Loop Quantum Gravity

Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. As a candidate for quantum gravity, LQG competes with string theory.

Loop quantum gravity is an attempt to develop a quantum theory of gravity based directly on Einstein’s geometric formulation rather than the treatment of gravity as a force.

To do this, in LQG theory space and time are quantized analogously to the way quantities like energy and momentum are quantized in quantum mechanics. The theory gives a physical picture of spacetime where space and time are granular and discrete directly because of quantization just like photons in the quantum theory of electromagnetism and the discrete energy levels of atoms.

An implication of a quantized space is that a minimum distance exists. LQG postulates that the structure of space is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks.

The evolution of a spin network, or spin foam, has a scale on the order of a Planck length, approximately 10−35 metres, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure.

LQG never introduces a background and excitations living on this background, so LQG does not use gravitons as building blocks.

Instead one expects that one may recover a kind of semiclassical limit or weak field limit where something like “gravitons” will show up again. In contrast, gravitons play a key role in string theory where they are among the first (massless) level of excitations of a superstring.

The areas of research, which involves about 30 research groups worldwide, share the basic physical assumptions and the mathematical description of quantum space. Research has evolved in two directions: the more traditional canonical loop quantum gravity, and the newer covariant loop quantum gravity, called spin foam theory.

A detailed study of the quantum geometry of a black hole horizon has been made using loop quantum gravity. Loop-quantization does not reproduce the result for black hole entropy originally discovered by Bekenstein and Hawking, unless one chooses the value of the Immirzi parameter to cancel out another constant that arises in the derivation.

However, it led to the computation of higher-order corrections to the entropy and radiation of black holes.

Based on the fluctuations of the horizon area, a quantum black hole exhibits deviations from the Hawking spectrum that would be observable were X-rays from Hawking radiation of evaporating primordial black holes to be observed. The quantum effects are centered at a set of discrete and unblended frequencies highly pronounced on top of Hawking radiation spectrum.

The most well-developed theory that has been advanced as a direct result of loop quantum gravity is called loop quantum cosmology (LQC).

LQC advances the study of the early universe, incorporating the concept of the Big Bang into the broader theory of the Big Bounce, which envisions the Big Bang as the beginning of a period of expansion that follows a period of contraction, which one could talk of as the Big Crunch.

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