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From Wikipedia, the free encyclopedia

Loop quantum gravity (LQG), also known as loop gravity and quantum geometry, is a proposed quantum hypothesis of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity.

Loop quantum gravity postulates that space can be viewed as an extremely fine fabric or network "woven" of finite quantised loops of excited gravitational fields called spin networks. When viewed over time, these spin networks are referred to as "spin foam" (which should not be confused with quantum foam). The theory of LQG is considered a major quantum gravity contender, along with string theory, but has the perceived advantage of consistently incorporating general relativity without requiring the use of "higher dimensions".

LQG preserves many of the important features of general relativity while simultaneously employing quantization of both space and time at the Planck scale in the tradition of quantum mechanics. The technique of loop quantization was developed for the nonperturbative quantization of diffeomorphism-invariant gauge theory. LQG tries to establish a quantum theory of gravity in which space itself - where all other physical phenomena occur - becomes quantized.

LQG is one of a family of theories called canonical quantum gravity. LQG also includes matter and forces, but does not address the problem of the unification of all physical forces in the way some other quantum gravity theories (such as string theory) do.

Broad overview of LQG

The native mechanisms of quantum mechanics (successfully applied to other fields) fail to quantize gravity - indicating that something fundamental in the theory is missing, incomplete, or has to be changed. Several different approaches attempt to solve this problem, including string theory, asymptotic safety, and loop quantum gravity (LQG).

Essentially, LQG introduces new variables which replace the well-known metric in general relativity (GR) that describes spacetime and curvature. These new variables are rather close to fields that are known from gauge theory, like QED and QCD. In a certain sense gravity appears similar to QCD, but gravity has an additional property that allows the application of a second mathematical technique which replaces the fundamental fields with "fluxes through surfaces" or "fluxes along circles". These surfaces and circles are embedded into spacetime.

It thus becomes possible to eliminate the embedding of circles and surfaces into spacetime through so-called diffeomorphism invariance (which does not exist in other field theories). This is accomplished by replacing these entities with a so-called "spin network" - a graph with nodes and links among them, where each link and node carry numerical values which represent abstract entities from which certain properties of spacetime can be reconstructed. Conceptually, spacetime can be thought of as cells, each with a certain volume carried by a node. Each cell has certain surfaces, and the link between different nodes (sitting inside these cells) carry the areas of the surfaces.

It would not be correct to envision these cells as sitting in spacetime, since there is no "spacetime" anymore - only nodes and links, and certain numerical values associated with these nodes and links. Spacetime, therefore, is no longer fundamental, but is more accurately described as an entity emerging from the more fundamental graphs and their associated nodes and links.

Loop quantum gravity (LQG), also known as loop gravity and quantum geometry, is a proposed quantum hypothesis of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity.

Loop quantum gravity postulates that space can be viewed as an extremely fine fabric or network "woven" of finite quantised loops of excited gravitational fields called spin networks. When viewed over time, these spin networks are referred to as "spin foam" (which should not be confused with quantum foam). The theory of LQG is considered a major quantum gravity contender, along with string theory, but has the perceived advantage of consistently incorporating general relativity without requiring the use of "higher dimensions".

LQG preserves many of the important features of general relativity while simultaneously employing quantization of both space and time at the Planck scale in the tradition of quantum mechanics. The technique of loop quantization was developed for the nonperturbative quantization of diffeomorphism-invariant gauge theory. LQG tries to establish a quantum theory of gravity in which space itself - where all other physical phenomena occur - becomes quantized.

LQG is one of a family of theories called canonical quantum gravity. LQG also includes matter and forces, but does not address the problem of the unification of all physical forces in the way some other quantum gravity theories (such as string theory) do.

Broad overview of LQG

The native mechanisms of quantum mechanics (successfully applied to other fields) fail to quantize gravity - indicating that something fundamental in the theory is missing, incomplete, or has to be changed. Several different approaches attempt to solve this problem, including string theory, asymptotic safety, and loop quantum gravity (LQG).

Essentially, LQG introduces new variables which replace the well-known metric in general relativity (GR) that describes spacetime and curvature. These new variables are rather close to fields that are known from gauge theory, like QED and QCD. In a certain sense gravity appears similar to QCD, but gravity has an additional property that allows the application of a second mathematical technique which replaces the fundamental fields with "fluxes through surfaces" or "fluxes along circles". These surfaces and circles are embedded into spacetime.

It thus becomes possible to eliminate the embedding of circles and surfaces into spacetime through so-called diffeomorphism invariance (which does not exist in other field theories). This is accomplished by replacing these entities with a so-called "spin network" - a graph with nodes and links among them, where each link and node carry numerical values which represent abstract entities from which certain properties of spacetime can be reconstructed. Conceptually, spacetime can be thought of as cells, each with a certain volume carried by a node. Each cell has certain surfaces, and the link between different nodes (sitting inside these cells) carry the areas of the surfaces.

It would not be correct to envision these cells as sitting in spacetime, since there is no "spacetime" anymore - only nodes and links, and certain numerical values associated with these nodes and links. Spacetime, therefore, is no longer fundamental, but is more accurately described as an entity emerging from the more fundamental graphs and their associated nodes and links.

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