensional gravity gives rise to a Virasoro algebra, who's corresponding quantum theory is a 2 dimensional conformal field theory. The AdS/CFT correspondence of Maldacena on the other hand is also known as the Maldacena-Conjecture which is due to the fact that it still lacks a mathematical proof.

Variations of the holographic principle

There are variations of the holographic known as the strong and weak holographic principles.

The Strong Holographic Principle

The strong holographic principle states that the information which an outside observer can derive from the surface of a black hole is directly proportional to the surface area of the event horizon. The "strong" version of the holographic principle states that an observer derives information from something through its surface which acts like a "screen" of sorts through which to view that information. However there is still a particle behind the screen projecting the information it holds onto the "screen" or surface.

The Weak Holographic Principle

The weak holographic principle states that all the information entering the event horizon of a black hole is encoded on the surface of the event horizon of that black hole and is proportional to the surface area of the event horizon. Unlike the "strong" version the weak holographic principle states that there is no particle behind the "screen" and that the physical processes of the universe can be wholly described by the "screens" or surfaces through which the information is observed.

Explanation of the Holographic Principle by Micheal Talbot

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