Everything about The Holographic Principle totally explained
The
holographic principle is a speculative conjecture about
quantum gravity theories, proposed by
Gerard 't Hooft and improved and promoted by
Leonard Susskind and
John A. Wheeler, claiming that all of the
information contained in a volume of
space can be represented by information which lives in the boundary of that region. In other words, if you've an empty sphere, all of the events within can be explained by the arrangement of information on the surface of the sphere. In a larger sense, the theory suggests that the entire universe can be seen as a two dimensional information structure "painted" on a boundary surface, and that the three dimensions we observe are illusory. The holographic principle also states that at most there's one
degree of freedom (or 1
Boltzmann constant k unit of maximum entropy) for every four
Planck areas in that theory, for example
in
natural units.
Using theoretical arguments based on the
holographic principle, many physicists suggest that 11-dimensional
M-theory, which is described in many sectors by
matrix string theory, in other sectors by
perturbative string theory could ultimately form a complete
theory of everything.
High level summary
The physical universe is widely seen to be composed of "matter" and "energy". In his 2003 article published in
Scientific American magazine,
Jacob Bekenstein summarized a current trend started by
John Archibald Wheeler, a collaborator of
Albert Einstein, which suggests scientists may
"regard the physical world as made of information, with energy and matter as incidentals." Bekenstein quotes
William Blake and questions whether the Holographic principle implies that seeing
"the world in a grain of sand," could be more than "poetic license".
Unexpected connection
Bekenstein's topical overview "A Tale of Two Entropies" describes potentially profound implications of Wheeler's trend in part by noting a previously unexpected connection between the world of information theory and classical physics. This connection was first described shortly after the seminal 1948 papers of American applied mathematician
Claude E. Shannon introduced today's most widely used measure of information content, now known as
Shannon entropy. As an objective measure of the quantity of information, Shannon entropy has been enormously useful, as the design of all modern communications and data storage devices, from cellular phones to modems to hard disk drives and DVDs, all rely on Shannon entropy.
In
Thermodynamics (the branch of physics dealing with heat) Entropy is popularly described as a measure of the "disorder" in a physical system of matter and energy. In 1877 Austrian physicist
Ludwig Boltzmann described it more precisely in terms of the
number of distinct microscopic states that the particles composing a macroscopic "chunk" of matter could be in while still
looking like the same macroscopic "chunk". As an example, for the air in a room, its thermodynamic entropy would equal the count of all the ways that the individual gas molecules could be distributed in the room, and all the ways they could be moving.
Energy, matter and information equivalence
Shannon's efforts to find a way to quantify the information contained in, for example, an e-mail message led him unexpectedly to a formula with the
same form as Boltzmann's. Bekenstein summarizes that
"Thermodynamic entropy and Shannon entropy are conceptually equivalent: the number of arrangements that are counted by Boltzmann entropy reflects the amount of Shannon information one would need to implement any particular arrangement..." of matter and energy. The only salient difference between the thermodynamic entropy of physics and the Shannon's entropy of information is in the units of measure; the former is expressed in units of energy divided by temperature, the latter in
essentially dimensionless "bits" of information, and so the difference is merely a matter of convention.
Reasons for the holographic principle
Black holes are
maximal entropy objects, and theoretical results of
Black hole thermodynamics suggest that the
Second law of thermodynamics is violated when matter crosses the event horizon of a
Black hole.
This conflict may be reconciled if black holes are accorded an
entropy whose increase more than compensates for the entropy carried by the matter "swallowed", so
Black hole entropy is the
entropy of a
black hole.
Jacob Bekenstein posited that this black hole entropy is directly proportional to the area of the spherical
event horizon divided by the
Planck area. Later,
Stephen Hawking was able to confirm Bekenstein's idea and showed that the constant of proportionality is 1/4.
According to the second law of thermodynamics, greater mass entails greater entropy. 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), the holographic principle is
counter-intuitive to many physicists, as it states that the maximal limit of entropy is directly proportional to the
surface area of the region, not its
volume.
The holographic principle states that the entropy of
ordinary mass (not just black holes) is also proportional to surface area and not volume; that volume itself is illusory and the universe is really a
hologram which is
isomorphic to the information "inscribed" on the spherical surface of its boundary .
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 rigorously proved already in 1986, that the asymptotic symmetry of 2+1 dimensional gravity gives rise to a Virasoro algebra, whose 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's 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's 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.
Further Information
Get more info on 'Holographic Principle'.
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